AN4 Abstracts

Home , He Jifeng, James Glimm, Jennifer Tour Chayes

AN4 Abstracts

Abstracts are printed as submitted by the authors.

Society for Industrial and Applied Mathematics 3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA Telephone: +1-215-382-9800 Fax: +1-215-386-7999 Conference E-mail: [email protected] Conference web: www.siam.org/meetings/ Membership and Customer Service: 800-447-7426 (US & Canada) or +1-215-382-9800 (worldwide) AN14 Abstracts 1

IC1 Laplacians of graphs. The talk will describe these tech- Equilibrium Analysis of Large Populations Dynam- niques, starting with Vaidya’s 1991 solver and ending with ics very recent algorithms by Kelner and others. The talk will focus on how the graph-matrix isomorphism is used The first part of the talk will review several applica- in these solvers, on the class of matrices that they can be tions, including bird flocking, information percolation in applied to, and on the gap between theory and practice in social networks, valuation of exhaustible resources, high this area. frequency market making, emissions regulation, , for which models of large populations dynamics can be brought to Sivan A. Toledo bear. These models will be framed in the context of the Tel Aviv University theory of mean field games. The second part of the talk [email protected] will present recent equilibrium existence results, and discuss some of the nagging computational challenges raised by the need for reasonable numerical approximations to IC5 these equilibria. Optimization Algorithms for Machine Learning

Rene Carmona The extraordinary success of search engines, recommenda- Princeton University tion systems, and speech and image recognition software Dpt of Operations Research & Financial Engineering suggests that future advances in these technologies could [email protected] have a major impact in our lives. In this talk, we discuss modern intelligent-algorithmic systems based on sophisticated statistical learning models and powerful optimization IC2 techniques. One can envision new algorithms that operate Solving Stochastic Inverse Problems Using Sigma- in the stochastic or batch settings, and that take full ad- Algebras on Contour Maps vantage of parallelism. We review our remarkable understanding of classical stochastic approximation techniques, We describe recent work on the formulation and numerical and pose some open questions. The lecture concludes with solution of stochastic inverse problems for determining pa- a discussion of modern neural nets and the demands they rameters in differential equations with stochastic data on impose on optimization methods. output quantities. The new approach involves approximating the generalized contour maps representing set-valued Jorge Nocedal inverse solutions, using the approximate contour maps to Department of Electrical and Computer Engineering define a geometric structure on events in the sigma-algebra Northwestern University for the probability space on the parameter domain, and [email protected] exploiting the structure to define and approximate probability distributions in the space. We will present various examples, including high-dimensional problems involving IC6 spatially varying parameter fields in storm surge models. The Mathematical Problems of Isotropic-Nematic Interface Donald Estep Colorado State University Liquid crystals represent a vast and diverse class of [email protected] or [email protected] anisotropic soft matter materials which are intermediate between isotropic liquids and crystalline solids. The various liquid crystal phases can be characterized by the type IC3 of ordering,one of the most common liquid crystal phases Computational Biology in the 21st Century: Mak- is the isotropic phase, another is the nematic phase. In ing Sense out of Massive Data this talk, a wide spectrum of mathematical problems of isotropic-nematic interface will be considered. One set of The last two decades have seen an exponential increase problems to be considered is the relationship between these in genomic and biomedical data, which will soon outstrip different levels of modeling, for example how one can make advances in computing power to perform current methods a rigorous passage from molecular/statistical descriptions of analysis. Extracting new science from these massive to continuum theories. Special consideration will be given datasets will require not only faster computers; it will re- to the existence, uniqueness and regularity of the solutions quire smarter algorithms. We show how ideas from cutting- of the Landau-de Gennes theory. edge algorithms, including spectral graph theory and modern data structures, can be used to attack challenges in Pingwen Zhang sequencing, medical genomics and biological networks. Peking University [email protected] Bonnie Berger Department of Mathematics Massachusetts Institute of Technology IC7 [email protected] The Statistics Behind the Discovery of the Higgs Boson IC4 The standard model of particle physics is a wildly suc- The Evolution of Combinatorial Solvers for Lapla- cessful theory of fundamental particles and their interac- cian Linear Systems tions. The Higgs boson is a particle that was predicted nearly 50 years ago to address a serious theoretical consis- Fast solvers that are based on combinatorial techniques tency issue in the Standard Model of particle physics, but have been investigated for more than two decades now. it has never been observed. The Large Hadron Collider is a The most successful of these (at least theoretically) solve multi-national, multi-billion dollar experiment to search for symmetric diagonally linear systems, a class that includes the Higgs boson and other new phenomena. I will discuss 2 AN14 Abstracts

the statistical aspects of the recent discovery of the Higgs information on model parameters. Based on this property boson, including the collaborative statistical modeling of we design MCMC methods that adapt to the structure of the data and the statistical procedures we employ. With the posterior probability and exploit an eﬀectively-reduced multi-petabyte datasets and complex statistical models, we parameter dimension, thereby rendering Bayesian inference are arguably pushing a frontier of statistical analysis and tractable for high-dimensional Antarctic ice sheet ﬂow in- quickly outstripping our most advanced tools. verse problems.

Kyle Cranmer Omar Ghattas New York University The University of Texas at Austin [email protected] [email protected]

IC8 IP3 Random Braids Pattern Recognition with Weakly Coupled Oscilla- tory Networks Braids are mathematical objects closely related to knots. They consist of a set of strings embedded in three dimen- One outstanding property of biological neural networks is sions, anchored at both ends. Plotted in a spacetime di- the ability to perform pattern recognition tasks. To mimic agram, trajectories of two-dimensional systems naturally this property with a man-made device that processes inform braids. When the trajectories correspond to peri- formation in parallel has been a great challenge. Tradi- odic orbits they form closed braids, and there are powerful tional approaches employ many interconnected units and mathematical techniques available to analyze the dynam- are inherently difficult to construct. In the lecture, we will ics. If the trajectories are chaotic, then the analysis is not focus on neural network models of weakly coupled oscilla- so simple. I will describe the types of braids that arise tors with time-dependent coupling. In these models, each when dealing with chaotic orbits, and discuss their connec- oscillator has only one or a few connections to a common tion to surface dynamics. I will also discuss applications support, which makes them predestinated for hardware im- to sparse trajectory datasets. plementation. We will discuss the dynamics of different network architectures, compare their scalability, present Jean-Luc Thiffeault experimental realizations of the networks and point out Dept. of Mathematics open challenging mathematically problems. University of Wisconsin - Madison [email protected] Katharina Krischer Technische Universität München [email protected] IP1 Age of Networks IP4 Networks are becoming increasingly relevant in a host of Scientific Computing in Movies and Virtual domains. In the tech industry, we see the Internet, the Surgery WWW, and many online social networks. In economics, we are experiencing both the positive and negative effects New applications of scientific computing for solid and fluid of a global networked economy. In biomedical applications, mechanics problems include simulation of virtual materials the structure of gene regulatory networks is relevant for for movie special effects and virtual surgery. Both disci- the treatment of many human diseases. In this talk, I de- plines demand physically realistic dynamics for such mate- scribe quite generally models we are using to describe these rials as water, smoke, fire, and brittle and elastic objects. networks, processes we are studying on the networks, algo- These demands are different than those traditionally en- rithms we have devised for the networks, and finally, meth- countered and new algorithms are required. This talk will ods we are developing to indirectly infer network structure address the simulation techniques needed in these fields and from measured data. I then focus on a couple of specific some recent results including: simulated surgical repair of applications, including one to cancer genomics. biomechanical soft tissues, extreme deformation of elastic objects with contact, high resolution incompressible flow, Jennifer Tour Chayes clothing and hair dynamics. Also included is discussion of Microsoft Research a new algorithm used for simulating the dynamics of snow [email protected] in Disneys animated feature film, ”Frozen”. Joseph Teran IP2 UCLA Big Data, Sparse Information: Bayesian Inference [email protected] for Large-scale Models, with Application to Inverse Modeling of Antarctic Ice Sheet Dynamics IP5 Predictive models of complex geosystems often contain Big Data Visual Analysis numerous uncertain parameters. Rapidly expanding volumes of observational data present opportunities to re- We live in an era in which the creation of new data is duce these uncertainties via solution of inverse problems. growing exponentially such that every two days we create Bayesian inference provides a systematic framework for as much new data as we did from the beginning of mankind inferring model parameters with associated uncertainties until the year 2003. One of the greatest scientific challenges from (possibly noisy) data and prior information. How- of the 21st century is to effectively understand and make ever, solution of Bayesian inverse problems via conven- use of the vast amount of information being produced. Vi- tional MCMC methods remains prohibitive for expensive sual data analysis will be among our most important tools models and high-dimensional parameters. Observational to understand such large and often complex data. In this data, while large-scale, typically can provide only sparse talk, I will present state-of-the-art visualization techniques, AN14 Abstracts 3

including ways to visually characterize associated error and the opportunities for new applied mathematics research uncertainty, applied to Big Data problems in science, en- that will enable exascale computing. This work performed gineering, and medicine. under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract Christopher Johnson DE-AC52-07NA27344. LLNL-ABS-645318. University of Utah Department of Computer Science Jeffrey A. Hittinger [email protected] Center for Applied Scientific Computing Lawrence Livermore National Laboratory [email protected] IP6 Virtual Electrophysiology Laboratory IP9 We present the development of a highly innovative patient- Physics-based Animation Sound: Progress and specific MRI-based heart modeling environment that rep- Challenges resents cardiac functions from molecular processes to electrophysiological and electromechanical interactions at the Decades of advances in computer graphics have made it organ level. This environment is termed ”virtual electro- possible to convincingly animate a wide range of physical physiology lab”. We present our attempts to translate this phenomena, such as fracturing solids and splashing water. environment into the clinic and apply it to the non-invasive Unfortunately, our visual simulations are essentially ”silent diagnosis and treatment of heart rhythm and contractile movies” with sound added as an afterthought. In this talk, disorders in patients with structural heart disease. This pi- I will describe recent progress on physics-based sound syn- oneering effort offers to integrate, for the first time, compu- thesis algorithms that can help simulate rich multi-sensory tational modeling of the heart, traditionally a basic-science experiences where graphics, motion, and sound are syn- discipline, within the milieu of contemporary patient care. chronized and highly engaging. I will describe work on spe- The robust and inexpensive non-invasive approaches for in- cific sound phenomena, and highlight the important roles dividualized arrhythmia risk stratification and guidance of played by precomputation techniques, and reduced-order electrophysiological therapies presented here are expected models for vibration, radiation, and collision processing. to lead to optimized therapy delivery and reduction in health care costs. Doug L. James Cornell University Natalia A. Trayanova [email protected] Johns Hopkins University Institute for Computational Medicine [email protected] SP1 AWM-SIAM Sonia Kovalevsky Lecture: The Evo- lution of Complex Interactions in Non-Linear Ki- IP7 netic Systems Unilever, Science and eScience: The Challenges Ahead Recent developments in statistical transport modeling, ranging from rarefied gas dynamics, collisional plasmas and Unilever is a large multinational and a market leader in electron transport in nanostructures, to self-organized or the fast moving consumer goods business, with well known social interacting dynamics, share a common description products in the sectors of home care, personal care, re- based in a Markovian framework of birth and death pro- freshments and foods. We are embracing new ways of do- cesses. Under the regime of molecular chaos propagation, ing R&D to deliver bigger, better, faster innovations to their evolution is given by kinetic equations of non-linear market. The digital revolution, eScience, is already per- collisional (integral) Boltzmann type. We will present an meating everything we do at home: how could we pay our overview of analytical issues and novel numerical methods bills without eBanking, connect with our friends without for these equations that preserve the expected conserved Facebook, or find our way around without SatNav? The properties of the described phenomena, while enabling rig- same revolution is helping us move faster at work. But how orous stability, convergence and error analysis. can we make this digital eScience revolution work for us? Irene M. Gamba Massimo Noro Department of Mathematics and ICES Unilever, United Kingdom University of Texas [email protected] [email protected]

IP8 SP2 Evolutionary or Revolutionary? Applied Mathe- Fast, Accurate Tools for Physical Modeling in matics for Exascale Computing Complex Geometry

Themovetoexascalecomputingisexpectedtobedisrup- During the last two decades, fast algorithms have brought tive due to significant changes in computer architectures. a variety of large-scale physical and biophysical modeling Advances in applied mathematics will be necessary to re- tasks within practical reach. This is particularly true of in- alize the full potential of these supercomputers, but will tegral equation approaches to electromagnetics, acoustics, these advances be incremental changes to existing methods gravitation, elasticity, and fluid dynamics. The practical or will exascale computing require a substantial rethinking application of these methods, however, requires analytic of how we compute? To answer this question, the DOE representations that lead to well-conditioned linear sys- Advanced Scientific Computing Research Program char- tems, quadrature methods that permit the accurate evalu- tered a working group, which Dr. Hittinger co-chaired. In ation of boundary integrals with singular kernels, and tech- this talk, he will discuss the findings of the working group: niques for a posteriori error estimation that permit robust 4 AN14 Abstracts

mesh reﬁnement. I will give an overview of recent progress control the shape of growing bubbles. Experiments conﬁrm in these areas with a particular emphasis on wave scatter- the feasibility of the control strategy. Extensions to other ing problems in complex geometry. pattern-forming systems will be discussed.

Leslie Greengard John Lowengrub Courant Institute Department of Mathematics New York University University of California at Irvine [email protected] [email protected]

SP3 SP6 W. T. and Idalia Reid Prize in Mathematics Lec- Theodore Von Karman Prize Lecture: Materials ture: On the Master Equation in Mean Field The- from Mathematics ory We present examples of new materials whose synthesis was One of the major founders of Mean Field Games, P.L. LI- guided by some essentially mathematical ideas from pde ONS has introduced in his lectures at College de France and the calculus of variations. These materials undergo the concept of Master Equation. It is obtained through a phase transformations from one crystal structure to an- formal analogy with the set of partial differential equations other, without diffusion. The underlying mathematical derived for the Nash equilibrium of a differential game with theory was designed to identify alloys that show excep- a large number of players. The objective of this lecture is tional reversibility of the transformation. The new alloys to explain its derivation, not by analogy, but through its do show unprecedented reversibility, but raise fundamen- interpretation. We do that for both Mean Field Type Con- tal new questions for theory. Some of these alloys control and Mean Field Games. We obtain complete solutions vert heat to electricity (without a separate electrical gen- in the linear quadratic case. We analyze the connection erator), and provide an interesting possible route to re- with Nash equilibrium. cover the vast amounts of energy stored on earth at small temperature difference. The lecture will be mathemati- Alain Bensoussan cally/experimentally nontechnical and suitable for a broad The University of Texas, at Dallas audience. (http://www.aem.umn.edu/ james/research/) [email protected] Richard James Department of Aerospace Engineering and Mechanics SP4 University of Minnesota I. E. Block Community Lecture: Search and Dis- [email protected] covery in Human Networks

In the past few years, we have seen a tremendous growth in CP1 public human communication and self-expression, through blogs, microblogs, and social networks. In addition, we Filtering Algorithm For Pod-Based Reduced Order are beginning to see the emergence of a social technol- Modeling Techniques ogy stack on the web, where profile and relationship in- Principal component analysis (PCA) is a technique that formation gathered by some applications can be used by canbeusedtodeterminethemost important components other applications. This technology shift, and the cultural on a set of varying data. PCA algorithms produces stati- shift that has accompanied it, offers a great opportunity cally independent score variables that determines the im- for computer scientists, artists, and sociologists to study portance of each component. In this manuscript, we in- (and organize) people at scale. In this talk I will discuss troduce a new filtering algorithm that can be used to how the changing web suggests new paradigms for search down-select a smaller number of directions from the POD- and discovery. I will discuss some recent projects that use determined basis in order to render a more effective re- web search to study human nature, and use human nature duction of dimensionality. The error resulting from this to improve web search. I will describe the underlying prin- filtering can be upper bounded using a randomized range ciples behind these projects and suggest how they might finding algorithm (RFA), employed in some of our previ- inform future work in search, data mining, and social com- ous developments. A neutron transport model is used to puting. demonstrate the proof of principle and exemplify the imple- Sep Kamvar mentation and mechanics of the proposed algorithm. The Massachusetts Institute of Technology, USA proposed algorithm can be classified as a PCA algorithm, [email protected] yet, it uses the error metric associated with the RFA to generate a set of principal components with a certain probability. SP5 Hany S. Abdel-Khalik Julian Cole Lecture: Growth, Patterning, and Con- North Carolina State Univ. trol in Nonequilibrium Systems [email protected] Dense-branching morphologies are among the most common forms of microstructural patterning in systems driven Bassam A. Khuwaileh out of equilibrium. Prediction and control of the emergent North Carolina State University patterns are difficult due to nonlocality, nonlinearity and [email protected] spatial heterogeneity. Focusing on viscous fingering in a circular Hele-Shaw cell as a paradigm for such phenomena, we use theory and numerics to demonstrate that by con- CP1 trolling the injection rate of the less viscous fluid, we can An Efficient Output Error Bound for Reduced Ba- precisely suppress the evolving interfacial instabilities and sis Methods Applied to Parametrized Evolution AN14 Abstracts 5

Equations [email protected]

We present an efficient a posteriori output error bound for the reduced basis method applied to nonlinear parameter- CP1 ized evolution equations. With the help of a dual system and a simple representation of the residual in the primal Using Snapshots of the Derivatives in Proper system, the output error can be estimated sharply. Such an Orthogonal Decomposition (POD)-Based Reduced error bound is successfully applied to reduced order model- Order Methods (ROM) for Dynamical Systems ing of nonlinear chromatography, and the underlying optimization can be solved efficiently using the reduced model. POD-based ROM methods use solution snapshots (SS) or snapshot difference quotients. We explore a POD ROM method that, apart from SS, also uses time derivative snap- Yongjin Zhang shots (TDS), calculated from the right-hand side of the dy- Max Planck Institute for Dynamics of Complex Technical namical system. In general, TDS do not belong to the span Systems of the SS. We develop error estimates, supported by numer- [email protected] ical tests, suggesting that a ROM utilizing both TDS and SS approximates the solution better than one based only Lihong Feng on SS. Max Planck Institute for Dynamics of Complex Technical Systems Tanya Kostova-Vassilevska, Geoffrey Oxberry, Kyle [email protected] Chand, Bill Arrighi Lawrence Livermore National Laboratory [email protected], [email protected], [email protected], ar- Suzhou Li [email protected] Max Planck Institute for Dynamics of Complex Technical Systems, Germany [email protected] CP1 Peter Benner Adaptive Proper Orthogonal Decomposition Re- Max Planck Institute, Magdeburg, Germany duced Order Models Via Incremental SVD [email protected] Meeting approximation error tolerances may require global reduced order models (ROMs) with unacceptably large CP1 numbers of ROM basis vectors. To overcome this prob- Employing Non-Converged Iterates for Reduced lem, adaptive sampling and incremental singular value de- Order Modeling composition are used to construct smaller, locally accurate proper orthogonal decomposition (POD) ROMs. Replac- Recently, reduced order modeling (ROM) is being used ing a global POD ROM with a collection of local POD in various engineering fields. Model-specific basis can be ROMs generally reduces approximation error for a fixed constructed utilizing a randomized range finding algorithm number of ROM basis vectors. (RFA) where snapshots of the models response are used to construct the basis. However, this process might be com- Geoffrey M. Oxberry, Tanya Kostova-Vassilevska, putationally taxing. This work proposes an algorithm that William Arrighi, Kyle Chand utilizes the non-converged iterates of the model of interest Lawrence Livermore National Laboratory to construct the basis. A mathematical proof showed that [email protected], [email protected], [email protected], the resulting subspace in equivalent to that constructed us- [email protected] ing the converged snapshots. The two subspaces were compared numerically in terms of the dominant angle and an error metric that has been developed in a previous work. CP1 Results indicate that the proposed algorithm produces a Robust Reduced-Order Models Via Fast, Low- subspace that is representative and inclusive of the sub- Rank Basis Updates space obtained by the converged snapshots.In addition to that, a numerical test is implemented to illustrate the ap- The large computational cost associated with high-fidelity plication of the proposed algorithm in nuclear engineering physics-based simulations has limited their use in practi- design calculations. cal situations. Model Order Reduction (MOR) is an attempt to reduce the computational cost of such simula- Bassam A. Khuwaileh tions by approximating the solution in well-chosen, low- North Carolina State University dimensional affine subspaces. Recent developments in non- [email protected] linear MOR theory that achieves increased parametric robustness and additional speedup using fast, online reduced- Congjian Wang basis updates will be presented. These new techniques will NCSU be demonstrated on parametric, large-scale, 3D fluid me- [email protected] chanical problems.

Youngsuk Bang Matthew J. Zahr Department of Nuclear Engineering, North Carolina State Stanford University University, P.O.Box 7909, Raleigh, NC 27695, USA University of California, Berkeley [email protected] [email protected]

Hany S. Abdel-Khalik Kyle Washabaugh, Charbel Farhat North Carolina State Univ. Stanford University 6 AN14 Abstracts

[email protected], [email protected] [email protected]

CP2 CP2 Two-Point Riemann Problem for Inhomogeneous A Free Boundary Approach for Solving a Two- Conservation Laws: Geometric Construction of So- Dimensional Riemann Problem for the Isentropic lutions Gas Dynamics Equations We consider a two-dimensional Riemann problem for the We consider the following conservation law: ∂tu(x, t)+ isentropic gas dynamics equations modeling strong (or ∂xf(u(x, t)) = g(u) The following boundary conditions are transonic) regular reflection. We write the problem in self- specified: u(0 − 0,t)=u0− and u(X +0,t)=uX+.In similar coordinates and obtain a free mixed boundary prob- addition, we specify the initial condition u(x, 0) = ux0 for lem for the reflected shock and the subsonic state behind x ∈ (0,X). Method of characteristics is used to show the the shock. Using the theory of 2nd order elliptic equations evolution of the initial profile and the discontinuities at with mixed boundary conditions as well as various fixed the boundaries as well as appearance and in some cases point arguments, we prove existence of a solution to the disappearance of internal discontinuities. For illustration above Riemann problem in a neighborhood of the reflec- purposes the function f(u) will be assumed to have 3 crit- tion point. ical points. Katarina Jegdic Dmitry A. Altshuller University of Houston-Downtown Dassault Systemes [email protected] [email protected]

CP2 CP2 Singular Behavior of the Navier Stokes Flow On Eigenfunction Expansion Solutions for the Through a Non-Convex Polyhedral Cylinder Start-Up of Fluid Flow This result is a mathematical background to solve the com- Textbooks describe the process of “subtracting off’ the pressible flow near the sharp edge. We consider the com- steady state of a linear parabolic PDE as means for ob- pressible viscous Navier-Stokes equations in a non-convex taining a homogeneous BVP to solve by eigenfunction ex- polyhedral cylinder. We split the edge singularity occur- pansions. While this works for the start-up problem for a ring at the non-convex edge from the velocity vector and Newtonian fluid between parallel plates, it leads to erro- show the high regularity for the velocity remainder. The neous solutions to the corresponding problem for a class of local sound wave is propagated into the region along the non-Newtonian fluids. We show this is due to non-rigorous streamline emanated from the non-convex edge and its enforcement of the start-up condition, violating the princi- derivatives blow up across the streamline. ple of causality. Oh Sung Kwon Ivan C. Christov Postech Princeton University [email protected] [email protected] Jae Ryong Kweon POSTECH(Pohang University of Science and Technology) CP2 Korea [email protected] Transport in Confined Structures As a Multiscale Problem and Numerical Results for Nanopores CP2 Charge transport through confined structures such as Higher Order Analyses of Laminated Composite nanopores differs from transport in bulk. Confined struc- Shells and Plates tures give rise to multiscale problems; more precisely, transport and scattering occur in the longitudinal direc- The free Vibration analyses of laminated cylindrical shells tion, while the particles are confined in the two transver- by using higher order shear deformation theories. Equilib- sal directions. We have derived a conservation law of the x η rium equations are formulated using the equations of stress form ∂tρ(x, η, t)+∂xF (x, η, t)+∂ηF (x, η, t)=0from resultants to attain a system of differential equations and the Boltzmann equation, where ρ is the concentration, η is x η are solved for free vibrations. Boundary conditions con- energy, and F and F are fluxes given explicitly by the sidered are simply supported and lamination is cross ply. harmonic confinement potential. We also present several The third orders shear deformation theory of that considers recent numerical results for artificial nanopores and for ion transverse normal stress, shear deformation and rotary in- channels such as certain antibiotics. ertia has been developed and used. An exact analytical solutions and boundary condition of shell has been obtained. Clemens F. Heitzinger The (first five) natural frequency parameters are reported Arizona State University & and compared with previously published research using a Technical University Vienna (TU Vienna) first order approximation. Results are also compared with [email protected] an accurate 3D finite element analyses.

Christian Ringhofer Mohammad Zannon School of Mathematical and Statistical Sciences Central Michigan University Arizona State University (ASU) [email protected] AN14 Abstracts 7

Mohamad Qatu [email protected], [email protected] CMU [email protected] CP3 Leela Rakesh Billiard Dynamics of Bouncing Dumbbell Central Michigan University Applied Mathematics Group A system of two masses connected with a weightless [email protected] rod(called dumbbell) interacting with a flat boundary is considered. The sharp bound on the number of collisions with the boundary is found using billiard techniques. In CP3 case the ratio is large and the dumbbell rotates fast, an adiabatic invariant is obtained. Pushing and Showing in Hallways and Doorways Ki Yeun Kim We investigate the location of macroscopic equilibrium University of Illinois at Urbana-Champaign states, both stable and unstable, in systems of interact- Department of Mathematics ing particles, modelling the evolution of flocks, swarms [email protected] and pedestrian crowds constrained by walls and obstacles. Unstable equilibrium states provide valuable infor- Yuliy Baryshnikov mation about qualitative system behaviour, boundaries be- University of Illinois at UrbanaChampaign tween stability regions, and transitions between modes of Department of Mathematics flow. Equation-free methods connecting macroscopic and [email protected] microscopic descriptions are employed to perform analysis and parameter continuation of equilibria and bifurcation Victoria Blumen, Vadim Zharnitsky points. University of Illinois at Urbana-Champaign [email protected], [email protected] Poul G. Hjorth Technical Univ of Denmark Department of Mathematics CP3 [email protected] Solitary Waves and the N-particle Algorithm for a Class of Euler-PoincaréEquations Kristian Berg Thomsen, Christian Marschler Technical University of Denmark Nonlinearity arises generically in mathematical models of Department of Mathematics and Computer Science physical phenomena, and the interplay between nonlinear- [email protected], [email protected] ity and dispersion is thought to be responsible for many of these phenomena, such as the existence of traveling Jens Starke waves. We explore the relation between nonlinearity and Technical University of Denmark dispersion by studying the N-particle system of the Euler- Department of Mathematics Poincaré differential equations, or the EPDiff equations. [email protected] In particular, we illustrate the existence and dynamics of traveling wave solutions of the EPDiff equations. Solitary waves for this class of equations can be made to correspond CP3 to interacting particles of a finite-degree-of-freedom Hamil- tonian system. We analyze the dynamics of two-solitary Spatial Localization in Heterogeneous Systems wave interaction and show that two solitons can either scatter or capture each other. The scattering or capture orbits We study spatial localization in the generalized Swift- depend on the singularity level of the solitons, while singu- Hohenberg equation larity of a soliton is determined by the power of the linear elliptic operator associated with the EPDiff equations. 2 ut = r(x)u − (1 + ∂xx) u + N(u) Long Lee Department of Mathematics with either quadratic-cubic or cubic-quintic nonlinearity University of Wyoming N(u) subject to spatially heterogeneous forcing through [email protected] the spatially varying parameter r(x). Different types of forcing with different spatial scales are considered and the Roberto Camassa corresponding localized structures are computed. The re- University of North Carolina sults indicate that spatial heterogeneity exerts a significant [email protected] influence on the location of spatially localized structures in both parameter space and physical space, and on their sta- Dongyang Kuang bility properties. The results are expected to assist in the University of Wyoming interpretation of experiments where departures from spa- [email protected] tial homogeneity are unavoidable.

Hsien-Ching Kao CP3 Wolfram Research Inc. The Gaussian Semiclassical Soliton Ensemble [email protected] We study a particular family of perturbed initial data for C´edric Beaume, Edgar Knobloch the focusing nonlinear Schr¨odinger equation. This family of Department of Physics data arises naturally in the analysis of the zero-dispersion University of California at Berkeley limit. However, the ellipticity of the associated modulation 8 AN14 Abstracts

equations raises questions about the impact of even small plete dictionary of piecewise-constant orthonormal bases. perturbations of the data. Remarkably, our experiments We adapt the best-basis selection algorithm to this setting, show that the rate of convergence of the perturbed data allowing us to choose a basis most suitable for the task at to the true data is propagated to positive times including hand. We conclude with some results from approximation times after wave breaking. and classiﬁcation experiments.

Gregory Lyng Jeffrey Irion Department of Mathematics UC Davis University of Wyoming [email protected] [email protected] Naoki Saito Department of Mathematics CP3 University of California, Davis Phyllotaxis As a Pattern-Forming Front [email protected] Some of the most spectacular patterns in the natural world can be found on members of the plant kingdom. Further- CP4 more, the regular configurations of organs on plants, collec- Alternating Direction Approximate Newton tively termed phyllotaxis, exhibit a remarkable predisposi- (ADAN) Method for Partially Parallel Imaging tion for Fibonacci-like progressions. Starting from a biochemical and mechanical growth model, we derive a PDE ADAN method is developed for problems that arise in similar to the classic Swift-Hohenberg equation and find partially parallel magnetic resonance image reconstruction that nearly every property of Fibonacci phyllotaxis can be (PPI). The reconstruction amounts to solving a problem of explained as the propagation of a pushed pattern-forming the form min{φ(Bu)+1/2Au−f2},whereu is the image. front. It is shown that ADAN converges to a solution of the image reconstruction problem without a line search. It performs Matthew Pennybacker at least as well as the recent variable stepsize Bregman op- University of New Mexico erator splitting algorithm (BOSVS), which requires a line [email protected] search and a suitable choice for many algorithm parameters.

CP4 William Hager, Cuong K. Ngo Automatic Segmentation of Microscopy Images University of Florida Based on the Starlet Wavelet Transform Department of Mathematics hager@ufl.edu, ngocuong@ufl.edu We propose an automatic method based on starlet wavelets to perform the segmentation of photomicrographs. The Maryam Yashtini proposed segmentation method is given applying starlets Department of Mathematics in an input image, resulting in L detail levels. First and University of Florida second detail levels are ignored; then, third to last detail myashtini@ufl.edu levels are summed. From the original image and its Ground Truth, Matthews Correlation Coefficient (MCC) is calculated for each level application. Therefore, the optimal Hongchao Zhang segmentation level has the highest MCC. Department of Mathematics and CCT Louisiana State University Alexandre F. De Siqueira,Flávio Cabrera, Wagner [email protected] Nakasuga DFQB - Faculty of Sciences and Technology CP4 UNESP - Univ Estadual Paulista [email protected], fl[email protected], Topology and Numerical Analysis in Molecular [email protected] Simulations Topological changes are significant during molecular sim- Aylton Pagamisse ulations. Our research focuses upon accurate display of DMC - Faculty of Sciences and Technology these changes through dynamic visualizations to domain UNESP - Univ Estadual Paulista scientists. Most topological characteristics are formulated [email protected] in terms of infinite precision, raising challenges within the approximations seen for graphics. Problems and partial Aldo Job solutions will be presented. DFQB - Faculty of Sciences and Technology UNESP - Univ Estadual Paulista Thomas J. Peters [email protected] University of Connecticut [email protected]

CP4 The Generalized Haar-Walsh Transform (GHWT) CP4 for Data Analysis on Graphs and Networks Per-Class Pca-Src: Increased Flexibility and Speci- ficity in Sparse Representation-Based Classification We present a new multiscale transform for data on graphs and networks which is a generalization of the classical Haar Sparse Representation-based Classification (Wright, et al.) and Walsh-Hadamard Transforms. Using a recursive parti- seeks the sparsest decomposition of test samples over the tioning of the graph, the transform generates an overcom- dictionary of training samples. This method assumes that AN14 Abstracts 9

the number of classes is large and test samples lie in the erties. We leverage our results to obtain insight into nonlinear subspaces spanned by their class’ training data. We linear dimension reduction. propose a modification that builds class-specific dictionaries containing approximate bases to points on the class Heather Harrington manifold using the “local PCA’ technique of Singer, et al. University of Oxford We show our modifications improve performance. [email protected]

Chelsea Weaver Florian Klimm University of California, Davis Master of Science (Physics) [email protected] Humboldt-Universit¨at, Berlin [email protected] Naoki Saito Department of Mathematics Miro Kramar, Konstantin Mischaikow University of California, Davis Department of Mathematics [email protected] Rutgers, The State University of New Jersey [email protected], [email protected] CP4 Peter J. Mucha Synchrosqueezed Wave Packet Transforms and Dif- University of North Carolina feomorphism Based Spectral Analysis for 1D Gen- [email protected] eral Mode Decompositions

We develops new theory and algorithms for 1D general Mason A. Porter mode decompositions. First, we introduce the 1D syn- University of Oxford chrosqueezed wave packet transform (SSWPT) and prove Mathematical Institute its ability to estimate the instantaneous information of [email protected] well-separated modes from their superposition. The SS- WPT has a better resolution than the synchrosqueezed Dane Taylor wavelet transform. Second, we present a new approach Statistical and Applied Mathematical Sciences Institute based on diﬀeomorphisms for the spectral analysis of gen- Dept of Mathematics, University of North Carolina, eral shape functions. These two methods lead to a frame- Chapel Hi work for general mode decompositions. [email protected]

Haizhao Yang Stanford University CP5 Math Dept, Stanford University On Continuous Time Bounded Conﬁdence Opinion [email protected] Dynamics with Multidimensional Opinions

In the bounded confidence opinion dynamics model, the CP5 opinion of each agent is only affected by other agents whose Two Mode Matrix of Urban Structure opinions lie within a confidence bound. In the case of continuous time bounded confidence opinion dynamics model We present an urban network that takes into account with scalar opinions, trajectories have been proven to reach how streets and neighborhoods interact and influence each an equilibrium asymptotically in time. We generalize this other. This two-mode urban structure presents another result for vector opinions by introducing Dissipation func- approach to analyze urban environments. We use GIS to tions and studying omega-limit sets of the trajectories. construct a network map of an American city and then apply network analysis to evaluate how the network structure Serap Tay, Muruhan Rathinam influences such features as traffic flow, density and housing University of Maryland, Baltimore County considerations. Also, given the rise of African cities, where [email protected], [email protected] some are being completely designed and developed in lieu of developing organically, the results of this project will make recommendations for effective metropolitan growth CP5 structures. Numerical Study on G-Expectation

James R. Gatewood We will present some numerical methods for the G-Heat Rensselear Polytechnic Institute equation which is related to the nonlinear expectation, in- [email protected] troduced by Shige Peng:

2 n ut − G(D u)=0, (x, t) ∈ R × (0,T); u(x, 0) = φ(x), CP5 1 ⊂ { t Classifying Contagion Dynamics on a Noisy Net- where G(A)=supQ∈Θ( 2 tr(AQ)), Θ S+(n)= BB : work Using Persistent Homology B ∈ Rn×n} Numerous numerical experiments will be carried out to show the eﬃciency, accuracy and stability of the A contagion can exhibit complicated dynamics on a net- proposed methods. The eﬀect of the boundary conditions work and its spread may be constrained by an underly- is also numerically investigated. Some numerical analysis ing geometry. We embed nodes of a complex-contagion 2 is given to show the convergence of the numerical solutions model on a manifold (e.g. R ). We study the extent that to the viscous solutions of the G-Heat equation. a contagion adheres to the underlying geometry with noisy non-geometric edges by embedding the nodes as points in a Xingye Yue metric space and analyse the geometrical/topological prop- Soochow University, Suzhou, China 10 AN14 Abstracts

[email protected] [email protected]

CP5 CP6 Eigenvalue Problems for Rapidly Growing Opera- Support System for Mathematical Models Based tors in Divergence Form on Optimization Problems of Economic Agents In an Orlicz-Sobolev setting, the spectrum of an exponen- This paper presents a support system for economic model- tial type perturbation of the Laplace operator is completely ing. It supports development, numerical computations and characterized by means of an asymptotic analysis of a class analytical study of models. It also controls balances and di- of eigenvalue problems involving the p-Laplacian. This talk mensions of a model for correctness and consistency. It was isbasedonjointworkwithMihaiMih˘ailescu (University successfully applied to intertemporal equilibrium models of of Craiova and “Simion Stoilow” Institute of Mathematics the Russian and the Kazakhstan economies. The system is of the Romanian Academy, Bucharest, Romania). particularly efficient for structures similar to general economic equilibrium with nonstandard descriptions of agents. Marian Bocea The system is supplemented by special procedures of reg- Loyola University Chicago ularization of complementary slackness conditions, subsys- [email protected] tem for analysis of stationary (or more exactly self-similar) solutions, based on the dimensions of the system, as well as an algorithm for solving the model as a boundary value CP6 problem and its implementation on a supercomputer. Simulating Non-Dilute Transport in Porous Media Using a TCAT-Based Model Aleksandra A. Zhukova Computing Center of RAS Predicting the transport of non-dilute species in fluids of Division of mathematical modelling of economy variable density in porous media is a challenging problem. [email protected] We use a thermodynamically constrained averaging theory (TCAT)-based model, which consists of a flow equation, Igor Pospelov a species transport equation, and closure relations. We Computing Center of RAS rewrite the model as a system of two partial differential- na algebraic equations. We use a stiff temporal integrator to perform 1D simulations. The model is nonlinear and non- Mikhail Khokhlov smooth. We will discuss results and numerical difficulties. Yandex LLC na Deena Hannoun Giffen NCSU Valentin Vrzhesch [email protected] Computing Center of RAS na C.T. Kelley North Carolina State University [email protected] CP6 Solution of a 2D Electrodiffusion Problem: Mathe- Casey Miller, William Gray, Pamela Schultz matical Modeling of Contact Resistance in Silicon University of North Carolina Photovoltaic Cells casey [email protected], [email protected], [email protected] In screen-printed silicon-crystalline solar cells, the presence of a thin interfacial glass layer of varying thickness between CP6 the silicon and silver electrode inhibits electron flow. In this paper we analyze a model for electron transport across A General Methodology for Approximating the the glass, based on the 2D drift-diffusion equations. We Discrete Chemical Master Equation with Short solve the model numerically using a spectral method and Range Spatial Correlations in Homogeneous Sys- compare results to asymptotic solutions. We are able to tems determine the effect of different glass layer topographies on the contact resistance. The chemical master equation is used to describe a wide variety of chemical kinetic processes, however the resulting system is posed in an infinite dimensional space. Often, Jonathan P. Black, Christopher Breward this system is solved via realizations of stochastic differ- University of Oxford ential equations via kinetic Monte Carlo methods, however [email protected], [email protected] these techniques may have high computational cost and require statistical sampling over many realizations. In cases Peter D. Howell where the system of interest may be assumed to have short University of Oxford range spatial correlations and have translational symme- Mathematical Institute tries, we demonstrate a general methodology of approxi- [email protected] mating the chemical master equation by a finite dimensional system of ordinary differential equations. We then Gareth Fuge demonstrate this methodology with a concrete example of DuPont (UK) Ltd surface catalysis and compare our results with those from AN14 Abstracts 11

kinetic Monte Carlo simulations. Antonios Armaou Department of Chemical Engineering Gregory J. Herschlag The Pennsylvania State University Department of Mathematics [email protected] University of North Carolina at Chapel Hill [email protected] CP7 Anytime A* for Continuous Optimal Path Plan- CP6 ning On the Initial-Boundary Value Problem for the Korteweg-De Vries Equation Eikonal PDE can be used to ﬁnd the value function of an isotropic optimal control problem. These PDE can be The Korteweg-de Vries Equation (KdV Equation) is one solved eﬃciently using the Fast Marching Method, and A* of the most important nonlinear PDEs of applied mathe- methods provide additional computational savings. We matics. We will discuss the initial-boundary problem for present an Anytime algorithm using FMM and ideas from the PDE and show, depending on boundary conditions, Weighted A*, quickly producing an initial suboptimal solu- that it can behave like a hyperbolic PDE such as the wave tion that is iteratively improved. This ensures early avail- equation and has time reversible solutions, and it can also ability of a suboptimal path before the completion of the behave like a parabolic equation such as the heat equation search for a globally optimal path. and has smooth solutions that are not time reversible. Zachary D. Clawson Steve Taylor Cornell University University of Auckland, New Zealand [email protected] [email protected] Alexander Vladimirsky Dept. of Mathematics CP6 Cornell University Transmission Eigenvalues for Regions on a Con- [email protected] ducting Surface

We consider the interior transmission problem correspond- CP7 ing to inverse scattering for a bounded isotropic dielectric A Proper Orthogonal Decomposition Based medium lying on an infinite conducting surface. In partic- Method for Solving Algebraic Riccati Equations ular, we investigate the 2-D scalar case where the dielectric medium is illuminated by time harmonic Transverse- We present a new method to solve algebraic Riccati equa- Electric or Transverse-Magnetic polarized electromagnetic tions by employing a projection method based on Proper waves. In both cases we show that transmission eigenvalues Orthogonal Decomposition. The method only requires sim- exist and form a discrete set. Numerical results are given ulations of linear systems to compute the solution of a showing that real transmission eigenvalues can be found Lyapunov equation. The leading singular vectors of the from near field data. Lyapunov solution are then used to construct a projector which is employed to produce a reduced order sys- Fan Yang tem.Computational results and comparisons to other meth- University of Delaware ods will be discussed. [email protected] Boris Kramer Peter B. Monk Virginia Tech Department of Mathematical Sciences [email protected] University of Delaware [email protected] CP7 A New Semi-smooth Newton Multigrid Method for CP7 Parabolic PDE Optimal Control Problems Robust Dynamic Shaping of Distributed Parameter Systems Via Recursively Updated Empirical Basis A new semi-smooth Newton (SSN) multigrid algorithm is Functions proposed for solving the discretized first order necessary optimality systems that characterizing the optimal solu- We focus on shaping the dynamic response of distributed tions of a class of 2D semi-linear parabolic PDE optimal parameter systems in the presence of parameter uncer- control problems with control constraints. To achieve a tainty using adaptive model order reduction. The prob- second-order accurate finite difference discretization, we lem is addressed by enforcing the desired spatio-temporal use a leapfrog scheme (with the second-order backward dynamics in the closed-loop system via an observer-based differentiation formula (BDF2)) in time and a standard robust nonlinear feedback controller specifically designed 5-point stencil in space. The derived well-structured dis- based on the reduced order model that is refined by re- cretized Jacobian matrices greatly facilitate the develop- cursively updated empirical basis functions. The proposed ment of effective smoother in our multigrid algorithm. Nu- method is illustrated on the thermal dynamic shaping in a merical simulations are provided to illustrate the efficiency catalytic reactor. of the proposed method, which validates the second-order accuracy in solution approximations and the optimal linear Davood Babaei Pourkargar complexity in computational time. Department of Chemical Engineering The Pennsylvania State University, University Park Jun Liu [email protected] Southern Illinois University 12 AN14 Abstracts

[email protected] posed method for ranking fuzzy numbers to develop a new method for dealing with fuzzy risk analysis problems. Mingqing Xiao Southern Illinois University at Carbondale Tayebeh Hajjari [email protected] Department of Mathematics Firoozkooh Branch of Islamic Azad University [email protected] CP7 Computationally-Based Technique for Bifurcation Control CP8 Reduced Basis Methods for Maxwell’s Equations In this paper, a computationally-based methodology to ob- with Stochastic Coefficients tain chaos controllers for PWM buck power converters is proposed, developed and proven. The mathematical model We consider parametrized partial differential equations of a PWM is highly nonlinear (and non-smooth) and sim- in many-query settings. We discuss the Reduced Basis ulations show rich phenomena. The controller is easy to Method (RBM) for time-harmonic Maxwell’s equations un- implement with an analog circuit, and it improves the per- der stochastic parameters. The RBM model reduction sig- formance of the system. Additionally, it reduces the per- nificantly reduces the system size while preserving a certi- centage of regulation error and eliminates non-desired or- fied accuracy by employing rigorous error estimators. To bits. Computational and experimental results validate the quantify the statistical outputs like mean and variance for controller design. Maxwell’s equations under stochastic uncertainties, we use sparse collocation and weighted RBM. Numerical experi- Gerard Olivar ments are performed on 3D models of microwave devices. Department of Electrical and Electronics Engineering Universidad Nacional de Colombia, sede Manizales [email protected] Martin W. Hess Max-Planck-Institute for Dynamics of Complex Technical Daniel Morcillo Systems Magdeburg Universidad Nacional de Colombia - Manizales [email protected] [email protected] Peter Benner Daniel Burbano Max Planck Institute, Magdeburg, Germany Universita degli Studi di Napoli [email protected] [email protected] CP8 Fabiola Angulo Department of Electrical and Electronics Engineering Use of Polynomials of Chaos as Regression Func- Universidad Nacional de Colombia, sede Manizales tions for Universal Kriging Models and Application [email protected] to Numerical Dosimetry In the computer experiments domain, Universal Kriging CP8 and Polynomial Chaos are two widely used metamodel- Accelerated Hierarchical Stochastic Collocation - ing approaches. Considering a sparse representation of the Finite Element Methods for PDEs with Random Polynomial Chaos expansion gathering the most influent Inputs polynomials with the Least Angle Regression, this communication proposes to use these polynomials as regression The dominant cost of stochastic collocation methods for functions in the Universal Kriging model. The optimal PDEs with high-dimensional random inputs are the cost of performances of the proposed approach are illustrated with solving large numbers of linear systems. For non-intrusive several benchmark functions and with a dosimetry exam- methods like stochastic collocation, each linear system can ple. be solved separately. Instead we consider global and local, hierarchical, semi-intrusive methods that accelerate Pierric Kersaudy the performance of the finite element solvers and look at Orange Labs the conditions under which computational costs can be re- [email protected] duced. Bruno Sudret Diego Galindo, Clayton G. Webster, Guannan Zhang ETH Zurich Oak Ridge National Laboratory [email protected] [email protected], [email protected], [email protected] Odile Picon CP8 UniversitéParis-Est [email protected] Uncertainty Qualification Based on Ranking Fuzzy Numbers Joe Wiart In this paper, we present a new method for uncertainty Orange Labs qualification based on ranking fuzzy number. First, we [email protected] present a new method for ranking fuzzy numbers. It considers left and right area deviation. The proposed method can overcome the drawback of some existing meth- CP8 ods for ranking fuzzy numbers. Then, we apply the pro- Quasi Optimal Sparse-Grid Approximations for El- AN14 Abstracts 13

liptic PDEs with Stochastic Coeﬃcients [email protected]

Solution of PDEs depending on random coefficients can be conveniently approximated by polynomial expansions on CP9 the parameter space, that suffer however from a perfor- Mixing and Piecewise Isometries on a Hemisphere mance degradation as the number of random parameters increases (“curse of dimensionality’ effect). In this talk we We study chaotic nonlinear dynamics and mixing on a will propose an “a-priori/a-posteriori knapsack approach’ hemispherical surface using piecewise isometries (PWI) to minimize such effect for sparse grids approximations. motivated by cutting and shuffling in 3-D granular flow. The efficiency of the proposed technique will be supported Mapping singularities with simple PWI for different pa- by theoretical convergence results and numerical tests. rameters yield a variety of complex patterns on the hemisphere’s surface termed the exceptional set (E). Coarse- Lorenzo Tamellini grained measures of E suggest that E exhibits properties EPF-Lausanne, Switzerland, of fat fractals that may provide deeper insight into mixing lorenzo.tamellini@epfl.ch by cutting and shuffling.

Fabio Nobile Paul Park EPFL, Switzerland Northwestern University fabio.nobile@epﬂ.ch [email protected]

Raul F. Tempone Paul Umbanhowar, Julio Ottino Mathematics, Computational Sciences & Engineering Northwestern University King Abdullah University of Science and Technology Evanston, IL 60208-3109 [email protected] [email protected], [email protected]

CP9 Richard M. Lueptow Subharmonic Response and Threshold of Chirp Northwestern University Driven Microbubbles Department of Mechanical Engineering [email protected] Recent experimental results have shown that acoustically driven microbubbles may exhibit an enhanced subharmonic response if driven by nonstationary (chirp) waveforms. CP9 However, the previous theory on the subharmonic thresh- Variational Integrators for Interconnected Dirac old has been limited to single frequency forcing. We present Mechanical Systems a method for predication of the threshold using a energy ratio of the IMFs from a Empirical Mode Decomposition Dirac mechanics simultaneously generalizes Lagrangian of the scattered acoustic signal. Results are compared for and Hamiltonian mechanics to reveal the geometric struc- linear and finite elastic models of an encapsulating shell for ture of systems with forces, constraints and degeneracies. ultrasound contrast agent microbubble applications. Jacobs and Yoshimura recently elucidated the relationship between the Dirac mechanical structure of an intercon- John S. Allen nected system and those of its components. The varia- University of Hawaii-Manoa tional integrator construction derives structure-preserving [email protected] integrators from discrete variational principles, producing symplectic, momentum preserving integrators where ap- Rintaro Hayashi plicable. This talk will discuss extensions of existing Dirac University of Hawaii at Manoa variational integrators to accommodate interconnections. [email protected] Helen F. Parks University of Pittsburgh CP9 [email protected] A Global Bifurcation of Mixed-Mode Oscillations Melvin Leok Mixed-mode oscillations (MMOs) are trajectories of dy- University of California, San Diego namical systems in which large and small oscillations oc- [email protected] cur with a distinct gap between the two. Over two decades ago, Koper first observed the seemingly paradoxical emergence of complex MMOs in a (now canonical) model. We CP9 describe the successful detection of an elusive global bi- Different Wave Solutions Associated with Singular furcation that only now resolves this paradoxical dynam- Lines on Phase Plane ics. Our techniques are based on computation of invariant manifolds and continuation methods. The bifurcation phenomena of a compound K(m,m) equation are investigated. Three singular lines have been found Ian M. Lizarraga in the associated topological vector field, which may evolve Center for Applied Mathematics in the phase trajectories of the system. The influence of Cornell University parameters as well as the singular lines on the properties of [email protected] the equilibrium points has been explored in details. Tran- sition boundaries have been obtained to divide the param- John Guckenheimer eter space into regions associated with different types of Cornell University phase trajectories. The existence conditions and related 14 AN14 Abstracts

discussions for diﬀerent traveling wave solutions have been hence predicts bounded stress and strain at the crack-tip. presented in the end. Mallikarjunaiah S. Muddamallappa Yu V. Wang Department of Mathematics York College, The City University of New York Texas A&M University [email protected] [email protected]

Jay R. Walton CP10 Department of Mathematics A Domain Decomposition Method for Cavitation Texas A&M Computation in Nonlinear Elasticity [email protected] A domain decomposition method is applied to compute cavity growth in nonlinear elasticity. The idea is that the CP10 material is ﬁrst tailored into nonoverlapping circular ring Peridynamics As a Multiscale Method sub-domains so that each one is a scaling of the other; then, the standard Dirichlet to Neummann boundary conditions The peridynamic theory of solid mechanics is a strongly are applied to pass the information from a subproblem to nonlocal theory that contains a length scale represent- its neighbors; ﬁnally, some special measures are taken to ing the maximum interaction distance between material stabilize the method. The convergence speed is greatly points. Recent work shows that by varying this length improved by the method. scale, we can achieve a multiscale model of solids within a single theory, without the need to couple dissimilar meth- Zhiping Li ods. In this talk I will describe a hierarchical multiscale School of Mathematical Sciences, Peking University method based on the peridynamic equations and appropri- [email protected] ate coarse graining of material properties.

Wulin Luo Stewart Silling School of Mathematical Sciences Sandia National Laboratories Peking University [email protected] [email protected] CP10 CP10 Light Beam Interaction in Nonlinear Optical Media On Strong Ellipticity for Implicit and Strain- The dynamics of light beam interaction in Nonlinear Op- Limiting Theories of Elasticity tical Media is studied numerically and analytically. The Implicit constitutive theories for elastic material bodies beam dynamics is simulated by the beam propagation have received increasing attention in the literature. The method. The numerical results agree with the results of theories are used to formulate strain limiting models of the analytic model. The results show that the reflection elasticity, and to develop nonlinear constitutive relations and transmission can be predicted and controlled by the between linearized strain and stress. We study strong el- trapped beam at the interface of two nonlinear optical me- lipticity for a general class of elastic implicit constitutive dia. Some interesting new results will be presented in this relations and apply it to specific examples. For the con- talk. sidered examples, strong ellipticity is shown to hold for Rajah P. Varatharajah sufficiently small strain and fail for suitably large strain. North Carolina A&T State University Tina Mai [email protected] Department of Mathematics, Texas A&M University College Station, TX 77843-3368 CP11 [email protected] Variance Reduction in the Simulation of Stochastic Differential Equations Jay R. Walton Department of Mathematics Variance reduction techniques are commonly used to en- Texas A&M hance the efficiency of Monte Carlo simulations. This talk [email protected] focuses on variance reduction for single and coupled systems of stochastic ordinary differential equations. Variance reduction techniques such as antithetic variates and control CP10 variates will be described and results presented. Direct Numerical Simulation of Anti-Plane Shear Fracture in New Class of Elastic Bodies David J. Horntrop Dept of Mathematical Sciences, Center for Applied Math In this work we study Finite Element Method (FEM) for New Jersey Institute of Technology the problem of anti-plane shear fracture in the setting of a [email protected] strain-limiting theory of elasticity. Recently Rajagopal and Walton used a new class of such models to study anti-plane strain fracture. Using asymptotic analysis of the model CP11 near the tip of crack, they showed that both stress and A Guaranteed Automatic Integration Library for strain vanish at the crack-tip, and the crack separation Monte Carlo Simulation displacement has a cusp-shaped profile. The FEM based direct numerical simulation indicates that the present ap- This talk introduce the Guaranteed Automatic Integration proach removes the classical square root singularity and Library (GAIL), which was developed within last year. It AN14 Abstracts 15

contains four algorithms, which perform function approxi- local smoothing multigrid approach, which uses informa- mation, numerical integration(using Monte Carlo method tion about geometry near the interface to perform a single and 1-D trapezoidal rule) and Monte Carlo for evaluat- geometric coarsening to a problem with volume-averaged ing the mean. All routines come with theoretical guaran- materials. tees of success, something that is missing, say, for MAT- LAB’s integral.m and nearly all other automatic algo- Christopher Siefert,RichardKramer rithms. Moreover, GAIL has been carefully designed with Sandia National Laboratories a friendly user-interface, thorough documentation, and ex- [email protected], [email protected] tensive testing. Also, this talk discuss the theoretical research on the reliable relative error estimation based on the previous work, which comes with the numerical results and CP11 proved theorems. Various Strategies for the Numerical Stochastic Homogenization of the Stochastic Poisson and Lan Jiang Helmholtz Equations Dpet. of Applied Mathematics Illinois Institute of Technology We consider stochastic versions of the Poisson equation [email protected] as well as of the Helmholtz equation with discontinuous coefficients. These equations arise, e.g., when modeling nanowire sensors and metamaterials with a random struc- CP11 ture. Although there are some theoretic homogenization Reliable Error Estimation for Quasi-Monte Carlo results, the question of how to compute solutions effi- Methods ciently still remains. Here, we discuss approximations of the stochastic dimensions by various quasi-MC strategies This project aims to build an efficient algorithm based on and which boundary conditions and size of the domain to extensible rank-1 lattice rules for multidimensional integra- use when approximating the problem on the whole space. tion with guarantees. In order to proceed, we compute the a Fast Fourier Transform on the integrand values sampled Gerhard Tulzer on an integration lattice and use them to approximate the TU Vienna, Austria Fourier coefficients of the integrand. The decay rate of the [email protected] Fourier coefficients and the assumption that the integrands lie inside a given cone helps us approximate the error. Clemens F. Heitzinger Arizona State University & Lluis Antoni Jimenez Rugama, Fred J. Hickernell Technical University Vienna (TU Vienna) Illinois Institute of Technology [email protected] [email protected], [email protected]

CP12 CP11 Iron-dependent Oxidative Stress Response Path- Split-Step Balanced Milstein Methods for Multi- way in Human Mammary Epithelial Cells Channel Stiff Stochastic Differential Systems It has been known that iron plays an important role in We discuss systems of ordinary SDEs with non- the development of breast cancer and cancer cells are un- commutative multi-channel noise arising in chemical net- der persistent oxidative stress. However, the effect of iron works that involve reactions at different time scales. Such overload on the oxidative stress response pathway in nor- systems are inherently stiff, both in deterministic and mal and cancer cells is still under study. This project fo- stochastic components, and can change stiffness with un- cuses on a mathematical model of an oxidative stress re- certainty. To resolve this issue we consider fully implicit sponse pathway in normal human breast cells in order to split-step balanced methods with optimal parameter selec- understand how normal cells transition malignant cells. tions with respect to the desired convergence, stability and positivity properties. Numerical examples are provided to Seda Arat show the effectiveness of these methods. Virginia Tech [email protected] Viktor Reshniak, Abdul Khaliq Middle Tennessee State University Julia Chifman [email protected], [email protected] Wake Forest School of Medicine [email protected] David A. Voss Western Illinois University Suzy Torti, Reinhard Laubenbacher [email protected] University of Connecticut Health Center [email protected], [email protected] CP11 Local Smoothers for Cdfem with Sub-Element Dis- CP12 continuities A Mathematical Model for Glucose and Fatty Acid Metabolism The conformal decomposition finite element method (a technique for handling sub-cell discontinuities) allows for A model is presented for the rate of utilization and stor- Lagrangian-like interfaces in a (basically) Eulerian mesh. age of carbohydrates and fats. It is based on differential As the physics ”chooses” the location of the interface, it equations for the chemical kinetics converting glucose and can lie very close to element boundaries, which can hurt fatty acids to pyruvate and acetylCoA, which then enter matrix conditioning and the linear solver. We present a the Krebs cycle to produce energy. The molecules can also 16 AN14 Abstracts

be stored as glycogen and fat. The conversion rates are with Timecourse Data modeled as Hill’s reactions. Results are presented for different conditions of supply and usage. Due to the limit of current experimental techniques, identifying biochemical network among genes and proteins un- Donald A. Drew derlying biological systems is one of the most challenging Rensselaer Polytech Institute works. On the other hand, output of the networks, time- Dept of Mathematical Sciences courses of genes and proteins can be easily acquired with [email protected] recent advances in technology (e.g. microarray analysis). In this work, we will describe how to use oscillating time- Julienne LaChance course data to reveal the biochemical network structure by Rensselaer Polytechnic Institute using a fixed-point criteria. [email protected] Jae Kyoung Kim Department of Mathematics CP12 University of Michigan, Ann Arbor, Michigan 48109, USA Multiscale Simulation of Reaction-Diffusion Sys- [email protected] tems in Living Cells Daniel B. Forger III We present a simulation algorithm that allows for dynamic University of Michigan switching between a microscopic and a mesoscopic model- [email protected] ing framework for stochastic reaction-diffusion kinetics. By discretizing space with an unstructured mesh we can carry out simulations in complex and realistic geometries. The CP12 accuracy and efficiency of the algorithm is demonstrated Using Machine Learning and in numerical examples inspired by biological applications. Metabolomic/transportomic Systems Model- We show that by simulating only parts of a system at the ing to Identify Bacterial Ecotype from Genomic more detailed, microscopic level, we can reduce the compu- Sequence of Uncharacterized Environmental Or tational cost significantly while retaining the accuracy of Clinical Isolates the full microscopic model. The method can be combined with microscopic simulations of dynamic lower dimensional The ability to genomically sequence bacteria from envi- structures such as DNA or fibers, where the microscopic ronmental or clinical isolates that are not or cannot be simulations are used close to the complex parts of the ge- cultured in the laboratory requires development of compu- ometry, and the more efficient mesoscopic simulations are tational tools to predict bacterial ecotypes from genomic used in the other parts of space. data. Using Psuedomonads for which complete genomes Stefan Hellander are available and ecotype is known or inferred, we demon- Uppsala University, Sweden strate that support vector machines using features derived [email protected] from computational modeling of bacterial metabolome and transportome is more predictive of Psuedomonads ecotype than using only genomic data. Andreas Hellander Uppsala University Peter E. Larsen, Frank Collart [email protected] Argonne National Laboratory [email protected], [email protected] Linda Petzold University of California, Santa Barbara Yang Dai [email protected] Laboraory of Computational Functional Genomics University of Illinois at Chicaho CP12 [email protected] A Simulator of the Multi-Scale Dynamics of Gene Regulatory Networks CP13 We propose a simulator of an ODE model class of the multi- Non-Parametric Clustering with Rank- scale dynamics of gene regulatory networks with steep sig- Constrained Least-Squares moidal interactions. The threshold-dependent dynamics divides the phase space into domains. Under specific as- Unsupervised clustering is a problem of great practical im- sumptions, trajectories through any sequence of domains portance, from genetics to marketing, extreme events mod- are derived by iterating a local computation of transitions elling or even financial engineering. Although most avail- between domains. The parameter values can be expressed able techniques perform well in practice, most of them re- either qualitatively by inequalities or by probability dis- quire solving an NP-hard optimization problem or require tribution. In the latter case, the probability of trajectory to know the number of clusters ahead of time. Our goal occurrence is calculated. is to present a simple technique for fast joint estimation of the number of clusters and their respective center of mass. Liliana Ironi Assuming the data can be represented as a d × n matrix IMATI - CNR X = C + E,whereC = MT, E is a matrix-noise, M is Pavia (Italy) the center of mass matrix, and Tk,i =1ifXi belongs to [email protected] custer k and Tk,i = 0 otherwise. This representation leads to searching for a low rank approximation of X. The rank of C is the number of clusters and is efficiently estimated CP12 using recent work in model selection. The approximation Bioechemical Network Structure can be Revealed itself can be performed using the power method and its AN14 Abstracts 17

recent analysis by Hardt. We also study the marginal distribution of the number of occupied secondary spaces, as well as various conditional Stephane Chretien distributions. Universite de Franche Comte [email protected] Eunju Sohn University of Georgia [email protected] CP13 Stationary Stability for Evolutionary Dynamics in Charles Knessl Finite Populations University of Illinois at Chicago [email protected] We extend the theory of evolutionary stability to multidimensional finite populations with mutation, connecting the theory of the stationary distribution of the Moran process CP14 with the Lyapunov theory of evolutionary stability for the replicator dynamic. We show essentially that the local ex- Using Lasso Model to Predict Cell-Type-Specific trema of the stationary distribution minimize the relative Transcription Factors in Low Methylated Regions entropy of the current population state and the ”expected next state” computed by weighting the adjacent states by Low Methylated Regions (LMRs) have been implied to the appropriate transition probabilities. This holds for be potential distal regulatory regions. Using the tran- a variety of selection processes including the increasingly scription factor binding sites (TFBSs) predicted from both popular Fermi selection. We present several complete com- LMRs and promoters, we apply LASSO models to pre- putational examples for illustration and we show that the dict directions of gene expression among multiple cell types classical stability theory of the replicator dynamic is re- based on the similarity score of TFBSs. By analyzing the covered in the large population limit. If time allows, we LASSO results, we demonstrate that the model can fa- describe extensions to populations evolving on graphs. cilitate the identification of cell-type-specific transcription factors binding that may potentially regulate directions of Dashiell Fryer gene expression. Pomona College [email protected] Hong Hu Bioinformatics Program, Department of Bioengineering Marc Harper University of Illinous at Chicago UCLA [email protected] [email protected] Yang Dai Laboraory of Computational Functional Genomics CP13 University of Illinois at Chicaho A Novel Concept of Normal Exponential ROC [email protected] Model

Receiver Operating Characteristic (ROC) Curve is used to CP14 quantify and compare the accuracy of diagnostic tests. In Moment Fitting for Parameter Inference in Re- this paper, Normal Exponential ROC model is proposed peatedly and Partially Observed Stochastic Biolog- and its properties are studied when healthy test scores ical Models follow Normal distribution and diseased test scores follow Exponential distribution. Area under the proposed ROC The inference of reaction rate parameters in biochemical curve and its standard error are derived. The utility of network models from time series concentration data is a this model is explored using simulation studies and Serum central task in computational systems biology. Under the concentrations of CA 19-9 (Carbohydrate antigen) for pan- assumption of well mixed conditions the network dynam- creatic cancer. At the end, it is found that proposed ROC ics are typically described by the chemical master equation. model gives better accuracy as compared to the traditional Based on the latter we derive closed systems of parameter Binormal ROC model. dependent nonlinear ordinary differential equations that predict the time evolution of the statistical moments. For Sudesh Pundir inferring the reaction rate parameters we suggest to not Pondicherry University only compare the sample mean with the theoretical mean [email protected] prediction but also to take the residual of higher order moments explicitly into account. Cost functions that involve CP13 residuals of higher order moments may form landscapes in the parameter space that have more pronounced curvatures Storage Allocation Models with Finite Capacity at the minimizer and hence may weaken or even overcome parameter sloppiness and uncertainty. We consider a stochastic storage allocation model, which has m primary holding spaces and R secondary ones. All of the spaces are numbered and ordered, and an arriving cus- Philipp Kuegler tomer takes the lowest ranked available space. We define RICAM, Austrian Academy of Sciences the traffic intensity ρ to be λ/μ where λ is the customers’ Austria arrival rate and μ is the service rate of the processor. If we [email protected] let m+R = N, the total number of stored items behaves as an M/M/N/N queue, which is the Erlang loss model. We obtain the joint probability distribution of the numbers CP14 of occupied primary and secondary spaces, for ρ →∞. Mathematical Modeling of the Antibiotic Er- 18 AN14 Abstracts

tapenem [email protected]

Ertapenem is an antibiotic commonly used to treat a broad spectrum of infections. A physiologically-based pharma- CP14 cokinetic model was developed to investigate the uptake, Discovery of Multi-Dimensional Modules in Cancer distribution, and elimination of ertapenem following a Genomic Data once-a-day, single one gram dose. Blood concentrations of ertapenem found by the model were compared to data Recent technology has made it possible to simultane- from published experimentation for normal height, normal ously perform multi-platform genomic profiling of bio- weight males. Simulations were performed to consider the logical samples, resulting in so-called ’multi-dimensional distribution of the antibiotic in underweight, overweight, genomic data’. However, integrative analysis of multi- and obese men of normal height. dimensional genomics data for the discovery of combinatorial patterns is currently lacking. Here, we develop a set Cammey Cole Manning of matrix factorization techniques to address this challenge. AWM and Meredith College We applied this method to the data from the The Cancer [email protected] Genome Atlas project, and show that our tools can uncover hidden patterns in multi-dimensional cancer ’omic’ data. Michele Joyner East Tennessee State University Xianghong J. Zhou [email protected] Biological Science and Computer Science University of Southern California [email protected] CP14 Connecting Motifs and Molecular Mechanisms To- CP15 ward Control of Complex Networks Fourth Order Compact Simulation of the One Di- Advances in high throughput biological assays have pro- mensional Euler Equations of Gas Dynamics moted statistical inference of large experimental datasets; This paper introduces a class of higher order compact the subsequent networks are then used as models to dis- schemes for the solution of one dimensional (1-D) Euler cover therapeutic targets. However, these networks yield equations of Gas Dynamics. These schemes are fourth little mechanistic insight into the cornerstones of complex order accurate in space and second or lower order accu- biological systems: regulation and dynamics. Comprehen- rate in time and unconditionally stable. To test the effi- sive analysis of networks inferred from in silico models that ciency of our proposed schemes, we first apply it to three represent biological mechanisms (e.g., competitive inhibi- shock tube problem of gas dynamics, including the famous tion) elucidates our understanding of large network dynam- SOD shock tube problem. Later on, we apply our pro- ics and informs novel control strategies. posed schemes to the subsonic-supersonic isentropic flow through a convergent-divergent nozzle and compare our Aaron Oppenheimer solution with the exact solutions. In all the cases, our Northwestern University computed numerical solutions are found to be in excellent Department of Chemical and Biological Engineering match with the exact ones. Lastly, we show ways to extend [email protected] the schemes to problems of higher spatial dimensions.

Neda Bagheri Jiten C. Kalita Chemical and Biological Engineering Indian Institute of Technology Guwahati Northwestern University Guwahati INDIA [email protected] [email protected]

Bidyut Gogoi CP14 Indian Institute of technology Guwahati INDIA A Combined Method of Model Reduction for Bio- [email protected] chemical Reaction Networks

This talk introduces a combined model reduction algorithm CP15 with particular application to biochemical reaction net- High Order Parametrized Maximum-Principle- works within the context of systems pharmacology. This Preserving and Positivity-Preserving Weno method brings together versions of proper lumping and em- Schemes on Unstructured Meshes pirical balanced truncation to reduce nonlinear, stiff dynamical systems that are typical in the modelling of bio- We will talk about the generalization of the maximum- chemical reactions. Modifications and enhancements to the principle-preserving (MPP) flux limiting technique devel- established methods are discussed. Finally, the algorithm oped in [Z. Xu, Math. Comp., (2013)] to develop a class is demonstrated with application to two published systems high order MPP finite volume schemes for scalar conser- biology models, with good results. vation laws and positivity-preserving (PP) finite volume WENO schemes for compressible Euler system on two di- Tom J. Snowden, Marcus Tindall mensional unstructured meshes. The key idea of this pa- University of Reading rameterized technique is to limit the high order schemes [email protected], [email protected], towards first order ones which enjoy MPP property, by decoupling linear constraints on numerical fluxes. Error Piet van Der Graaf analysis on one dimensional non-uniform meshes is pre- Universiteit Leiden sented to show the proposed MPP schemes can maintain Pfizer high order of accuracy. Similar approach is applied to solve AN14 Abstracts 19

compressible Euler systems to obtain high order positivity- oped an algorithm that extracts the 3D geometry of the preserving schemes. Numerical examples coupled with deployed stent from real patients OCT images. Visualiza- third order Runge-Kutta time integrator are reported. tion of the blood flow in stented vessel for the first time becomes a reality. Combined with an adaptive meshing Yuan Liu method, real inflow, and real vessel curvature, our CFD Department of Mathematics simulations can best approximate the real hemodynamic Michigan State University conditions of the stented vessel and provide many desirable [email protected] results, which demonstrates the great power of numerical PDEs in biomedical engineering.

CP15 Boyi Yang Scalable High-Order Non Conforming Finite Ele- Emory University ment Methods For Time Domain Acoustic-Elastic Department of Mathematics & Computer Science Problems [email protected]

High-order numerical methods for solving time-dependent Alessandro Veneziani acoustic-elastic coupled problems are introduced. These MathCS, Emory University, Atlanta, GA methods, based on Discontinuous Galerkin and Classical [email protected] Finite Element techniques, allow for a flexible coupling between the fluid and the solid domain by using non- conforming meshes and curved elements. Importantly, CP15 physical domains may be independently discretized and the A Finite Element Method for the Second Order structural geometry is faithfully represented upon a chosen Linear Elliptic Equation in Non-Divergence Form degree of fidelity, enabling for higher flexibility and efficient computation. In order to illustrate the accuracy and scal- We design a finite element method for the linear elliptic ability properties of a parallel implementation, we present equation in non-divergence form, which satisfies discrete representative numerical tests for large-scale seismic wave maximum principle. We show that the method guaran- propagation. tees convergence to the viscosity solution provided that coefficient matrix A(x) and function f(x) are continuous. Angel Rodriguez-Rozas In order to establish a rate of convergence, we derive a Center for Mathematics and its Applications discrete version of Alexandroff-Bakelman-Pucci estimate. Department of Mathematics - Instituto Superior Técnico Using this discrete estimate, we show that angel.rodriguez [email protected] α/(2+α) 2 1 u − uh L∞ ≤ C h ln Julien Diaz h Team-Project Magique-3D INRIA Bordeaux Sud-Ouest for u ∈ C2,α(Ω), f ∈ Cα(Ω), and [email protected] 1/2 2 1 u − uh L∞ ≤ C ln h h CP15 Advances in Adaptively Weighted Finite Element for u ∈ C3,1(Ω), f ∈ C0,1(Ω). Methods Wujun Zhang The overall effectiveness of finite element methods may Department of Mathematics be limited by solutions that lack smoothness on a rela- University of Maryland tively small subset of the domain. By enhancing norms [email protected] and and/or inner products in the variational framework with weight functions chosen according to a coarse-scale Richardo Nochetto approximation, it is possible to recover near-optimal con- University of Maryland vergence rates. In this talk we give an overview of the Department of Mathematics general approach, both in the least-squares and Galerkin [email protected] settings, and illustrate with numerical examples.

Chad Westphal CP16 Wabash College The Influence of Stochastic Parameters on Calcium [email protected] Waves in a Heart Cell In this study, we investigate the effects of stochastic release CP15 from calcium release units (CRUs) on generating calcium Numerical Simulations of Bioresorbable Vascular waves considering a distribution for the flux density term Stent with Automatic Patient-Specific Geometry sampled (i) once for all CRUs and (ii) for each CRU in- Construction and Adaptive Meshing dependently. We include a stochastic flux density term as more physiologically appropriate than a fixed release rate. The invention of Bioresorbable Vascular Stent(BVS) We use an array of statistical techniques as well as paral- opened a new era for cardiovascular intervention technol- lel computing to facilitate the large number of simulation ogy as it offers numerous benefits for patients. Patient- runs. specific CFD Simulation of stented vessel is a great tool to analyze potential risks of BVS such as restenosis. Cur- Matthew W. Brewster rent work in BVS research is limited to geometries with University of Maryland, Baltimore County no clear appearance of the stent. However, we have devel- [email protected] 20 AN14 Abstracts

Xuan Huang [email protected] Department of Mathematics and Statistics University of Maryland, Baltimore County [email protected] CP16 Stochastic Homogenization of the One- Matthias K. Gobbert Dimensional Keller-Segel Chemotaxis System University of Maryland, Baltimore County Department of Mathematics and Statistics In this talk, we focus on the one-dimensional Keller-Segel [email protected] chemotaxis system in a random heterogeneous domain. We assume that the corresponding diffusion and chemotaxis coefficients are given by stationary ergodic processes, Bradford E. Peercy and we apply methods pertaining to stochastic two-scale Department of Mathematics and Statistics convergence to derive the homogenized macroscopic equa- University of Maryland, Baltimore County tions. Special attention is paid to developing numerical [email protected] algorithms for approximating the homogenized asymptotic coefficients. This is joint work with Mariya Ptashnyk. Padmanabhan Seshaiyer George Mason University Anastasios Matzavinos [email protected] Division of Applied Mathematics Brown University [email protected] CP16 Simulation of Calcium Waves in a Heart Cell on Mariya Ptashnyk Modern Parallel Architectures Division of Mathematics University of Dundee Simulating calcium induced calcium flow in a heart cell [email protected] requires solving a system of advection-reaction-diffusion equations in three space dimensions. Efficient parallel computing is necessary to enable long-time simulations on CP16 high-resolution meshes. Modern architectures with multi- Neural Implementation of Shape-Invariant Touch ple memory hierarchies in CPU and coprocessors such as CounterBasedonEulerCalculus GPUs and the Intel Phi offer opportunities to speed up the numerical kernels of PDE solvers dramatically. One goal of neuromorphic engineering is to imitate the brain’s ability to count the number of objects based on Xuan Huang the global consistency of the information from the pop- Department of Mathematics and Statistics ulation of visual or tactile sensory neurons whatever the University of Maryland, Baltimore County objects’ shapes are. To achieve this flexibility, it is essen- [email protected] tial to utilize topological methods rather than ad hoc algorithms. Although latest works by mathematicians tackled Matthias K. Gobbert fundamental problems for shape-invariant count, they lack University of Maryland, Baltimore County the circuit implementations to save computational time for Department of Mathematics and Statistics big data. Here we propose a fully parallelized algorithm [email protected] for a shape-invariant touch counter for 2D pixels. The touch number is counted by the Euler integral, a general- Bradford E. Peercy ized integral, in which a connected component counter for Department of Mathematics and Statistics binary images (Betti number) was used as elemental mod- University of Maryland, Baltimore County ule. Through examples, we demonstrate how the proposed [email protected] circuit embodies the Euler integral in the form of recursive vector operations, with scalability to high resolutions of pixels.

CP16 Keiji Miura A Model of Brain Neuro-Mechanics Tohoku University [email protected] Brain tissue is sensitive to mechanical forces and chemical imbalances which can alter brains functions and/or Kazuki Nakada structure and lead to neurological diseases. Mathematical The University of Electro-Communications models of brain neuro-mechanics can increase our under- [email protected] standing of how brain works and help develop better diagnostic and therapeutic tools. We propose to model the brain as a mixture material and investigate the linkages CP17 between neural activity and mechanical behavior of brain Interface Tracking Using Level Set and A Fast Al- tissue through computer simulations. gorithm

Bradford J. Lapsansky Although moving interface problem is an interesting prob- The Pennsylvania State University lem in physics, it is challenging to obtain accurate and sta- [email protected] ble numerical solution because interface problems are singular and sensitive with small perturbations. In this talk, Corina Drapaca we will discuss an interface tracking method for the solution Department of Engineering Science and Mechanics of 2D incompressible Stokes ﬂow problems within an unit Pennsylvania State University disk as an application of a fast algorithm [L. Borges and AN14 Abstracts 21

P. Daripa, A fast parallel algorithm for the Poisson equa- the Curl operator using Gauss’ Theorem instead. This re- tion on a disk, J. Comput. Phys., 16 (2001), pp. 151–192.] definition allows us to present a discretization framework which is based on the principle of convolution of integrals that naturally inherits all the desirable properties of the involving Green’s function and exact analysis. mimetic differential operators. We present the mathematical justification for this redefinition and we implement this JoungDong Kim mimetic Curl operator testing it on 2 and 3D test cases. Texas A&M University Physical applications concern the computational study of [email protected] hurricanes.

Prabir Daripa Eduardo J. Sanchez Department of Mathematics Computational Science Research Center Texas A&M University San Diego State University [email protected] [email protected]

Guillermo Miranda CP17 San Diego State University Field-split Preconditioned Inexact Newton Algo- Computational Science Research Center rithms [email protected]

To improve the convergence of systems with unbalanced Jose Castillo nonlinearities, the field-split preconditioned inexact New- Computational Science Research Center ton (FSPIN) algorithm is introduced as a complementary San Diego State University form of the additive Schwarz preconditioned inexact New- [email protected] ton (ASPIN) algorithm, based on partitioning of degrees of freedom in a nonlinear system by field type rather than by subdomain. We introduce two types of FSPIN algorithms: CP17 Jacobi-type and Gauss-Seidel-type, and we augment the classical Jacobi-type convergence theory for the latter. Fast Structured Direct Spectral Methods for Dif- ferential Equations with Variable Coefficients Lulu Liu King Abdullah University of Science and Technology We study the rank structures of the matrices in Fourier- [email protected] and Chebyshev-spectral methods for differential equations with variable coefficients in one dimension. We show analytically that these matrices have a so-called low-rank prop- David E. Keyes erty, and develop a matrix-free direct spectral solver, which KAUST has nearly O(N) complexity and O(N)memory.Numerical [email protected] tests for several important but notoriously difficult problems show the superior efficiency and accuracy of the direct CP17 solutions, especially when iterative methods have severe difficulties in the convergence. A Dual Iterative Substructuring Method with An Optimized Penalty Parameter Yingwei Wang Purdue University In this talk, we will present a domain decomposition Purdue University method based on augmented Lagrangian. The proposed [email protected] method imposes the continuity on the interface not only by using Lagrange multipliers but also by adding a penalty term which consists of a positive penalty parameter and a Jie Shen measure of the jump across the interface. The study for Purdue University the proposed method with an optimized penalty parame- [email protected]. edu ter will be discussed in terms of its convergence analysis and practical efficiency. Jianlin Xia Purdue Eun-Hee Park [email protected]. edu KAIST [email protected] CP17 Chang-Ock Lee A Hybrid Fd-Fv Method for First-Order Hyper- Department of Mathematical Sciences bolic Systems KAIST [email protected] We describe a hybrid FD-FV approach to solve first-order hyperbolic systems. These methods use cell averages and nodal values as dependent variables, and evolve them in CP17 time by the method of lines. They use the integral form Redefining a Mimetic Curl Operator Using Gauss’ of the PDE and Hermite interpolation polynomials to dis- Theorem with Applications in Computational Cli- cretize the cell averages and nodal values in space, respec- mate and Weather Modeling tively. We present the accuracy and stability analysis of these methods to solve problems in one and two dimen- The common way to define a Curl operator considers sions. Stoke’s Theorem and the concept of circulation. Com- mon numerical discretizations for this operator also use Xianyi Zeng this approach. In this work, we present a redefinition of Duke University 22 AN14 Abstracts

[email protected] Li Ming, Eric De Sturler Virginia Tech [email protected], [email protected] CP18 Block Preconditioners for Biot’s Equations CP18 Biot’s equations are a popular model for geomechanical Sensitivity of Leverage Scores to Perturbations simulations of fluid flow in elastic porous media. These simulations are run on a very large scale, resulting in a The leverage scores of a matrix A with full column rank large number of unknowns. Further complicating matters are the squared row norms of any matrix that contains is that the domains have complex geometry and a vast an orthonormal basis for the range of A. Leverage scores range of material parameters. The linear systems that arise describe the importance of rows in regression problems after discretization of Biot’s equations are large enough and are used as sampling probabilities in randomized al- that iterative methods are required. They are also badly gorithms for matrix computations. We bound the differ- conditioned, making effective preconditioners essential. In ence between the leverage scores of A and a perturbation this work we investigate the effectiveness of several different A +ΔA when the orthonormal basis is computed by a QR preconditioners over a wide range of material parameters. factorization or SVD.

Geoﬀrey Dillon John Holodnak Texas Tech University North Carolina State University geoﬀ[email protected] [email protected]

Victoria Howle Ilse Ipsen Texas Tech North Carolina State University [email protected] Department of Mathematics [email protected] Rob Kirby Baylor University CP18 robert [email protected] Symmetric Tensor Decompositions

CP18 A tensor is a multi-way or n-way array. A tensor is sym- A Model for Tempo Synchronization in Music Per- metric if its entries are invariant to any permutation of its formance indices. A tensor may also be symmetric with respect to a subset of its modes, i.e., if its entries are invariant to A model is derived for the manner in which performers any permutation of a speciﬁc subset of its modes. We sur- of music establish and maintain tempi in the presence of vey the landscape of symmetric tensor decompositions and a conductor, other performers, and noise. The model as- compare various methods. sumes that a performer sets a tempo in response to several stimuli. This tempo, or period, correction, occurs as a su- Tamara G. Kolda perposition of responses of the form of sensitivity times Sandia National Laboratories stimulus. The model is solved and results obtained for [email protected] several cases. A model for phase correction is also derived.

CP18 Donald A. Drew Indefinite Preconditioning of the Coupled Stokes- Rensselaer Polytech Institute Darcy System Dept of Mathematical Sciences [email protected] We propose the use of an indefinite (constraint) preconditioner for the iterative solution of the linear system arising CP18 from the finite element discretization of coupled Stokes- Darcy flow. We provide spectral bounds for the precon- Recycling and Updating Preconditioners for Se- ditioned system which are independent of the underlying quences of Linear Systems mesh size. We present numerical results showing that the indefinite preconditioner outperforms both standard block For sequences of related linear systems, the computation diagonal and block triangular preconditioners both with of a preconditioner for every system can be expensive. Of- respect to iteration count and CPU times. ten a fixed preconditioner is used, but this may not be effective as the matrix changes. We analyze cheap updates Scott Ladenheim to preconditioners: Incremental updates (Calgaro et al) Temple University and sparse approximate inverse updates to ILUTP precon- [email protected] ditioners and updates to factorized sparse approximate inverse preconditioners (Bellavia et al.) Applications include model reduction, the Quantum Monte Carlo method, and Princ Chidyagwai others. Loyola University [email protected] Arielle K. Grim Mcnally Virginia Tech Daniel B. Szyld Eric de Sturler Temple University [email protected] Department of Mathematics AN14 Abstracts 23

[email protected] by Total Least-Squares Adjustment

Over a century ago Pearson (1901) solved the problem of CP19 fitting lines in 2-space to points with noisy coordinates in Optimisation and Conditioning in Variational Data all dimensions. Surprisingly, however, the case of fitting Assimilation lines in 3-space has seen little attention. We solve this problem using a new algorithm for the Total Least-Squares Data assimilation merges observations with a dynamical solution within an Errors-In-Variables (EIV) Model, re- model to find the optimal state estimate of a system given spectively an equivalent Gauss-Helmert Model. Follow- a set of observations. It is cyclic in that it is applied at ing Roberts (1988), only four parameters are estimated, fixed time intervals and the beginning of each cycle in- thereby avoiding over-parameterization that may lead to corporates the previous cycle known as the background unnecessary singularities. or apriori estimate. Variational data assimilation aims to Kyle B. Snow, Burkhard Schaffrin minimise a non-linear, least-squares objective function that School of Earth Sciences is constrained by the flow of the (perfect) dynamical model The Ohio State University (4DVAR).Relaxing the perfect model assumption gives rise [email protected], aschaff[email protected] to weak-constraint 4DVAR, which has two formulations of interest. Gradient-based iterative solvers are used to solve the problem. We gain insight into accuracy and conver- CP19 gence by studying the condition number of the Hessian. Bounds on the condition number are demonstrated using a A Block-Coordinate Descent Approach for Large- simple model and are utilised to illustrate the effect of dif- Scale Sparse Inverse Covariance Estimation ferent assimilation components on the conditioning which can highlight interesting architectural differences between The Sparse Inverse Covariance Estimation problem arises both formulations. in many statistical applications in Machine Learning. In this problem, the inverse of a covariance matrix of a multi- Adam El-Said variate normal distribution is estimated, assuming that it University of Reading is sparse. An l-1 regularized log-determinant optimization [email protected] problem is solved to compute such matrices. Because of memory limitations, most algorithms are unable to handle Nancy K. Nichols large scale instances of this problem. We present a new University of Reading block-coordinate descent approach for solving the prob- Department of Mathematics lem for such large-scale data sets. Our method treats the [email protected] sought matrix block-by-block using quadratic approximations. Numerical experiments demonstrate the potential of this approach. Amos Lawless University of Reading Eran Treister [email protected] Computer Science Department, Technion [email protected] CP19 Javier Turek A Primal-Dual Simplex Algorithm to Enumerate Computer Science Department the Mixed Cells of a Polynomial System Technion [email protected] When the polyhedral homotopy continuation method is used to locate all isolated zeros of a polynomial system, the Irad Yavneh process of enumerating all the mixed cells plays a critical Computer Science Department, Technion role: it provides starting points for the solution paths and [email protected] governs the efficiency of the continuation method. When locating mixed cells, one must deal with a large number of linear programming problems. Rather than the more pop- CP19 ular interior point method, the simplex method is used for those LP problems because its underlying pivoting struc- Coupled Spring Forced Multiagent Coordination ture provides indispensable information in the process. An Optimization for Mixed-Binary Nonlinear Pro- efficient primal-dual algorithm to enumerate all the mixed gramming cells will be presented. Mixed-binary nonlinear programming(MBNP) optimizing Tsung-Lin Lee the network structure and network parameters simultane- National Sun Yat-set University ously has been seen widely applications in cyber-physical [email protected] system nowadays. Swarm intelligence based optimization algorithms simulate the cooperation and interaction behaviors from social or nature phenomena as optimization Tien-Yien Li to solve complex, non-convex and/or ill-conditioned non- Department of Mathematics linear problems of high efficiency. In this research, we pro- Michigan State University pose a coupled spring forced multiagent coordination op- [email protected] timization (CSFMCO) algorithm by considering that each particle is a spring and is coupled with the optimal solution founded so far as the second abstract spring to offer a new CP19 efficient algorithm to solve the MBNP problem. Contin- Fitting a Straight Line in Three-Dimensional Space uous optimizer, binary optimizer and the switch between 24 AN14 Abstracts

continuous and binary optimizers will be investigated. Princeton Plasma Physics Laboratory [email protected] Haopeng Zhang,QingHui Department of Mechanical Engineering Texas Tech University CP20 [email protected], [email protected] A Performance-Portable Implementation of the Al- bany Ice Sheet Model: Kokkos Approach

CP20 Modern HPC applications need to be run on many different Modeling Accidental Explosions and Detonations platforms and performance portability has become a critical issue: parallel code needs to be executed correctly and The physical mechanism and constraints required for a De- performant despite variation in the architecture, operating flagration to Detonation Transition (DDT) in a large num- system and software libraries. In this talk we’ll present ber of explosive devices is investigated. The Uintah Com- our progress towards a performance portable implementa- putational Framework is utilized to model explosives using tion of the finite element assembly in the Albany Ice Sheet large computational platforms. Current efforts are focused Model code, based on Kokkos programming model from on a parametric study to determine if inertial confinement Trilinos. could cause a transition to detonation. These simulations will give insight into the physical mechanism of DDT for Irina Demeshko, H. Carter Edwards large-scale explosions and help determine safe packaging Sandia National Laboratories configurations to eliminate DDT in transportation acci- [email protected], [email protected] dents. MichaelA.Heroux Jacqueline Beckvermit Sandia National Laboratories Department of Chemsitry Albuquerque, New Mexico, USA University of Utah [email protected] [email protected] ERIC T. Phipps, ANDREW G. Salinger Todd Harman Sandia National Laboratories Department of Mechanical Engineering [email protected], [email protected] University of Utah [email protected] CP20 Andrew Bezdjian Matrix-Free Krylov Subspace Methods on Modern University of Utah CPUs and Many-Core Processors [email protected] We study methods to implement Krylov Subspace methods in matrix-free form that take advantage of the memory hi- Qingyu Meng erarchy of modern CPUs and many-core processors such as SCI Institute GPUs and the Intel Phi. We also work to develop an effec- Univeristy of Utah tive preconditioner for Krylov subspace methods for linear [email protected] systems arising from the discretization of PDEs that is easy to program. We use a finite difference approximation of an Alan Humprey, John Schmidt elliptic test problem for the computational experiments. University of Utah [email protected], [email protected] Samuel Khuvis Department of Mathematics and Statistics Martin Berzins University of Maryland, Baltimore County Scientific Computing and Imaging Institute [email protected] University of Utah [email protected] Matthias K. Gobbert University of Maryland, Baltimore County Chuck Wight Department of Mathematics and Statistics Weber State University [email protected] [email protected] Andreas Meister University of Kassel CP20 Institute of Mathematics Finite Elements in Flux Coordinates in Gyrokinetic [email protected] Turbulence Simulation

A series of finite elements with C0 and C1 continuity are CP20 constructed in curved flux coordinates in gyrokinetic tur- Parallel Techniques for the Incomplete-LU Factor- bulence modeling. The difficulties with flux coordinate Ja- ization cobian and periodic domain and the solution strategies will be demonstrated. This is the first time two-dimensional fi- The incomplete-LU factorization (ILU) is one of the most nite elements are constructed in this type of coordinate popular black-box preconditioning techniques. However, systems which are used everywhere in fusion plasma simu- incomplete factorizations are challenging to effectively im- lation. plement on massively parallel computer architectures, such as GPUs. In this talk we present an in-depth study of dif- Jin Chen ferent existing parallelization techniques for ILU, such as AN14 Abstracts 25

level-scheduling, multi-coloring and multi-level approaches, cal predictions match well with full numerical simulations, as well as more recent communication avoiding algorithms and suggest optimal geometries. This work may also aid and related power(q)-pattern method. We discuss their designs in microfluidic manipulation, microswimmer engi- properties and relationships. Finally, we present relevant neering, and the mixing of viscous fluids. numerical experiments. Lei Li, Saverio Spagnolie Maxim Naumov University of Wisconsin-Madison NVIDIA [email protected], [email protected] [email protected] CP21 CP20 Mathematical Model and Simulation of Particle Effective Parallel Preconditioners for CFL Appli- Flow Around Choanoflagellates Using the Method cation of Regularized Stokeslets

We focus on the fast iterative solution of linear systems on Choanoflagellates are unicellular organisms whose intrigu- GPUs, in particular, for problems from computational fluid ing morphology includes a set of collars/microvilli emanat- dynamics. Krylov subspace solvers mostly can be imple- ing from the cell body, surrounding the beating flagellum. mented efficiently on GPUs; however, the preconditioner We investigate the role of the microvilli in the feeding and is often a bottleneck. In fact, many of the most effective swimming behavior of the organism using the method of preconditioners perform poorly on GPUs, such as ILUT, regularized Stokeslets. This model allows us to depict the taking much more time than the matrix-vector product in effective capture of nutritional particles and bacteria in the spite of similar complexity. Therefore, we discuss precon- fluid and the hydrodynamic cooperation between the cell, ditioners like sparse approximate inverse preconditioners, flagellum, and microvilli of the organism. which are matrix-vector product like, as alternatives, possibly accelerated with deflation techniques like Krylov sub- Hoa Nguyen,NitiNararidh space recycling. Trinity University [email protected], [email protected] Katarzyna Swirydowicz, Eric De Sturler Virginia Tech CP21 [email protected], [email protected] Swimming Efficiently: An Analytical Demonstra- tion of Optimal Strouhal Number in Fish Xiao Xu, Christopher J Roy Virginia Tech, Department of Aerospace and Ocean Using Lighthills large amplitude elongated body theory it Engineering is shown that the kinematics of fish swimming can be re- [email protected], [email protected] duced to a single variable, Strouhal Number (St). This is accomplished by applying mathematical constraints to enforce constant velocity, low drag swimming. Using this CP21 result, it is demonstrated that Froude efficiency for swim- Equilibrium and Bifurcation Analysis of Discoidal ming can be defined directly as a function of St. This func- Lipoproteins tion correctly predicts the behavior of swimmers across a wide range of sizes. A discoidal lipoprotein particle consists of a lipid bilayer bounded by a protein polymer chain. In isolation, the free Alexander J. Wiens energy of such a particle is the sum of the bending-energy Massachusetts Institute of Technology of the bilayer and the bending and torsional energy of the [email protected] chiral protein loop. The Euler–Lagrange equations governing the equilibrium of such particles are derived. Also, Anette Hosoi a finite-element solver is employed to obtain approximate Massachusetts Institute of Technology numerical solutions and analyze possible conformations of 77 Massachusetts Avenue, Room 3-173, Cambridge MA these particles. 02139 Aisa Biria [email protected] McGill University [email protected] CP22 Analysis of a Large Time Step and Overlapping Eliot Fried Grids Method for Hyperbolic Conservation Laws Okinawa Institute of Science and Technology [email protected] We propose a numerical method for approximate solving of hyperbolic conservation laws. The method is based on a finite volume method and our novelties are twofold. First, CP21 our method is a Large Time Step method which enables us Swimming and Pumping of Helical Bodies in Vis- to march faster in time. Secondly, the method incorporates cous Fluids overlapping grids which is a very important issue in many practical applications. In one space dimension, we prove Many flagellated microorganisms including E. coli swim that the method converges to the entropy solution of the by rotating slender helical flagella, while ciliated organ- conservation law. We also present numerical simulations isms like Paramecia swim by passing helical waves along for Burger’s equation and the Lax problem for the Euler their surfaces. We will discuss a framework for study- gas dynamics equations. ing such problems where the Stokes equations describing viscous flow are written in helical coordinates. Analyti- Ilija Jegdic 26 AN14 Abstracts

Department of Mathematics, University of Houston the distribution function in spherical harmonics (i.e., the i [email protected] Pn approximation). One key difficulty in solving such systems is that standard numerical schemes have maximum time-step restrictions that vanish in the singular limit. Sev- CP22 eral approaches have been proposed in the literature that Filtered Positive PN Closure for Kinetic Transport overcome this difficulty, many of which are based on split- Equations ting the equation into stiff and non-stiff pieces and using appropriate semi-implicit time-stepping methods. In this We propose a modification to the standard spherical har- work we employ a different strategy in order to achieve monic closure, known as PN closure, used for linear kinetic asymptotic-preservation. We develop a scheme using a dis- equations. The modification produces smooth, nonnega- continuous Galerkin semi-Lagrangian scheme. Several nu- tive polynomial particle distributions by using two-step fil- merical test cases are used to validate the proposed scheme. tering on the oscillatory, partially negative PN solutions; closes the moment system using filtered polynomial ansatz; Anna Lischke and integrates the closed moment system with filtered mo- Iowa State University ments. We formulate the filtering process as a quadratic [email protected] program, and demonstrate numerical results on the challenging line source benchmark problem. James A. Rossmanith Deparment of Mathematics Ming Tse P. Laiu Iowa State University Department of Electrical and Computer Engineering [email protected] University of Maryland - College Park [email protected] CP22 Cory Hauck Positivity-Preserving WENO Schemes with Con- Oak Ridge National Laboratory strained Transport for Ideal MHD [email protected] We will discuss a novel positivity-preserving flux limiting Dianne P. O’Leary technique developed for WENO schemes to solve idea mag- University of Maryland, College Park netohydrodynamic (MHD) equations. There are two main Department of Computer Science steps in our MHD solver: first updating conservative quan- [email protected] tities by WENO scheme with positivity-preserving limiter and then correcting the magnetic field and total energy by AndréTits a high-order constrained transport approach. Several ex- University of Maryland at College Park amples are presented to verify the order of accuracy and to [email protected] demonstrate the efficiency of positivity-preserving limiter. Qi Tang, Andrew J. Christlieb, Yuan Liu CP22 Department of Mathematics Michigan State University Unconditionally Optimal Error Estimates of Fully [email protected], [email protected], Discrete Fems for Parabolic Equations [email protected] Error analysis of fully discrete finite element methods for nonlinear parabolic equations often requires certain time- Zhengfu Xu step size conditions (or stability conditions) such as Δt = Michigan Technological University O(hk), which are widely used in the analysis of the nonlin- Dept. of Mathematical Sciences ear PDEs from mathematical physic. In this talk, we sug- [email protected] gest a new approach to analyze the discretization error of fully discrete FEMs for nonlinear parabolic equations. By this new approach, we found that the time-step size restric- CP22 tions are not necessary for most problems. To illustrate our Partially Penalized Immersed Finite Element idea, we analyze some models from mathematical physics, Methods for Elliptic Interface Problems e.g. the thermistor problem, miscible flow in porous media and gradient flows, with linearized backward Euler scheme In this talk, we present new immersed finite element (IFE) for the time discretization. Previous works on the these methods for the second order elliptic interface problems models all required certain time-step size conditions. on Cartesian meshes. Closely related to traditional IFE methods which are based on Galerkin formulation, these Buyang Li new IFE methods contain extra stabilizing terms at inter- Nanjing University, China face edges to penalize the discontinuity in IFE functions. [email protected] Error estimation shows that these IFE methods converge optimally in an energy norm. Numerical examples demonstrate that these new methods outperform traditional IFE CP22 methods at the vicinity of the interface. Asymptotic-Preserving Semi-Lagrangian Discon- tinuous Galerkin Schemes for a Class of Relaxation Xu Zhang Systems Purdue University [email protected] We consider in this work a class of singularly perturbed hyperbolic balance laws that admit a diffusive limit. Such systems arise naturally in radiative transport applications CP23 if one starts with a Boltzmann description and expands Lagrangian Particle Methods for Global Atmo- AN14 Abstracts 27

spheric Flow [email protected]

We present a particle method for global atmospheric ﬂow in James Glimm spherical geometry based on the Lagrangian formulation of State University of New York, Stony Brook the ﬂuid equations. Poisson equations for the stream func- [email protected] tion and velocity are solved using integral convolution with Green’s function for the sphere, which is approximated numerically with singular point vortices and point sources Baolian Cheng using midpoint rule quadrature. An adaptive remeshing LosAlamosNationalLab procedure is applied at regular time intervals to maintain [email protected] spatial accuracy on the Lagrangian particles. Solutions of the barotropic vorticity equation are presented, and on- David Sharp going work with the shallow water equations is discussed. Los Alamos National Laboratory [email protected]

Peter A. Bosler University of Michigan CP23 Applied and Interdisciplinary Mathematics [email protected] Continuum Boundary Force Method for Multiscale Modeling of Flows Subject to Slip Boundary Con- ditions CP23 Numerical Derivation of a D˙ −D−κ Relation for An When fluid flow velocity at fluid-solid interfaces is non-zero, Expanding Detonation Wave in the Mie-Gruneisen the flow is said to have “slip’ at the fluid-solid boundary. Equation of State This phenomenon is commonly described by the Navier boundary condition or, more generally, Robin-type bound- The propagation behavior of a detonation wave expansion ary conditions. Here we propose the Continuous Boundary can be described asymptotically by Taylor blast wave the- Force (CBF) method for imposing Robin boundary condi- ory (TBW) in the limit of a small, rapid wave, and by tions in Smoothed Dissipative Particle Dynamics (SDPD) geometrical shock dynamics (GSD) in the limit of a large, simulations. We demonstrated the efficiency and accuracy steady wave. We use a hydrodynamic solver to find a nu- of the SDPD-CBF method for modeling slip flows subject merical relationship between the curvature, velocity, and to the Robin boundary conditions with arbitrary (constant, acceleration of the detonation wave that describes the tran- space-dependent, or non-linear) slip lengths at flat and sition between the limits in the ideal and Mie-Gruneisen curved boundaries. Furthermore, the consistent thermal equations of state. scaling in the SDPD-CBF method allows it to also be used for multiscale modeling, i.e., bridging scales in concurrent Brandon A. Lieberthal coupling from the continuum hydrodynamic scale all the University of Illinois at Urbana-Champaign way to the molecular scale. [email protected] Wenxiao Pan D. Scott Stewart Pacific Northwest National Laboratory Mechanical Science and Engineering [email protected] University of Illinois at Urbana Champaign [email protected] Alexandre Tartakovsky University of South Florida [email protected] CP23 Turbulent Mix in Numerical Simulations for ICF Nathan Baker Capsules Pacific Northwest National Laboratory [email protected] We study the turbulent mixing zone in an Inertial Confine- ment Fusion (ICF) capsule, with a focus on the Rayleigh- Taylor (RT) unstable deceleration phase of hot spot forma- CP23 tion. Our main results are twofold: (i) a ”post shot” simulation with modifications to input parameters that better Hydrodynamic Calculations Using Reale: An resemble experimental observations and (ii) examination of Arbitrary-Lagrangian-Eulerian Framework with the resulting hot spot and turbulent mixing zone proper- Mesh Reconnection ties. We examine a new ALE hydro scheme that allows for on- Hyunkyung Lim the-fly mesh reconnection based on the Voronoi diagram SUNY at Stony Brook [Loubere et al, ReALE: A Reconnection-Based Arbitrary- Department of Applied Mathematics and Statistics Lagrangian-Eulerian Method, JCP, 2010]. Reconnection [email protected] allows the mesh to follow Lagrangian features in the flow more closely than standard ALE schemes while avoiding Jeremy Melvin the problem of mesh tangling typical of pure Lagrangian Stony Brook University schemes. We outline our methodology for ReALE and Stony Brook NY present results demonstrating its effectiveness on several [email protected] challenging compressible hydrodynamic tests.

Verinder Rana David Starinshak, John Owen, Douglas Miller Stony Brook University Lawrence Livermore National Laboratory 28 AN14 Abstracts

[email protected], [email protected], [email protected] [email protected]

CP23 CP24 Modeling the Progression and Development to A Smoothed Particle Hydrodynamics Model for Hepatocellular Carcinoma for Hepatitis C Virus In- Electrokinetic Flows fection

Theoretic description of electrokinetic phenomena includes The mathematical model considered here is the first at- the Poisson-Boltzmann equation relating the electric field tempt to encapsulate the long-term dynamics of hepatitis to ion concentration and Navier-Stokes equations relating C virus (HCV) infection and the influence of viral and im- the flow velocity to the pressure and electrostatic forces mune processes in the gradual progression and development acting on the system. A Lagrangian particle model based to hepatocellular carcinoma (HCC). The key basis for the on smoothed particle hydrodynamics is proposed to nu- model formulation is that the long-term implications are merically solve the coupled equations. And a fast multi- random and are very likely caused by cell-mediated im- level pre-conditioned method by means of auxiliary space mune response. The chances of development of cancer are is incorporated as the linear solver for the associated Pois- modeled by way of a stochastic model which takes into ac- son equation. The efficiency and accuracy of the proposed count the dynamics over the infection duration. Sampling model are examined through modeling the electroosmotic based simulations show that the development rate of HCC flow in microchannels and flow through charged mem- over a period of 40 years is about 9%, which is in conso- branes. A good agreement is found in comparison with the nance with estimates available in literature. Simulations corresponding analytical or finite-element solutions. The also show that the chance of developing HCC increases lin- diffusion-advection equation relating the species mass con- early along with the length of period of infection at a rate centration to flow velocity is then coupled to investigate of 2.4 incidents per year for every thousand infected indi- the influence of surface heterogeneity on electrokinetically viduals. driven microfluidic mixing. Siddhartha P. Chakrabarty Dept. of Mathematics Wenxiao Pan Indian Institute of Technology Guwahati Pacific Northwest National Laboratory [email protected] [email protected] John Murray Hongxuan Zhang, Xiaozhe Hu School of Mathematics The Pennsylvania State University University of NSW [email protected], hu [email protected] [email protected]

Jinchao Xu Pennsylvania State University CP24 [email protected] Quantifying the Relationships among Natural Se- lection, Mutation, and Stochastic Drift in Multidi- mensional Finite Populations CP24 The interrelationships of the fundamental biological pro- Mutational History Dominates Clonal Selection cesses natural selection, mutation, and stochastic drift are Within Evolving Tumors quantified by the entropy rate of Moran processes with mutation, measuring the long-run variation of a Markov pro- Natural selection acting on clonal diversity within tumors cess. The entropy rate is shown to behave intuitively with is thought to drive tumor progression, but details remain respect to evolutionary parameters such as monotonicity obscure. Evolutionary mathematical models of the angio- with respect to mutation probability (for the neutral land- genic switch predict the emergence of hypovascular necro- scape), relative fitness, and strength of selection. Strict sis caused by hypertumors—“cheating” clones that free- upper bounds, depending only on the number of replicat- ride on vasculature organized by cooperative clones. Here ing types, for the entropy rate are given and the neutral we show that hypertumors should rarely evolve because fitness landscape attains the maximum in the large popu- the deterministic evolutionary trajectory is overwhelmed lation limit. by stochastic mutational history. These results highlight mutation pressure as a significant evolutionary force in can- Marc Harper cer. UCLA [email protected] Scott T. Bickel Arizona State University CP24 Scottsdale Community College Competition Between Oysters and Invasive Mus- [email protected] sels in the Presence of Water Releases

Joseph Juliano The Asian green mussel competes with oyster populations Arizona State University in parts of Florida, displacing some reefs in Tampa Bay. [email protected] However, oysters are more tolerant of salinity changes that can occur, such as when large freshwater releases are made. John D. Nagy Releases along waterways can take diﬀerent forms, with Scottsdale Community College some recent ones being large in volume relative to time. We Arizona State University present an ODE system modeling the population dynamics, AN14 Abstracts 29

including the eﬀect of fresh water releases. Some numerical Department of Mathematics results are included. Virginia Tech [email protected] Daniel L. Kern Florida Gulf Coast University Tao Lin Dept of Chemistry and Mathematics Virginia Tech [email protected] [email protected]

CP24 CP25 A Mixed-Strategy Game Theoretical Approach for Flow Control by Adjoints and Sensitivities Infectious Disease Prevention by Social Distancing I will present an algorithm for flow control which is based We describe a population game in which individuals are al- on the derivation of adjoint equation using Lagrange mul- lowed to decide between adopting different social distanc- tipliers. This algorithm involves computing gradient of an ing strategies in order to lower infection risk and maximize user-defined objective function that has the system control payoffs. When the reduction in infection risk is a convex settings resulting in sensitivity expressions. Characteris- function of the cost of social-distancing, there is a unique tic analysis is incorporated in this methodology to derive pure-strategy game equilibrium. When the reduction in sensitivity expressions that yield more information on flow infection risk is not convex, the existence of equilibria be- control as compared to sensitivity expressions that are de- comes more complicated. We will discuss three cases vis-- rived without characteristic analysis. Finally, I will show vis different costs of infection. results obtained by applying these algorithms to partial differential equations that model atmospheric flows. Jing Li California State University Northridge Vani Cheruvu [email protected] Department of Mathematics and Statistics The University of Toledo, Toledo, OH 43606 Timothy Reluga [email protected] Pennsylvanian State University [email protected] CP25 A Realizability Preserving Discontinuous Galerkin CP24 Method for the M1 Model for Radiative Transfter Traveling Wave Fronts in Population and Disease in 2D Models with Nonlocal Reaction and Delay We consider the M1 moment model for radiative transfer. We will discuss the stability of traveling wavefronts for non- In order to ensure well-possedness the moment variables of linear reaction diffusion equations with nonlocal reaction the model have to satisfy certain realizability conditions. and delay. We will prove stability of both non-critical and We present the necessary modifications to the Runge-Kutta critical wavefronts, and their rates of convergence. Appli- discontinuous Galerkin method in 2D that ensure realiz- cations will be made to a host-vector disease model, a gen- ability of the moment variables. Our goal is to resolve the eralized Nicholson blowflies model, and a modified vector time evolution of isolated sources or beams of particles in disease model. This work generalizes results of Lv-Wang heterogeneous media on unstructured triangular meshes. and Mei-et-al, and allows us to treat more realistic models. Prince Chidyagwai Peter Y. Pang Temple University National University of Singapore Department of Mathematics [email protected] [email protected]

Martin Frank CP25 RWTH Aachen University A Q2−iso−Q1/Q1 Immersed Finite Element for Center for Computational Engineering Science Stokes Interface Problems [email protected]

We present the bilinear immersed ﬁnite element (IFE) Florian Schneid methods for solving Stokes interface problems with struc- TU Kaiserslauten tured Cartesian meshes that is independent of the location [email protected] and geometry of the interface. Basic features of the bilinear IFE functions, including the unisolvent property, will Benjamin Seibold be discussed. Numerical examples are provided to demon- Temple University strate that the bilinear IFE spaces have the optimal ap- [email protected] proximation capability, and that numerical solutions produced by a Q2−iso−Q1/Q1 method with these IFE functions for Stokes interface problem also converge optimally CP25 2 1 in both L and H norms. Optimal Error Estimates of a Linearized Backward Euler Galerkin Fem for the Landau-Lifshitz Equa- Nabil Chaabane tion Virginia Tech [email protected] We present a fully discrete linearized backward Euler Galerkin FEM for the Landau–Lifshitz equation in which Slimane Adjerid a new linearization is proposed for the gyromagnetic term. 30 AN14 Abstracts

Optimal error estimates are proved almost unconditionally [email protected] (i.e. when the stepsizes h and τ are smaller than given constants). Numerical results are provided to confirm our Bruno Després theoretical analysis and show the unconditional stability of UPMC Univ Paris 06, LJLL the scheme. [email protected] Huadong Gao Department of Mathematics, CityU of HK Ricardo Weder Kowloon, Hong Kong Universidad Nacional Autonoma de México, IIMAS [email protected] [email protected]

CP25 CP26 A Particle-In-Cell Method Based on An Implicit Juxtaposition of Evaporation, Gravity and Darcian Wave Solver Resistance in Seepage Through a Silt Block Ad- jacent to a Coarse Sand Compartment: Solutions A recently developed implicit wave solver removes the CFL Based on Theory of Holomorphic Functions and condition while maintaining computational cost compara- Computer Algebra ble to explicit wave solvers. We present the application of this wave solver in a particle-in-cell (PIC) method for the 2-D wicking of soil water is analytically studied by tension- simulation of plasmas in an approach that can handle both saturated model. Along 3 sides of a transient flow tube the electrostatic and fully electromagnetic cases. We show the type of boundary conditions is fixed but the 4-th side con- results of some standard one- and two-dimensional electro- sists of no-flow boundary and constant-potential segment. static test problems, and discuss the extension to the fully In the complex potential domain, the shrinking rectangle is electromagnetic case. conformally mapped onto the rectangle in the flow domain. The Schwarz-Christoffel formula and Mobius transforma- Eric Wolf tion are used. Cauchys problem for an integro-differential Michigan State University equation with respect to an affix of the conformal mapping [email protected] is numerically solved. Physical and mathematical conditions of solvability of the equation are established. The seepage flow rate as a function of time is presented and CP26 related to the classical hydrological taxonomy of evapora- Generalization of Pade Approximation from Ra- tion stages. Applications in agricultural engineering, e.g. tional Functions to Arbitrary Analytic Functions desiccation of a coarse-textured under-canopy zone of irri- - Applications gated trees in arid conditions, is related to the developed mathematical model. We extended the basic idea of Pade approximation to any arbitrary function holormorphic in a neighborhood of the Anvar Kacimov Taylor series expansion point. This provides the flexibil- Sultan Qaboos University ity of using other functions in a Pade-type approximation, [email protected] yielding highly accurate approximations with additional desirable properties such as asymptotic behavior. In this Yurii Obnosov talk, we present applications of our method to approxima- Kazan Federal University, Russia tion of sine/cosine, Fresnel integral functions, representa- [email protected] tion of band-limited functions, and constructing multires- olution representations, i.e., chirplet decomposition. Dani Or Evren Yarman Eidgenössische Technische Hochschule Zürich Schlumberger Switzerland [email protected] [email protected]

Garret Flagg CP26 Schlumberger, Houston, TX gfl[email protected] Unexpected Fooling Functions We often rely on automatic quadrature rules to compute CP26 definite integrals that cannot be expressed in terms of el- Analysis of a Singular Integral Equation Modeling ementary functions. Unfortunately, we have found that Waves Propagating in a Fusion Plasma nearly all such algorithms can be fooled because their error estimates are based on the difference of two quadrature A singular integral equation models resonant waves in a rules. Using this insight, we have constructed fooling func- fusion plasma. This resonance called hybrid is linked to tions that are not particularly spiky, but for which the heating of a magnetic plasma. This presentation is dedi- automatic quadrature rule is grossly incorrect. This high- cated to the analysis of this equation, see [B. Després, L.-M. lights the need for better rules. Imbert-Gérard, R. Weder, Hybrid resonance of Maxwell’s equations in slab geometry, J. Math. Pures et Appl., DOI: Martha Razo 10.1016/j.matpur.2013.10.001]. A singular solution is ob- Illinois Institute of Technology tained thanks to a limit absorption principle, which pro- [email protected] vides a formula for the plasma heating. Lise-Marie Imbert-Gérard CP26 Courant Institute of Mathematical sciences, NYU Generalization of Pade Approximation from Ra- AN14 Abstracts 31

tional Functions to Arbitrary Analytic Functions of these results to chemical EOR will be discussed. -Theory Prabir Daripa We present a method for extending the basic idea of Pade Texas A&M University approximation by using an arbitrary analytic function in- Department of Mathematics stead rational functions to match a prescribed number of [email protected] terms in the Taylor series. The choice of analytic function can be used to construct highly accurate approximations. In this talk, we discuss the theory and error analysis be- CP27 hind our method. Several examples of its application will Iterative Algorithms for Geosounding Inversion be discussed in a separate talk. For most of Geosounding problems, an iterative scheme is Evren Yarman usually implemented after linearization of forward equa- Schlumberger tions. Bachmayr and Burger propossed iterative algo- [email protected] rithms for TV functionals. Those iterative algorithms are based on Bregman distance, that can be interpreted as a generalization of the mean-square distance for general func- Garret Flagg tionals. In this contribution, several novel algorithms for Schlumberger, Houston, TX nonlinear inversion of electrical, electromagnetic and re- gfl[email protected] sistivity soundings based on Bregman iterations are presented. Results are reported of algorithm implementation for several geosounding methods applying Bregman dis- CP27 tance to minimize the TV and MS functionals. The linear Rate-Limited Sorption in Production Transport approximation for electromagnetic soundings at low induc- Codes tion numbers is implemented on the inversion algorithm. A comparison of developed models for Bregman based al- Computational models of contaminant transport are used gorithms with those obtained with a linear programming regularly for designing subsurface environmental remedi- package is also presented for synthetic and field data. ation systems. In many soils, the contaminant sorbs to the solid matrix in the porous media. As a result, the Hugo Hidalgo rate of removal by traditional pump-and-treat flushing is CICESE-Ciencias de la Computacion much slower than predicted with equilibrium models. This [email protected] phenomenon is called rate-limited sorption (RLS) and it is particularly problematic in cases where the contaminant Enrique Gomez-Trevino has been in place for a long period of time. Although RLS CICESE-Geofisica Aplicada is well known in academic literature, production models [email protected] used for field work have failed to incorporate the effect. As a result, remediation designs and cleanup time projections are often inaccurate. In this project, a well-validated CP27 production subsurface transport model is modified with a A Higher-Order Robert-Asselin Type Time Filter simple analytical model for layers and lenses that incorporates RLS effects with reasonable computational costs. We propose and analyze a higher-order Robert-Asselin Preliminary results show good agreement with RLS behav- (hoRA) type time filter for weather and climate models. ior. While requiring the same amount of computational effort as the Robert-Asselin-Williams filter, the hoRA filter ef- David L. Coulliette fectively suppresses the leapfrog schemes computational Mathematics and Computer Science Department modes and achieves third-order accuracy. The hoRA fil- Asbury College ter is shown to be suitable for long-time simulations. In [email protected] addition, the filter is non-intrusive, and so it would be easily implementable in the existing legacy codes. Kenneth Rietz Asbury University Yong Li [email protected] University of Pittsburgh [email protected] Edward Heyse Parsons Corporation Catalin S. Trenchea [email protected] Department of Mathematics University of Pittsburgh [email protected] CP27 Fingering Instability in the Presence of Visco- CP27 elasticity Coupled Multi-Physics Analysis of Caprock In- tegrity and Joint Reactivation During Co2 Seques- With the motivation of understanding the effect of com- tration plex rheological properties of complex fluids often used in chemical enhanced oil recovery, we study linear instabil- Structural trapping beneath a low-permeable caprock layer ity of the displacement of a visco-elastic complex fluid and is the primary trapping mechanism for long-term subsur- quantify the effect of elasticity on fingering instability. An face sequestration of CO2. We modeled the effects of exact formula is provided which shows that the elasticity caprock jointing on the caprock sealing. The modeling ef- has a destabilizing effect on fingering instability. Relevance fort uses a 3D-FEM based coupled multiphase flow and ge- 32 AN14 Abstracts

omechanics simulator. Various injection schedules as well that the proposed heuristics perform signiﬁcantly better as caprock jointing conﬁgurations within a proto-typical than the existing heuristics in terms of both error and com- sequestration site have been investigated. The resulting putation time. leakage rates through the caprock and fault are compared to those assuming intact material. Ali Allahverdi Pania Newell Kuwait University Sandia National Laboratory [email protected] [email protected] Harun Aydilek, Asiye Aydilek Mario, J. Martinez, JOSEPH, E. Bishop Gulf University for Science and Technology Sandia National Laboratories [email protected], [email protected] [email protected], [email protected]

CP28 CP27 Modeling of Arctic Melt Ponds and Sea-Ice Computing Spectra of Laplace Beltrami Operator Albedo-Feedback Using Cylindrical Radial Basis Functions

We study possibility of the climate system to pass through The spectrum of the Laplace-Beltrami (LB) Operator is a bifurcation point - irreversible critical threshold as the known to provide an intrinsic shape signature for 3D shape system progresses toward ice-free summers. This study matching. Given point clouds on a 2 manifold, we utilize is based on the nonlinear phase transition model for melt a novel cylindrical Radial Basis function to eﬃciently ap- ponds and bifurcation analysis of a simple climate model proximate the surface and compute the Eigen values of the with the positive sea ice - albedo feedback as a key mech- LB operator. At the end, we perform numerical tests to anism potentially driving the system to the bifurcation demonstrate the generality and eﬃciency of our method point.

Ivan A. Sudakov Emmanuel O. Asante-Asamani University of Utah Department of Mathematical Sciences Mathematics Department University of Wisconsin-Milwaukee [email protected] [email protected]

Sergey Vakulenko Zeyun Yu Institute for Mechanical Engineering Problems University of Wisconsin-Milwaukee Russian Academy of Sciences [email protected] [email protected] Lei Wang University of Wisconsin-Milwaukee CP28 Department of Mathematical Science Multi-Echelon Supply Chain Inventory Optimiza- [email protected] tion: An Industrial Perspective

Mathematical programming based multi-echelon inventory optimization models developed in the literature quantify CP28 uncertain demand or lead time assuming a Normal or Pois- Sub-Linear Sparse Fourier Algorithm for High Di- son distribution. We demonstrate how such assumptions mensional Data can severely impact and underestimate optimal inventory, and discuss the drawbacks of mathematical programming approaches. We present a novel simulation-optimization In this talk, we discuss how to implement a sub-linear framework that not only generates more accurate results sparse Fourier algorithm on data in high dimensional space. by bootstrapping historical data, but is also versatile to We already have the efficient algorithm with O(klogk) run- capture non-standard inventory policies and decisions. In- time for one dimensional problem with k data. We propose dustrial examples are presented. a method to embed higher dimensional data in lower space without overlap so that the existent algorithm is applica- Anshul Agarwal, John Wassick ble to modified data. In this way, we can retain the com- The Dow Chemical Company putational efficiency. It can be shown theoretically and [email protected], [email protected] computationally.

CP28 Bosu Choi University of Michigan Single Machine Scheduling Problem with Interval [email protected] Processing Times

In this paper, the single machine scheduling problem Andrew J. Christlieb with uncertain and interval processing times is addressed Michigan State Univerity with the objective of minimizing mean weighted comple- Department of Mathematics tion time. Some polynomial time heuristics, utilizing the [email protected] bounds of processing times, are proposed. The proposed and existing heuristics are compared by extensive compu- Yang Wang tational experiments. The computational results indicate Michigan State University AN14 Abstracts 33

[email protected] sion Problems

It is well known that whenever central finite difference CP28 schemes (second order or higher order central schemes) are Interpolation Using the Min Kernel applied to solve convection diffusion singularly perturbed problems (SPP) numerically on uniform meshes, non physi- We find a relationship between the second derivative of cal oscillations observed in the numerical solution and their a function f ∈ C2[0,b], such that f(0) = 0, and the magnitude increases in the layers (boundary and interior) coefficients cj obtained from the interpolation problem regions. The presence of these large non physical oscillations in the approximated solution shows that central Sf (xj )=f(xj)atpointsxj ,j =1,...,n where xj ∈ n finite difference operators on the uniform meshes are un- (0,b], Sf (x)= j=1 cj K(x, xj ), and K is the min kernel stable. To eliminate these oscillations while retaining the K(x, z)=min(x, z). We find an integral representation order of accuracy, one needs either a fine mesh at the layer. formula, then, adding the boundary condition f (b)=0, This maybe done either via uniformly fine meshing or via show that min(x, z) is the Green’s function for the Lapla- an adaptive mesh strategy. In this paper, a new adaptive cian, and we give an elementary derivation of the native mesh strategy has been developed for solving SPP with space of the min kernel. higher order central compact schemes. Our strategy uses Martin A. Dillon a novel, entropy-like variable as the adaptation parameter Illinois Institute of Technology for convection diffusion SPP. [email protected] Vivek K. Aggarwal Assistant Professor, Department of Applied Mathematics, CP28 Delhi Technological University [email protected] On the Entringer and Slater Problem Balaji Srinivasan In 1981, Entringer and Slater proposed the problem of de- Deptt. of Applied Mechanics, IIT Delhi termining Ψ(r), where Ψ(r) is the maximum number of Hauz Khas, New Delhi - 110016 cycles in a connected graph G of order p with q edges and [email protected] r = q − p + 1 (see Aldred R. E. L., Thomassen Carsten, On the maximum number of cycles in a planar graph, J. Graph Theory 57 (2008), no. 3, 255–264). In this talk, CP29 some results on this problem and related conjectures are summarized. Are Spectrally-Accurate Radial Basis Functions Obsolete? Gaussian-Mollified Polynomial Interpo- Chunhui Lai lation Zhangzhou Normal University [email protected]; [email protected] Spectrally-accurate radial basis functions (RBFs) such as Gaussians often succeed where polynomial interpolation fails because of the Runge Phenomenon. Why? Compar- CP28 ative analysis of RBF and polynomial cardinal functions (nodal bases) shows that RBF cardinals are much more Tractability of Function Approximation Problems localized. This motivated us to abandon RBFs in favor with General Kernels of Gaussian-mollified polynomial cardinal functions: much more accurate, cheaper to construct and much better con- This talk addresses the problem of approximating functions ditioned than RBFs. Using potential theory, we prove an belonging to a reproducing kernel Hilbert space H.Often exponential, geometric rate of convergence. On a uniform convergence rates deteriorate quickly as the dimension of grid, the Runge Phenomenon is not completely annulled, problem increases. Such a behavior is known as the curse but the Runge Zone is an order of magnitude smaller than of dimensionality. Therefore it is desirable to have dimen- for polynomial interpolation. Applications to solving dif- sion independent convergence rates, which corresponds to ferential equations, especially in complicated geometry, are the concept of strong polynomial tractability. We study in progress. A note was published as “Hermite Function the conditions for strong tractability on more general ker- Interpolation ..., Appl. Math. Letters, 26, 10, 995-997 nels of product form. The shape parameter, γ,governs (2013). the horizontal scale of a function in H with respect to the variable x. We also introduce a parameter α,whichgov- John P. Boyd erns the vertical scale of the function with respect to the University of Michigan variable x. The exponent of strong tractability depends ∞ Ann Arbor, MI 48109-2143 USA on how quickly the sequence (αγ)=1 tends to zero. [email protected] Xuan Zhou Illinois Institute of Technology CP29 [email protected] Solutions of Boltzmann Equation for Simulation of Particle Distributions in Plasmas Fred J. Hickernell Illinois Institute of Technology We are investigating the time evolution of the electron and Department of Applied Mathematics excited state distribution functions. We solve the time [email protected] dependent Boltzmann equation to overcome some typical limitations of modeling high pressure plasmas using Monte Carlo methods. Here we focus on the numerical approach CP29 to solving the time dependent Boltzmann equation using a An Adaptive Mesh Strategy for Convection Diffu- multi-term approximation of the electron distribution func- 34 AN14 Abstracts

tion. We also compare Boltzmann results for electron dis- Department of Mathematics tribution evolution against multiple plasma simulations us- City University of Hong Kong ing experimental collisional cross-section data. [email protected]

Jason F. Hammond Zhiyong Si University of Colorado School of Mathematics and Information Science Department of Applied Mathematics Henan Polytechnic University [email protected] [email protected]

CP29 Weiwei Sun Investigation and Numerical Solution of Initial- City University of Hong Kong Boundary Value Problem to One Nonlinear [email protected] Parabolic Equation In the presented work the difference scheme for specific CP30 initial-boundary value problem to the following nonlinear The Heuristic Static Load-Balancing Algorithm parabolic equation Applied to the Community Earth System Model 2 ∂U ∂ U 3 We propose to use the heuristic static load-balancing al- = a (x, t) + U + f (x, t) ∂t ∂x2 gorithm for solving load-balancing problems in the Com- is investigated. The coefficient a (x, t)isrequiredtobe munity Earth System Model, using fitted benchmark data continuous and positive. The function f (x, t)isrequired as an alternative to the current manual approach. The to be continuous. For the mentioned difference scheme the problem of allocating the optimal number of CPU cores to theorem of convergence of its solution to the solution of the CESM components is formulated as a mixed-integer nonlinear optimization problem which is solved by using an source problem is proved. The rate of convergence is established and it is equal to O τ + h2 . The corresponding optimization solver implemented in MINLP/MINOTAUR. numerical experiments are conducted which confirm the Our algorithm was tested on 163,840 cores of IBM Blue validity of the theorem. Gene/P.

Mikheil Tutberidze Yuri Alexeev Ilia State University Argonne National Laboratory Associated Professor [email protected] [email protected] CP30 CP29 Roadmapping An Obstacle Forest Coupled Orbital And Thermal Evolution of Major A growing spectrum of applications targeted for au- Uranian Satellites tonomous vehicles drives demand for robust path planners. We have developed a model of the orbital and thermal evo- Environment obstacle information determines route selec- lution of the five major Uranian satellites over millions tion in cluttered domains but is only partially exploited of years. The model consists of detailed ordinary differ- by sample-based algorithms. A geometric terrain-based ential equations for the orbital evolution coupled to the roadmapping approach is discussed that builds, explores one-dimensional heat equation for the thermal evolution. and updates Morse navigation functions for forests of ob- We present preliminary results that show how the differ- stacle trees. Exploiting a known mathematical character- ent terms in the orbital equations such as the oblateness of ization of valleys and ridges on the function landscape, a Uranus affect the orbital semi-major axis and eccentricity high-level roadmap connecting landscape critical points is of the satellites. constructed.

Attique Ur Rehman Thomas A. Frewen The University of Auckland United Technologies Research Center [email protected] [email protected]

CP29 CP30 A New Optimal Error Analysis of Characteristics- Optimal Control Approach and Numerical Meth- Mixed Fems for Miscible Displacement in Porous ods for Constrained Smoothing Splines Media Constrained smoothing splines are an efficient array of es- In this talk, we establish unconditionally optimal error estimators, whose performance often surpasses that of their timates for a modified method of characteristics with a unconstrained counterparts. The computation of smooth- mixed finite element approximation for the miscible dis- ing splines subject to general dynamics and control con- placement problem in Rd (d =2, 3), while all previous straints and initial state constraints is considered. The work required certain time-step restrictions. By introduc- optimal control formulation of such splines is developed. ing a characteristic time-discrete system, we prove that the Several algorithms to compute these splines, including a di- numerical solution is bounded in W 1,∞-norm uncondition- rectional derivative based nonsmooth Newton method, are ally. Thus, optimal error estimates can be obtained in a introduced. The convergence analysis of these algorithms traditional way. Numerical results are presented to confirm and numerical examples are presented. our theoretical analysis. Teresa Lebair Jilu Wang University of Maryland Baltimore County, USA AN14 Abstracts 35

[email protected] [email protected]

Jinglai Shen University of Maryland Baltimore County CP31 [email protected] On the Existence of Classical Solutions for a Two- Point Boundary Value Problem for the Navier- Stokes Equations CP30 A Cut Approach for Solving the Single-Row Ma- We consider the motion of a liquid surface between two chine Layout Problem parallel surfaces that are non-ideal, and hence, subject to contact angle hysteresis effect. This effect implies that the A cut approach is developed for the machine configura- contact angle of the capillary surface at the interface is tion in a single-row linear layout, with objective to mini- set-valued. We study the problem of existence of classical mize the total material movement cost. We show that the solutions to the two point boundary value problem in time above equidistant linear layout problem is equivalent to the whereby a liquid surface with one contact angle is deformed locale network problem by graph theory. The minimum to another with a different contact angle. cut, which has the minimum capacity in each locale network, is the corresponding optimal layout that minimizes Bhagya U. Athukorallage,RamIyer the material handling cost. The computational complexity Texas Tech University of the cut approach is O(n3), where n is the number of [email protected], [email protected] workstations in the layout problem. In addition, the non- equidistant linear layout problem can be transformed into CP31 an equidistant linear layout problem. High-Order L-Stable Schemes for the Nonlinear Shine-Der Lee Parabolic Equation Using Successive Convolution National Cheng Kung University Dept. of Industrial & Information Management We present a numerical implementation of an L-stable, 3rd [email protected] order accurate solution of the Cahn-Hilliard model using successive convolution combined with the high order multi- derivative time integrators. The primary advantage is that CP30 the operators can be computed quickly and effectively with various boundary conditions using parallel computing. Study of Weak Stationarity for a Class of Stochastic Mpcc Problems Hana Cho Michigan State University In this talk we shall discuss the weak stationarity for a [email protected] particular class of stochastic mathematical programming problem with complementarity constraints (SMPCC, for short). Our aim here is to show why concept of weak sta- Andrew Chrislieb tionarity is important for SMPCC problems even if the Dept. of Mathematics problem data is smooth. In fact, a well known technique Michigan State University to solve stochastic programming problems, namely sam- [email protected] ple average approximation (SAA) method will show the strength of weak stationarity for SMPCC problems. David C. Seal Department of Mathematics Arnab Sur Michigan State University Indian Institute of Technology, Kanpur [email protected] [email protected] Matthew F. Causley Michigan State University CP30 [email protected] Real-Time Power Dispatch with Renewables Using Stochastic Admm CP31 Leveraging stochastic programming techniques, energy A Scalable, Parallel Implementation of Weighted, management problems are formulated to account for the Non-Linear Compact Schemes intrinsically stochastic availability of renewable energy sources. Both economic dispatch and demand response Weighted, non-linear compact finite-difference schemes, setups are considered to minimize the microgrid net cost. such as the CRWENO scheme (Ghosh and Baeder, SIAM Based on the stochastic alternating direction method of J. Sci. Comput., 2012) and the hybrid compact-WENO multipliers (ADMM), a novel decentralized solver with scheme (Pirozzoli, J. Comput. Phys., 2002), are well suited guaranteed convergence is developed for real-time power for the numerical solution of compressible, turbulent flows. dispatch. Numerical tests illustrate the merits of the novel We propose a scalable, parallel implementation of these approach. schemes based on an iterative sub-structuring of the tridiagonal system. We apply our algorithm to benchmark flow Yu Zhang problems and demonstrate its scalability on extreme-scale University of Minnesota computing platforms. Department of ECE and DTC [email protected] Debojyoti Ghosh Mathematics and Computer Science Division Georgios Giannakis Argonne National Laboratory University of Minnesota [email protected] 36 AN14 Abstracts

Emil M. Constantinescu tween the elliptic solutions in the perforated domains and Argonne National Laboratory the solution of the homogenized elliptic equation are de- Mathematics and Computer Science Division rived. [email protected] Li-Ming Yeh Jed Brown Department of Applied Mathematics Mathematics and Computer Science Division National Chiao Tung University, Taiwan Argonne National Laboratory [email protected] [email protected]

MS1 CP31 Network Adaption for Leader-Follower Networks Robust Design of Boundary Conditions for Stochastic Incompletely Parabolic Systems of We examine a networked multi-agent system running con- Equations sensus susceptible to mis-information from its environment. The influenced dynamics are modeled with leader- We consider an incompletely parabolic system in one space follower dynamics and the impact of the foreign input is dimension with uncertainty in the boundary and initial measured through the open loop H2 norm of the net- data. Our aim is to show that different boundary con- work dynamics. The measure has a graph-based effec- ditions gives different convergence rates of the variance of tive resistance interpretation which allows one to reason the solution. This means that we can with the same knowl- about the graph’s topological robustness. Consequently, edge of data get a more or less accurate description of the to dampen the external disturbances, decentralized game- uncertainty in the solution. A variety of boundary con- theoretic and online edge rewiring methods are proposed. ditions are compared and both analytical and numerical estimates of the variance of the solution is presented. Airlie Chapman Jan Nordstrom Aeronautics & Astronautics Department of Mathematics, Linköping University University of Washington SE 581 83 Linköping, Sweden [email protected] [email protected] Mehran Mesbahi Markus Wahlsten University of Washington Department of Mathematics [email protected] Linköping University SE 581 83 Linköping, Sweden [email protected] MS1 On Leader Selection for Performance and Control- CP31 lability Multilevel Monte Carlo Finite Element Method for Time-Dependent Wave Equation A standard approach to controlling multi-agent systems is to select a subset of agents, denoted as leaders, that We propose multilevel Monte Carlo Finite Element method are directly controlled in order to steer the remaining (fol- (MLMC-FEM) for time-dependent stochastic wave equa- lower) agents to a desired state. Approaches to selecting tion. Our method leads to decrease to log-linear work and the leader agents currently depend on the design criteria of memory in the number of unknowns of a single level calcu- the system, with continuous optimization techniques em- lation of the deterministic wave equation. We analyze the ployed to guarantee performance and robustness to distur- MLMC-FEM of the solution based on the nested mesh for bances, and discrete optimization used to ensure controlla- Finite Element spaces. bility, and hence do not give optimality guarantees for joint selection based on performance and controllability. I will Imbo Sim, Myoungnyoun Kim present a unifying approach to leader selection in multi- National Institute for Mathematical Sciences agent systems based on both performance (e.g., robustness [email protected], [email protected] to noise and convergence rate) and controllability. My key insight is that leader selection for joint performance and CP31 controllability can be formulated within a matroid optimization framework, implying provable guarantees on the Pointwise Estimate for Elliptic Equations in Peri- optimality of the chosen leader set. Furthermore, I define odic Perforated Domains a novel graph controllability index, equal to the cardinal- ity of the largest controllable subgraph from a given leader Pointwise estimate for the solutions of elliptic equations in set, and prove that it is a submodular function of the leader periodic perforated domains is concerned. Let denote the set, leading to a submodular relaxation of the problem of size ratio of the period of a periodic perforated domain to achieving controllability. the whole domain. It is known that even if the given functions of the elliptic equations are bounded uniformly in , 1,α 2,p Andrew Clark the C norm and the W norm of the elliptic solutions Electrical Engineering may not be bounded uniformly in .Itisalsoknownthat University of Washington when closes to 0, the elliptic solutions in the periodic per- [email protected] forated domains approach a solution of some homogenized elliptic equation. In this work, the Hölder uniform bound in and the Lipschitz uniform bound in for the elliptic solutions in perforated domains are proved. The L∞ and MS1 the Lipschitz convergence estimates for the difference be- Joint Centrality and Optimal Leader Selection in AN14 Abstracts 37

Noisy Networks oRdinAte descent method for solving loss minimization problems with big data. We initially partition the coor- We discuss the leader selection problem in a model where dinates (features) and assign each partition to a different networked agents, subject to stochastic disturbances, track node of a cluster. At every iteration, each node picks a an external signal. The optimal leader set minimizes random subset of the coordinates from those it owns, inde- steady-state variance about the external signal. We prove pendently from the other computers, and in parallel com- the single optimal leader is the agent with maximal infor- putes and applies updates to the selected coordinates based mation centrality and show the optimal set of m leaders on a simple closed-form formula. We give bounds on the maximizes a measure of joint centrality. Finally, we solve number of iterations sufficient to approximately solve the explicitly for optimal leader locations in special cases. problem with high probability, and show how it depends on the data and on the partitioning. We perform numerical Katherine Fitch experiments with a LASSO instance described by a 3TB Mechanical Engineering matrix. Princeton University kfi[email protected] Martin Takac, Peter Richtarik University of Edinburgh Naomi E. Leonard [email protected], [email protected] Princeton University [email protected] MS2 Efficient Quasi-Newton Proximal Method for Large MS1 Scale Sparse Optimization Leader Selection in Noisy Multi-agent Systems: A Resistance Distance Approach Recently several methods were proposed for sparse optimization which make careful use of second-order informa- We select a number of agents and control them to effec- tion [10, 28, 16, 3] to improve local convergence rates. tively reject noise in multi-agent systems. This optimiza- These methods construct a composite quadratic approx- tion problem is equivalent to grounding nodes in resistance imation using Hessian information, optimize this approxi- networks such that total effective resistance is minimized. mation using a first-order method, such as coordinate de- For structured networks in which resistance distances have scent and employ a line search to ensure sufficient de- analytical expressions, we obtain globally optimal selection scent. Here we propose a general framework, which in- of leaders. For unstructured networks in which resistance cludes slightly modified versions of existing algorithms and distances can be computed efficiently, we speed up existing also a new algorithm, and provide a global convergence rate greedy algorithms by exploiting sparsity techniques. We analysis in the spirit of proximal gradient methods, which illustrate our results with several examples. includes analysis of method based on coordinate descent.

Fu Lin Xiaocheng Tang Mathematics and Computer Science Division Lehigh Argonne National Laboratory [email protected] [email protected] MS2 MS2 Nomad: Non-Locking, Stochastic Multi-Machine Bayesian Estimation for Mixtures of Linear Sub- Algorithm for Asynchronous and Decentralized spaces with Variable Dimension Matrix Factorization

We assume i.i.d. data sampled from a ﬁnite mixture distri- Abstract not available at time of publication. bution over variable dimension linear subspaces. An em- S V N Vishwanathan bedding of linear subspaces onto a Euclidean sphere allows Department of Statistics - Purdue University us to deﬁne a joint prior on each subspace and its dimen- [email protected] sion. The embedding and use of a Gibbs posterior yield model parameter estimates. MS3 Brian St. Thomas Krylov Subspaces for Approximation of the Spec- Department of Statistical Science - Duke University tral Embedding [email protected] Spectral embedding problems are solved with truncated Sayan Mukherjee spectral decompositions (tSDs); approximation of the tSD Duke University may allow for substantial compute savings. Minimal [email protected] Krylov subspaces have been advocated as tSD alternatives; minimal Krylov subspaces present the greatest po- Lek-Heng Lim tential for compute savings over the tSD, but they also University of Chicago have nontrivial approximation error. We observe that this [email protected] error is due both to lack of convergence of eigenvalues used in the spectral embedding and convergence of unde- sired eigenvalues from the opposite end of the spectrum. MS2 We also note that eigenvalue approximations may be far Distributed Coordinate Descent Method for Learn- more converged than canonical error bounds suggest. We ing with Big Data propose preconditioning to produce lower-error minimal Krylov subspaces without incurring much extra computa- In this paper we develop and analyze Hydra: HYbriD co- tional cost. We demonstrate polynomial preconditioning 38 AN14 Abstracts

for approximations of the spectral embedding and develop periments and with analyses of well-balancing, dispersion error bounds for more tightness. These results hint towards relations, and numerical stability. minimal Krylov subspace-speciﬁc preconditioners. Robert L. Higdon Alexander Breuer Oregon State University U.S. Army Research Laboratory [email protected] [email protected]

MS4 MS3 Analysis of Adaptive Mesh Refinement for Imex Algebraic Distance on Graphs with Applications to Discontinuous Galerkin Solutions of the Compress- Large-Scale Optimization and Data Analysis ible Euler Equations with Application to Atmo- spheric Simulations Measuring the connection strength between vertices in a graph is one of the most important concerns in many nu- We investigate the performance of a tree-based AMR algo- merical tasks in graph mining. We consider an iterative rithm for the high order discontinuous Galerkin method on process that smooths an associated value for nearby ver- quadrilateral grids with non-conforming elements. We pay tices, and we present a measure of the local connection particular attention to the implicit-explicit (IMEX) time strength (called the algebraic distance) based on this pro- integration methods and show that the ARK2 method is cess. Algebraic distance is attractive in that the process is more robust with respect to dynamically adapting meshes simple, linear, and easily parallelized. than BDF2. Preliminary analysis of preconditioning reveals that it can be an important factor in the AMR over- Jie Chen, Ilya Safro head. Argonne National Laboratory [email protected], [email protected] Michal A. Kopera, Francis X. Giraldo Naval Postgraduate School [email protected], [email protected] MS3 Numerical Analysis of Spectral Clustering Algo- rithms (SCAs) MS4 A Unified Discontinuous Galerkin Approach for An SCA employs eigensolves to cluster vertices and edges Solving the Two- and Three-Dimensional Shallow so that graph topology is better understood. Given a Water Equations graph, a desired cluster type, and an SCA, how many eigensolver iterations are required for the constituent eigenprob- In this talk, we present a novel discontinuous Galerkin lems to have adequate data mining quality? We present (DG) method that provides a unified approach for solv- in-depth analysis of the simplest cases: power method ap- ing the two- (depth-integrated) and three-dimensional shal- plied to synthetic data mining problems, with an eye for low water equations. A key feature of the developed DG developing convergence theory for real-world problems and method is the discretization of all the primary variables us- faster iterative methods. ing discontinuous polynomial spaces of arbitrary order, including the free surface elevation. In a standard Cartesian- Geoffrey D. Sanders coordinate system, this results in elements in the surface Center for Applied Scientific Computing layer having mismatched lateral faces (a staircase bound- Lawrence Livermore National Lab ary). This difficulty is avoided in the current method by [email protected] employing a sigma-coordinate system in the vertical, which transforms both the free surface and bottom boundaries Lance Ward into coordinate surfaces. The top sigma coordinate surface, Lawrence Livermore National Lab which corresponds to the free surface, is discretized using [email protected] triangular and/or quadrilateral elements that are extended in the vertical direction to produce a three-dimensional Tobias Jones mesh of one or more sigma layers of triangular prism and University of Colorado, Boulder hexahedral elements. The polynomial spaces over these Dept. of Applied Mathematics elements are constructed using products of Jacobi polyno- [email protected] mials of varying degrees in both the horizontal and vertical directions. The DG approach is unified in the sense that in the case of a single sigma layer and a piecewise constant MS4 approximation in the vertical, the method collapses to a Pressure Forcing and Time Splitting for Discontin- “standard” DG method for the two-dimensional, depth- uous Galerkin Approximations to Layered Ocean integrated shallow water equations. The approach also Models makes use of new (in many cases optimal) sets of nonprod- uct integration rules and strong-stability-preserving time This work concerns the application of DG methods to the steppers that have been specifically designed for efficient numerical modeling of the general circulation of the ocean. calculation when used with DG spatial discretizations. The One step performed here is to develop an integral weak efficiency, robustness and h (mesh) and p (polynomial or- formulation of the pressure forcing that is suitable for us- der) convergence properties of the method will be demon- age with a DG method and with a generalized vertical co- strated on a set of test cases. ordinate that includes level, terrain-fitted, and isopycnic coordinates as examples. The computation of pressure at Ethan Kubatko cell edges is facilitated by some ideas that are also used Department of Civil, Environmental and Geodetic for barotropic-baroclinic time splitting. This formulation Engineering is tested, in special cases, with some computational ex- The Ohio State University AN14 Abstracts 39

[email protected] conclusions about what to look for in a mentor. And I will reflect on the related topic of community, where the supports and the engagement are bi-directional and dynamic. MS4 A Discontinuous Galerkin Non-Hydrostatic Model with An Operator-Split Semi-Implicit Time Step- Margot Gerritsen ping Scheme Dept of Energy Resources Engineering Stanford University A new two-dimensional non-hydrostatic (NH) DG model [email protected] (compressible Euler or Navier-Stokes system) based on efficient spatial discretization has been developed on (x, z) plane. However, the fast-moving acoustic waves together MS5 with a high aspect ratio (Δx = 1000Δz) between the hori- From Law of Large Numbers... zontal and vertical spacial discretization impose a stringent restriction on explicit time-step size for the resulting ODE I would like to share some aspects from my own academic system. We consider a semi-implicit time-split method experiences, such as holding positive attitudes, planning which employs so-called horizontally explicit and vertically and making preparation, and the importance of having implicit (HEVI) approach through an operator-split pro- good mentors. cedure for the DG discretization. The vertical component of the dynamics, which deals with the acoustic waves and Fengyan Li very small grid-spacing (Δz), is solved implicitly while the Rensselaer Polytechnic Institute horizontal part solved in an explicit manner. For the DG [email protected] model with HEVI time integration, the CFL limit is only restricted to the horizontal grid-spacing (Δx). The model MS5 is tested for various NH benchmark test-cases, and the results will be presented in the seminar. On the Road Again: My Experience as an Early- career Mathematician Ram Nair NCAR As a mathematician in the transition between postdoc and Institute for Mathematics Applied to Geosciences tenure-track, I will reflect on my experiences thus far and [email protected] highlight some of the resources that have supported my career. I will also discuss my experience with the academic job market, the two-body problem, pursuing funding op- Lei Bao portunities, and seeking a balance between work and per- University of Colorado, Boulder sonal/family commitments. [email protected] Anne Shiu University of Chicago MS5 [email protected] My Intertwined Paths: Career and Family

A rich mixture of both career and family characterizes my MS5 life during the past twenty years since I earned a PhD in On the Importance of Good Mentoring and having applied mathematics. I’ll discuss my intertwined paths – an Engaging Community as a researcher at Argonne National Laboratory and as a parent. I will highlight career paths at national laborato- We all need mentors and to connect with a community in ries, with emphasis on the diverse opportunities for impact our work, and we need this at every career stage. I will tell in interdisciplinary computational science. Also, I will re- some stories of successes and failures with these from my ﬂect on my ongoing choices for work-life balance, including own career. I will draw some key conclusions about what to addressing the ’two-body’ problem, parenting, and care for look for in a mentor. And I will reﬂect on the related topic aging parents. of community, where the supports and the engagement is bi-directional and dynamic. Lois Curfman McInnes Argonne National Laboratory Mary Silber [email protected] Northwestern University Dept. of Engineering Sciences and Applied Mathematics [email protected] MS5 Beating the Imposter Syndrome MS6 Many competitive and successful students and profession- Parallel Preconditioning for All-at-Once Solution als at times feel like impostors. ”I am not as smart as of Time-Dependent Navier-Stokes Optimization they think I am”, or ”One sure day, I will disappoint my Problems advisor” are frequently occurring thoughts. In a study of several hundred graduate students at Stanford, we asked We explore domain decomposition strategies for accelerat- about this Impostor Syndrome. I’d like to share some of ing the convergence of all-at-once numerical schemes for the results, as well as my own thoughts on how the often the solution of time-dependent Navier-Stokes optimization negative and sometimes paralyzing thoughts that surface problems on parallel computers. Special attention is paid can be turned around. We all need mentors and to connect to developing preconditioners that are robust with respect with a community in our work, and we need this at every to parameters, such as the regularization parameter, the career stage. I will tell some stories of successes and fail- Reynolds number, and the timestep size. We describe ures with these from my own career. I will draw some key a parallel preconditioning strategy for these systems that 40 AN14 Abstracts

uses domain decomposition algorithms in the time domain straints (α, yD and Ω are given). The box constraints and Schur complement approximations for the resulting might be state constraints (y ≤ y ≤ y) or control con- local saddle point systems. Finally, we present numerical straints (u ≤ u ≤ u). One possibility to solve such prob- results and discuss possible applications. lems using multigrid methods is to use a (semi-smooth) Newton solver. Here, a standard multigrid method would Andrew Barker be used as an solver for linear sub-problems that occur Max Planck Institut, Magdeburg within this iteration. Recently, it was possible to con- [email protected] struct and analyze multigrid solvers that can be directly applied to elliptic problems with box constraints (like obstacle problems). Those methods have shown good con- MS6 vergence behavior in practice. In the present talk we will A Block Diagonal Preconditioner for All-at-Once discuss how the ideas of such methods can be extended to Solution of Time-Dependent PDE-Constrained Op- control problems. timization Problems Stefan Takacs All-at-once schemes aim to solve all time-steps of parabolic TU Chemnitz PDE-constrained optimization problems in one coupled [email protected] computation, leading to exceedingly large linear systems requiring efficient iterative methods. We present a new block diagonal preconditioner which is both optimal with MS7 respect to the mesh parameter and parallelizable over time, Algorithms That Satisfy a Stopping Criterion, thus can provide significant speed-up. We will present nu- Probably merical results to demonstrate the effectiveness of this preconditioner. Numerical algorithms are typically equipped with a stopping criterion where the calculation is terminated when Eleanor McDonald some error or misfit measure is deemed to be below a given University of Oxford tolerance. However, in practice such a tolerance is rarely [email protected] known; rather, only some possibly vague idea of the desired quality of the numerical approximation is available. Andrew J. Wathen Indeed, fast codes for initial value ODEs and DAEs heavily Oxford University rely on the underlying philosophy that satisfying a toler- Numerical Analysis Group ance for the global error is too rigid a task; such codes [email protected] proceed to control just the local error. Another instance of soft error control is when a large, complicated model for fitting data is reduced, say by a Monte Carlo sampling MS6 method. If calculating the misfit norm is in itself very Fast Iterative Solvers for Reaction-Diffusion Con- expensive then the option of satisfying the stopping crite- trol Problems from Biological and Chemical Pro- rion only in a probabilistic sense naturally arises. We will cesses discuss this in the context of inverse problems involving systems of PDEs, when many experiments are employed in In this talk, we develop fast and robust preconditioned it- order to obtain reconstructions of acceptable quality. Ma- erative methods for solving matrix systems arising from jor computational savings can then be realized by using reaction-diffusion control formulations of biological and unbiased estimators for the misfit function in the stopping chemical processes. To construct these methods, we ex- criterion. ploit the saddle point structure of the matrices to derive good approximations of the (1,1)-block and Schur comple- Uri M. Ascher ment. For the problems considered, we motivate our rec- University of British Columbia ommended preconditioners, discuss parallel solution strate- Department of Computer Science gies, and present numerical results to demonstrate the per- [email protected] formance of our methods.

John W. Pearson Farbod Roosta-Khorasani University of Edinburgh Computer Science [email protected] UBC [email protected] Martin Stoll Max Planck Institute, Magdeburg MS7 [email protected] Time Varying RBFs for Wave-Like Solutions of Pdes MS6 We introduce radial basis functions (RBFs) whose time- All-at-Once Multigrid Methods for Optimal Con- varying coeﬃcients determine not only the amplitude and trol Problems position of each RBF but also their shape. The intended use of these Time Varying-RBFs (TV-RBFs) is in the local- In this talk we will discuss the solution of all-at-once multi- in-time representation of low-dimensional approximations grid methods for optimal control problems of tracking type of functions that arise in solving spatiotemporal evolution with inequality constraints, which might look as follows: problems; in particular, for time-varying spatially local- 1 2 α 2 ized solutions with a temporal translation component such Minimize J(y,u)= y − yD 2 + u 2 2 L (Ω) 2 L (Ω) as traveling waves, modulated pulses or soliton-like solutions of evolutionary diﬀerential equations. This paper subject to −Δy = u on Ω and y =0on∂Ωandbox con- is restricted to the one-dimensional spatial case. We also AN14 Abstracts 41

present an algorithm that places the Time Varying-RBFs [email protected] (TV-RBFs) over spatiotemporal data that may come from experiments, from finely discretized PDE simulations, or even from multiscale, particle-based simulations. It first MS8 approximates the function at a single time instant (a temporal snapshot) as a sum of RBFs using a novel weighted Optimizing Snake Locomotion in the Plane minimization that causes each RBF to primarily approximate one of the localized parts of the function. It then We develop a numerical scheme to determine which planar extends that approximation to TV-RBFs over a sequence snake motions are optimal for locomotory efficiency, across of snapshots of the function at different times. We con- frictional parameter space. With large transverse friction, clude by discussing the potential uses of these TV-RBFs. retrograde traveling waves are optimal. Our asymptotic analysis shows that the optimal wave amplitude decays as the -1/4 power of the coefficient of transverse friction. At the other extreme, zero transverse friction, we find a tri- C.W. Gear angular direct wave which is optimal. Between these ex- Princeton University tremes, a variety of locally optimal motions are found, in- Department of Chemical Engineering cluding ratcheting motions. We also extend the study to [email protected] motion on inclines.

Arta Jamshidi Silas Alben Princeton University University of Michigan, USA [email protected] [email protected]

Yannis Kevrekidis Matt Osborne Dept. of Chemical Engineering University of Toledo Princeton University [email protected] [email protected] Xiaolin Wang Georgia Institute of Technology MS7 [email protected] On High Index Differential-Algebraic Equations MS8 In this talk we discuss solvability of high index differential From Animal to Robot and Back: Sidewinding on algebraic equations. In this context, exponentially faster Granular Media time scale of evolution of the algebraic variables is pointed out. A numerical method that elucidates the above result Sidewinders locomote in granular medium through compli- by regularizing the Jacobian of the method and producing cated internal shape changes and body-terrain interactions, smoothed solutions is given. The results are illustrated hence making it is difficult to predict their trajectories. We with numerical examples. propose an approach which predicts motions according to body shapes. This approach is built on geometric tech- Soumyendu Raha niques to prescribe the internal motions and observations SERC, Indian Institute of Science, Bangalore 560012, from live sidewinders moving on sandy terrain. We demon- India strate these ideas on the CMU snake robot. [email protected] Howie Choset Robotics Institute MS7 Carnegie Mellon University [email protected] Sensitivity Analysis of Stochastic Chemical Kinet- ics Chaohui Gong, Matthew Travers Carnegie Mellon University Monte Carlo methods of parametric sensitivity analysis for [email protected], [email protected] stochastic dynamics consist of the Girsanov Transforma- tion (GT), Pathwise Derivative (PD) and Finite Difference (FD) methods. The GT differs significantly from the PD MS8 and FD methods which are closely related. While each Lessons from Animal Locomotion: Extending Flo- method has its advantages and drawbacks, it has been ob- quet Theory to Hybrid Limit Cycle Oscillators served that PD and FD have lower variance than GT in many examples. We provide a theoretical explanation for Animal locomotion is often modeled as a limit cycle oscilla- this in the chemical kinetics context. tor with hybrid (discontinuous) vector field, where classical results of Floquet theory do not apply. We will discuss sev- Muruhan Rathinam eral recent theoretical results extending Floquet theory to University of Maryland, Baltimore County hybrid limit cycle oscillators, as well as ongoing work on [email protected] numerical/statistical tools for Data Driven Floquet Anal- ysis of legged locomotion systems. Ting Wang Department of Mathematics and Statistics Shai Revzen University of Maryland Baltimore County University of Michigan 42 AN14 Abstracts

[email protected] [email protected]ﬀord.edu

MS8 MS9 Chaotic Scattering during Legged Locomotion on Billiard Motion of Microorganisms in Conﬁned Do- Granular Media mains

We study locomotion on heterogeneous granular media us- Models of ciliated ”squirmer” microorganisms indicate that ing laboratory experiments and a granular resistive force the body rotates passively away from a wall before, during, theory (RFT). By combining RFT with a multi-body simu- and after collision. We explore the billiard-like motion of lator, we model in detail the dynamics of a small open-loop such a body as it swims inside a confined domain. Solutions controlled legged sand-running robot. To gain insight into for stable periodic trajectories inside of regular polygons the long-term trajectories, we use cycle expansion theory are derived, and criteria for the existence of other trajec- to study a simplified (scattering potential) model of the tories in complex domains are investigated. The results locomotor. may provide insight on entrapment and sorting of microorganisms and other active particles. Advisors: Jean-Luc Tingnan Zhang Thiffeault and Saverio E. Spagnolie, UW-Madison Georgia Institute of Technology [email protected] Colin Wahl, Joseph Lukasik UW-Madison [email protected], [email protected] Chen Li University of Califonia, Berkeley [email protected] MS10 Multiscale Modeling and Numerical Simulation of Predrag Cvitanovic Calcium Cycling in Cardiac Myocyte Center for Nonlinear Science Georgia Institute of Technology In this talk we present the detailed model of the intra- [email protected] cellular calcium dynamics in a cardiac myocyte and their efficient numerical techniques. We adopted a detailed CRU Daniel Goldman model to describe the source functions in the PDE model Georgia Tech and the dynamics of the membrane potential is based on School of Physics the Mahajan membrane Model. We developed a finite el- [email protected] ement simulator interface for the 452 CRUs arrangement. The numerical convergence of solutions and parallel results are demonstrated. MS9 An Initial Modeling of Fractal Nets for the Sier- Nagaiah Chamakuri pinski Gasket Radon Institute for Computational and Applied Mathematics The Sierpienski tetrahedron is obtained by applying an it- Austrian Academy of Sciences erated function system (IFS) method to a regular tetrahe- [email protected] dron. We give a sketch and algorithm for a folding method that allows us to construct the n-th iteration of a modified Sierpinski gasket, then fold it to form the Sierpienski MS10 tetrahedron. We also provide an initial exploration of con- Modeling the Molecular Basis of Calcium En- struction methods for minimal volume objects that retain trained Arrhythmia their surface area under refinement. This idea has potential applications at nanoscale. Advisor: Gregory Fasshauer Heart disease is the leading cause of death in the developed world and an increasing problem developing nations Barrett Leslie most often as result of cardiac arrhythmia. Here we exam- Illinois Institute of Technology ine the cellular and subcellular basis of calcium dependent [email protected] arrhythmias. In order to understand how calcium dynamics, plays a role in arrhythmogenesis, we have investigated normal and dysfunctional calcium signaling in heart cells MS9 at high temporal and spatial resolution using multiscale A Bioinformatic Approach to Cancer Research stochastic models. Aman Ullah The purpose of the study was to identify potential proto- Department of Molecular Neuroscience oncogenes and tumor suppressor genes for further research George Mason University, Fairfax, VA 22030 by culture. The R programming language was used to ac- [email protected] cess metadata from the cBio portal. Methylation, mutation, and phosphorylation data were used to distinguish the most likely candidate genes. As a result of this study, two Tuan Hoang-Trong significant candidates were identified, and the oncogenic School of Systems Biology nature of a family of genes was characterized. Research George Mason University, Manassas, VA 20110 is ongoing. Advisors: Mingli Yang and Yeatman, Gibbs [email protected] Cancer Research Center, Spartanburg, SC Geoge Williams, William Lederer Nicolas Limogiannis Biomedical Engineering and Technology Wofford College University of Maryland, Baltimore, MD 21201 AN14 Abstracts 43

[email protected], [email protected] University of Michigan at Flint lxhan@umﬂint.edu Mohsin S. Jafri Department of Molecular Neuroscience George Mason University,Manassas,VA 20110 MS11 [email protected] Dynamical Systems Analysis of Swamps in ALS

MS10 The Alternating Least Squares (ALS) algorithm for ap- Cellular Mechanisms of Calcium-Mediated Trig- proximating a tensor by a low-rank tensor is prone to peri- gered Activity in Cardiac Myocytes ods of very slow convergence, known as swamps. Although the existence of swamps is well-known and various fixes The main chambers of the heart are made up of electrically have been proposed, the mechanisms that cause swamps coupled ventricular myocytes, which are excitable cells that are mysterious. I will discuss progress on analyzing and only transit from the resting to the excited states (fire an understanding swamps using tools from Dynamical Sys- action potential) under a finite current stimulus. However, tems. under abnormal conditions, those cells can spontaneously fire a single action potential, or even a burst of several Martin J. Mohlenkamp action potentials, after a normal stimulated action poten- Ohio University tial. This talk will present results of a computational study [email protected] that sheds new light on the dynamical origin of those ar- rhythmogenic ”afterdepolarizations” by quantifying the relationship of stochastic intracellular calcium dynamics and MS11 whole-cell voltage dynamics. Canonical Polyadic Decomposition for Symmetric Alain Karma Tensor Distinguish Professor Northeastern University We propose a method for finding symmetric outer prod- [email protected] uct decomposition for fully and partially symmetric tensor. These are iterative algorithms which are based on Zhen Song matricizations, least-squares and finding roots of quartic Physics Department polynomials. The methods work well for third-order par- Northeastern University tially symmetric tensors and fourth-order fully symmetric [email protected] tensors. Our numerical examples indicate a faster convergence rate than the standard alternating least-squares method. MS10 Alternans As An Order-Disorder Transition in Carmeliza Navasca Heart Cells University of Alabama at Birmingham [email protected] Electrical alternans is a beat-to-beat alternation in the amplitude of the electrocardiogram (ECG) which has been Na Li shown to be a precursor to various cardiac arrhythmias. MathWorks In this talk I will argue that nonlinear signaling between [email protected] stochastic ion channels can explain the onset of alternans. Furthermore, I will present evidence that the transition to alternans occurs via an order-disorder phase transition which exhibits universal features common to a wide range MS11 of physical systems. Towards Better Computation-statistics Trade-off in Tensor Decomposition Yohannes Shiferaw California State University New approaches for tensor decomposition with worst case Northridge d−1 performance guarantee have recently emerged. O(rn )is [email protected] the number of samples required for recovering an n×n××n d-way tensor that admits a Tucker decomposition with × ×× MS11 r r r core proved for one of these methods called overlapped trace norm. Although this method is com- Computing Eigenvalues and Eigenvectors of Sym- putationally very efficient, the rate is rather disappoint- metric Tensors: A Survey ing. A newer approach called square norm achieves lower O d/2 d/2 Eigenvalues and eigenvectors of symmetric tensors have (r n ) samples at the cost of higher computational found applications in automatic control, data analysis, demand. There is also a more theoretical approach that O d− higher order diffusion tensor imaging, image authenticity could achieve optimal (rn 1) but seem to be computa- verification, optimization, and other areas. In the past few tionally intractable. I will overview these recent develop- years several algorithms have been proposed for comput- ments and discuss how we could achieve a better trade-off ing certain eigenpairs of symmetric tensors. In this talk, we between what we can provably achieve in terms of statisti- will survey these methods. We will also describe some new cal accuracy and how much computation we need to spend. ideas such as the use of deflation method that can assist the existing algorithms to find other eigenpairs. Ryota Tomioko Lixing Han Toyota Technological Institute at Chicago 44 AN14 Abstracts

[email protected] behavior at nano sized structures, using cell cultures to study biological fluid flow against gravity, and engineering artificial cilia to study directed flow and enhanced mixing MS12 in actuated arrays. Mixing and Transport by Ciliary Flows: A Numer- ical Study Richard Superfine Department of Physics & Astronomy Motile cilia often serve the dual function of transporting University of North Carolina fluid across the cell surface and sensing of environmental [email protected] cues. The performance of cilia in fluid transport was studied extensively. However, the way by which cilia serve the simultaneous tasks of transport and sensing is less well un- MS13 derstood. We use a 3D computational model to examine the transport and mixing properties of ciliary flows. We Frictional and Heat Transfer Characteristics of find that the metachronal wave improves both the trans- Flow in Square Porous Tubes of Diesel Exhaust port and mixing rates, often simultaneously. These results Particulate Filters suggest that cilia use chaotic advection and mixing as a mechanism to enhance sensing. In the 1D modeling of flow in the channels of wall-flow monoliths used in diesel particulate filters for engine ex- Eva Kanso haust emissions control, it is common to use friction coeffi- University of Southern California cients and Nusselt numbers from idealized 2D/3D channel [email protected] flows. Previously, this idealization suffered from lack of flow through the porous filter walls. As wall flow increases for the simpler geometries of circular tubes and parallel MS12 planes, there is a rich literature describing multiple solu- The Capture of Symbiotic Bacteria from the Envi- tions. We extend the practical portion of these results to ronment by Host Ciliated Epithelia the computationally challenging, but realistic, square channel geometry that is necessary for mathematical modeling Most, if not all, animals have epithelial cells whose apical and settle certain long-standing controversies. surfaces have cilia, elongate mechanosensory appendages that are evolutionarily conserved in their structure and Edward Bissett biochemical composition. Cilia often occur in dense, Gamma Technologies, Inc behaviorally- coordinated assemblages along the mucosal Westmont, IL 60559 surfaces. In these locations, the cilia work in concert with [email protected] the secreted mucus to capture and translocate suspended materials, notably environmental bacteria. This presen- Margaritis Kostoglou tation will focus on what is known about the biology of Aristotle University of Thessaloniki cilia-bacteria interactions. [email protected] Margaret McFall-Ngai Athanasios Konstandopoulos University of Wisconsin-Madison Aristotle University of Thessaloniki [email protected] [email protected]

MS12 MS13 A Cilia-Driven Hydrodynamic Sieve for Selective Particle Capture Solution Verification in Simulations of Drop Impact of Flexible Containers Juvenile Hawaiian bobtail squids reliably capture and iso- late a single species of bacteria from inhaled coastal water Solution Verification is an important part of the credibility containing a huge background of other particles. Here I of a computational model. This activity is focused on de- present experimental data showing how arrangement and termining the rate of convergence of the computed solution coordination of the cilia that capture the bacteria create a as the computational grid gets refined, with the assump- 3D flow field that facilitates advection, sieving and selective tion that it will reach an asymptotic regime of convergence. retention of flow-borne particles, including bacteria. These The talk will show some approaches on verifying the solu- studies may inspire novel microfluidic tools for detection tion of a fluid structure interaction problem where flexible and capture of specific cells and particles. container filled with fluid impacts the ground after being dropped. Janna C. Nawroth Harvard School of Engineering Carlos A. Corrales [email protected] BAXTER HEALTHCARE CORPORATION Round Lake, IL 60073 carlos [email protected] MS12 Cilia Generated Flows: Insights from Cell Cultures Mark Perry and Engineered Arrays Baxter Healthcare Corporation The lung stays sterile due to the cilia-generated flow of mark [email protected] mucus that sweeps the airway clean. We are studying each aspect of this process: Using a magnetic microbead assay to measure the force developed by individual cilia, using MS13 driven microbead rheology to understand strain thickening Estimating Shape and Motion Information from AN14 Abstracts 45

Radar Data [email protected]

Due to the relatively short microwave wavelengths involved, radar imaging relies on exquisite knowledge of the MS14 relative geometry between the antenna(s) and the scene Hybrid Parallelism for Large-scale Adaptive-mesh to be imaged (i.e., the target). Radar image formation of Simulations non-cooperative targets, such as ships in a rolling sea, is particularly challenging because the target may undergo With the advent of supercomputers featuring one million signiﬁcant unknown and unpredictable motion. In this talk processing units or more, maybe the most important guide- we discuss our recent progress in estimating arbitrary tar- line for algorithm development is to maximize the concur- get motion from radar measurements. rency of computational tasks. This is at odds with common solution algorithms for elliptic or hyperbolic PDEs, which Matthew Ferrara, Gregory Arnold are most eﬀective in the mathematical sense but rely on a Matrix Research, Inc. multilevel structure of causality. In this talk, we discuss [email protected], options in parallel algorithm design to reduce causality in [email protected] favor of concurrency.

Mark Stuff Carsten Burstedde Michigan Tech Research Institute Universität Bonn mastuff@mtu.edu [email protected]

Jason T. Parker Donna Calhoun AFRL/RYRT Boise State University [email protected] [email protected]

Bram Metsch MS13 University of Bonn Regularization in the Real World [email protected]

The inverse problem of determining cardiac electrical patterns from measurements on internal or external electrodes MS14 has received increasing attention from medical-device com- Plate Boundary-resolving Nonlinear Global Man- panies in recent years. This talk will describe new ideas tle Flow Simulations using Parallel High-order Ge- for regularization methods, simulation and preclinical ex- ometric Multigrid Methods on Adaptive Meshes periments to evaluate and optimize them, and some of the clinical factors that make reliable solutions more difficult The simulation of global mantle flow with associated plate in vivo. motion at global scale is challenging due to the extreme nonlinearity, the viscosity variations, and the different spa- Eric Voth tial scales inherent in the problem. We discretize the St. Jude Medical, USA governing nonlinear incompressible Stokes equations using [email protected] high-order finite elements on highly adapted meshes, which allow us to resolve plate boundaries down to a few hundred meters. Crucial components in our scalable solver are an MS14 efficient, collective communication-free, parallel implemen- Towards τ Adaptivity for Lithosphere Dynamics: tation of geometric multigrid for high-order elements, the Nonsmooth Processes in Heterogeneous Media use of a Schur complement preconditioner that is robust with respect to extreme viscosity variations, and the use of We propose a new form of adaptivity based on FAS multi- an inexact Newton solver combined with grid continuation grid, allowing fine grid work to be avoided in regions methods. We present results based on real data that are with nearly-linear behavior, despite arbitrarily rough co- likely the most realist global scale mantle flow simulations efficients. We present preliminary experiments with non- conducted to date. linear solvers for localized plastic yielding in lithosphere dynamics. Johann Rudi ICES Jed Brown The University of Texas at Austin Mathematics and Computer Science Division [email protected] Argonne National Laboratory [email protected] Hari Sundar Institute for Computational and Engineering Sciences Mark Adams University of Texas at Austin Columbia University [email protected] [email protected] Tobin Isaac, Georg Stadler Matthew G. Knepley University of Texas at Austin University of Chicago [email protected], [email protected] [email protected] Michael Gurnis Dave May California Institute of Technology ETH Zurich [email protected] 46 AN14 Abstracts

Omar Ghattas tools have historically been restricted to systems with lin- The University of Texas at Austin ear, analytical dynamics. We have recently developed a [email protected] framework for combining empirical data from nonlinear models with geometric gait evaluation methods. The resulting tools both reduce the computational costs of de- MS14 scribing sand-swimming and reveal fundamental aspects of Title Not Available at Time of Publication the motion.

Abstract not available at time of publication. Ross L. Hatton Sc. of Mechanical, Industrial, and Manufacturing Olaf Schenk Engineering USI - Universit`a della Svizzera italiana Oregon State University Institute of Computational Science [email protected] [email protected]

MS15 MS15 Coupling of Locomotion Control and Sensing in Bi- Geometric Locomotion with Passive Internal De- ological Systems grees of Freedom: Hovering Flight and Passive Swimming The hawkmoth Manduca sexta has a keen ability to nav- igate dense environments with incredible robustness. Al- This talk presents a general modeling approach for loco- though these animals utilize relatively simple, noisy sen- motion dynamics of mobile multibody systems contain- sors, they harness massively distributed sensing to estimate ing passive internal degrees of freedom concentrated into their state and the state of the surrounding environment. joints and/or distributed along deformable bodies of the Observability tools give us insight into what information system. The approach embraces the locomotion systems these sensing systems can encode and how locomotion can bioinspired by animals that exploit the advantages of soft be used to enhance sensing capabilities. appendages to improve their locomotion performance. It is illustrated through the passive swimming in von Karman Brian Hinson, Kristi Morgansen Vortex Street (KVS), and the hovering flight with twistable Dept. of Aeronautics and Astronautics flapping wings. U. of Washington [email protected], mor- Frédéric Boyer [email protected] Department of Automatic Control Ecole des Mines de Nantes [email protected] MS16 Fully-Automated Multi-Objective Optimization for Fitting Spatial and Temporal Constraints in a Neu- MS15 ronal Model with Real Morphology Mapping Effort: Cartographically-Inspired Meth- ods for Representing the Energetic Cost of Loco- We introduce a fully automated optimization methodology motion for fitting spatially extended neuronal models with multiple time scales. Using multi-objective optimization and In kinematic motion planning, Euclidean configuration dis- targeted experimental protocols, we model a hippocampal tance metrics often fail to encode nonlinear effort or power CA1 pyramidal cell, which exhibits a sodium channel with from changing shape. Cartographic techniques can project widely-separated time constants of recovery from inacti- the distorted configuration coordinates into representations vation. Our implementation uses Python to control the that more accurately portray such distances. We show that NEURON simulator on a multi-core cluster and features the kinematic cartography problem may be reformulated a clickable interface to explore the Pareto-optimal front of into one of nonlinear dimensionality reduction (NLDR), solutions. and compare the results of applying a well-known NLDR technique against a previous spring relaxation algorithm Aushra Abouzeid on a three-link low Reynolds swimmer. Department of Applied Mathematics, Northwestern University Howie Choset Department of Neurobiology, Northwestern University Robotics Institute [email protected] Carnegie Mellon University [email protected] William Kath Northwestern University Engineering Sciences and Applied Mathematics MS15 [email protected] Numerical-Geometric Analysis of Sandswimming

Sand-swimming, a form of desert burrowing, offers inter- MS16 esting potential as a locomotion mode for robots operat- Intrinsically Bursting AII Amacrine Cells Drive ing in loose, granular environments. Unfortunately, the Oscillations in the Degenerated Rd1 Retina computational cost of modeling the relevant physics raises obstacles to a thorough exploration of the system dynam- In retinal degeneration, spontaneous oscillations are ob- ics. Geometric mechanics offers techniques for reducing the served in retinal output neurons, interfering with signal complexity of evaluating gaits, thereby offering the poten- processing. Using compartmental modeling, based on slice tial for exploring a gait design space; unfortunately, these experiments, we show these oscillations are generated by AN14 Abstracts 47

intrinsic bursting of individual AII amacrine cells, which computational models we investigate how these processes are instrumental in transmitting photoreceptor signals to allow these coupled networks to learn to discriminate stim- the output cells. We explain the bursting mechanism by de- uli depending on their familiarity or their association with coupling the fast and slow subsystems, and investigate the non-olfactory cues. bistability between bursting and tonic ﬁring in the model. Hermann Riecke Applied Mathematics Hannah Choi Northwestern University Northwestern University [email protected] [email protected] Wayne Adams, James Graham, Cameron Dennis, Tom Lei Zhang Zhao, Siu Fai Chow University of Maryland Northwestern University [email protected] [email protected], jngra- [email protected], [email protected], Mark Cembrowski [email protected], siu- HHMI Janelia Farm [email protected] [email protected] MS17 Joshua Singer University of Maryland Hardcore Eﬃcient Computation of Atmospheric [email protected] Flows Using High-Order Local Discretization Methods

William Kath The High-order Adaptively Refined Dynamical Core Northwestern University (HARDcore) composes several compact numerical methods Engineering Sciences and Applied Mathematics to easily facilitate intercomparison of atmospheric flow cal- [email protected] culations on the sphere and in rectangular domains. This framework includes the implementations of Spectral Ele- Hermann Riecke ments, Discontinuous Galerkin, Flux Reconstruction, and Applied Mathematics Hybrid Finite Element methods with the goal of achieving Northwestern University optimal accuracy in the solution of atmospheric problems. [email protected] Several advantages of this approach are discussed such as: improved pressure gradient calculation, numerical stability by vertical/horizontal splitting, arbitrary order of accu- MS16 racy, etc. The local numerical discretization allows for high Synchrony and Phase-Locking of Mixed-Mode Os- performance parallel computation and efficient inclusion of cillations in a System of Pulse-Coupled Neurons parameterizations. These techniques are used in conjunction with a non-conformal, locally refined, cubed-sphere Our study is motivated by the experimental observation grid for global simulations and standard Cartesian grids of fast and slow rhythms in the mammalian olfactory sys- for simulations at the mesoscale. A complete implemen- tem. We develop a minimal model in which the interac- tation of the methods described is shown with verification tion of three relevant populations of neurons is reduced to test case simulation results based on standard literature. an effective pulse-coupling amongst a single population of mixed-mode oscillators, and explore the dynamics of this Jorge E. Guerra system as a function of the shape and delay of the pulses. Department of Land, Air and Water Resources We interpret our findings in the context of the observed University of California, Davis rhythms. [email protected]

Avinash J. Karamchandani Paul Ullrich Department of Engineering Sciences and Applied University of California, Davis Mathematics [email protected] Northwestern University [email protected] MS17 Hermann Riecke Using the Multilayer Shallow Water Equations for Applied Mathematics Storm Surge Modeling Northwestern University [email protected] Coastal hazards related to strong storms, in particular storm surge, are one of the most frequently recurring and wide spread hazards to coastal communities. In this talk MS16 we will present a modiﬁcation of the standard shallow wa- Network Restructuring Guided by Associative ter model that adds an additional layer to represent the Feedback for Enhanced Stimulus Discrimination boundary layer of the ocean so that the storm wind forcing is properly taken into account. A demonstration of the The neuronal network performing the initial information utility of this approach will also be presented as applied to processing of olfactory stimuli in mammals exhibits ex- Hurricane Ike. tensive neuronal turnover and a slow restructuring of its connectivity. This network evolution and the activity on Kyle T. Mandli this network are modulated by feedback from a network University of Texas at Austin that has properties of an associative memory. Using simple ICES 48 AN14 Abstracts

[email protected] description of the problem and how it can be addressed.

John A. Dodson MS17 Options Clearing Corporation Transport Methods for the Community Atmo- Chicago, IL 60606 sphere Model’s Spectral Element Dynamical Core [email protected]

Transport algorithms are highly important in atmospheric modeling for climate where hundreds of tracer species must MS18 be efficiently transported and it is critical that they satisfy Using Social Influence to Predict Subscriber Churn physical bounds and conservation laws. We describe and compare two new transport algorithms that are being de- With the saturation of mobile phone markets operators fo- veloped for the Community Atmosphere Model’s (CAM) cus their energies on identifying potential churners for re- Spectral Element (SE) Dynamical Core for use on unstruc- tention campaigns. Typical churn prediction algorithms tured meshes. The first is a finite-volume based approach identify churners based on service usage metrics, net- where cell intersections between a Lagrangian departure work performance indicators, and demographic informa- grid and the Eulerian computational grid are computed tion while social influence to churn is usually not consid- with the Mesh Oriented Data Base (MOAB). This method ered. We present a churn prediction algorithm that incor- is stable for large time steps and is efficient for large num- porates the influence churners spread to their social peers bers of tracer species because the computationally inten- and show that social influence improves churn prediction sive intersection algorithm needs to be called only once and is among the most important factors. per timestep for multiple tracers. The second method is Veena Mendiratta a nodal semi-Lagrangian scheme that has the advantage Bell Labs, ALCATEL-LUCENT of directly using the spectral element degrees-of-freedom. Naperville, IL 60563 This method is coupled with an optimization algorithm to [email protected] enforce mass conservation and bounds preservation. We evaluate the new methods using several standard two- and three-dimensional transport problems on the sphere and Chitra Phadke, Huseyin Uzunalioglu, Dan Kushnir compare to existing approaches. Bell Labs, Alcatel-Lucent [email protected], Kara Peterson [email protected], Sandia Natl. Labs [email protected] [email protected] MS18 Mark A. Taylor Sandia National Laboratories, Albuquerque, NM Efficient High-Precision Numerical Computation [email protected] This talk provides an overview of the methods used to compute numerical functions using high precision in Mathe- MS18 matica. The main focus will be on computation of elementary functions, but applications to special functions will Interpreting the Impact of Constraints for Mean also be mentioned. An outline of the algorithms used will Variance and Cvar Optimization be given together with a description of recent work on more efficient implementation. A comparison with some state- In this presentation, we study the effect linear constraints of-the-art special purpose software will also be presented. have on risk in the context of both mean variance optimization (MVO) and conditional value at risk (CVaR) optimization. Jagannathan and Ma (2003) establish an equiva- Mark Sofroniou lency between certain constrained and unconstrained MVO Wolfram Research Inc problems via a modification of the covariance matrix. We 40139 Bologna, Italy extend their results to both the general case of arbitrary [email protected] constraints in MVO problems and to CVaR optimization, where the joint density is modified. MS19 Chris Bemis Changing Directions Whitebox Advisors Minneapolis, MN 55416 We were often told to choose a research area we love. But [email protected] there are a lot of different kinds of math I love; in fact, any math is fun! In this talk I will share my reflections on how I came to the research area I work in now and factors you MS18 can consider when making that difficult choice yourself. Addressing the Potential Non-Robustness of Sub- additive Portfolio Risk Measures May Boggess Arizona State University The modern approach to managing financial market risk [email protected] is to define an acceptance set for portfolio net asset value at some fixed time horizon according to some probability measure and to impose limits in the current period on the MS19 portfolio composition in order to assure acceptable out- Two Jobs, Two Children, and Two Cars: What can comes. Estimating these limits present practical and theo- Possibly go Wrong? retical challenges (cf Cont et al. [2010]), particularly where outcomes are highly leptokurtotic. We present a concise Some time in the last millennium but it seems longer ago AN14 Abstracts 49

than that my husband and I set out to start a family and solve systems of parameterized PDEs faster, such as model find permanent academic jobs, more or less at the same reduction for parameterized systems, Krylov subspace re- time. Employer-provided daycare, spousal accommoda- cycling, and updating preconditioners, and we discuss links tion, and parental leave were yet to be invented. Nonethe- between these approaches, and results from recent projects. less, we benefited from many factors: The novelty of the situation, our willingness to explore different parts of the country and different types of institutions, and our opti- Eric De Sturler mism and our determination to do the best we could for Virginia Tech our careers and for our family. This talk will summarize [email protected] our strategies, and will consider what we could have done better. MS20 Barbara Lee Keyfitz Computational Complexity of Stochastic Galerkin The Ohio State University and Collocation Methods for PDEs with Random Department of Mathematics Coefficients bkeyfi[email protected] We developed a rigorous cost metric, used to compare the computational complexity of a general class of stochas- MS19 tic Galerkin methods and stochastic collocation methods, Perspectives of an Assistant Professor when solving stochastic PDEs. Our approach allows us to calculate the cost of preconditioning both the Galerkin and I will reflect on my career path, which did not follow the collocation systems, as well as account for the sparsity of trajectory I expected. Instead of continuing in a career fo- the Galerkin projection. Theoretical complexity estimates cused solely on teaching, I moved from being an assistant will also be presented and validated with use of several professor at a teaching university to one at a research uni- computational examples. versity. Along with my career path, I will share the advice I received along the way that shaped this journey. In addi- Nick Dexter tion, I will reflect on my experiences of being an assistant University of Tennessee professor at two different types of institutions. [email protected]

Joan Lind Clayton G. Webster, Guannan Zhang University of Tennessee Oak Ridge National Laboratory [email protected] [email protected], [email protected]

MS20 MS20 A Linear Algebra Perspective on Modeling and Compressive Sensing Method for Solving Stochas- Computation with Stochastic PDEs tic Diﬀerential Equations

Computational solutions of PDE models with uncertain We solve stochastic partial differential equations (SPDEs) inputs often begin by representing the randomness in the with random coefficients by expanding the solution with system with a set of random variables, which become ad- generalized polynomial chaos (gPC). We employ the com- ditional coordinates of the PDE solution. One must dis- pressive sensing method to recover the coefficients of the cretize both the physical domain (space, time) and the gPC expansion given the knowledge that the solution is random domain (added coordinates) to approximate the ”sparse”. We also combine this method with a special solution numerically. Discretization methods yield a host sampling strategy to further increase the accuracy of the of interesting linear systems to solve. We will compare the recovery of the gPC coefficients. Our method is especially linear systems arising in Galerkin methods, pseudospectral suitable for exploiting information from limited sources. methods, and least-squares methods with the goal of offering some practical guidelines for discretization. Xiu Yang Brown University Paul Constantine xiu [email protected] Colorado School of Mines Applied Mathematics and Statistics George E. Karniadakis [email protected] Brown University Division of Applied Mathematics David F. Gleich george [email protected] Purdue University [email protected] MS21 Stochastic Turing Patterns: Analysis of MS20 Compartment-based Approaches Strategies for the Efficient Solution of Parameter- ized or Stochastic PDEs Turing patterns can be observed in reaction-diffusion systems where chemical species have different diffusion con- Many applications, such as stochastic PDEs and uncer- stants. In recent years, several studies investigated the tainty quantification, lead to a large collection or sequence effects of noise on Turing patterns and showed that the of parameterized PDEs. Taking into account that we need parameter regimes, for which stochastic Turing patterns to solve a collection or sequence of related PDEs can lead are observed, can be larger than the parameter regimes to a substantially shorter total solution time (over all sys- predicted by deterministic models. In this talk, the tems). We provide a brief overview of methods that help dependence of stochastic Turing patterns on the com- 50 AN14 Abstracts

partment size is investigated. we propose and study a in the models will vary due to external sources. We will compartment-based model of Turing patterns where each discuss how diffusion can be modeled on meshes of poor chemical species is described using a different set of com- quality and how to include and analyze extrinsic noise in partments. It is shown that the parameter regions where the simulations of an oscillatory system. spatial patterns form are different from the regions obtained by classical deterministic PDE-based models, but Per Lotstedt they are also different from the results obtained for the Department of Information Technology stochastic reaction-diffusion models which use a single set Uppsala University, Sweden of compartments for all chemical species. In particular, it [email protected] is argued that some previously reported results on the effect of noise on Turing patterns in biological systems need to be reinterpretted. MS21 SParSE: Efficient Stochastic Parameter Search Al- Yang Cao gorithm for Events Computer Science Department Virginia Tech High-performance computing empowers scientists to run [email protected] large in-silico stochastic models that accurately mimic the behavior of the represented system. As the predic- Radek Erban tive power of such models improve, the need for an algo- University of Oxford rithm that efficiently determines system configurations for Mathematical Institute achieving a specific outcome increases. In this presenta- [email protected] tion, we present a novel parameter estimation algorithm— Stochastic Parameter Search for Events (SParSE)—that automatically computes parameter configurations for prop- MS21 agating the system to produce an event of interest at user- Adaptive Accelerated Spatial Stochastic Simula- specified success rate and error tolerance. tion of Biochemical Systems Min K. Roh Spatial stochastic simulation is an extremely computation- Intellectual Ventures Laboratory ally intensive task. This is due to the large number of [email protected] molecules, which along with the refinement of the discretized spatial domain, results in a large number of diffusive transfers between voxels (sub-volumes). Previously, MS23 we presented a novel formulation of the Finite State Pro- jection (FSP) method, called the Diffusive FSP (DFSP) Machine Learning Models for Terrestrial Space method, for the efficient and accurate simulation of diffu- Weather Forecasting sive processes. Using the FSP method’s ability to provide a bound on the error, we are able to take large diffusion Earths magnetosphere experiences loading and unloading timesteps with confidence in our solution. We used this to processes in response to the incoming energy from the so- construct an operator split algorithm for spatial stochastic lar wind, creating geomagnetic storms. Predicting these simulation of reaction-diffusion processes that solves diffu- storms is a key priority of space agencies. Due to the sion with DFSP and reactions with SSA. However, one of scarcity of available data, this system is difficult to sim- the biggest challenges faced by scientists utilizing DFSP ulate with first-principle techniques, inspiring significant is correct selection of the appropriate operator splitting research in data-driven models. We investigate the use timestep. A correctly chosen timestep will produce results of advanced graphical machine learning methods includ- at the optimum speed without violating the specified error ing Elman Recurrent Neural Networks and Hidden Markov tolerance. Choosing an appropriate timestep requires esti- Models for predicting solar storms. Advisor: Dhruv Batra, mation of the error due to operator splitting. The error is Virginia Tech a function of the spatial discretization of the domain, the Brendan Avent, Nicholas Sharp diffusion coefficients of the molecules within the system, Virginia Tech and the stiffness of the chemical reaction channels. Here, [email protected], [email protected] we present an extension to the DFSP algorithm that automatically and adaptively selects the appropriate timestep for performance and error control. We demonstrate the MS23 utility of this method with a traditional CPU implementation, and its parallel efficiency with a many-core imple- Optimal Control in Time-Varying Velocity Fields mentation. using Alpha Hulls

Brian Drawert Vehicles in current fields present a difficult optimization University of California Santa Barbara problem in charting optimal navigational paths. Recent [email protected] progress has been made on the general optimal control problem by using front propagation to track the boundary of a reachable set. This work presents a significant MS21 advancement by using alpha hulls to dynamically mesh a Stochastic Simulation of Biochemical Networks: set boundary in three dimensional space. This method per- Diffusion and Parameter Sensitivity mits higher order optimization, including mixed time-fuel cost metrics and trajectories in three dimensions. Advisor: At the level of a single biological cell, random fluctuations Shane Ross, Virginia Tech have a significant effect on the biochemistry of the cell. The intrinsic noise in the system with reactions and diffusion Nicholas Sharp is simulated on an unstructured mesh. The parameters Virginia Tech AN14 Abstracts 51

[email protected] vations about the spread of calcium within an atrial myocyte. Furthermore, I will demonstrate that altering the strength of calcium release, the refractoriness of calcium MS23 release channels, the magnitude of initiating stimulus, or An Extensible Test Matrix Collection the introduction of stochastic calcium channel activity can cause the nucleation of pro-arhythmic travelling calcium We describe the design and implementation of a test ma- waves. trix collection. The matrices are grouped into subclasses and their key properties are documented, such as struc- Ruediger Thul ture, eigenvalues, inverse and condition number. Users University of Nottingham can access to matrices by matrix name, by number and [email protected] by property. They can also include their own matrices by creating new subclasses, which can be easily shared with Steve Coombes others. The package is written in Fortran 95 and includes University of Nottingham a Python interface. Advisor: Nicholas Higham, University Division of Applied Mathematics, School of Mathematical of Manchester Scie [email protected] Weijian Zhang University of Manchester [email protected] Martin Bootman The Open University [email protected] MS24 Mathematical Modelling of Excitation Contraction MS25 Coupling Complexity and Approximability of Tensor Nuclear We present a spatially resolved Ca2+ release unit model. It Norm reproduces experimental ﬁndings like gain and gradedness, spark life time and the dependence of release currents and We show that computing the nuclear norm of a 3-tensor RyR open probability on lumenal Ca2+. A crucial question is an NP-hard problem. We discuss its approximability for the early phase of release is whether the activation of and deduce polynomial-time computable upper and lower the RyRs is triggered by one or by multiple open LCCs. bounds. We address the problem by modelling. We conclude that the activation of RyRs requires multiple open LCCs. Shmuel Friedland Department of Mathematics ,University of Illinois, Martin Falcke Chicago MDC for Molecular Medicine [email protected] Berlin, Germany [email protected] Lek-Heng Lim University of Chicago [email protected] MS24 Ca2+ Signaling in the Cardiomyocyte: An Atom- istic to Cellular Multi-Scale Perspective MS25 Combinatorial Interpretation of the Mesner- Abstract not available at time of publication. Bhattacharya Algebra with Application to Hyper- matrix Spectral Decomposition Peter Kekenes-Huskey UCSD In this talk we will present an overview of the hyperma- [email protected] trix generalization of matrix algebra proposed by Mesner and Bhattacharya in 1990. In connection with the Mesner- MS24 Bhattacharya algebra we discuss a spectral decomposition theorem for hypermatrices, a generalization of the Cayley- Subcellular Calcium Dynamics in a Whole-cell Hamilton theorem to Hypermatrices with application to Model of an Atrial Myocyte computing new hypergraph invariants.

Intracellular calcium waves play a crucial role in coordi- Edinah Gnang nating contraction of cardiac myocytes. I will present Institute of Advanced Study an innovative mathematical modelling approach that al- [email protected] lows detailed characterisation of calcium movement within the 3-dimensional volume of an atrial myocyte. Essential aspects of the model are the geometrically realistic rep- Vladimir Retakh resentation of calcium release sites and physiological cal- Rutgers University cium ﬂux parameters, coupled with a computationally in- [email protected] expensive framework. By translating non-linear calcium excitability into threshold dynamics, we avoid the compu- Ahmed Elgammal tationally demanding time-stepping of the full parabolic Department of Computer Science partial diﬀerential equations that are often used to model Rutgers University calcium transport. Our approach successfully reproduces [email protected] key features of atrial myocyte calcium signalling observed during excitation-contraction coupling. Beyond this val- Ori Parzanchevski idation of the model, our simulation reveals novel obser- Institute of Advanced Study 52 AN14 Abstracts

[email protected] ity. The slime mold Physarum polycephalum provides an excellent model organism for the study of amoeboid motion. In this research, we develop a computational model MS25 of crawling Physarum. Our model incorporates the effects Randomized Methods for Higher-Order SVD of the cytoplasm, cellular cortex, the internal cytoskeleton and adhesions to the substrate. Of particlary interest are We adapted the work of Halko, Martinsson and Tropp of stresses generated by cytoplasmic flow and how transmis- the randomized range finder in finding the low multilinear sion of stresses to the substrate is coordinated. In our nu- rank of tensors. merical model, the Immersed Boundary Method is used to account for such stresses. We investigate the relationship Deonnia Pompey, Carmeliza Navasca between contraction waves, flow waves, adhesion, and loco- Department of Mathematics motive forces in an attempt to characterize conditions nec- University of Alabama at Birmingham essary to generate directed motion. Cytoplasmic flows and [email protected], [email protected] traction stresses generated by the model are compared to experimentally measured stresses generated by Physarum. MS25 Tensor Linear Discriminant Analysis for Object Owen Lewis Recognition University of California, Davis [email protected] In this talk we explore a tensor based approach to linear discriminant analysis and object recognition. Similar to matrix LDA we determine a basis for projection by mini- MS26 mizing the within class scatter and maximizing the between Simulation of Fluid Flow Past Conic Obstacles with class scatter. We measure the accuracy of the method and Applications to Leaves compare to the traditional LDA approach by varying the number of eigenvectors and eigenmatrices used for classifi- We present findings from 2 and 3 dimensional simulations cation. of fluid flow past conic obstacles to compare to experiments of leaves in wind tunnels conducted by the Miller Lab. The William E. Sorenson goal is to study vortex formation at different cone angles, South Dakota School of Mines and Technology compare boundary layers to asymptotics and if given time [email protected] potentially measure the impact of elasticity on the obstacle.

Randy Hoover, Karen S. Braman South Dakota School of Mines Jeremy L. Marzuola [email protected], [email protected] Department of Mathematics University of North Carolina, Chapel Hill [email protected] Nels Leonard South Dakota Schoold of Mines and Technology [email protected] MS26 Plant Leaves Reconfigure into Cone Shapes to Re- duce Drag and Flutter MS26 Leaf Compliance and Foliar Disease Transmission We examine how leaves roll up into drag reducing shapes in strong flows. The dynamics of the flow around the leaves Foliar diseases in plants are a major cause of crop loss of the wild ginger and tulip poplar are described and com- worldwide. Following a recent study which identified vari- pared to simplified sheets using 3D numerical simulations ous modes of foliar pathogen ejections from contaminated and physical models. In the actual leaf, a stable recircu- leaves during rainfalls, we here present a theoretical model lation zone is formed within the wake of the reconfigured that rationalizes the effect of foliage compliance on such cone. In physical and numerical models that reconfigure mechanisms. The laws of fluid dynamics set tight limits into cones, a similar recirculation zone is observed. on this epidemiological problem of foliar disease transmission and suggest mitigation strategies to the onset of foliar Laura A. Miller disease spread. University of North Carolina - Chapel Hill Department of Mathematics Lydia Bourouiba [email protected] Department of Mathematics #2-348 Massachusetts Institute of Technology [email protected] MS27 Demon Design: Circumnavigating Landauer’s Limit MS26 Hydrodynamic Contributions to Amoeboid Cell Maxwells Demon is a century old thought experiment Motility which has challenged physicists understanding of thermodynamics. We develop a new classical formalism for con- Understanding the methods by which cells move is a funda- structing generalized Maxwellian Demons. We call this mental problem in modern biology. Cell locomotion is inte- new class of systems information engines. These engines gral to physiological processes such as wound healing, can- use ”intelligent” information processing to extract energy cer metastasis, embryonic development, and the immune from a thermal bath. Although these processes appear to response. Recent evidence has shown that the fluid dy- violate the second law of thermodynamics on first inspec- namics of cytoplasm can play a vital role in cellular motil- tion, information processing has an energy cost. This cost AN14 Abstracts 53

was once thought to be described by Landauers limit on eﬃcient machine which merely copied the input would nec- erasure. We discuss how to design the microscopic and essarily predict the input. macroscopic architecture of the information engine in order to circumnavigate Landauers Principle, developing a Sarah Marzen diﬀerent set of energetic bounds on information process- University of California Berkeley ing. [email protected]

Alec Boyd, James P. Crutchfield James Crutchfield University of California Davis Computational Science & Engineering Center and Physics [email protected], [email protected] Dept. University of California at Davis [email protected] MS27 Information Processing and the Second Law of Thermodynamics: An Inclusive, Hamiltonian Ap- MS28 proach Scalable Nonlinear Solvers for Geophysical Prob- lems We obtain generalizations of the Kelvin-Planck, Clausius, and Carnot statements of the second law of thermodynam- Robustness and efficiency of nonlinear solvers, especially ics for situations involving information processing. To this for complex multiphysics problems, is a major concern end, we consider an information reservoir (representing, for large scale problems. We present the new framework e.g., a memory device) alongside the heat and work reser- for nonlinear preconditioning developed in PETSc, and voirs that appear in traditional thermodynamic analyses. show its application to problem in crustal dynamics from We derive our results within an inclusive framework in the PyLith package, and lithospheric dynamics from the which all participating elementsthe system or device of in- pTatin3d package. terest, together with the heat, work, and information reser- voirsare modeled explicitly by a time-independent, classical Matthew G. Knepley Hamiltonian. We place particular emphasis on the limits University of Chicago and assumptions under which cyclic motion of the device [email protected] of interest emerges from its interactions with work, heat, and information reservoirs. MS28 Sebastian Deffner University of Maryland Performance and Scalability of Multigrid Solvers sebastian.deff[email protected] for Geophysical Flow this talk, we present the abstract concept of hierarchical MS27 hybrid grids to design scalable and fast multigrid solvers for the incompressible Stokes that lead to saddle point for- TowardsAPhysicsofInformation:BitbyBit mulations. Based on a hierarchy of block-wise uniformly refined grids, a semi-structured mesh is obtained that con- Energy and information are fundamental concepts in sci- stitutes the starting point for the design and implementa- ence, and yet, most would struggle to cite results relat- tion of a massively parallel Stokes solver. In this presen- ing the two, with Landauer’s principle, perhaps, being the tation, we investigate and analyze experiments for Earth most well-known. However, there has been renewed inter- Mantle Convection simulations on peta-scale clusters. est in relating these concepts, especially as researchers en- gage the nanoscale. We review information-theoretic mea- Björn Gmeiner sures of memory and organization as developed in compu- Computer Science 10 - System Simulation tational mechanics, an approach that emphasizes informa- Friedrich-Alexander-University Erlangen-Nuremberg, tion storage and processing in physical systems. Existing Germany and future applications will also be discussed. [email protected] Christopher J. Ellison Center for Complexity and Collective Computation Christian Waluga University of Wisconsin-Madison M2 Center of Mathematics [email protected] Technical University of Munich [email protected]

MS27 Ulrich J. Ruede Predictive Inference in Non-equilibrium Steady University of Erlangen-Nuremberg State Department of Computer Science (Simulation) [email protected] Biological sensory systems could be very efficient lossy predictive feature extractors, and a common goal is to engineer systems which learn to extract predictive features of sen- MS28 sory input. One theoretical framework for lossy predictive Computational Environments for Modeling Multi- feature extraction is that of predictive rate-distortion the- phase Flow, Geochemistry, and Geomechanics ory. We discuss how to find predictive information curves of output generated by partially-deterministic finite au- We discuss multiphase models for modeling coupled flow, tomata. We discuss how input-dependent dynamical sys- geochemistry and geomechanics in a porous medium that tems can extract predictive features of their input automat- includes history matching using EnKf. We will present ically. And finally, we ask whether or not an energetically- results for a carbon sequestration storage problem and a 54 AN14 Abstracts

chemical flood. fine-grained parallelism. We then measure the resulting performance improvements on emerging multicore archi- Mary F. Wheeler tectures in the context of sparse linear algebra. Center for Subsurface Modeling, ICES University of Texas at Austin Eric Phipps [email protected] Sandia National Laboratories Optimization and Uncertainty Quantification Department [email protected] MS29 A Hyperspherical Method for Discontinuity Detec- H. Carter Edwards tion Sandia National Laboratories [email protected] The objects studied in uncertainty quantification may in- conveniently have discontinuities or be contained in an implicitly defined irregular subvolume. Standard techniques MS29 are likely to fail; even an adaptive sparse grid method may A Generalized Clustering-based Stochastic Collo- require excessive sampling to achieve a tolerance. The hy- cation Approach for High-dimensional Approxima- persphere approach detects and unfolds discontinuity sur- tion of SPDEs faces, greatly reducing the influence of highly curved geometry, and allowing good estimates of shape and proba- We developed a novel generalized clustering-based stochas- bilistic volume. tic collocation (gSC) approach, constructed from, e.g., a latinized hCV tessellation (hCVT), with locally supported Guannan Zhang, Clayton G. Webster hierarchical radial basis function defined over each hCVT Oak Ridge National Laboratory cell. This gSC method permits low-discrepancy adaptive [email protected], [email protected] sampling according to the input probably density function (PDF), and whose accuracy decreases as the joint PDF ap- John Burkardt proaches zero; effectively approximating the solution only Department of Computational Science in the high-probability region. Theoretical and computa- Florida State University tional comparisons to classical sampling and SC methods [email protected] will also be examined.

Clayton G. Webster, Guannan Zhang MS29 Oak Ridge National Laboratory A Hierarchical Stochastic Collocation Method for [email protected], [email protected] Adaptive Acceleration of PDEs with Random In- put Data MS30 We will present an approach to adaptively accelerate a se- Matching Exponential and Resolvent Based Cen- quence of hierarchical interpolants required by a multilevel trality Measures in Complex Networks sparse grid stochastic collocation (aMLSC) method. Tak- ing advantage of the hierarchical structure, we build new Centrality measures are used to numerically define the no- iterates and improved pre-conditioners, at each level, by us- tion of importance of a node to the entire network. In this ing the interpolant from the previous level. We also provide talk we consider in particular centrality measures based on rigorous complexity analysis of the fully discrete problem the matrix exponential and resolvent functions. It has been and demonstrate the increased computational efficiency, as observed that the ordinal node ranking the resolvent based well as bounds on the total number of iterations used by measure yields can be particular sensitive to the choice of the underlying deterministic solver. the parameter involved. We show that the parameter can be chosen so that the resolvent measure gives similar rank- Peter Jantsch ings to the exponential measure. University of Tennessee [email protected] Mary Aprahamian School of Mathematics Guannan Zhang, Clayton G. Webster The University of Manchester Oak Ridge National Laboratory [email protected] [email protected], [email protected] Des Higham Univ. Strathclyde MS29 [email protected] Improving Performance of Sampling-Based Uncer- tainty Quantification on Advanced Computing Ar- Nicholas J. Higham chitectures Through Embedded Ensemble Propa- University of Manchester gation School of Mathematics [email protected] We explore approaches for improving the performance of sampling-based uncertainty quantification methods on emerging computational architectures. Our work is moti- MS30 vated by the trend of increasing disparity between floating- Anticipating Behavior During Twitter Spikes point throughput and memory access speed. We describe rearrangements of sampling-based uncertainty propagation We propose and test a novel mathematical model for the methods to propagate ensembles of samples simultaneously activity of microbloggers during an external, event-driven leading to improved memory access patterns and increased spike. The model leads to a computable prediction of who AN14 Abstracts 55

will become active during a spike. This information is of in- University of Cagliari, Italy terest to commercial organisations, governments and char- [email protected], [email protected] ities, as it identifies key players who can be targeted with information in real time. The main expense is a large-scale, Lothar Reichel sparse linear system solve that is comparable with the cost Kent State University of computing Katz centrality. We will illustrate the new [email protected] algorithm on Twitter data around sporting events and TV shows, where spikes in social media activity are driven by external events such as referees’ decisions or dramatic plot MS31 developments. A Family of Numerical Methods for Large Scale DFN Flow Simulations avoiding Complex Mesh Desmond Higham Generation University of Strathclyde, UK [email protected] A novel optimization method for Discrete Fracture Net- work (DFN) simulations of subsurface flows is presented. Peter Laflin Large scale DFN problems are iteratively split in quasi- Bloom Agency, UK independent smaller problems on the fractures that can be peter.lafl[email protected] efficiently solved on parallel computers, applying several discretization approaches on fractures, with independent Peter Grindrod meshes. The approach leads to a flexible, efficient and re- University of Oxford, UK liable method. The approach is also used for Uncertainty [email protected] Quantification of flow properties in DFNs. Matias Benedetto, Stefano Berrone, Caludio Canuto, Alex Mantzaris Sandra Pieraccini, Stefano Scialo University of Strathclyde, UK Politecnico di Torino [email protected] Dipartimento di Scienze Matematiche [email protected], [email protected], Amanda Otley [email protected], [email protected], Bloom Agency, Leeds, UK [email protected] [email protected]

MS31 MS30 Adaptive Mesh Reﬁnement for Flow in Fractured A Matrix Analysis of Diﬀerent Centrality Measures Porous Media

Node centrality measures including degree, eigenvector, Discrete fracture models are typically large due to the ex- Katz and subgraph centralities are analyzed for both undi- plicit representation of fractures. For these systems, the rected and directed networks. We show how parameter- fracture connectivity often has the largest impact on flow. dependent measures, such as Katz and subgraph centrality, In some cases fracture connectivity can restrict the flow to can be ”tuned” to interpolate between degree and eigenvec- a limited area, leaving large parts of the reservoir essen- tor centrality, which appear as limiting cases of the other tially inactive. In this work we show how well-driven flow measures. Our analysis gives some guidance for the choice solutions can be used to efficiently adapt the unstructured of parameters in Katz and subgraph centrality, and pro- grid to resolve key flow regions. vides an explanation for the observed correlations between different centrality measures. Mohammad Karimi-Fard Stanford Christine Klymko [email protected] Emory University [email protected] Louis Durlofsky Stanford University Michele Benzi [email protected] DepartmentõfMathematics˜ and Computer Science Emory University [email protected] MS31 Meshing Strategies and the Impact of Finite El- ement Quality on the Velocity Field in Fractured MS30 Media Low-rank Approximation Methods for Ranking the Nodes of a Complex Network For calculating flow in a fracture network, the mixed hybrid finite element (MHFE) method is a method of choice as it Various network metrics have been introduced to identify yields a symmetric, positive definite linear system. How- the most important nodes in a graph. Some of them are ever, a drawback to this method is its sensitivity to bad defined as a function of the adjacency matrix associated to aspect ratio elements. For poor-quality triangles, elemen- the network. We propose a new method to compute such tary matrices are ill-conditioned, and inconsistent velocity matrix functions, based on a low rank approximation of the vectors are obtained by inverting these local matrices. Here adjacency matrix, which allows us to determine a subset we present different strategies for better reconstruction of that contains the most important nodes, followed by the the velocity field. application of Gauss quadrature to refine the result. Géraldine Pichot Giuseppe Rodriguez, Caterina Fenu INRIA-Rennes, France 56 AN14 Abstracts

Campus de Beaulieu [email protected] [email protected]

Patrick Laug MS32 INRIA - Rocquencourt Oscillation of Nabla Dynamic Equations on Time France Scales [email protected] In this talk we discuss the oscillatory behavior of the second-order nonlinear nabla functional dynamic equation Jocelyne Erhel ∇ ∇ INRIA-Rennes, France p(t)y (t) + q(t)f(y(τ(t))) = 0 Campus de Beaulieu [email protected] on a time scale (a nonempty subset of the real numbers) T with sup T = ∞. We establish a sufficient and neces- Jean E. Roberts sary condition which ensures that every solution oscillates. INRIA Paris-Rocquencourt Next we establish the oscillatory equivalence of the above France dynamic equation and the second-order nonlinear nabla dy- [email protected] namic equation ∇ ∇ ρ Jérôme Jaffré p(t)y (t) + q(t)f(y (t)) = 0 INRIA-Rocquencourt Jerome.Jaff[email protected] on time scales. We close with an example. Raegan Higgins Jean-Raynald de Dreuzy Texas Tech University Geosciences Rennes, UMR6118 CNRS Department of Mathematics and Statistics Université de Rennes 1 [email protected] [email protected]

MS32 MS31 Fetal Heart Rate and EEG Modeling: Predicting XFEM for Flow in Fractured Porous Media Fetal Distress in Labor Simulations of flows in porous media in geological appli- During labor, fetal well-being is typically monitored by cations are challenging due to geometric complexity and measuring fetal heart rate (FHR). It is known that more strong variability of properties. To obtain a flexible nu- reliable monitoring modalities are needed. To address this, merical discretization we employ the XFEM. Grids can be we present a mathematical model which explores the mon- set irrespectively of regions of different permeability since itoring of two signals, FHR and EEG, as a way to predict we can represent discontinuous coefficients within elements fetal distress. Our modeling approach includes blood flow accurately. Fractures can cut grid elements thanks to suit- to the heart and brain and incorporates several key fea- able enrichments of the pressure and velocity spaces. Fi- tures such as, oxygen delivery, blood flow redistribution, nally, n − 1 dimensional XFEM are employed to treat the blood pressure, chemo and baro-receptor mechanisms. intersections between fractures. Aisha Najera Chesler Anna Scotti Claremont Graduate University MOX, Department of Mathematics, Politecnico di Milano [email protected] [email protected] Ami Radunskaya Luca Formaggia Pomona College Department of Mathematics Mathematics Department Politecnico di Milano, Italy [email protected] [email protected]

MS32 MS32 A Biological Application of the Oriented Skein Re- Mathematical Models of Metabolic Dysfunction in lation Type 2 Diabetes The tangle model was developed in the 1980’s by profes- Type 2 diabetes is a slowly progressing and complex sors DeWitt Sumner and Claus Ernst. This model uses the metabolic disease with a multitude of etiological factors. mathematics of tangles to model protein-DNA binding. An Although it is primarily caused by reduced cellular uptake n-string tangle is a pair (B,t)whereB is a 3-dimensional of glucose (insulin resistance) and insufficient insulin pro- ball and t is a collection of n non-intersecting curves prop- duction (β-cell dysfunction), many of its underlying mech- erly embedded in B. In the tangle model for DNA site- anisms remain unknown. We develop a series of math- specific recombination, one is required to solve simultane- ematical models to describe cellular and molecular pro- ous equations for unknown tangles which are summands cesses involved in the progression of insulin resistance and of observed DNA knots and links. This presentation will β-cell dysfunction and discuss implications for metabolic give a review of the tangle model for site specific recombi- irreversibility and disease onset time. nation, discuss another tangle model that utilizes the oriented skein relation for knots and give an application for Erica J. Graham these models to biological processes. North Carolina State University Department of Mathematics Candice Price AN14 Abstracts 57

United States Military Academy, West Point system is a model used to describe the evolution of proba- Department of Mathematical Sciences bility density function of charged particles under self con- [email protected] sistent electric filed in plasmas. It conserves many physical quantities, including the total energy which is comprised of the kinetic and electric energy. Unlike the total particle MS33 number conservation, the total energy conservation is chal- Fast Sweeping Methods for Steady State Problems lenging to achieve. For simulations in longer time ranges, for Hyperbolic Conservation Laws negligence of this fact could cause unphysical results, such as plasma self heating or cooling. In our work, we develop Fast sweeping methods are efficient interactive numer- the first Eulerian solvers that can preserve fully discrete ical schemes originally designed for solving stationary total energy conservation. The main components of our Hamilton-Jacobi equations. Their efficiency relies on solvers include explicit or implicit energy-conserving tem- Gauss-Seidel type nonlinear iterations, and a finite num- poral discretizations, an energy-conserving operator split- ber of sweeping directions. We generalize it to hyperbolic ting for the VA equation and discontinuous Galerkin finite conservation laws with source terms. The algorithm is ob- element methods for the spatial discretizations. We vali- tained through finite difference discretization, with the nu- date our schemes by rigorous derivations and benchmark merical fluxes evaluated in WENO fashion, coupled with numerical examples such as Landau damping, two-stream Gauss-Seidel iterations. High order accuracy and the ca- instability and bump-on-tail instability. pability of resolving shocks are achieved. In further study, we incorporate multigrid method to improve the efficiency. Xinghui Zhong Michigan State University [email protected] Weitao Chen University of California, Irvine [email protected] MS34 Bayesian Inference with Reduced-order Models and Statistical Error Estimates MS33 Nonlinear Traveling Waves for a Model of the Bayesian inversion for parameterized PDEs requires sam- Madden-Julian Oscillation pling from the posterior distribution, which can entail thousands of forward simulations; this is infeasible with The Madden-Julian oscillation (MJO) is a planetary-scale large-scale models. To make this tractable, we 1) replace wave envelope of cloud and storm activities in the trop- the large-scale model with a reduced-order model (ROM), ics. MJO significantly affects other components of the and 2) rigorously account for the ROM error using the atmosphere-ocean-earth system. Recently, a nonlinear novel ROMES method. ROMES provides a statistical model is presented for capturing MJO’s features. I will model of this error by constructing a stochastic process present the exact nonlinear traveling wave solutions based mapping error indicators (e.g., residual norm) to a distri- on the model’s energy conservation. The solution allows for bution over the ROM error. explicit comparisons between features of linear and nonlinear waves, such as dispersion relations and eligible traveling Kevin T. Carlberg wave speeds. Sandia National Laboratories [email protected] Shengqian Chen University of Wisconsin, Madison Martin Drohmann [email protected] University of Münster Institute for Computational and Applied Mathematics [email protected] MS33 Nonlinear Neutral Inclusions: Assemblages of Matthias Morzfeld, Fei Lu Spheres and Ellipsoids Department of Mathematics Lawrence Berkeley National Laboratory If a neutral inclusion is inserted in a matrix containing [email protected], fl[email protected] a uniform applied electric field, it does not disturb the field outside the inclusion. The well known Hashin coated sphere is an example of a neutral coated inclusion. In this MS34 talk, we consider the problem of constructing neutral in- Partial Eigenvalue Assignment in Large-Scale Lin- clusions from nonlinear materials. In particular, we discuss ear Stochastic Dynamic Systems assemblages of coated spheres and ellipsoids. The objective of the proposed work is to characterize feed- Silvia Jimenez Bolanos back matrices for large-scale linear dynamic systems within Department of Mathematics the framework of nonlinear eigenvalue problem and robust Colgate University design optimization under uncertainty. The proposed for- [email protected] mulation takes into account the effects of constraint vio- lations associated with certain risk assessment for the dynamic system under consideration. It is based on the con- MS33 cept of quantiles and tail conditional expectations. Numer- Energy-Conserving Discontinuous Galerkin Meth- ical examples will be presented to illustrate the proposed ods for the Vlasov-Ampere System framework.

In this talk, we propose energy-conserving numerical Sonjoy Das, Kundan Goswami schemes for the Vlasov-Ampere (VA) systems. The VA University at Buﬀalo 58 AN14 Abstracts

sonjoy@buﬀalo.edu, kundango@buﬀalo.edu [email protected]

Biswa N. Datta Northern Illinois University MS35 [email protected] Intrinsic and Extrinsic Fluctuations in a Spa- tiotemporal Oscillatory System

MS34 Appropriate modeling and simulation frameworks for studying extrinsic noise in spatial settings will be increas- Optimal Sampling of Polynomial Chaos Expansions ingly important as cell biologists dissect the relative contributions of intrinsic and extrinsic fluctuations to total We investigate Monte Carlo sampling of random inputs for stochasticity on ever finer scales. Here we present an ex- the estimation of coefficients in a sparse polynomial chaos tension to URDME to incorporate extrinsic noise into a expansion, with a particular focus on high-dimensional spatial, mesoscopic setting. As an example, the method is random inputs. Sampling from the distribution of the demonstrated on a model of experimentally observed, spa- random variables is typically sub-optimal in a statistical tiotemporal Min protein oscillations in E. Coli cells. When sense. Asymptotic properties of orthogonal polynomials extrinsic fluctuations are modelled as a coloured noise pro- yield sampling schemes with reduced dependence on the cess the sensitivity of a system may depend critically on order and dimension of polynomial basis. We present alter- the typical lifetime of the noise. This phenomenon is ob- native sampling schemes including a Markov Chain Monte served here and illustrates the importance of taking the Carlo sampling with a statistical optimality. timescale of interacting processes into account when analyzing a models robustness to noise. Alireza Doostan Department of Aerospace Engineering Sciences Andreas Hellander University of Colorado, Boulder Department of Computer Science [email protected] University of California, Santa Barbara [email protected] Jerrad Hampton University of Colorado, Boulder [email protected] MS35 Multi-Physics Multiscale Simulations for Dusty Proto-Planetary Disks MS34 We develop a numerical package to simulate the interaction High-Dimensional Approximation with Discrete between the protoplanetary disks and embedded proto- Leja Sequences planets. The disk motion is described as PDEs(hyperbolic, parabolic, and elliptic type). The planet motion is de- We investigate weighted Leja sequences for non-intrusive scribed as ODEs. The coupled system contains multiple interpolatory/approximation schemes of differential equa- length and time scales. Several numerical techniques in- tions parameterized by a random variable. Leja sequences cluding multiscale method have been developed to accel- are attractive for building surrogates of parametric depen- erate the time integration. Adaptive mesh refinement and dence because of their asymptotically optimal properties in parallel-in-time methods are also used to speed up the cal- the pdf-weighted norm. In this talk we discuss the applica- culation. tion and construction of discrete approximations to these sequences, the latter of which involves canonical numeri- Shengtai Li cal linear algebra routines and maximum-volume subspace Los Alamos National Laboratory selection. [email protected]

Akil Narayan University of Massachusetts Dartmouth MS35 [email protected] Understanding the Network of Oscillators in the Mammalian Circadian Clock

MS35 The mammalian circadian clock is comprised of thousands of heterogeneous intracellular oscillators synchroniz- Integration of Molecular Science and Engineering ing their rhythms via intercellular communication. It is not well understood how such a diverse set of cells synchronizes. Electrodeposition is a key process step in the fabrication Using a mechanistic ordinary differential equation model, of high-value products. Deposit formation involves a wide we have identified an inverse relationship between intrinsic variety of physical phenomena that span multiple time- amplitude and phase response properties as a key factor in and length-scales. Although new scientific knowledge at synchronization. Using a simple phase-amplitude model, the atomic-scale is revolutionizing understanding, the de- we relate our earlier findings to the ability to synchronize sign of well-engineered products presents significant com- increasingly heterogeneous populations. putational challenges. This presentation describes use of kinetic Monte Carlo and First Passage Time algorithms Stephanie Taylor from an engineering perspective that requires massively it- Colby College erative optimization calculations based on incomplete fun- [email protected] damental knowledge.

Richard C. Alkire MS36 University of Illinois at Urbana-Champaign Inertial Particles in Turbulence, Caustics and Col- AN14 Abstracts 59

lisions will split into two niches, one with large ornaments and one with small, a phenomenon observed in many species. Abstract not available at time of publication. Sara Clifton Gregory Bewley Northwestern University, USA Max Planck Institute for Dynamics and Self-Organization [email protected] [email protected] Danny Abrams Northwestern University MS36 [email protected] Capillary Fracture

I will describe the initiation and growth of fractures in gels MS37 close to their solid-liquid transition. In experiments, chan- Qualitative and Asymptotic Theory of Detonations nel fractures form at the surface of the gel, driven by ﬂuid propagating away from a central droplet. Their initiation We derive a multidimensional weakly non-linear asymp- is governed by two processes. First, surface-tension forces totic model of detonation waves capable of reproducing exerted by the droplet deform the gel substrate and break the rich nonlinear dynamics observed in solutions of the azimuthal symmetry. We model the substrate as an incom- reactive Euler equations, both in one and multiple space pressible, linear-elastic solid and characterize the elastic re- dimensions. Quantitative and qualitative comparison be- sponse to provide a prediction for the number of fracture tween the asymptotic equations and the full system they arms as a function of material properties and geometric pa- approximate are also presented. rameters. Second, a thermally-activated process initiates a starburst-shaped collection of fractures corresponding to Luiz Faria this strain-patterning. Once initiated, the fractures grow KAUST with a universal power law L = t3/4, with the speed limited [email protected] by the transport of an inviscid ﬂuid into the fracture tip. Aslan R. Kasimov Karen Daniels Applied Mathematics and Computational Science North Carolina State University King Abdullah University of Science and Technology [email protected] [email protected]

Joshua Bostwick Rodolfo R. Rosales Northwestern University Massachusetts Inst of Tech [email protected] Department of Mathematics [email protected] MS36 Low Energy Cardiac Deﬁbrillation MS37 A Linear Quadratic Programming Method for Non- Abstract not available at time of publication. linear Model Predictive Control

Stefan Luther Nonlinear Model Predictive Control (NMPC) requires iter- Max Planck Institute for Dynamics and Self-Organization ative approximative solution of optimal control problems. [email protected] After discretization these are given as nonlinear programs. State-of-the-art solvers use Sequential Quadratic Program- ming to this end. Several industrial applications demand MS36 the solution of Mixed-Integer NMPC Problems with com- Nonlinear Waves and Wave Turbulence binatorial constraints leading to Mathematical Programs with Equilibrium Constraints. We investigate an SLEQP Abstract not available at time of publication. method that uses LPs to determine active sets and steps given by a combination of Linear and equality constrained Nicolas Mordant Quadratic Programs. Laboratoire des Ecoulements G´eophysiques et Industriels Univ. J. Fourier / CNRS / Grenoble INP / IUF Felix Lenders [email protected] Heidelberg University, Germany [email protected]

MS37 Christian Kirches A Mathematical Model for the Sexual Selection of Interdisciplinary Center for Scientiﬁc Computing Extravagant and Costly Mating Displays University of Heidelberg, Germany [email protected] The evolution of extravagant and costly ornaments on animals has intrigued biologists since Darwin suggested that female preference for exaggerated courtship displays drives MS37 the sexual selection of these ornaments. We propose a min- Mathematical Model of Transplant Rejection: imal mathematical model which incorporates two compo- Roles of T cells, Antigen Presenting Cells, and Cy- nents of ornament evolution: an intrinsic cost of ornamen- tokines tation to an individual, and a social beneﬁt of relatively large ornaments within a population. Using bifurcation A mathematical model of the immune-mediated rejection analysis and perturbation theory, we show that animals of transplants predicts a 50% decrease in graft mass within 60 AN14 Abstracts

two weeks of transplantation. Effector T cells propagate Lukas Horny rejection while regulatory T cells limit it; the model is used Czech Technical University in Prague to test graft tolerance-promoting interventions. Decreasing [email protected] the effector T cell translocation rate into the graft typically delays rejection, although this effect depends on relative cytokine concentrations. Doubling the initial number of MS38 regulatory T cells delays rejection by two weeks. Hamilton-Jacobi Equations for the Continuum Limits of Sorting and Percolation Problems Andrew Maturo Indiana University-Purdue University, Indianapolis, USA We show that two related combinatorial problems have [email protected] continuum limits that correspond to solving Hamilton- Jacobi equations, and give convergent numerical schemes. Giorgio Raimondi The first problem is non-dominated sorting, which is fun- Johns Hopkins School of Medicine, Baltimore, MD damental in multi-objective optimization, and the second is [email protected] directed last passage percolation (DLPP), which is an important stochastic growth model closely related to directed polymers and the totally asymmetric simple exclusion pro- Julia Arciero cess (TASEP). Department of Mathematical Sciences Indiana University-Purdue University Indianapolis Jeff Calder [email protected] Department of Mathematics University of Michigan [email protected] MS37 Solving Differential Algebraic Equations Using Structural Analysis Based Dummy Derivatives MS38 Fast and Accurate Redistancing Via Directional Differential algebraic equations, DAEs, appear frequently Optimization in applications involving equation based modelling. A common way of making a DAE amenable to numerical solution A fast and accurate algorithm for the reinitialization of is by reducing it to a corresponding (usually implicit) ODE. the signed distance function in two and three spatial di- The signature matrix method instead solves the DAE dimensions is presented. The algorithm has computational rectly via Taylor series [1]. We draw comparisons between complexity O(N log N ) for the reinitialization of N grid these two different approaches and show the signature ma- points. The order of accuracy of the reinitialization is trix method is in some sense equivalent to the dummy demonstrated to depend primarily on the interpolation al- derivative index reduction method [2]. gorithm used. Bicubic interpolation is demonstrated to result in fourth-order accuracy for smooth interfaces. Sim- Ross McKenzie ple numerical examples demonstrating the convergence and Cardiff University, Wales, UK computational complexity of the reinitialization algorithm McKenzieR1@cardiff.ac.uk in two and three dimensions are presented as verification of the algorithm.

John Pryce Selim Esedoglu Cardiﬀ University, Wales, United Kingdom University of Michigan [email protected] [email protected]

Guangning Tan McMaster University, Hamilton, Canada MS38 [email protected] Numerical Solution of the Second Boundary Value Problem for the Monge-Ampère Equation Ned Nedialkov McMaster University The second boundary value problem for the Monge- [email protected] Ampere equation consists of a fully nonlinear elliptic partial differential equation (PDE) with a global constraint on the image of the gradient map. The state constraint is MS37 replaced by a more tractable local PDE on the boundary. Using wide-stencil finite difference schemes, we construct a A Mathematical Model of an Arterial Wall numerical method that converges to the viscosity solution of the underlying problem. Elastic arteries are significantly prestretched in axial direction and this has great influence on the mechanical behav- Brittany Froese ior during the pressure cycle. Our study presents results of University of Texas at Austin a simulation of the inflation-extension behavior and com- [email protected] parisson of several different models of the wall. The constitutive parameters and geometries for 17 aortas adopted from the literature were supplemented with initial axial MS38 prestretches obtained from the statistics of 365 autopsy Convergent Filtered Schemes for the Eikonal Equa- measurements. tion

Marek Netuil The approximation theory of Barles and Souganidis Charles University in Prague, Czech Republic [Asymptotic Anal. 4 (1991), pp. 271-283] guarantees the [email protected] convergence of numerical schemes to the viscosity solution AN14 Abstracts 61

provided they are monotone, stable and consistent. How- Department of Electrical Engineering (ESAT) ever, theses schemes are in general only 1st order accu- KU Leuven rate. Froese and Oberman [Siam J. Numer. Anal. 51 [email protected] (2013), pp. 423-444] introduced recently convergent filtered schemes which achieve high order where the solu- Lieven De Lathauwer tions are sufficiently smooth. In this talk, we construct Katholieke Universiteit Leuven filtered schemes to the Eikonal equation, present results in [email protected] one and two dimensions and compare them to the ENO schemes [Siam J. Numer. Anal. 28 (1991), pp. 907-922]. MS40 Tiago Salvador McGill University Hydrodynamics and Control of Microbial Locomo- [email protected] tion Interactions between swimming cells, surfaces and fluid MS39 flow are essential to many microbiological processes, from the formation of biofilms to the fertilization of human egg Using Krylov Subspace Method for the Canonical cells. Yet, relatively little remains known quantitatively Polyadic Decomposition about the physical mechanisms that govern the response of bacteria, algae and sperm cells to flow velocity gradi- We propose method based on Krylov subspace methods in ents and solid surfaces. A better understanding of cell- finding the minimum sum of rank one tensors. For rank surface and cell-flow interactions promises new biological deficient least-squares problems, this iterative method is insights and may advance microfluidic techniques for con- efficient with respect to the computational cost and mem- trolling microbial and sperm locomotion, with potential ory. applications in diagnostics and therapeutic protein synthe- Christina Glenn sis. Here, we report new experimental measurements that Department of Mathematics quantify surface interactions of bacteria, unicellular green University of Alabama at Birmingham algae and mammalian spermatozoa. These experiments [email protected] show that the subtle interplay of hydrodynamics and surface interactions can stabilize collective bacterial motion, that direct ciliary contact interactions dominate surface Carmeliza Navasca scattering of eukaryotic biflagellate algae, and that rheo- University of Alabama at Birmingham taxis combined with steric surface interactions provides a [email protected] robust long-range navigation mechanism for sperm cells.

Jorn Dunkel MS39 Mathematics, MIT Source Apportionment of Time and Size Resolved [email protected] Ambient Particulate Matter

The proposed weighted alternating least squares method Vasily Kantsler was used to analyze size- and time-resolved particle sam- University of Warwick ple compositional tensor data. The algorithm identi- Skolkovo Institute of Technology fied five emission sources: soil, deicing road salt, air- [email protected] craft landings, transported secondary sulfate, and local sulfate/construction. The largest source associated with the Raymond E. Goldstein airport operations was aircraft landing that had not been Department of Applied Mathematics and Theoretical previously considered as a significant source of particles. Physics University of Cambridge Na Li [email protected] MathWorks [email protected] MS40 Carmeliza Navasca Orientational Order in Two-Dimensional Confined University of Alabama at Birmingham Active Suspensions [email protected] Geometric confinement in physical space is important for the studies of the collective motion of suspensions of ac- MS39 tive swimmers. The reasons are two-fold: motile biolog- Stochastic Approximation Algorithms for the ical micro-organisms or active colloids are always subject Polyadic Decomposition to different types of confinement in the swimming environment; The existence of confinement can have signifi- In a polyadic decomposition, a tensor is written as a sum of cant effects on the hydrodynamic interactions between the rank-1 terms. The computation of this decomposition often swimmers and thus changes the nature of the collective involves the minimization of the distance between the ten- motion. We focus on the situation when the swimmers are sor and the decomposition. Most iterative algorithms use confined between two parallel plates (Hele-Shaw cell) such every known element in each iteration. By using stochastic that the motion of the particles are restricted to two di- approximation techniques, only a few points are accessed in mensions. In this case, the far-field hydrodynamic effect each iteration. The number of data point accesses can thus of a swimmer is no longer given by a force-dipole, which be reduced, which is important in big data applications. has been used in numerous studies on discrete numerical simulations and continuum theories. Instead, the far-field Nico Vervliet effect of a confined swimmer is given by a potential-dipole. 62 AN14 Abstracts

Using a potential-dipole model in doubly-periodic domain, the long time dynamics of the continuum equations. we perform numerical simulations to probe into the collective dynamics of conﬁned active suspensions. We show Patrick Underhill,YaserBozorgi that, depending on whether the swimmers have head-and- Rensselaer Polytechnic Institute tail symmetry, the isotropic suspensions of swimmers can Department of Chemical and Biological Engineering develop either long time polar orientation order, local align- [email protected], [email protected] ments and non-mobile clusters or combination of the above, which are novel collective behavior compared to swimmer suspensions in unconﬁned geometries. MS41 Low-Dimensional Dynamics Embedded in Echo- Alan Cheng Hou Tsang, Eva Kanso State Networks University of Southern California [email protected], [email protected] Abstract not available at time of publication.

MS40 Andrea K. Barreiro Department of Mathematics Surface Interactions in Suspensions of Swimming Southern Methodist University Cells [email protected] Interactions between swimming cells and surfaces are essential to many microbiological processes, from bacterial MS41 biofilm formation to human fertilization. However, despite their fundamental importance, relatively little is known Metastability and Coherent Structures in Large about the physical mechanisms that govern the scatter- Stochastic Neuronal Networks ing of flagellated or ciliated cells from solid surfaces. In the talk I will reveal recent advances in understanding of We will consider stochastic dynamical systems defined on flagella interaction with surfaces, provide mechanisms for networks where the individual dynamics mimic standard utilizing our knowledge about these interactions to control neuronal models, and show that the systems can exhibit swimming of flagellated cells. In addition, I will describe various types of coherent and metastable behavior. We our very recent results on sperm rheotaxis near surfaces. will demonstrate that there is a naturally occurring, but The key focus will be on the experimental results, sup- non-standard, spectral problem in problems of this type; ported by numerical simulation using minimal models. analysis of this spectral problem will show that its salient features are determined by a certain homology group. Vasily Kantsler University of Warwick Lee DeVille Skolkovo Institute of Technology University of Illinois, Department of Math [email protected] [email protected]

Jorn Dunkel Mathematics, MIT MS41 [email protected] Integrate-and-Fire Model of Insect Olfaction

Raymond E. Goldstein When a locust detects an odor, the stimulus triggers a Department of Applied Mathematics and Theoretical series of synchronous oscillations of the neurons in the an- Physics tenna lobe. These oscillations are followed by slow dy- University of Cambridge namical modulation of the firing rates which continue after [email protected] the stimulus has been turned off. I model this behavior by using an Integrate-and-Fire neuronal network with excitatory and inhibitory neurons. The inhibitory response MS40 of both types of neurons contains a fast and slow component. The fast component, together with the excitation, Modeling of Hydrodynamic Interactions of Large creates the initial oscillations while the slow component Groups of Swimming Microorganisms in Viscoelas- suppresses them and aids in the creation of the slow pat- tic Fluids ters that follow. During the initial oscillations the stimulus can be identified by determining which excitatory neurons Hydrodynamic interactions of swimming microorganisms participate consistently in every cycle of the oscillations. can lead to coordinated behaviors of large groups. The impact of viscoelasticity on the collective behavior of active particles driven by hydrodynamic interactions has Pamela B. Fuller been quantified with the inclusion of rotational diffusion. Rensselaer Polytechnic Institute Oldroyd-B, Maxwell, and generalized linear viscoelastic [email protected] modeled are considered as the constitutive equation of the suspending fluid, inspired by some biological fluids. A mean field assumption is used to model the suspension dy- MS41 namics near an isotropic state. The onset of instability Generalized Linear Models for Networks of Spiking has been quantified by a linear stability analysis in terms Neurons of wavenumber, diffusivities, and constitutive equation parameters. Some key results are in contrast to suspensions Abstract not available at time of publication. in Newtonian fluids. The maximal growth rate can occur at a particular wavelength, and diffusion can act to make Sara A. Solla the system more unstable. Viscoelasticity can also affect Northwestern University AN14 Abstracts 63

[email protected] [email protected]

MS42 MS42 Cytoplasm Rheology and Its Role Cellular Bleb- bing Dynamics Exploring the Effect of Glass-Forming Sugars on Vesicle Membrane Dynamics During Drying We present a computational model to describe the dynamics of blebbing, which occurs when the cytoskeleton de- When immersed in a liquid, certain sugars have a ”glass- taches from the cell membrane, resulting in the pressure- forming” effect on the liquid at large enough concentration. driven flow of cytosol towards the area of detachment and In particular, the viscosity of the liquid is found to be heav- the local expansion of the cell membrane. The model is ily dependent on the sugar concentration, reaching that of used to explore the relative roles in bleb dynamics of cy- a glass in optimal conditions. These sugars, and their affect toplasmic rheology, permeability of the cytoskeleton, and on cellular structures, are of interest to the biological com- elasticity of the membrane and cytoskeleton. We show that munity for various reasons, one of which is their use in the the multiphase poroelastic nature of cytoplasm is essential preservation of biological material. Whereas cryopreserva- to explain experimental observations. tion stores material using extremely low temperatures to reduce cellular mobility, a new technique named lyopreser- Robert Guy vation uses the aforementioned glass-forming effect to re- Deptartment of Mathematics, U.C. Davis duce mobility. However, current attempts to achieve lyop- [email protected] reservation have less than successful. The work discussed in this talk focuses on modeling a single cell undergoing drying similar to that involved in current lyopreservation MS42 techniques. This is done by considering a vesicle placed in a fluid containing a spatially varying concentration of sugar. An Analytic Framework for Pairwise Correlations The model incorporates the bending resistance and inex- in Active Swimming tensibility of the membrane, the viscosity dependence on the sugar, the flow of liquid across the vesicle membrane, as In recent years there has been considerable interest in well as the surrounding concentration and velocity fields. active fluids, such as suspensions of swimming micro- It is solved using the level set, immersed boundary, and im- organisms. A key observation for such suspensions is the mersed interface methods. The results focus on identifying tendency of ”pushing” swimmers (typically bacteria, e.g. how the various material parameters affect the vesicle dy- E. coli) to develop long range orientational correlations; in namics and attempt to identify ideal regimes for achieving stark comparison to ”pulling” organisms (typically algae, lyopreservation. e.g. C. reinhardtii) which tend to remain uncorrelated. This observation is consistent with analytical results in mean field theories for hydrodynamically interacting swim- Chris Vogl mers, where the uniform isotropic state is stable for pullers University of Washington but unstable for pushers. However, a mean field theory can Department of Applied Mathematics not be used to actually predict correlation length scales, as [email protected] it assumes independence of distinct swimmers. Being able to predict such two-point statistics is an important step in characterizing the macroscopic rheological properties of the MS43 suspension as a whole. In this talk an analytical framework for computing the correlations in a simplified phenomeno- Qualitative Reasoning with Modelica Models logical model for swimming will be discussed. Qualitative reasoning allows us to reason about physical Kajetan M. Sikorski systems using simplified systems of qualitative differential University of California Santa Barbara equations, in a way which preserves important behavioral Departament of Mathematics aspects of those systems. However, a continuing challenge [email protected] in that work is the construction of appropriate qualitative models of those systems. Meanwhile, designers are increasingly using the Modelica language to create simula- MS42 tion models of proposed designs for numerical simulation. Finite Length Undulatory Swimmers: Whether to Our group at PARC has addressed the model construction Kick Or to Burrow in a Viscoelastic Fluid bottleneck of qualitative reasoning by automatically trans- forming Modelica models into qualitative models. In this We explore finite length undulatory swimmers in viscoelas- talk, we describe that process, and discuss the challenges in tic fluids. The worm is modeled as an inextensible infinitely abstracting equations into constraints, determining initial thin sheet in 2 dimensions and the swimming is driven us- conditions and discrete events, and identifying appropriate ing a prescribed target curvature. We look at front-back continuous behavior. We identify places where additional asymmetries in the prescribed stroke pattern and consider qualitative constraints can be derived from Modelica equa- the effect on swimming speed and efficiency. The impor- tions, and describe how we bridge the gaps between Mod- tance of passive dynamics, where swimmers are given pre- elica and existing qualitative simulation work on discrete scribed torques rather than prescribed shapes, is explored. behavior. Our system has been integrated with existing We show that kickers can get a larger boost from viscoelas- Modelica tools; we describe its potential applications to ticity than burrowers. mechatronic engineering design.

Becca Thomases Bill Janssen University of California at Davis PARC 64 AN14 Abstracts

[email protected] systems and to NLPs for solving optimal control problems.

Hubertus Tummescheit MS43 Modelon, Inc. tba Enabling Technologies for Web-Based Engineering Analysis MS43 The web and cloud have become ubiquitous in our every- Modelica for Building and Community Energy Sys- day lives. The societal impact of these technologies is sig- tems nificant. Everyday, new tools and technologies are introduced to facilitate the creation of web-based applications. Building energy and control systems can be represented But most of these applications are targeted at consumer by systems of coupled stiff differential equations, algebraic level applications. Although these applications are driven equations and discrete equations. These equations couple by very interesting mathematical principles (for machine models from multiple physical domains. We will present intelligence, data correlation, etc), they are successful be- how these systems can be modeled using the equation- cause they use these principles to create a significant im- based, object-oriented Modelica language. We discuss nu- pact for non-technical users (i.e. consumers). In the engi- merical challenges and opportunities to use such models neering world, many interesting mathematical techniques for analysis that is outside the capabilities of conventional have only a limited impact because there are fewer tech- building simulation programs. The talk closes with an nologies available to wrap these techniques up so they can overview of the international project ”new generation com- impact non-expert users. The first step in connecting en- putational tools for building and community energy sys- gineering and software technologies is understanding the tems based on the Modelica and Functional Mockup Inter- role of technology standards in streamlining the develop- face standards”. This project is a collaboration among 16 ment and deployment process. The next step is identifying countries under the Energy in Buildings and Communities applications where these technologies can have a signifi- Programme of the International Energy Agency. cant impact on the the customers of engineered products. Along the way, we need to consider how to educate engi- Michael Wetter neers, mathematicians and scientists about the possibilities LBNL that these technologies present and how to leverage them. [email protected] This talk will discuss these issues and demonstrate examples of how engineering standards combined with cutting edge software technologies can help bridge the gap allow- MS44 ing engineers and mathematicians to have a greater impact Dynamics Constrained Optimization of Power Grid on engineering product development and, ultimately, con- Using Adjoint Sensitivity Analysis sumers. Specific topics will include mathematical models of products, cloud computing technologies and user expe- We present a DAE-constrained optimization problem for rience in web-based engineering applications. theelectricpowergridwherethesteadystateoperating point has path constraints on the trajectory when the Michael Tiller power grid is subjected to severe disturbances. We use Xogeny constraint aggregration and adjoint sensitivity approach [email protected] for efficiently solving this optimal control problem. This talk discusses the problem formulation, solution approach, and the preliminary results obtained.

MS43 Shrirang Abhyankar Introduction and Overview of Modelica Argonne National Laboratory [email protected] Modelica is a declarative, equation based, object oriented language for the physics-based modeling of large scale en- Mihai Anitescu gineering systems. Modelica is unique in being a vendor- Argonne National Laboratory neutral and widely accepted standard to describe such Mathematics and Computer Science Division cyber-physical systems as the composition of Differential- [email protected] Algebraic Equations (DAE) to describe the system physics and the software to control such systems. For the software Vishwas Rao part, several models of computation can be expressed in Department of Computer Science Modelica: signal oriented modeling, state machines, and Virginia Tech synchronous declarative descriptions can all be expressed [email protected] within the scope of Modelica. This combination makes Modelica useful through all phases of model based engineering, from the early phases of system design to the veri- MS44 fication of the control software, and even reaching into sys- Global Error Estimation for Differential Equations tem operation, where Modelica based models are used for non-linear model predictive control of complex and safety- Global error represents the actual discretization error re- critical plants. This talk will give an introduction to var- sulting after solving a system of differential equations. I ious aspects of Modelica from the perspective of applied will focus on time-stepping methods for ordinary and differ- mathematics and introduce how high-level Modelica code ential algebraic equations. Calculating a posteriori errors is transformed in several of the Modelica compilers to a is generally viewed as an expensive process, and therefore range of numerical algorithms that are then used to ana- in practice only the (local) error from one step to the next lyze engineering design problems. In particular we will look is used to estimate the global errors. However, local er- at the transformation of Modelica code into hybrid DAE ror estimation is not always suitable and may lead to error AN14 Abstracts 65

underestimation. I will review several strategies for a pos- per MC sample. Implementation on GPU. teriori error estimation and discuss new approaches that generalizes the classical strategies. Zane Colgin, Abdul Khaliq Middle Tennessee State University Emil M. Constantinescu [email protected], [email protected] Argonne National Laboratory Mathematics and Computer Science Division Guannan Zhang, Clayton G. Webster [email protected] Oak Ridge National Laboratory [email protected], [email protected] MS44 Viktor Reshniak Predicting the Future with Faster Than Real-Time Middle Tennessee State University Power System Dynamics Simulation [email protected] “Faster than real-time dynamics simulation” is a key goal of DOE’s Advanced Modeling Grid program. IIT is lead- MS45 ing a project to (eventually) predict complex, large-scale power system behavior based on real-time measurements. A Multilevel Stochastic Collocation Methods for The team is leveraging computational and hardware ad- SPDEs vances (e.g., PETSc solvers, time-stepping algorithms, and multi-core processors) to increase speed. Furthermore, the Multilevel methods for SPDEs seek to decrease computa- team is integrating modeling advances (e.g., three-phase tional complexity by balancing spatial and stochastic dis- unbalanced models, protection system models) to improve cretization errors. Multilevel techniques have been success- accuracy. The ultimate goal is to avoid blackouts. fully applied to Monte Carlo methods (MLMC), but can be extended to accelerate stochastic collocation (SC) approxi- Alexander J. Flueck mations. In this talk, we present convergence and complex- Illinois Institute of Technology ity analysis of a multilevel SC (MLSC) method, demon- fl[email protected] strating its advantages compared to standard single-level approximations, and highlighting conditions under which a sparse grid MLSC approach is preferable to MLMC. MS44 Max Gunzburger Dynamic-Feature Extraction, Attribution and Re- Florida State University construction (dear) Method for Power System School for Computational Sciences Model Redution [email protected] This paper presents a method of deriving the reduced dynamic model of power systems based on dynamic response Aretha L. Teckentrup measurements. The method consists of three steps, namely Florida State University dynamic-feature extraction, attribution, and reconstruc- [email protected] tion (DEAR), and results in a quasi-nonlinear reduced model of the original system. The network topology is Peter Jantsch unchanged. Tests on several IEEE standard systems show University of Tennessee that the proposed method yields better reduction ratio and [email protected] response errors than the traditional coherency based reduction methods. Clayton G. Webster Oak Ridge National Laboratory Shuai Lu, Shaobu Wang, Ning Zhou, Marcelo Elizondo, [email protected] Guang Lin Pacific Northwest National Laboratory [email protected], [email protected], MS45 [email protected], [email protected], A Comparison of Algebraic Multigrid Precondi- [email protected] tioning Approaches for Sampling-Based Uncer- tainty Propagation on Advanced Computing Ar- M.A. Pai chitectures University of Illinios, Champion [email protected] Algebraic multigrid (AMG) methods are known to be effective, scalable preconditioners for linear systems arising in various application areas. Sampling-based uncertainty MS45 propagation methods provide an opportunity to extend Improved Multilevel Monte Carlo for High Perfor- such techniques to what are essentially groups of closely mance Computing coupled systems. We compare AMG approaches in the context of ensemble propagation on advanced architectures, Since models at extreme scales may have high dimensional where sampling rearrangement has occurred in order to random space, it is important to continue the development improve access and parallelism. Examples will be given of dimension-independent methods of uncertainty quantifi- using the Trilinos solver framework. cation. Here we accelerate MLMC for PDEs by using a FEM iterative solver that improves the initial guess during Jonathan J. Hu sampling. By using previous samples to build an inter- Sandia National Laboratories polant that predicts the solution value at subsequent sam- Livermore, CA 94551 ple points, we can greatly reduce the number of iterations [email protected] 66 AN14 Abstracts

Eric Phipps [email protected] Sandia National Laboratories Optimization and Uncertainty Quantification Department [email protected] MS46 Exponential Iterative Methods of Runge-Kutta- type (EPIRK): Construction, Analysis and Soft- MS45 ware Calibration of a Computer Model with Functional Inputs Exponential integrators have recently emerged as an efficient alternative to the explicit and implicit methods We investigate the use of specialized experimental data for time integration of large stiff systems of differential to find Bayesian estimates of a functional parameter in equations. A distinct feature of these techniques is that a model of the system. Ideas are illustrated using a case the approximation of the solution uses exponential and study on the action potential of ventricular myocytes. exponential-like functions of the Jacobian or the matrices corresponding to the stiff linear part of the problem. Matthew Plumlee Exponential integrators possess better stability properties ISYE, Georgia Tech compared to explicit methods and can require fewer calcu- [email protected] lations per time step then implicit schemes. We introduce a new class of Exponential Propagation Iterative methods of Runge-Kutta type (EPIRK). These schemes are designed MS46 to offer computational savings and allow construction of Overview of High-Performance Algorithms for very efficient schemes compared to other exponential and Functions of Matrices implicit methods. We describe three different types of EPIRK methods - the unsplit, the split and the hybrid In this talk I will present an overview of recent develop- EPIRK schemes - as well as discuss a new type of implicit- ments in high performance algorithms for matrix functions, exponential (IMEXP) methods. Both the classical and stiff with a focus on topics not covered by the subsequent talks order conditions for EPIRK integrators will be discussed in this minisymposium. I will discuss a selection of recent and we will present a new software package EPIC (Expo- algorithms and results on condition estimation, the action nential Propagation Integrators Collection) which imple- of matrix functions on large, sparse matrices, and the im- ments most efficient of these methods for serial and parallel plementation and testing of matrix function algorithms. computational platforms. I will also discuss some of the open problems and challenges involved in developing high-performance algorithms Mayya Tokman for matrix functions. University of California, Merced School of Natural Sciences Edvin Deadman [email protected] University of Manchester [email protected] MS46 Blocked Algorithms for the Matrix Sign Function MS46 The talk will describe two different blocked (partitioned) Efficient and Stable Arnoldi Restarts for Matrix algorithms for the matrix sign functions. These algorithms Functions Based on Quadrature offer improved performance over Higham’s adaptation of the Schur-Parlett method for this problem. The improved Arnoldi’s method is a popular tool for approximating performance is a result of reduced communication (fewer f(A)b, the action of a function f of a large sparse matrix A cache misses or less inter-processor communication). One ontoavectorb. The practical applicability of this method variant uses existing efficient building blocks but requires is limited by the storage requirements of the Arnoldi ba- the reordering of the Schur form, while the others has more sis. We will discuss a new restarting technique based on overhead in the inner loop, but can utilize any ordering of quadrature which removes this limitation and is more sta- the eigenvalues. ble and efficient than previously proposed restarting techniques. The new technique is applicable for a large class Sivan A. Toledo of functions f, including the so-called Stieltjes functions Tel Aviv University and the exponential function, both of which have applica- [email protected] tions in complex network analysis. Our method is applicable for functions of Hermitian and non-Hermitian matrices, requires no a-priori spectral information, and runs with es- MS47 sentially constant computational work per restart cycle. Gradient Discretization of Hybrid Dimensional Two-Phase Darcy Flows in Fractured Porous Me- Stefan Guettel dia The University of Manchester [email protected] We present a gradient discretization, including a large family of schemes, in a case of a two-phase Darcy flow in dis- Andreas J. Frommer crete fracture networks (DFN) . We consider the asymp- Bergische Universitaet Wuppertal totic model for which the fractures are represented as inter- Fachbereich Mathematik und Naturwissenschaften faces of codimension one immersed in the matrix domain [email protected] with continuous pressures at the matrix fracture interface. The convergence is proved under the assumption that the Marcel Schweitzer relative permeabilities are bounded from zero but cover Bergische Universität Wuppertal the discontinuous capillary pressures. The numerical tests AN14 Abstracts 67

are performed on the 3D fracture networks using Hybrid dia Flow Finite Volume and the novel Vertex Approximate Gradi- ent (VAG) discretizations. Compared with Control Vol- We consider the dynamics of multiphase flow in heteroge- ume Finite Element (CVFE) approaches, the VAG scheme neous porous media with randomly located interfaces. In has the advantage to avoid the mixing of the fracture and the deterministic case the modeling of such systems re- matrix rocktypes, while keeping the low cost of a nodal dis- quires the usage of nonlinear discontinuous flow functions. cretization on unstructured meshes. The efficiency of VAG Based on the capillarity-free fractional flow formulation for scheme is shown in the case of a high permeability contrast two-phase flow, a hybrid stochastic Galerkin finite volume between fracture network and matrix. method (HSG-FV) is presented. The method accounts for the spatially random change of the mobilities and is par- Konstantin Brenner ticularly well-suited for parallel computations. University of Nice Sophia Antipolis Laboratoire de Mathematiques J.A. Dieudonné Markus Köppel [email protected] University of Stuttgart Institute for Applied Analysis and Numerical Simulation Cindy Guichard [email protected] LJLL, University Paris 6 [email protected] MS47 A Fracture Indicator to Identify Fractures in Mayya Groza Porous Media LJAD, University Nice Sophia Antipolis COFFEE team, Inria We study the identification of fractures in porous media. [email protected] The problem is formulated as a least squares minimization of a function evaluating the misfit between a mea- Gilles Lebeau sured pressure and a pressure calculated using a particular LJAD, University Nice Sophia Antipolis reduced discrete model for flow in porous media with frac- [email protected] tures. Inspired by the idea of refinement indicators, we develop fracture indicators to search for fractures as well Roland Masson as their hydraulic conductivities through an iterative pro- University of Nice Sophia Antipolis cess. [email protected] Vincent Martin UTC MS47 [email protected] A Double-Layer Reduced Model for Flow in Fault Zones Using Hybrid Finite Volume Schemes MS48 We consider single-phase flows for subsurface porous media Learning Hierarchical Invariant Spatio-Temporal with faults, the latter along which the surrounding domain Features for Human Action and Activity Recog- on one side of the fault has slipped with respect to that on nition the other. The fault width being smaller by several orders We propose a neural-network based learning scheme which of magnitude than other characteristic sizes, we propose computes a manifold in a bag of spatio-temporal features a hybrid finite volume method based on a double-layer, through regression based modeling. The action class mod- reduced model. We allow non-matching grids along the els are designed to be independent of time without the faults. Numerical and theoretical results are shown. need for sequence length normalization and initialization of Isabelle Faille states. Using the bag of spatio-temporal features as a time IFP Energies Nouvelles series data, a time-independent orthogonal basis is com- France puted where a low-dimensional manifold is learned. Ex- [email protected] perimental results prove its efficiency on public data sets. Binu Nair, Vijay Asari Alessio Fumagalli, Alessio Fumagalli University of Dayton Institut Franais du Pétrole Energies´ nouvelles [email protected], [email protected] [email protected], [email protected] MS48 Jerome Jaffre An Inverse Kinematic Approach Using Groebner INRIA-Roquencourt Basis Theory Applied to Gait Analysis of the Lower 78153 Le Chesnay cedex France Extremity Joint Angles Jerome.Jaff[email protected] This research highlights the results obtained from an experimental study of the lower limbs of a human gait cycle to Jean E. Roberts extract and identify gait signatures. This biometric analy- INRIA Paris-Rocquencourt sis was carried out by capturing the gait cycles in a normal France and load bearing gait, using modalities such as passive in- [email protected] frared and passive optical. The challenge of this study is to distinguish between normal and abnormal gait signatures due to a concealed load on the lower body. MS47 Controlling Uncertainty in Fractured Porous Me- Anum Barki 68 AN14 Abstracts

NASA Langley Research Center adjoint and direct differentiation gradients, and proper or- [email protected] thogonal decomposition are some of some of the topics of interest that continue to develop optimal design of devices. Kimberly Kendricks Central State University Carmen Caiseda [email protected] Inter American University Bayamón, PR [email protected] Ronald Tuttle, David Bunker, Borel Christoph Air Force Institute of Technology ronald.tuttle@afit.edu, david.bunker@afit.edu, MS49 chris.borel@afit.edu A Characterization of the Reflected Quasipotential

MS48 Our purpose here is to characterize the reflected quasipotential in terms of a first-order Hamilton-Jacobi equa- Game-Theoretic and Reliability Methods in Coun- tion. Because it is continuous but not differentiable in terterrorism and Security general the characterization will be in terms of viscos- The routine application of reliability analysis is not ade- ity solutions. Using conventional dynamic programming quate in the security domain. Protecting against inten- ideas, along with a complementarity problem formulation tional attacks is fundamentally different from protecting of the effect of the Skorokhod map on absolutely continu- against accidents or acts of nature. In particular, an in- ous paths, we will derive necessary conditions in the form telligent and adaptable adversary may adopt a different of viscosity-sense boundary conditions. offensive strategy to circumvent or disable protective security measures. Game theory provides a way of taking this Kasie Farlow into account. Thus, security and counter-terrorism require United States Military Academy a combination of reliability analysis and game theory. [email protected]

Vicki Bier University of Wisconsin- Madison MS49 [email protected] Analysis of Finite Difference Schemes for Diffusion in Spheres with Variable Diffusivity MS48 Biomechanical Analysis of Pack Load Influence on Three finite difference schemes are compared for discretiz- Gait Signatures Derived from Grobner Basis The- ing the spatial derivatives of the diffusion equation in ory spherical coordinates for the general case of variable diffusivity, D. Five diffusivity cases are considered: 1) con- This project examines kinematic gait patterns as predic- stant D, 2) time-dependent D, 3) spatially-dependent D, tors of the influence associated with individuals carrying 4) concentration-dependent D, and 5) implicitly time- concealed weighted packs up to 20% of their body weight. dependent and spatially-dependent D. The results point to An initial inverse dynamics approach combined with com- one of the schemes as the preferred finite difference method putational algebra provided lower limb joint angles during for numerically solving the diffusion equation in spheres the stance phase of gait as measured from 12 human sub- with variable diffusivity. jects during normal walking. This talk describes the additional biomechanical analysis of the joint angle data to Ashlee Ford Versypt produce kinetic and kinematic parameters further charac- Massachusetts Institute of Technology terizing human motion [email protected] Sean Kohles Oregon Health and Science University MS49 [email protected] Analysis of Si Models with Multiple Interacting Anum Barki Populations Using Subpopulations with Forcing NASA Langley Research Center Terms [email protected] As a system of differential equations describing an epidemi- Kimberly Kendricks ological system becomes large with multiple connections Central State University between subpopulations, the expressions for reproductive [email protected] numbers and endemic equilibria become algebraically complicated, which makes drawing conclusions based on biological parameters difficult. We present a new method MS49 which deconstructs the larger system into smaller subsys- Numerical Optimization Method for Simulation tems, captures the bridges between the smaller systems as Based Optimal Design Problems external forces, and bounds the reproductive numbers of the full system in terms of reproductive numbers of the The numerical optimization of simulation based problem smaller systems, which are algebraically tractable. This is an interdisciplinary area of study that includes the op- method also allows us to analyze the size of the endemic timization with PDE constraints area in applied mathe- equilibria. matics. The Finite Element Method to find the numerical solution of a PDE subject to third-type boundary condi- Evelyn Thomas tions as the ones that model electromagnetic phenomena, Bennett College AN14 Abstracts 69

[email protected] called ‘secant method’ could be generalized to systems of N nonlinear equations with N unknowns, just for showing the students that there is something behind the hori- MS50 zon. Before starting to read everything on the subject, Krylov Subspace Methods for Solving Singular Lin- the author always tries to think about it unbiased, and ear Systems or Least-Squares Problems so he started with, probably, re-inventing the wheel. Had he seen the book by Ortega and Rheinboldt at that time, GMRES (Saad and Schultz 1986) is a famed generalized CGS, BiCGSTAB and IDR(s) probably wouldn’t exist to- minimal-residual method for solving nonsingular unsym- day. Actually a new wheel was discovered, that appeared metric or non-Hermitian linear systems. It may suffer to be useful in the machinery of solving large sparse non- non-benign breakdown on nearly singular systems (Brown symmetric linear systems. The first application of the new and Walker 1997). When working, the solver returns only wheel was called IDR − Induced Dimension Reduction. a least-squares solution for a singular problem (Reichel Afterwards, CGS − Conjugate Gradients Squared − was and Ye 2005). We present GMRES-QLP and GMRES- developed as an ‘improvement’ of IDR, and also for other URV, both successful revamps of GMRES, for returning reasons. After CGS, in cooperation with Henk van der the unique pseudoinverse solutions of (nearly) singular lin- Vorst, (Bi-)CGStab was constructed, followed by a lot of ear systems or linear least-squares problems. On non- other methods of this kind, developed by others. This went singular problems, they are numerically more stable than on until about 10 years ago. In this short presentation a GMRES. In any case, users do not need to know a pri- reconstruction will be given of the strange history of these ori whether the systems are singular, ill-conditioned, or so-called ‘Lanczos-type Product Methods’. It will be ex- incompatible; the solvers constructively reveal such prop- plained why this ‘sleeping theory’ woke up just after the erties. The solvers leverage the QLP and URV decom- author’s retirement in 2006, resulting in a brand new family positions (Stewart 1998 and 1999) to reveal the rank of of methods: IDR(s). History is a continuing story, there- the Hessenberg matrix from the Arnoldi process, incurring fore some recently established features of IDR(s) will be only minor additional computational cost in comparison to mentioned. GMRES. We present extensive numerical experiments to demonstrate the scalability and robustness of the solver, Peter Sonneveld with or without preconditioners or restart. Delft Inst. of Appl. Mathematics Delft University of Technology Sou-Cheng T. Choi [email protected] University of Chicago and Argonne National Laboratory [email protected] MS50 MS50 Multiple Preconditioners for GMRES Probabilistic Bounds for Randomized Precondi- tioner for a Krylov Least Squares Solver We propose a variant of GMRES which we call MPGM- RES, whereby multiple (two or more) preconditioners are The Blendenpik algorithm by Avron, Maymounkov and applied simultaneously, while maintaining minimal resid- Toledo solves least squares problems min ||Ax−b|| for m×n ual optimality properties. To accomplish this, a block ver- matrices A with rank(A)=n, by computing a random- sion of Flexible GMRES is used, but instead of considering ized preconditioner and applying the Krylov method LSQR blocks starting with multiple right hand sides, we start to the preconditioned matrix. The preconditioner is com- with the initial residual and grow the space by applying puted by randomly sampling rows from A.Wepresent each of the preconditioners to all current search directions probabilistic bounds for the condition number of the pre- and minimizing the residual norm over the resulting larger conditioned matrix, when rows are sampled with replace- subspace. To alleviate the difficulty of rapidly increas- ment, and the sampling probabilities are uniform or based ing storage requirements and make the method practical, on leverage scores. Our bounds are derived from singular we further propose a selective algorithm that uses limited value bounds for a Monte Carlo matrix multiplication al- memory, and show theoretically and experimentally that gorithm for computing the cross product AA. For uniform this approach is highly effective. Convergence bounds for a sampling, the bounds imply that the number of sampled special case are presented. Numerical results for problems rowscanbeasmuchas30percentlowerthanexisting in domain decomposition, PDE-constrained optimization, bounds. For leverage-score based sampling, our bounds and fluid flow problems are presented, illustrating the vi- imply that the number of sampled rows must at least be a ability and the potential of the proposed method. This is multiple of n ∗ ln(n). This is joint work with John Holod- joint work with Chen Greif and Tyrone Rees. nak. Daniel B. Szyld Ilse Ipsen Temple University North Carolina State University Department of Mathematics Department of Mathematics [email protected] [email protected]

MS51 MS50 IDR-CGS-BiCGSTAB-IDR(s)-aCaseofTitle Not Available at Time of Publication Serendipity Abstract not available at time of publication. In about 1976, the author was preparing a renovation of an elementary course on numerical analysis in Delft Uni- Robert P. Gilbert versity. In relation to the problem of solving a single non- Department of Mathematical Sciences linear equation iteratively, he wondered whether the so- University of Delaware 70 AN14 Abstracts

[email protected] [email protected]

MS51 MS52 Analysis of the Volume-Constrained Peridynamic Computer-Assisted Existence and Multiplicity Navier Equation of Linear Elasticity Proofs for Semilinear Elliptic Boundary Value Problems Well-posedness results for the state-based peridynamic nonlocal continuum model of solid mechanics are estab- Abstract not available at time of publication. lished with the help of a nonlocal vector calculus. The Michael Plum peridynamic strain energy density for an elastic constitu- Karlsruhe University (KIT) tively linear anisotropic heterogeneous solid is expressed in Germany terms of the field operators of that calculus, after which [email protected] a variational principle for the equilibrium state is defined. The peridynamic Navier equilibrium equation is then derived as the first-order necessary conditions and are shown MS52 to reduce, for the case of homogeneous materials, to the classical Navier equation as the extent of nonlocal inter- Rigorous Computation of Connecting Orbits actions vanishes. Using standard results, well-posedness is Abstract not available at time of publication. also established for the time-dependent peridynamic equation of motion. Jan Bouwe Van Den Berg VU University Amsterdam Richard B. Lehoucq Department of Mathematics Sandia National Laboratories [email protected] [email protected]

MS52 MS51 Rigourous Computation of a Bifurcation Diagram Is Dynamic Fracture at the Macroscale a Distin- for the Ohta-Kawasaki Model guished Limit of Unstable Nonlocal Bond Models? The Ohta-Kawasaki, or non-local Cahn-Hilliard, model is a We investigate a new class of models for solving problems simple description of energy-driven pattern formation with of free crack propagation described by the peridynamic for- competing short- and long-range effects. One of the funda- mulation. In the peridynamic formulation material points mental problems in this area is to identify which patterns interact through short-range forces acting over a prescribed have lowest energy in which regions of parameter space. horizon. The formulation allows for discontinuous defor- We address this problem by finding the curves along which mations and free propagation of cracks. We upscale the different solutions have the same energy. We use methods peridynamic model, passing to a small horizon limit, to from rigourous computing to prove the existence of such find that the macroscopic evolution corresponds to the si- curves and to get bounds between our discrete numerical multaneous evolution of the fracture surface and the linear approximations and the true infinite-dimensional solutions. elastic displacement away from the crack set. This provides Results from both two and three dimensions will be pre- a new connection between the dynamics of nonlocal short- sented and discussed. This is joint work with JB van den range forces acting at the microscale to a brittle fracture Berg. evolution at the macroscale. J.F. Williams Robert P. Lipton Simon Fraser University Department of Mathematics Dept. of Mathematics Louisiana State University [email protected] [email protected] MS54 MS51 The Exponential Formula for The Wasserstein Peridynamics as a Multiscale Method Metric Many evolutionary partial differential equations may be Abstract not available at time of publication. rewritten as the gradient flow of an energy functional, a perspective which can provide useful estimates concerning Stewart Silling the behavior of solutions. The notion of gradient flow re- Sandia National Laboratories quires both the specification of an energy functional and [email protected] a metric with respect to which the gradient is taken. In particular, much recent work has considered gradient flow in the Wasserstein metric. Given the formal nature of the MS52 gradient in this setting, a useful technique for constructing Rigorous Computations for Nonlinear PDEs: An solutions to the gradient flow and studying their stability is Introduction to consider the ”discrete gradient flow”, a time discretization of the gradient flow problem analogous to the implicit Abstract not available at time of publication. Euler method in Euclidean space. In this talk, I will present a new proof that the discrete gradient flow converges to Jean-Philippe Lessard the continuous time gradient flow inspired by Crandall and UniversitéLaval Liggett’s result in the Banach space case. Along the way, AN14 Abstracts 71

I will discuss theorems of independent interest concerning method comes from a careful discretization of the singular transport metrics. integral. We apply rigorous numerical analysis methodology to the study of the fractional Laplacian. We derive Katy Craig a finite difference/quadrature method, and establish accu- Rutgers University racy, a proof of convergence, careful truncation of the oper- [email protected] ator outside the computational domain, and numerical validation against exact solutions. Our method is compared favorably against existing methods, which do not have a MS54 rigorous foundation. We also apply the method to solve A Finite-Volume Method for Nonlinear Nonlocal the obstacle problem. Equations with a Gradient Flow Structure Adam M. Oberman We consider a finite volume method for the general equa- McGill U. tion [email protected] d ρt = ∇· ρ∇ H (ρ)+V (x)+W ∗ ρ , x ∈ R Yanghong Huang with the density of internal energy H(ρ), the confinement Imperial College London potential V (x) and the interactional potentail W (x). A [email protected] large variety of equations arises from physical or biological modelscanbewritteninthisgeneralform,andmanyim- MS54 portant theoretical advances like optimal transportations are developed in certain special cases. The finite method Error Estimates for Approximations to Fully Non- is carefully designed to preserve the non-negativity of the linear PDE solutions, and the total energy We discuss error estimates for finite difference approxima- 1 tions to nonlinear elliptic and parabolic PDE. In particular, E(ρ)= H(ρ) dx+ V (x)ρ(x) dx+ W (x−y)ρ(x)ρ(y)dx dy Rd Rd 2 Rd Rd we highlight the relationship between error estimates and the regularity of solutions of the original equation. We is shown to be non-increasing in the semi-discrete form. present some recent progress and applications. We demostrate the effectiveness of this method with many examples, and show that it can be used to perform a nu- Olga Turanova merical study of other unknown equations of similar types. Department of Mathematics University of Chicago [email protected] Yanghong Huang Imperial College London [email protected] MS55 Active Nano-Rod Dispersions José Carrillo Department of Mathematics Within the large space of fluids that behave nonlinearly, we Imperial College London consider a niche fluid system between liquid crystals and [email protected] active micro scale swimmers: active nano scale rod dispersions. We first highlight physical and biological systems Alina Chertock that motivate our modeling, analysis, and simulations, and North Carolina State University then take liberty to explore the models for rich phenomena Department of Mathematics that are reminiscent of behavior in either liquid crystals or [email protected] bacterial suspensions. M. Gregory Forest MS54 University of North Carolina at Chapel Hill Dept of Math & Biomedical Engr. Numerical Methods for the Fractional Laplacian [email protected] The fractional Laplacian is the seminal example of a nonlocal diffusion operator. Nonlocal diffusions are increasingly Qi Wang popular, and the fractional Laplacian is the prototypical University of South Carolina model. Recent work by analysts including Caffarelli and [email protected] Silvestre, among others, has studies nonlinear equations involving this operator, starting with the obstacle prob- Ruhai Zhou lem. But it solving even the one dimensional linear Frac- Old Dominion University tional Laplacian equation on a bounded domain is a chal- [email protected] lenge which has not yet been addressed. It might appear that it should be quite simple to build schemes for the fractional Laplacian. For example the work of Valdinoci MS55 suggests that convolution kernels with the right decay will Physiological Boundary Conditions for Hemody- converge. The difficulty turns out to be accuracy: build- namics ing even a first order accurate discretization is a challenge. The operator can be defined (and, in simple situations, A common goal in computational hemodynamics is the pre- approximated) using its Fourier symbol, which is multipli- diction of local blood flow downstream from stem arteries cation by a power. However, when bounded domains are in which measurements are available. Due to computa- involved, the Fourier method is not as practical. The op- tional complexity and uncertainties about the geometry erator can also be represented as a singular integral: our and topology of the vasculature, such calculations are typ- 72 AN14 Abstracts

ically performed in a relatively small number of contigu- Shawn W. Walker ous vessels. At the downstream edge of the computational Louisiana State University domain, outflow boundary conditions have to be imposed. Department of Mathematics and CCT Choices of parameter values and type of conditions strongly [email protected] impact the results, putting in question the significance of the entire modeling endeavor. We will discuss a new type of outflow boundary conditions allowing for a reduced re- MS56 liance on calibration which is a major obstacle toward reli- Mechanics and Evolution in Bacterial Biofilms able patient specific simulations. Our approach allows the computation of the impedance of tiered structured vascu- Bacteria frequently occupy densely populated surface- lar trees. It extends previous work from periodic to generic bound communities, termed biofilms. Biofilms behave like transient flows and relies on Laplace transforms and con- viscoelastic fluids at the macroscopic level. It is largely un- volution quadratures. Joint work with Will Cousins (MIT) known how bacteria organize their behavior inside biofilms, and Daniel Tartakovsky (UCSD) and how biofilms behave in natural environments. In this talk, I will focus on how biofilms solve a classical evolution- Pierre Gremaud ary theory problem, the public goods dilemma, and how Department of Mathematics and Center for Research in fluid physics shapes the dynamics of biofilms in complex Scientific Computing, North Carolina State University environments. [email protected] Knut Drescher,HowardStone Princeton University MS55 [email protected], [email protected] Two-Fluid Flow in a Capillary Tube

A phase field model for two-phase flow in a capillary tube, MS56 developed by Cueto-Felgueroso and Juanes, results in a Hydrodynamics Affects Ordering and Organization PDE with higher-order terms. We find traveling wave so- in Bacterial Suspensions lutions of the PDE and determine a bound on parameters to obtain physically relevant solutions. We observe that the We explore the nature and causes of the spontaneous or- traveling wave height decreases monotonically with capil- dering and organization that emerges in bacterial suspen- lary number. Finite difference simulations of the injection sions under confinement. Using simulations that capture of a gas finger into water show a traveling wave advanc- oriented cell-cell and cell-fluid interactions, we show that ing ahead of a rarefaction, leaving a plateau region of fluid hydrodynamics is crucial in reproducing and explaining the adjacent to the tube wall. The residual thickness of this phenomena observed in recent experiments using bacteria region was measured in experiments by G.I. Taylor in his B. Subtilis. We give new insights into the microscopic ar- famous 1961 paper. We find agreement between the trav- rangement of the bacteria, which are confirmed by new eling wave heights and the plateaus seen in the PDE sim- experiments. ulations, and the results also compare favorably with the residual fluid thickness observed in the experiments. This Enkeleida Lushi is joint work with Rachel Levy, Ruben Juanes, and Luis Imperial College London Cueto-Felgueroso. and Courant Institute NYU enkeleida [email protected] Michael Shearer Mathematics NC State University MS56 [email protected] Active Suspensions in Confinement

Melissa Strait Active particle suspensions, of which a bath of swimming NC State University bacteria is a paradigmatic example, are characterized by [email protected] complex dynamics involving strong fluctuations and large- scale correlated motions. These motions, which result from the many-body interactions between particles, are biologi- MS55 cally relevant as they impact mean particle transport, mix- A Saddle-Point Formulation And Finite Element ing and diffusion, with possible consequences for nutrient Method For The Stefan Problem With Surface Ten- uptake and the spreading of bacterial infections. In this sion work, we use a combination of kinetic theory and numerical simulations to analyze these effects, with particular A dual formulation is proposed for the Stefan problem with focus on confined suspensions. I will specifically discuss surface tension (Gibbs-Thomson law). The method uses a the transport and effective rheology of dilute to semi-dilute mixed form of the heat equation in the solid and liquid suspensions in pressure-driven channel flows, as well as the domains, and imposes the interface motion law (on the pattern formation and complex dynamics arising in active solid-liquid interface) as a constraint. Well-posedness of suspensions confined in a Hele-Shaw geometry. the time semi-discrete and fully discrete (finite element) formulations is proved in 3-D, as well as an a priori bound, David Saintillan conservation law, and error estimates. Simulations are pre- Department of Mechanical Science and Engineering sented in 2-D. University of Illinois at Urbana-Champaign [email protected] Christopher B. Davis Louisiana State Univesity Barath Ezhilan Department of Mathematics University of Illinois at Urbana-Champaign [email protected] Department of Mechanical Science and Engineering AN14 Abstracts 73

[email protected] individual behavioral decisions in such interactions. Here, we study a rather unique instance of kleptoparasitic interactions, whereby seagulls attempt to ’rob’ flocks of aquatic MS56 seaducks of their food obtained from underwater dives. By Effects of Micro-swimmer Locomotion in Peri- reconstructing individual trajectories of both kleptopara- staltic Pumping site and prey, we analyze the evasion behavior of the seaducks. Peristaltic pumping is a form of fluid transport along the length of a tube containing liquid when the tube undergoes Ryan Lukeman a contraction wave. While much is known about the peri- Department of Mathematics, Statistics and Computer stalsis of Newtonian liquids, complex ones have received Science limited attention. If the fluid inside such a peristaltic St. Francis Xavier University micro-pump contains motile micro-particles (such as bac- [email protected] teria), then the net transport and mixing are affected by the micro-swimmer collective motion. We present a new numerical method that couples the motion of many micro- MS57 swimmers, the pump and the fluid flow. We show that the Collective Dynamics in Laboratory Insect Swarms type of swimmer affects not only the net transport but can be utilised for mixing passive material. Aggregations of social animals, think bird flocks or swarms Adam Stinchcombe of insects, are beautiful, natural examples of self-organized University of Michigan behavior far from equilibrium. Many models have been [email protected] proposed to describe these systems, including agent-based models that specify social forces between individuals. We discuss measurements of laboratory midge swarms in the Enkeleida Lushi context of model assessment. In particular, we focus on Imperial College London the question of the small-number limit: how large must and Courant Institute NYU the population be before collective properties emerge? enkeleida [email protected] James Puckett Charles S. Peskin School of Engineering and Applied Science Courant Institute of Mathematical Sciences Yale University New York University [email protected] [email protected]

MS57 MS57 Oscillatory Patch Formations from Social Foraging Social Aggregation in Pea Aphids: Experimental Measurement and Random Walk Modeling Dynamics of resource patches and foragers have been Biological aggregations are found across the natural world. shown to exhibit pattern formations. Simple taxis of for- An ongoing challenge in the mathematical modeling of ag- agers towards randomly moving prey cannot lead to spon- gregations is to strengthen the connection between mod- taneous formation of patchy environments. However, social els and biological data by quantifying the rules that in- interactions among foragers, specifically taxis in producer- dividuals follow. We model aggregation of the pea aphid, scrounger group, can create novel spatiotemporal oscilla- Acyrthosiphon pisum. Specifically, we conduct experiments tory patterns. I will also briefly discuss which of these be- to track the motion of aphids walking in a featureless cir- havior is more beneficial and how switching between strate- cular arena in order to deduce individual-level rules. We gies affect the resulting spatiotemporal patterns. observe that aphids follow a correlated random walk whose parameters depend strongly on distance to an aphid’s near- Nessy Tania est neighbor. We propose a random walk model and Smith College demonstrate that it reproduces the salient features of the Mathematics and Statistics Department observed macroscopic patterns of movement. [email protected]

Chad M. Topaz Macalester College MS58 [email protected] Elastic Swimmer in Viscous Fluid: How to Swim Efficiently? Andrew J. Bernoff Harvey Mudd College We use fully-coupled computer simulations to examine the Department of Mathematics low Re hydrodynamics of a self-propelling elastic swimmer. [email protected] The swimmer is modelled as a thin elastic plate plunging at the root. The swimmer is free to move in the forward direction. We probe how swimming speed and efficiency MS57 depend on swimmer parameters. Our simulations reveal Trajectory Dynamics of Aquatic Kleptoparasitic that the efficiency is maximized when the swimmer center Interactions of mass displacement is minimized. This regime reduces viscous losses, thereby enhancing the swimming efficiency. Predation is among the most common pressures leading to group formation in animals. Although predator-prey Alexander Alexeev, Peter Derek Yeh systems have been studied extensively at the population George W. Woodruff School of Mechanical Engineering level, relatively little work has been done to specify the Georgia Institute of Technology 74 AN14 Abstracts

[email protected], [email protected] hovska (Brown University). Y.-N. Young is partially supported by NSF grants DMS 1222550.

MS58 Yuan-Nan Young Mathematical Models for Microstructured Optical Department of Mathematical Sciences Fibre (MOF) Fabrication NJIT [email protected] We address various challenges arising in the fabrication of so-called microstructured optical fibres (MOFs) which Petia Vlahovska guide light by virtue of a specially designed geometrical Brown University arrangement of channels running along their length. The petia [email protected] fabrication involves placing a material (such as glass), heating it in a draw tower, and pulling it into a fibre so that the material is essentially a highly viscous (Stokes) fluid under MS59 an axial strain. The simultaneous effects of surface ten- Role of Network Topology in the Electromechanical sion on the fibre/channel boundaries and the axial strain Dynamics of Cascading Power Grid Failure lead to deformations in the global fibre geometry that must be understood in order to arrive at the desired fibre state. Recent work in analysis of cascading failure of electric This talk will describe recent progress in the mathemati- power networks has sought to augment the quasi-steady cal modelling of this process [joint with P. Buchak and Y. state representations of prior literature with faster time Stokes]. scale electromechanical dynamics, and with threshold- driven relay action that disconnects network links upon Darren G. Crowdy overload. In these dynamic models, cascading failure ap- Imperial College London pears as a sequence of transitions between locally stable [email protected] equilibria, each corresponding to a partially degraded network structure, and with the most vulnerable paths of transition passing through saddle point unstable equilib- MS58 ria. This work will explore the role of network topology Accelerated Boundary Integral Simulations for In- in predicting the location of these saddle exits in the state teractions of Drops and Solids in Micro-Fluidics space, and the interplay of topology and relay threshold values in determining the disturbance energy that must be In micro-fluidic applications where the scales are small and injected into the system to drive the state over such a sad- viscous effects dominant, the Stokes equations are often ap- dle point. plicable. Simulation methods can be developed based on boundary integral equations, which leads to discretizations Christopher DeMarco of the boundaries of the domain only, reducing the number University fo Wisconsin of unknowns. Two main challenges associated with bound- [email protected] ary integral methods are to construct accurate quadrature methods for singular and nearly singular integrands, as well Honghao Zheng as to accelerate the solution of the dense linear systems University of Wisconsin-Madison that arise. For drops and solids in 2D, including also ob- [email protected] jects with sharp corners, we will discuss how to apply a general special quadrature approach to achieve highly accurate simulations also for very complicated settings. The MS59 simulations are accelerated with either the Fast Multipole Centrality of Dynamical Graph Structures method or a spectrally accurate FFT based Ewald method (for periodic problems). Simulation results for very chal- We consider adapting well known graph centrality mea- lenging problems are presented. sures to the case of dynamic graphs or static graphs with dynamic forcing functions. For instance, we present the Anna-Karin Tornberg PageRank method on a static graph with time-varying tele- KTH portation and demonstrate a closed form analytical solu- [email protected] tion that involves complex valued teleportation parameter. We consider how these could be deployed for studying power systems and contingency analysis. MS58 Self-Propulsion of An Inextensible Elastic Mem- David F. Gleich brane in An Electric Field Purdue University [email protected] In this work we illustrate a novel mechanism for self- propulsion of an inextensible elastic (lipid-bilayer) membrane subject to an electric field. In the lubrication frame- MS59 work, the dynamics of an inextensible elastic membrane Stochastic Graph Modeling of Power Grids is governed by a sixth order nonlinear partial differential equation with an integral constraint. Through numerical Graph-theoretic approaches have long been used for char- simulations we find (1) sloshing motion of the membrane, acterizing the topological structure of power grids. The and (2) unit directional movement of the membrane, both central idea of such approaches is to use known algorithms in the direction transverse to the imposed electric field. We for generating random graphs and then using graph-based will also demonstrate how such movements of an elastic metrics to match the characteristics with those from real- membrane can be further controlled by pattern electrodes world power grid models, such as the Western and East- and/or varying the temporal dependence of the external ern Interconnects. In our work, we are exploring several electric field. This work is a collaboration with Petia Vla- variants of the random geometric graph algorithm for the AN14 Abstracts 75

purposes of generating synthetic models of the power grid. fl[email protected] By exploiting the inherent hierarchical structure in voltage levels, we show that random geometric graph models can be used to generating synthetic power grids. MS60 RBF-FD for Elastic Wave Propagation in Layered Mahantesh Halappanavar Media Pacific Northwest National Laboratory [email protected] Seismic exploration is used to map out hydrocarbon de- posits. In forward modeling, substructures are assumed to Eduardo Cotilla-Sanchez be known, and the task is to simulate elastic wave propaga- Oregon State University tion through the medium. Inversion programs then update [email protected] substructure assumptions to reconcile the model response with actual measurements. We have found that RBF-FD spatial discretization offers outstanding accuracy and al- Emilie Hogan gebraic simplicity for modeling elastic wave propagation, Pacific Nortwest National Lab especially in layered media with large numbers of irregu- [email protected] larly curved interfaces.

Paul Hines Bengt Fornberg University of Vermont University of Colorado [email protected] Boulder [email protected]

MS59 MS60 Algorithms for Monitoring Oscillations in the Power Grid Application of the RBF-FD Method to Laminar Flame Propagation Problems Monitoring the oscillations in the power grid in real-time Premixed flame propagation is an important topic in com- is an increasingly difficult challenge due to the large num- bustion research with many applications in energy and ber of components. Additionally, large numbers of Phasor safety. In this paper we apply the RBF Finite differ- Measurement Units (PMUs) are being deployed to gener- ence (RBF-FD) method to solve the equations describing ate large-scale data on the state of the grid. Algorithms for laminar fame propagation in two-dimensional and three- computing a few singular values and vectors and updating dimensional ducts. We use stencils with a relatively large these are critical components to monitor the oscillations. number of nodes in order to achieve high order accuracy. We describe efficient algorithms to compute and update Finally, we apply this methodology to solve a simplified the singular value decompositions in this context. mathematical model describing flame propagation in a rotary engine microcombustor. Alex Pothen Purdue University Manuel Kindelan Department of Computer Science Universidad Carlos III de Madrid [email protected] [email protected]

Mani Venkatasubramanian, Tianying Wu Washington State University MS60 [email protected], [email protected] Modeling Ocean Dynamics Using RBF-FD

Ananth Kalyanaraman RBFs have started to emerge as a powerful tool, not only Associate Professor for interpolation, but also for discretizing differential oper- School of EECS, Washington State University ators. Over the last few years, new approaches have been [email protected] developed to bypass the method’s well-known problems of stability and of large computational complexity. Such a new approach resulted in the RBF-FD method which en- MS60 joys high accuracy, has an intrinsic ability to represent complicated geometries in any dimension, still has a re- RBF-FD for Mesoscale Nonhydrostatic Atmo- markable algorithmic simplicity, and leads to a sparse dif- spheric Modeling ferentiation matrix. We will use this technique to solve the Navier-Stokes equations and discuss its potential as a In applications of radial basis functions (RBFs) for fluid high-order method for the modeling of oceanic phenomena. modeling, infinitely smooth RBFs have traditionally been used due to the spectral convergence properties. However, fluid flows in nature can exhibit complex features such that Cecile M. Piret spectral accuracy cannot be realized on resolutions that Université catholique de Louvain are observable or practical. A novel approach for model- [email protected] ing with RBF-generated finite differences (RBF-FD) is presented by using polyharmonic spline RBFs together with high-order polynomials. The approach is tested on nonhy- MS61 drostatic atmospheric flows. Electromagnetic Wave Propagation in Random Waveguides Natasha Flyer National Center for Atmospheric Research I will describe an analysis of electromagnetic wave propaga- Institute for Mathematics Applied to Geosciences tion in waveguides filled with heterogeneous media, mod- 76 AN14 Abstracts

eled by a random electric permeability. The waves are Fractured, Poroelastic Materials trapped by perfectly conducting boundaries and the goal of the analysis is to quantify the long range net scattering ef- We introduce a coupled system of PDEs for the modeling fects of the random medium. The result is a detailed char- of the fluid-fluid and fluid-solid interaction in a fractured, acterization of the transport of energy, the loss of coher- poroelastic material. The fluid flow in the fracture is mod- ence and the depolarization of the waves due to scattering. eled by a lower-dimensional equation, which interacts with I will give some numerical illustrations and will compare the surrounding rock matrix and the fluid it contains. To the theory with that of scalar (acoustic) wave propagation determine the mechanical and hydrological equilibrium of in random waveguides. the system numerically, we combine an XFEM discretization for the rock matrix deformation and pore pressure with Liliana Borcea a lower-dimensional grid for the fracture. The resulting University of Michigan coupled discrete problem is solved using a substructuring [email protected] method.

Katja Hanowski MS61 IGPM Homogenization of Interfaces Moving with Spatio- RWTH Aachen University temporal Periodic Velocity [email protected]

Abstract not available at time of publication. Oliver Sander IGPM RWTH Aachen University Wenjia Jing, Panagiotis Souganidis, Hung V. Tran [email protected] University of Chicago [email protected], sougani- [email protected], [email protected] MS62 Fracture Propagation in Porous Media Using Iso- MS61 geometric Analysis Imaging Multiply Scattering Point Targets Using Abstract not available at time of publication. Sparsity Promoting Optimization Trond Kvamsdal We study active array imaging of small but strong scat- Department of Applied Mathematics terers in homogeneous media when multiple scattering be- SINTEF ICT, Trondheim, Norway tween them is important. We discuss a non-iterative ap- [email protected] proach that solves the imaging problem in two steps using sparsity promoting optimization. We analize the uniqueness and stability of this imaging method using both single MS62 and multiple illuminations. To improve its robustness and Coupling Fluid Flow with Stresses Induced by the resolution of the images we also discuss the use of opti- Fracture Deformation in Discrete Fracture Net- mal illuminations. This is join work with Anwei Chai and works George Papanicolaou.

Miguel Moscoso Fluid flow in fractures can cause deformation, but in- Universidad Carlos III de Madrid duced stresses can be challenging to implement in nu- [email protected] merical models, especially in large DFNs. I will describe CFRAC, a simulator I developed that implicitly couples fluid flow, fracture deformation, transmissivity evolution, MS61 friction evolution, and fracture propagation, and is efficient enough to simulate (2D) networks with thousands of frac- Correlation Based Imaging and Applications tures. I will describe model behaviors that emerge from Abstract not available at time of publication. interactions between processes and which give insight into complex physical systems. George C. Papanicolaou Stanford University Mark McClure Department of Mathematics The University of Texas at Austin [email protected] Petroleum & Geosystems Engineering [email protected]

MS62 Numerical Assessment of the Risk of Rock Damage MS63 in the Vicinity of Salt Caverns for the Storage of Learning the Association of Multiple Inputs in Re- Gaseous Matter at Cyclic Operation Conditions current Networks

Abstract not available at time of publication. In spite of the many discoveries made in neuroscience, the mechanism by which memories are formed is still un- Norbert B¨ottcher clear. To better understand how some disorders of the Helmholtz-Centre for Environmental Research - UFZ brain arise, it is necessary to improve our knowledge of [email protected] memory formation in the brain. With the aid of a biological experiment, an artiﬁcial neural network is developed to provide insight into how information is stored and re- MS62 called. In particular, the bi- conditional association of dis- Numerical Simulation of Deformation and Flow in tinct spatial and non-spatial information is examined using AN14 Abstracts 77

computational model. This model is based on a combina- of this invasive ant species are discussed. tion of feedforward and recurrent neural networks and a biologically-inspired spike time dependent plasticity learn- Luis Melara ing rule. The ability of the computational model to store Shippensburg University and recall the bi-conditional object-space association task [email protected] through reward-modulated plastic synapses is numerically investigated. Victor Vidal SUNY Stony Brook Jeannine Abiva,RodicaCurtu na University of Iowa Department of Mathematics Valerie Cheathon [email protected], [email protected] ASU West na MS63 Agustin Flores Mechanistic Models of Retinitis Pigmentosa Noertheastern Illinois University na In this talk we will give a brief overview of our work as it pertains to Retinitis Pigmentosa (RP). With mathematics Octavius Talbot and computer (in silico) experiments, we explore the exper- Morehouse College imentally observed photoreceptor death and rescue in the na progression of RP. Using mechanistic mathematical models of photoreceptor interactions in the presence of RP we (1) trace the evolution of RP from one stage to another Adrian Smith in each main subtype, (2) capture the rod and cone wave University of Arizona deaths, and (3) explore various treatment regiments via [email protected] RdCVF. Our work highlights the delicate balance between the availability of nutrients and the rates of shedding and Marta Sarzynska renewal of photoreceptors needed for a normal functioning University of Oxford retina and to halt the progression of RP. This work pro- [email protected] vides a framework for future physiological investigations potentially leading to long-term targeted multi-faceted in- Dustin Padilla terventions and therapies dependent on the particular stage ASU Tempe and subtype of RP under consideration. na

Erika T. Camacho Arizona State University MS63 Division of Mathematics and Natural Sciences [email protected] Qualitative Inverse Problems Using Bifurcation Analysis in the Recurrent Neural Network Model

Stephen Wirkus We develop a framework for determining when there is Arizona State University bistability and multistability in the expression states of School of Mathematical and Natural Sciences systems described by the recurrent neural network (RNN) [email protected] model. Our results show that, although bistability can be generated with autoregulation, it is also the case that both autorepression or no autoregulation can yield bistability as MS63 long as a sigmoidal behavior is present. Additionally, our Dynamics and Control of An Invasive Species: The results suggest that allowing only a single connection when Case of the Rasberry Crazy Ant Colonies inferring a network may be a reason why parameter values in the inferred gene networks in the literature are not be This project is motivated by the costs related with the doc- realistic. umented risks of the introduction of non-native invasive species of plants, animals, or pathogens associated with Stephen Wirkus travel and international trade. Such invasive species of- Arizona State University ten have no natural enemies in their new regions. The School of Mathematical and Natural Sciences spatiotemporal dynamics related to the invasion/spread of [email protected] Nylanderia fulva, commonly known as the Rasberry crazy ant, are explored via the use of models that focus on the Erika T. Camacho reproduction of ant colonies. A Cellular Automaton (CA) Arizona State University simulates the spatially explicit spread of ants on a grid. Division of Mathematics and Natural Sciences The impact of local spatial correlations on the dynamics of [email protected] invasion is investigated numerically and analytically with the aid of a Mean Field (MF) model and a Pair Approx- Pamela Marshall imation (PA) model, the latter of which accounts for ad- Arizona State University jacent cell level eects. The PA model approach considers [email protected] the limited mobility range of N. fulva, that is, the grid cell dynamics are not strongly inuenced by non-adjacent cells. ThemodeldeterminestherateofgrowthofcoloniesofN. fulva under distinct cell spatial architecture. Numerical re- MS64 sults and qualitative conclusions on the spread and control Organism - Eﬀects of Nonlinearities on Lamprey 78 AN14 Abstracts

Locomotion to discriminate potential animal immune response mechanisms that can explain the variant shedding patterns for The lamprey is a basal vertebrate and a model organism each infected animal. Our results suggest that there are for neurophysiology and locomotion studies. Here a 2D, specific variant immune response mechanisms that could integrative, multi-scale model of the lamprey’s anguilli- be silent in other animals, however, these could be active form (eel-like) swimming is driven by neural activation and in other animals, hence varying MAP shedding patterns muscle kinematics coupled to body interactions with fluid and disease progression trends. surroundings. The fluid-structure interaction problem is solved numerically using an adaptive version of the im- Gesham Magombedze mersed boundary method (IBAMR). Effects on swimming NIMBioS speed and cost by nonlinear dependencies associated with University of Tennessee, Knoxville muscle force development are examined. [email protected]

Christina Hamlet Tulane University MS64 New Orleans LA Variability in Species Abundance Distributions [email protected] from Nonlinear Stochastic Competition Models

Eric Tytell Species abundance distributions (SADs) are metrics for Tufts University ecological communities, or sets of similar species in an Department of Biology ecosystem. Using a nonlinear stochastic competition [email protected] model, I will show that SADs of communities with neutral dynamics (demographic stochasticity and immigra- tion) differ from those of communities with niches (clusters Lisa J. Fauci of similar species) arising under trait-based competition, Tulane University and quantify the likelihood of being able to use this metric Department of Mathematics to distinguish between these two community types based [email protected] on abundance data alone. Rosalyn Rael,RafaelD’Andrea,György Barabás, MS64 Annette Ostling The Breadth of Mathematical Modelling of Biolog- Department of Ecology and Evolutionary Biology ical Systems: History and Opportunities University of Michigan [email protected], [email protected], dysor- An overview of a number of established areas in mathe- [email protected], [email protected] matical biology, as well as more recent opportunities that have emerged, will be presented as an introduction to this session. In particular, the importance that nonlinearities MS65 often pose, both in terms of reflecting realistic biological Block Preconditioners for Saddle-Point Linear Sys- dynamics and the mathematical challenges that arise in an- tems alyzing the resulting models, will be emphasized. Recent illustrations of integrative research in this area in which Symmetric indefinite 2×2and3×3 block matrices are fea- the mathematical sciences guide biological studies and ex- tured prominently in the solutions of constrained optimiza- perimental work and field data inform the modeling will be tion problems and partial differential equations with con- discussed. straints. When the systems are large and sparse, modern iterative methods are often effective. For block-structured Mary Ann Horn matrices it is often desirable to design block diagonal pre- Vanderbilt University & National Science Foundation conditioners. In this talk a few block preconditioning ap- [email protected] proaches are discussed. We focus on the case of a maxi- mally rank deficient leading block, which gives rise to interesting algebraic properties that can be exploited in the MS64 design of preconditioners. The use of Schur complements CellularNonlinear Models for Predicting Immune and null space matrices is illustrated. Response Mechanisms Chen Greif Johne’s disease, a persistent and slow progressing infection Department of Computer Science in ruminants such as cows and sheep is caused by Mycobac- The University of British Columbia terium avium subspecies paratuberculosis (MAP) bacillus. [email protected] Mycobacterial infections are associated with complex immune response mechanisms whose underlying biology is not clearly understood. Host immune response to MAP infec- MS65 tion is associated with predominance of a cell mediated Krylov Subspace Methods for Large Scale Matrix response in its early stages and a switch to the dominance Equations of antibody response with concomitant disease progression. How the switch in immune response predominance occurs is Given the square large matrices A, B, D, E and the matrix not clearly known. In this study, we developed series non- C of conforming dimensions, we consider the numerical so- linear models to predict the underlying immune response lution of the linear matrix equation AXE + DXB = C mechanisms associated with MAP-bacteria shed in cattle in the unknown matrix X. These matrix equations are feces. Immune response mechanisms are identified by fit- becoming a reliable tool in the numerical treatment of ad- ting these models to immune response data and longitudi- vanced mathematical models in engineering and scientific nal fecal shedding patterns of experimentally infected cat- computing. Our aim is to provide an overview of the major tle. Using statistical model selection methods, we were able algorithmic developments in projection methods based on AN14 Abstracts 79

Krylov-type subspaces, that have taken place in the past [email protected] few years.

Valeria Simoncini MS66 Universita’ di Bologna Forward and Inverse Homogenization of Maxwell’s [email protected] Equations in Time Domain

The talk discusses a time domain problem for Maxwell’s MS65 equations for a multiscale dispersive medium. Homoge- Krylov Subspaces and Dense Eigenvalue Problems nization results in time-convolution equations with a memory kernel. We relate this kernel to the spectral measure When we think of Krylov subspace methods, we normally of the local problem and use it to derive information about think of large, sparse problems. It is not widely appreciated the microgeometry of the ﬁnely structured medium. that Krylov subspace ideas are also applicable to dense linear algebra. In this talk, which is more pedagogy than Elena Cherkaev research, we show how thinking about Krylov subspaces University of Utah leads to a powerful algorithm for solving dense eigenvalue Department of Mathematics problems. Unfortunately the algorithm is not new; it was [email protected] invented over 50 years ago by John Francis.

David S. Watkins Niklas Wellander Washington State University Swedish Defence Research Agency Department of Mathematics [email protected] [email protected] Dali Zhang University of Calgary MS65 Department of Mathematics Computing Singular Values of Large Matrices with [email protected] an Inverse Free Preconditioned Krylov Subspace Method MS66 We present an efficient algorithm for computing a few On Reconstruction of Dynamic Permeability and extreme (largest and smallest) singular values and corre- Tortuosity of Poroelastic Materials sponding singular vectors of a large sparse m × n matrix C. Our algorithm is based on reformulation of the singular Dynamic permeability refers to the permeability of poroe- value problem as an eigenvalue problem for CT C and, to lastic media subjecting to oscillatory pressure gradient. It address the clustering of singular values, we use an inverse- depends on both the frequency and the pore space geom- free preconditioned Krylov subspace method to accelerate etry. The dynamic tortuosity is inversely related to the convergence. We consider preconditioning that is based dynamic permeability and plays an important role in the on robust incomplete factorizations and we discuss various mechanism of energy dissipation of waves through poroe- implementation issues. Extensive numerical tests are pre- lastic materials. Numerically, dynamic tortuosity is the sented to demonstrate efficiency and robustness of the new kernel in the memory term in the dissipation term for time algorithm. domain wave equations; it is known to be associated with fractional derivative of order 1/2. In this talk, we will Qiao Liang present our results on reconstructing the dynamic perme- University of Kentucky ability as a function of frequency from partial data by uti- [email protected] lizing its analytical properties when extending to the complex frequency plane. Using the relation between tortuosity Qiang Ye and permeability, a set of quadratures are constructed for Dept of Math handling the memory term in the poroelastic wave equa- Univ of Kentucky tions. [email protected] Miao-Jung Y. Ou University of Delaware, USA MS66 Department of Mathematical Sciences Closure-based Algorithms for Simulation of [email protected] Mesoscale Evolution of Large ODE Systems We study a problem of designing efficient methods based MS66 on space-time averaging for simulation of mesoscale dy- Kinetic Equation for Spatial Averages of Particle namics of large particle systems. Averaging produces exact Dynamics mesoscale partial differential equations but they cannot be simulated without solving the underlying microscale sys- Abstract not available at time of publication. tem. To simulate these mesoscale equations independently, we consider several closure methods including regularized Alexander Panchenko deconvolution closure and kinetic closure. We investigate Washington State University the relationship between their accuracy and computational [email protected] cost. Lyudmyla Barannyk MS67 University of Idaho Symmetry and Bifurcations in First-order PDEs Department of Mathematics with Nonlocal Terms Modelling Animal Aggrega- 80 AN14 Abstracts

tion mathematical model of the neuronal symmetry breaking as a nonlinear dynamical system, and show how symmetry Pattern formation in self-organised biological aggregation breaks by phase plane analysis. is a phenomenon that has been studied intensively over the past twenty years. I will present a class of models of an- Yuichi Sakumura imal aggregation in the form of two first-order hyperbolic School of Information Science and Technology partial differential equations on a one-dimensional domain Aichi Prefectural University with periodic boundary conditions, describing the motion [email protected] of left and right moving individuals. The nonlinear terms appear using nonlocal social interaction terms for attrac- Naoyuki Inagaki tion, repulsion and alignment. This class of models has Graduate School of Biological Sciences been introduced in the Ph.D thesis of R. Eftimie. In this Nara Institute of Science and Technology talk, I will show that the equations are O(2) equivariant [email protected] where the group O(2) is generated by space-translations and a reflection which interchanges left-moving individuals with right-moving individuals across the middle of the in- MS68 terval. I will discuss steady-states and their symmetry with Mathematical Modelling of Wind Turbines a focus on homogeneous O(2) symmetric states and the existence of codimension two steady-state/steady-state, America is home to one of the largest and fastest growing steady-state/Hopf and Hopf/Hopf bifurcation points. I wind markets in the world. In 2012 the United States wind will discuss how using existing symmetry-breaking bifur- power installations were more than 90% higher than in cation theory and new theoretical results, one can study 2011. With the growing demand for installations, the need the neighborhood of those bifurcation points and classify for mathematical modelling has become critical. In this the patterns obtained. This is joint work with R. Eftimie talk, I will describe a simple model of a wind turbine and (U. Dundee, Scotland). some of it’s applications. Future lines of research will also be discussed. Pietro-Luciano Buono University of Ontario Institute of Technology Andre Candido Oshawa, Ontario Canada State University of New York at New Paltz, USA [email protected] [email protected]

Raluca Eftimie University of Alberta, Edmonton, Canada MS68 [email protected] Well-Balanced Positivity Preserving Central- Upwind Scheme for the Shallow Water System with Friction Terms MS67 NetworkSymmetryandBinocularRivalryExper- Shallow water models are widely used to describe and study iments free-surface water flow. The friction terms will play a significant role when the depth of the water is very small. In Hugh Wilson has proposed a class of models that treat this talk, we introduce shallow water equations with fric- higher-level decision making as a competition between pat- tion terms and a well-balanced central-upwind scheme that terns coded as levels of a set of attributes in an appropri- is capable of exactly preserving physically relevant steady ately defined network. In this talk, I will propose that states. The data in the numerical example correspond to symmetry-breaking Hopf bifurcation from fusion states in the laboratory experiments designed to mimic the rain wa- suitably modified Wilson networks can be used in an algo- ter drainage in urban areas. rithmic way to explain the surprising percepts that have Shumo Cui been observed in a number of binocular rivalry experi- Tulane University, USA ments. [email protected] Casey Diekman Department of Mathematical Sciences Alina Chertock New Jersey Institute of Technology North Carolina State University [email protected] Department of Mathematics [email protected] Martin Golubitsky Ohio State University Alexander Kurganov Mathematical Biosciences Institute Tulane University [email protected] Department of Mathematics [email protected]

MS67 Tong Wu Spontaneous Symmetry-Breaking in Neural Mor- Tulane University phology [email protected]

A developing neuron initially extends several protrusions which are similar in length, but selects a single one which MS68 elongates much longer than the others and becomes an Membrane Deformation by Protein Inclusions axon. This morphological symmetry breaking is important for the neuron to form its input (dendrite) and out- I will explore various models for the deformation of put (axon) devices. In this talk, we introduce quantitative biomembranes by protein molecules which are embedded AN14 Abstracts 81

in or attached to the membrane, termed protein inclusions. Per Lötstedt Mathematically we focus on minimisation problems involv- Uppsala University ing the Helfrich energy functional. Inclusions will be mod- [email protected] elled by enforcing pointwise constraints on the membrane displacement or curvature. I will present results detailing the existence and behaviour of minimal energy states for MS68 some of these models. A Smoothing Trust Region Filter Algorithm for Nonsmooth Nonconvex Least Squares Problems Graham Hobbs University of Warwick, UK We propose a smoothing trust region filter algorithm for [email protected] nonsmooth and nonconvex least squares problems with zero residual. We present convergence theorems of the proposed algorithm to a Clarke stationary point or a global MS68 minimizer of the objective function under certain condi- Modeling Feral Hogs in the Great Smoky Moun- tions. Preliminary numerical experiments show the effi- tains National Park ciency of the proposed algorithm for finding zeros of a system of polynomial equations with high degrees on the Feral Hogs (Sus Scrofa) are an invasive species that have sphere and solving differential variational inequalities. occupied the Great Smoky Mountains National Park since the early 1900s. Recent studies have revitalized interest Yang Zhou in the pest and have produced useful data on vegetation, The Hong Kong Polytechnic University, China mast and harvest history. Using these data, a model with [email protected] discrete time and space was formulated to represent the hog dynamics in the park. Management strategies and Xiaojun Chen estimation of actual total population was investigated. Department of Applied Mathematics The Hong Kong Polytechnic University Benjamin Levy [email protected] University of Tennesse, USA [email protected] Shouqiang Du Qingdao University, China Bill Stiver [email protected] Great Smoky Mountains National Park bill [email protected] MS69 Rene Salinas Filtered Spectral Methods for Transport Problems Appalachian State University [email protected] We analyze the behavior of filtered spectral approximations that are used in the angular discretization of radia- Joseph Corn, Marguerite Madden tive transport equations. Recently the filtering approach University of Georgia has been recast as a transport equation with modified scat- [email protected], [email protected] tering cross-section. We examine this modified equation, prove some basic convergence properties, and show some Charles Collins supporting numerical results. University of Tennessee Knoxville, Tennessee Cory Hauck [email protected] Oak Ridge National Laboratory [email protected] Suzanne M. Lenhart University of Tennessee Martin Frank, Kerstin Kuepper Department of Mathematics RWTH Aachen University [email protected] Center for Computational Engineering Science [email protected], [email protected] MS68 Stochastic Diffusion Processes in Systems Biology MS69 In cell biology many species are only present at very low Hybrid Algorithms for Hybrid Computers: copy numbers, therefore a deterministic description by par- Kinetic-Continuum Models of Transport Phenom- tial differential equations often doesnt reproduce experi- ena mental results and a stochastic model is needed. We use a continuous-time discrete-space Markov process to simulate Recent developments in high-performance computing have diffusion stochastically. To represent complex geometries led to a hybrid architecture composed of multicore CPUs accurately we discretize the cell into an unstructured mesh and GPU coprocessors (e.g. ORNL Titan machine). In and compare the jump coefficients resulting from a finite such architectures, a premium is placed on algorithms element method and a first exit time approach. that require minimal communication between CPU/GPU nodes. We introduce a set of algorithms in this spirit Lina Meinecke based upon stochastic differential equation solvers for ki- Uppsala University, Sweden netic level models of transport phenomena, coupled with [email protected] high-order finite element models of the continuum (homog- 82 AN14 Abstracts

enized) scale. ary conditions.

Michael Malahe, Sorin Mitran Harbir Antil University of North Carolina Chapel Hill George Mason University [email protected], [email protected] Fairfax, VA [email protected]

MS69 Hydraulic Modeling for Quantum Absorption Cal- MS70 culation in Plasmonics Based on High-Order Spec- Numerical Investigations of Bouncing Jets tral Element Discontinuous Galerkin Approach The Kaye effect is a fascinating phenomenon of a leaping I will discuss about recent development of spectral element shampoo stream which was first described by Alan Kaye discontinuous Galerkin (SEDG) schemes for solving local in 1963 as a property of non-Newtonian fluid. It manifest interactions between electrons and the light in plasmonic itself when a thin stream of non-Newtonian fluid is poured systems. The dispersive material properties of the sys- into a dish of fluid. As pouring proceeds, a small stream of tem are described by a hydraulic model. This approach liquid occasionally leaps upward from the heap. We inves- is formulated by coupling the macroscopic Maxwell equa- tigate numerically the impact of the experimental setting tions with the equations of motion of the electron gas. The as well as the fluid rheology on the apparition of bouncing nonlocal polarization current induced by an external elec- jets. In particular, we observe the importance of the cre- tromagnetic field is represented by a system of the first- ation of a thin lubricating layer of air between the jet and order partial differential equations with an auxiliary ordi- the rest of the liquid. The numerical method consists of a nary differential equation. I will present efficient and stable projection method coupled with a level-set formulation for SEDG algorithms with properly designed numerical fluxes, the interface representation. Adaptive finite element meth- provided with stability analysis. We validate our compu- ods are advocated to capture the different length scales tational results for nano sized metallic cylinders for the inherent to this context. absorption cross sections and field distributions. Andrea Bonito MiSun Min Texas A&M University Argonne National Laboratory Department of Mathematics Mathematics and Computer Science Division [email protected] [email protected] Jean-Luc Guermond Department of Mathematics MS69 Texas A&M, USA Semi-Lagrangian Discontinuous Galerkin Schemes [email protected] for the Relativistic Vlasov-Maxwell System Sanghyun Lee The Vlasov-Maxwell system describes the evolution of a Texas A&M University collisionless plasma, represented through a probability den- Department of Mathematics sity function (PDF) that self-interacts via the electromag- [email protected] netic force. One of the main difficulties in numerically solving this system is the severe time-step restriction that arises from parts of the PDF associated with moderate-to-large MS70 velocities. The dominant approach in the plasma physics Splitting for Variable Density Flows community is the so-called particle-in-cell method. The focus of the current work is on semi-Lagrangian methods. We show the equivalence between the so-called gauge In particular, we develop a method based on high-order Uzawa method and the pressure correction schemes in ro- discontinuous Galerkin (DG) scheme in phase space, and tational form. Using this equivalence we show simpler sta- an operator split, semi-Lagrangian method in time. The bility proofs for known schemes and devise a new stable method is designed to be (1) high-order accurate, (2) mass scheme for the approximation of incompressible flows with conservative, and (3) positivity-preserving. The resulting variable density. The main feature of the new method is scheme is applied to laser-plasma acceleration problems. that only involves constant, in time, matrices.

James A. Rossmanith Abner J. Salgado Deparment of Mathematics Department of Mathematics Iowa State University University of Maryland [email protected] [email protected]

MS70 MS70 Optimal Control of Free Boundary Problems with Modeling Viscoelastic Networks in Stokes Flow Surface Tension Effects We present a simple method for modeling heterogeneous We will give a novel proof for the second order order suffi- viscoelastic media at zero Reynolds number. The method cient conditions for an optimal control problem where the can be extended to capture viscoelastic features as well state system is composed of Laplace equation in the bulk as some other models. Linking rules for the network are and Young-Laplace on the free boundary. Next, we will dis- based on linear viscoelastic models, then varying complex- cuss a novel analysis for a Stokes free boundary problem ity allows the model to exhibit different kinds of behavior. with surface tension effect. We will conclude with some re- A few rheology tests are used to analyze the mechanical cent results for the Navier-Stokes problem with slip bound- properties of the model networks and the effects of input AN14 Abstracts 83

parameters on these properties. curacy is realized without sophisticated quadrature rules), (ii.) seamless enforcement of the quasiperiodic boundary Jacek K. Wrobel conditions (no periodization of the fundamental solution, Department of Mathematics, Tulane University e.g. via Ewald summation, is required), and (iii.) reduced Center for Computational Science regularity requirements on the interface proles (derivatives [email protected] of the deformations do not appear explicitly in the formulation). We show how these can be efficiently discretized Ricardo Cortez, Ricardo Cortez and utilized in the simulation of scattering of linear acous- Tulane University tic waves by families of periodic layered media which arise Mathematics Department in geoscience applications. [email protected], [email protected] David P. Nicholls Lisa J. Fauci University of Illinois at Chicago Tulane University [email protected] Department of Mathematics [email protected] MS71 Numerical Algorithms for Simultaneous Determi- MS71 nation of Acoustic and Optical Coefficients in Pho- Interferometric Waveform Inversion: Geophysics toacoustic Tomography Meets Spectral Graph Theory Photoacoustic tomography (PAT) aims at reconstructing In seismic and SAR imaging, fitting cross-correlations of physical properties of optically heterogeneous media from wavefields rather than the wavefields themselves can result measured acoustic signals generated by the photoacoustic in improved robustness vis-a-vis model uncertainties. This effect. Image reconstructions in PAT are usually done in approach however raises two challenges: (i) new spurious a two-step process. In the first step, one solves an inverse local minima may complicate the inversion, and (ii) one wave propagation problem to recover the initial pressure must find a good subset of cross-correlations to make the field inside the media. In the second step, one solves an in- problem well-posed. I will explain how to address these verse diffusion/transport problem to recover optical prop- two problems with lifting, semidefinite relaxation, and ex- erties, using the result of the first step as the data. This pander graphs. This mix of ideas has recently proved to two-step procedure breaks down when the acoustic wave be the right approach in other contexts as well, such as speed is also assumed unknown and to be reconstructed. angular synchronization (Singer et al.) and phase retrieval We present here some numerical algorithms that solve the (Candes et al.). Joint work with Vincent Jugnon. inverse wave and inverse diffusion problems simultaneously to image both optical and acoustic properties. Laurent Demanet Professor of Mathematics, MIT Kui Ren [email protected] University of Texas at Austin [email protected]

MS71 Inverse Born Series for the Radiative Transport MS72 Equation Hydrodynamic Interaction of Swimming Microor- ganisms in Complex Fluids We propose a direct reconstruction method for the inverse radiative transport problem that is based on inversion of The interaction of motile microorganisms, surrounding flu- the Born series. We characterize the convergence and ap- ids and boundaries is of paramount importance in a va- proximation error of the method and illustrate its use in riety of physical and environmental phenomena including numerical simulations. the development of biofilms, colonization of microbes in viscoelastic mucus of human and animal bodies, bacterial Manabu Machida aggregating in oceanic gels, and swimming of spermatozoa Department of Mathematics in female reproductive tract. In this study, we scrutinize University of Michigan the role of rheological properties of background fluids on [email protected] the interaction of microorganisms with rigid surfaces.

John Schotland Gaojin Li University of Michigan University of Notre Dame [email protected] [email protected]

Arezoo Ardekani MS71 Notre Dame University Layered Media Scattering: Fokas Integral Equa- Department of Aerospace and Mechanical Engineering tions and Boundary Perturbation Methods [email protected]

In this talk we describe a class of Integral Equations to compute Dirichlet-Neumann operators for the Helmholtz MS72 equation on periodic domains inspired by the recent work Swimming Through Heterogeneous Networks of Fokas and collaborators on novel solution formulas for boundary value problems. These Integral Equations have I will present results for swimmers moving near similar-size a number of advantages over standard alternatives includ- microstructural heterogeneities. Spherical obstructions are ing: (i.) ease of implementation (high-order spectral ac- used to deduce physical principles linking the swimmer ﬂow 84 AN14 Abstracts

field, forces on obstructions, and changes in swimming ve- [email protected] locities. Then single rod-like obstructions are studied to deduce the effect of a network of filaments. The average and variance of the swimming speed reflect the density and MS73 orientation correlations of the microstructure, and hence Stochastic Mode-Reduction in Models with Con- swimming properties can be used as probes of microstruc- servative Fast Sub-Systems ture. We will consider application of the stochastic mode re- Henry Fu duction to multi-scale models with deterministic energy- University of Nevada, Reno conserving fast sub-system. In particular, we consider the Dept. Mechanical Engineering situation when the slow variables are driven stochastically [email protected] and interact with the fast subsystem in an energy conserving fashion. Since there is energy exchange between the fast conservative sub-system and the slow variables, it is MS72 necessary to explicitly keep track of the energy of the fast Mechanism of Microorganism Propulsion in Vis- sub-system. Therefore, we develop a new stochastic mode coelastic Fluids reduction process in this case by introducing energy of the fast subsystem as an additional hidden slow variable. We Abstract not available at time of publication. use several prototype models to illustrate the approach.

Alexander Morozov Ankita Jain University of Edinburgh Dept of Applied and Computational Mathematics and School of Physics & Astronomy Statistics [email protected] University of Notre Dame [email protected]

MS72 MS73 Flagellar Locomotion in Viscoelastic and Stochasticity in An Integrable System: Pulse Po- Anisotropic Environments larization Switching in An Active Optical Medium

We will discuss recent investigations of helical and Propagation of optical pulses through an active optical undulatory locomotion in viscoelastic (Oldroyd-B) and medium with two working levels, known as the Lambda- anisotropic (liquid crystal) fluids. Elastic and anisotropic configuration, is described by an initial-boundary value effects can either enhance or retard a microorganism’s problem for a set of completely integrable partial differ- swimming speed, and can even change the direction of ential equations. If the initial conditions are prepared swimming, depending on the body geometry and the fluid randomly, the resulting soliton solutions exhibit stochas- properties. Our findings connect studies showing situation- tic behavior, which can be described exactly in terms of ally dependent enhancement or retardation of swimming probability-density functions and first- and last-passage speeds, and may help to clarify phenomena observed in a time problems. The talk will present these soliton statis- number of biological systems. tics.

Saverio E. Spagnolie Gregor Kovacic University of Wisconsin Rensselaer Polytechnic Inst Department of Mathematics Dept of Mathematical Sciences [email protected] [email protected]

MS73 MS73 The Response of the Lyapunov Exponent to Exter- Dynamics of Ferromagnets nal Perturbations Driving nanomagnets by spin-polarized currents offers ex- We present a new approach to predict the response of the citing prospects in magnetoelectronics, but the response of largest Lyapunov exponent of a dynamical system to small the magnets to such currents remains poorly understood, external perturbations of different types. The connection even more so with the addition of thermal noise. For a between the external perturbation and the change in the single domain ferromagnet, I will show that an averaged largest Lyapunov exponent is approximately represented equation describing the diffusion of energy on a graph cap- through the corresponding response operator, computed tures the low-damping dynamics of these systems. I will for the original unperturbed system. The theory for the re- then present the problem of extending the analysis to spa- sponse operator of the largest Lyapunov exponent is based tially non-unifrom magnets, modeled by an infinite dimen- on the well-known Fluctuation-Dissipation theorem. We sional Hamiltonian systems, equivalently a non-linear wave also compute the response prediction for a simple model of equation with stochastic in space initial conditions. chaotic nonlinear dynamics, and compare it against the actual response of the largest Lyapunov exponent computed Katherine Newhall by directly perturbing the system, for a simple constant Courant Institute of Mathematical Science forcing perturbation. New York University [email protected] Rafail Abramov Department of Mathematics, Statistics and Computer Science MS74 University of Illinois at Chicago Data Analytics Throughout Undergraduate Math- AN14 Abstracts 85

ematics [email protected]

DATUM is an education/research program which trains freshman and sophomore students in the philosophy and MS74 tools of data analysis and modeling. The course, Intro- Computational and Data-Enabled Training in duction to Data Mathematics, introduces high-dimensional William & Mary modeling, data analytics, and their use in applications. Re- quiring only basic calculus, it prepares students for summer In this talk, I will talk about how EXTREEMS-QED is research on real-world data analytics problems. It teaches organized at W&M, how we recruit students, and how to data analytics methods along with a targeted examination run our summer research programs. I will also talk about of underlying high-dimensional mathematics including Eu- how we develop Data-related courses. clidean geometry, matrix algebra, eigenvalues, and spectral decomposition. Gexin Yu Department of Mathematics Kristin Bennett The College of William and Mary Mathematical Sciences [email protected] Rensselaer Polytechnic Institute [email protected] MS75 Bruce Piper A Stochastic-Oriented NLP Relaxation for Integer Rensselaer Polytechnic Institute Programming Dept of Mathematical Sciences [email protected] We introduce a nonlinear, nonconvex relaxation of integer constraints in certain linear programs. The relaxation is motivated by the interpretation of relaxed integer variables MS74 as probability of units to be on in energy systems applica- Research and Training in Computational and Data- tions. The relaxation depends on a complexity parameter Enabled Science and Engineering for Undergradu- that controls its strength that is derived from a quantile ates in the Mathematical Sciences at NJIT interpretation of a stochastic formulation. We analyze the dependence of the solution on this complexity parameter The NJIT EXTREEMS-QED program is designed to and provide numerical examples to support our claims. immerse undergraduates in courses and group research projects in the computational analysis of data and the John Birge modeling and simulation of complex systems in multidisci- University of Chicago plinary contexts. In this talk, we will describe the research Booth School of Business activities of our first cohort of undergraduates and the cur- [email protected] ricular enhancements in computational and data enabled science and engineering that have already been made. This Mihai Anitescu, Cosmin G. Petra project is supported by the NSF. Argonne National Laboratory Mathematics and Computer Science Division David J. Horntrop [email protected], [email protected] Dept of Mathematical Sciences, Center for Applied Math New Jersey Institute of Technology [email protected] MS75 Uncertainty Analysis of Wind Power Plant Dy- namic Model MS74 Data-Enabled Science and Computational Analy- In transient stability studies, large wind power plants sis Research, Training, and Education for Students (WPP) are usually represented by reduced model consist- (descartes) Program at UC Merced ing on one, or few, equivalent machines. However individual wind turbine generators (WTG), within a WPP, can The Data-Enabled Science and Computational Anal- produce diverse power outputs, because of terrain topog- ysis Research, Training, and Education for Students raphy and/or wake effect. Under these conditions, the ac- (DESCARTES) Program at UC Merced trains Applied curacy of the reduced WPP model has not been studied Mathematical Sciences majors in the computational tools yet. In this paper, we present an uncertainty analysis to needed to study modeling and simulation of complex sys- investigate the model accuracy of a WPP model under di- tems and analysis of large data sets. This program has verse power outputs of its individual WTGs. Wake effect three specific aims: (1) Provide exceptional undergraduate is considered as the reason for diverse power outputs. The students unique research opportunities and state-of-the-art impact of wake effect in dynamic WPP model uncertainty education and training in computational and data-enabled is investigated. The importance of diverse WTG power science; (2) Develop the Computational and Data-Enabled output is evaluated in full and reduced models of a large Science emphasis track within the Applied Mathematical 168-machine test WPP connected to the IEEE-39-bus sys- Sciences Major; and (3) Provide high school math teach- tem. The results show that diverse WTG output due to ers from the region the opportunity to learn the tools and wake effect can affect the transient stability outcome anal- methods of computational and data-enabled science. In ysis. The reduced WPP model misrepresents the dynamic this talk, we will describe current developments within the response observed with the full WPP representation. Engi- DESCARTES program and discuss new initiatives that we neers should be aware of this difference when using reduced have undertaken since the inception of the program. WPP models.

Arnold D. Kim Guang Lin, Marcelo Elizondo, Shuai Lu, Shaobu Wang University of California, Merced Paciﬁc Northwest National Laboratory 86 AN14 Abstracts

[email protected], [email protected], [email protected] [email protected], [email protected]

MS76 MS75 Dynamically and Kinematically Consistent Global Ocean State Estimation for Climate Research Global Optimization of Large Optimal Power Flow Problems The sparsity of observations for oceanographic (and cryospheric) research directed at climate requires the de- We propose a global optimization algorithm based on velopment and application of mathematical and computa- branch and bound for the Optimal Power Flow (OPF) tional tools, variously known as inverse methods, or state problem in power grids. The algorithm uses Semidefi- and parameter estimation, to infer poorly known or not nite Programming (SDP) relaxations of the OPF to pro- directly measurable quantities, and to provide useful un- vide strong lower bounds on the optimal objective function certainty estimates. Data assimilation commonly used in value. The algorithm is able to guarantee global optimality numerical weather prediction applies filtering methods that to a small tolerance for several IEEE benchmark instances are optimal for forecasting. However, to the extent that the and modified instances, orders of magnitude faster than focus is on understanding the dynamics of the ocean’s past general purpose global optimization solvers. We also ex- evolution such methods have limitations; they do not pre- tend the algorithm to the smart grid problem, which is a serve known conservation laws and evolution equations. In- multi period extension of the OPF to address integration stead, climate reconstruction is best solved using smoother of renewable energy sources and storage devices into the methods such that optimal use is made of the sparse obser- power grid. Results illustrate the effectiveness of storage vations while preserving known physical laws encapsulated in lowering costs and absorbing fluctuations due to inter- in the model used for data interpolation. Two examples mittent power sources in the grid. from global ocean state estimation and ice sheet modeling will be discussed. Lorenz T. Biegler Carnegie Mellon University Patrick Heimbach Pittsburgh, USA Massachusetts Institute of Technology [email protected] [email protected]

Bethany Nicholson Carnegie Mellon University MS76 [email protected] Computational Challenges in High-Resolution, Experimentally-Constrained Non-Newtonian Sub- duction Modeling MS75 Results from high-resolution, massively parallel, three- Exploiting Large-Scale Natural Gas Storage to Mit- dimensional numerical models of subduction zone deforma- igate Power Grid Uncertainty tion are presented. The models are observationally based, contain multiple plates, and use a non-Newtonian viscosity, We present a stochastic optimal control model to optimize making them among the highest fidelity convergent mar- gas network inventories in the face of system uncertainties. gin models to date. A scalable solver is used to solve the We demonstrate that gas network inventories can be used difficult variable viscosity stokes flow. Large viscosity gra- to mitigate volatility observed in power grid operations. dients emerge due to the strain-rate dependent viscosity, allowing for local decoupling and complex circulation semi- Victor Zavala independent from the larger scale mantle circulation. Argonne National Laboratory [email protected] Margarete A. Jadamec Brown University Department of Geological Sciences MS76 Margarete [email protected] Mathematical Models and Computational Soft- ware for Hazardous Earth-Surface Flows: from MS76 Tsunamis to Landslides Promoting the Development and Application of Mathematics, Statistics and Computational Sci- There is a large class of geophysical flows that can be cate- ence in the Geosciences gorized as hazardous, free-surface, gravity-driven inundat- ing flows. These problems include tsunami propagation I will begin by describing recent efforts of the Consortium and inundation; overland flooding; hurricane-generated for Mathematics in the Geosciences (CMG++) formed by storm surges; and a range of granular-fluid flows includ- members of the mathematical, statistical, computational ing landslides, debris flows and lahars. These problems and geoscience communities. The goal of the consortium is are often modeled with depth-averaged PDEs sharing com- to accelerate traditional interactions between these groups mon mathematical features and presenting similar compu- of scientists. Then I will discuss a computational inverse tational challenges. I will describe these models and show method developed by myself and colleagues that was mo- simulations of tsunamis, floods and landslides using these tivated by specific challenges in oceanographic data assim- methods. ilation and geophysics.

David George Jodi Mead U.S. Geological Survey Boise State University Cascades Volcano Observatory Department of Mathematics AN14 Abstracts 87

[email protected] [email protected]

MS77 MS78 Imaging of Extended Reflectors in Two- Flagellar Kinematics of Algal Cells in Viscoelastic Dimensional Waveguides Fluids The motility behavior of microorganisms can be signifi- We consider the problem of imaging extended reflectors in cantly affected by the rheology of their fluidic environment. waveguides using the response matrix of the scattered field In this talk, we experimentally investigate the effects of obtained with an active array. We employ selective imag- fluid elasticity on both the flagella kinematics and swim- ing techniques to focus onto the edges of a reflector which ming dynamics of the microscopic alga Chlamydomonas typically give raise to weaker echoes than those coming reinhardtii. We find that the flagellar beating frequency from its main body. A selective imaging functional based and wave speed are both enhanced by fluid elasticity. In- on Kirchhoff migration and the SVD of a weighted modal terestingly, the swimming speeds during the alga power projection of the response matrix is proposed and analyzed. and recovery strokes are enhanced by fluid elasticity for De 1. Despite such enhancements, however, the alga net forward speed is hindered by fluid elasticity by as much as Chrysoula Tsogka 30% compared to Newtonian fluids of similar shear viscosi- University of Crete and FORTH-IACM ties. The motility enhancements could be explained by the [email protected] mechanism of stress accumulation in the viscoelastic fluid.

Dimitrios Mitsoudis Paulo E. Arratia Institute of Applied and Computational Math Mechanical Engineering and Applied Mechanics Heraklion, Crete University of Pennsylvania, Philadelphia. [email protected] [email protected]

Symeon Papadimitropoulos Department of Applied Mathematics, University of Crete MS78 [email protected] The Dynamics of Sperm Detachment from Epithe- lium in a Coupled Fluid-Biochemical Model of Hy- peractivated Motility MS77 A mechanical advantage of the spermatozoa hyperactivated Imaging of Sparse Scatterers waveform has been hypothesized to be the promotion of detachment from oviductal epithelium. Using a Stokes Abstract not available at time of publication. fluid model that incorporates forces due to dynamic elastic bonds between the flagellar head and a surface, we find Alexei Novikov that hyperactive waveforms do result in the frequent de- Penn State University taching and binding dynamics that are observed in recent Mathematics lab experiments. [email protected] Lisa J. Fauci Tulane University MS77 Department of Mathematics Connecting the Dots: from Homogenization to Ra- [email protected] diative Transport Julie Simons Abstract not available at time of publication. Tulane University [email protected] Lenya Ryzhik Stanford University Sarah D. Olson [email protected] Worcester Polytechnic Institute [email protected] MS77 Ricardo Cortez, Ricardo Cortez Signal to Noise Ratio Analysis in Virtual Source Tulane University Array Imaging Mathematics Department [email protected], [email protected] We consider imaging a reflector located on one side of a passive array where the propagation medium is homogeneous. The reflector is illuminated by remote impulsive sources MS78 situated on the other side of the passive array where the The Phylogeny of Sperm Swimming Kinematics medium is complex and strongly scattering. We transform the passive array to an active virtual array by migrating Phylogenetic analyses have dominated the study of ecology the cross correlations of the field recorded on the passive and evolution. However, physical interactions between or- array. We will present an analysis of the signal to noise ganisms and their environment are mediated by organism ratio of the obtained image. form and function, highlighting the importance of mechanics to understanding evolutionary trajectories. We com- Chrysoula Tsogka bined high-speed video microscopy and singular value de- University of Crete and FORTH-IACM composition analysis to quantitatively compare the flagel- 88 AN14 Abstracts

lar waveforms of sperm from eight diverse species. The [email protected] emergence of dominant flagellar waveforms is suggestive of biological optimization, driven by environmental cues. MS79 Jeffrey Guasto Flight Stability of Mosquitoes using a Reduced Massachusetts Institute of Technology Model Jeff[email protected] We employ a reduced model that represents a mosquito as Lisa Burton, Filippo Menolascina a rigid body with two rigid wings to explore mosquito sta- MIT bility. Wing motions derived from analysis of high speed [email protected], fi[email protected] movies are used as inputs to a dynamical model of the mosquito body. We study uniform flight where flight tra- Richard Zimmer jectories are periodic orbits in a suitable translating refer- UCLA ence frame. We analyze the stability of body motions in [email protected] this frame by computing a linearized return map of the periodic orbit along with its eigenvalues and singular values. Long time stability corresponds to eigenvalues all smaller Anette Hosoi than one in magnitude and depends upon model param- Massachusetts Institute of Technology eters. For our mosquito geometry, we find that hovering 77 Massachusetts Avenue, Room 3-173, Cambridge MA flight is unstable but locate parameter ranges in which for- 02139 ward flight is stable. We also investigate the effect of vary- [email protected] ing the location of the joint between wings and body on stability of hovering flight. All cases are close to marginal Roman Stocker stability. MIT Civil and Environmental Engineering Sarah Iams [email protected] Northwestern University Evanston, IL [email protected] MS78

Flagellar Bundling and Unbundling in E. Coli MS79 On a Non-Linear Investigation of An Electrospin- Flagellar bundling and unbundling are important aspects ning Model under Combined Space and Time of locomotion in bacteria such as Escherichia coli. To study Evolving Instabilities the hydrodynamic behavior of helical flagella, we present a computational model that describes the motion of bacterial We study the nonlinear problem of axisymmetric electri- flagellar filament at the micrometer scale. Bundling occurs cally driven jets with applications to the electrospinning when all flagella are left-handed helices turning counter- process. We consider classical stability point of view in clockwise or when all flagella are right-handed helices turn- the early stage and then weakly nonlinear wave theory of ing clockwise. Helical flagella of the other combinations of certain dyad resonance modes that later involve the use of handedness and rotation direction do not bundle. Newton’s Method to solve a dispersion relation. Finally we present the Method of Lines (MOL) to solve a system of Sookkyung Lim PDEs that governs the combined time and space evolving University of Cincinnati amplitude instability functions. [email protected] Saulo Orizaga Department of Mathematics MS79 Iowa State University [email protected] Unifying the Equations of Life: Time Scale Calcu- lus and Evolutionary Dynamics MS79 Evolutionary dynamics is concerned with the evolution Analyzing Coherent Structure in Signals and Fluid of populations. In a general framework, each population Flows has its own geometry, method of adaptation (incentive), and time-scale (discrete, continuous, and others). Using We consider a dynamical systems based method for mea- an information-theoretic measure of distance, a widely- suring the complexity of particle trajectories in fluid flows. applicable stability result will be given for all of these sce- This complexity is measured in terms of ergodicity which narios. A wealth of examples leading up to and beyond the relates to how a trajectory samples a space and how it sam- main results is included. No prior knowledge of evolution- ples provides insight about the structure in the phenomena ary dynamics, information theory, Riemannian geometry, or region of interest. We discuss how this insight is used to or game theory is required. visualize the 2D and 3D Lagrangian coherent structures in ocean flows and how this information can in turn be used Dashiell Fryer to better understand the transport in the flow - e.g., trans- Pomona College port barriers and transport facilitators. As time permits, [email protected] other related diagnostics will also be presented.

Marc Harper Sherry Scott UCLA Marquette University AN14 Abstracts 89

[email protected] [email protected]

Richard B. Lehoucq MS80 Sandia National Laboratories Asymptotically Compatible Schemes for Robust [email protected] Discretization of Nonlocal Models

We present an abstract framework of asymptotically com- MS80 patiable (AC) schemes for robust discretizations of a family of parametrized problems. The AC schemes provide con- Modeling Anomalous Diffusion Using the Frac- vergent approximations to problems associated with fixed tional Bloch-Torrey Equation parameter values as well as their limiting values. This framework is then applied to study approximations of non- Contrast in magnetic resonance imaging (MRI) can be local models such as peridynamic models of nonlocal elas- manipulated to display the apparent diffusion coefficient ticity parametrzed by the horizon parameter and their local for water. In complex, heterogeneous materials, such as PDE limits (Navier equations) when the horizon parame- biological tissue, diffusion is anisotropic and often non- ter approaches zero. In particular, by combining with the Gaussian. Such anomalous diffusion can be succinctly de- theory of nonlocal calculus of variations, a precise char- scribed via the fractional order Bloch-Torrey equation - a acterization of AC schemes can be obtained for popular FPDE that captures both deterministic and stochastic pro- conforming finite element discretizations. cesses. Using this model, MRI can display spatial maps of tissue properties in terms of sub- and super-diffusion. Qiang Du Penn State University Richard Magin Department of Mathematics Department of Bioengineering [email protected] University of Illinois at Chicago [email protected] Xiaochuan Tian Pennsylvania State University MS80 tian [email protected] Fractional PDEs: Numerical Methods and Mathe- matical Analysis MS80 Analysis and Approximation of Finite-Range Jump We present a faithful and efficient numerical methods for Processes time-dependent space-fractional PDEs in three space dimensions, without resorting to any lossy compression, but The classical Brownian motion model for diffusion is rather by exploring the structure of the coefficient matrices. 3 not well-suited for applications with discontinuous sample The method reduces computational cost from O(N )to 2 paths. For instance, the mean square displacement of a O(N log N) per time step and memory requirement from 2 diffusing particle undergoing a jump process often grows O(N )toO(N). We also address some mathematical is- faster than that for the case of Brownian motion, or grows sues that are characteristic for fractional PDEs and report at the same rate but is of finite variation or finite activ- our recent progress in this direction. ity. Such jump processes are viable models for anomalous super-diffusion or nonstandard normal diffusion. In par- Hong Wang ticular, such jump diffusions are expedient models when University of South Carolina the process sample-path is discontinuous because nearly in- Department of Mathematics stantaneous price volatility, species migration or heat con- [email protected] duction is suggested by the length and time scales over which the data is collected. My presentation is on recent work for the associated deterministic equation on bounded MS81 domains where the jump process is of finite-range, i.e, the BANDITS: A Matlab Package of Band Krylov Sub- jump-rate is positive over a region of compact support. We space Iterations refer to the associated deterministic equation as a volume- constrained nonlocal diffusion equation. The volume con- Band Krylov subspace iterations are extensions of Krylov straint is the nonlocal analogue of a boundary condition subspace methods such as the Arnoldi process and the necessary to demonstrate that the nonlocal diffusion equa- Lanczos algorithm, which can handle only single starting tion is well-posed and be consistent with the jump process. vectors, to the case of multiple starting vectors. Band methods have a number of advantages over the more traditional block Krylov subspace methods. We describe the Marta D’Elia Matlab package BANDITS that provides implementations Department of Scientific Computing of band versions of the Arnoldi process, the general Lanc- Florida State University, Tallahassee, FL zos method, and the symmetric and Hermitian Lanczos [email protected] algorithms.

Qiang Du Roland W. Freund Penn State University University of California, Davis Department of Mathematics Department of Mathematics [email protected] [email protected]

Max Gunzburger Florida State University MS81 School for Computational Sciences Newton-Krylov Method for Problems with Embed- 90 AN14 Abstracts

ded Monte Carlo Simulations offering potentially multiplicative benefits of combined approaches. We analyze the behavior of inexact Newton methods for problems where the nonlinear residual, Jacobian, and Hong Zhang Jacobian-vector products are the outputs of Monte Carlo Argonne National Lab simulations. We propose algorithms which account for the [email protected] randomness in the iteration, develop theory for the behavior of these algorithms, and illustrate the results with an example from neutronics. MS82 Information Theoretic Projection of Cytoskeleton Carl T. Kelley Dynamics onto Surrogate Cellular Motility Models North Carolina State University tim [email protected] Lattice Boltzmann and lattice Fokker-Planck methods can readily handle the geometric and physical complexity of Jeffrey Willert the reactions underlying cytoskeleton formation and dy- Los Alamos National Laboratory namics from actin polymerization and myosin motor mo- [email protected] tion. The computational cost, even for such simplified discretizations of the flow velocity and cytoskeleton con- Xiaojun Chen figuration, is still prohibitive for study of cellular motion Hong Kong Polytechnic University over many cell diameters. This talk presents a non-linear [email protected] projection approach to the construction of surrogate models of cellular motility, as extracted from lattice computations. A mesoscale state is represented by a set of pa- MS81 rameters from a family of probability density functions. The Lanczos Algorithm and Extensions for Quater- The non-linear projection is induced by geodesic transport nionic Matrices in the non-Euclidean geometry of the space of probability functions, guided by information theoretic functionals Let A be an associative algebra containing one and A a that quantify the fidelity of a reduced model. Several in- square matrix with entries from A. Let there be a vector teresting links between microscopic parameters governing x = 0 with entries from A and λ ∈Asuch that cytoskeleton formation and overall cell motion are brought out by this approach. Ax = xλ, (1) Sorin Mitran where the multiplication on the right is carried out com- University of North Carolina Chapel Hill ponentwise. Then, λ will be called an eigenvalue of A [email protected] associated with an eigenvector x of A. If we multiply (1) from the right by an invertible element h ∈Awe obtain

−1 MS82 A[xh]=xλh =[xh][h λh], (2) Hybrid Models and Interfaces which shows that the set of eigenvalues of quaternionic ma- In various applications the traditional mathematical mod- trices can always be reduced to complex numbers. This els based on PDEs, with their empirically determined co- is not necessarily so in other algebras. The Lanczos al- efficients, and associated traditional numerical approxima- gorithm produces a series of tridiagonal j × j matrices tions, are not sufficient to describe all the relevant dynam- Tj ,j=1, 2,...from a symmetric matrix A,andtheeigen- ics and complexity. In the talk we describe our progress values of Tj (called Ritz values) approximate the eigenval- on hybrid computational models which combine tradi- ues of A (usually very quickly). We report on the results tional numerical PDEs with other computational methods for quaternionic matrices and on extensions to other non- from, e.g., statistical mechanics, and more broadly com- commutative algebras. Algebraic operations with quater- putational physics. We focus on a model which accounts nions are in general more effective than the corresponding for complicated physics occuring at a fixed interface in operations with their matrix counterpart. This research semiconductors, which involves a Density Function The- was supported by the DFG, GZ OP 33/19-1 ory model at microscale and a Domain Decomposition ap- Gerhard Opfer proach involving a traditional drift-diffusion equation at Universität Hamburg macroscale. [email protected] Timothy Costa Oregon State University MS81 [email protected] Hierarchical Krylov and Nested Krylov Methods Using PETSc for Extreme-Scale Computing Malgorzata Peszynska Department of Mathematics We develop hierarchical Krylov methods and nested Krylov Oregon State University methods to overcome the scaling difficulties for extreme- [email protected] scale computing. We demonstrate the impact at high core counts on the PFLOTRAN subsurface flow application. Because these algorithms can be activated at runtime via MS82 the PETSc library, application codes that employ PETSc Lagrangian Particle Methods for Multiphase Flows can easily experiment with such techniques. The principles of hierarchal Krylov methods and nested Krylov methods Here we present a novel formulation of the so-called mul- can be applied to complementary advances in synchroniza- tiphase Pairwise Force Smoothed Particle Hydrodynamics tion and communication-avoiding Krylov methods, thereby Method originally proposed by Tartakovsky and Meakin. AN14 Abstracts 91

We derive a relationship between parameters in the pair- can interrogate the pattern locally or globally, which pro- wise forces and the surface tension and static contact an- vides deeper insight into the dynamics of the process of pat- gle, validate the model and demonstrate its applicability tern formation. Because the quantification is being done for studying complex processes such as multiphase flow in in the space of persistence diagrams this technique allows porous media with variable wettability. us to compare directly numerical simulations with experimental data. Alexandre Tartakovsky University of South Florida Miroslav Kramar [email protected] Rutgers University Department of mathematics Alexander Panchenko [email protected] Washington State University [email protected] Konstantin Mischaikow Department of Mathematics Rutgers, The State University of New Jersey MS82 [email protected] Modeling Nanoscale Fluid-Solid Interfaces Mark Paul Structure and dynamics of soft matter are governed by Department of Mechanical Engineering molecular interactions and hydrodynamic fluctuations. As Virginia Tech the molecular and hydrodynamic aspects are coupled, com- [email protected] puter simulations of soft matter must confront this multiscale challenge. I will present a new scale-consistent simu- MichaelF.Schatz lation framework that combines molecular dynamics (MD) Center for Nonlinear Science and School of Physics and fluctuating hydrodynamics (FHD) to enable multiscale Georgia Institute of Technology modeling of complex systems. This method allows resolu- [email protected] tion of solute-solvent interfaces and realization of excluded volumes of particles in the presence of hydrodynamic coupling. Simulation results show that the hybrid FHD/MD Jeffrey Tithof method can reproduce the solvation free energies and scal- Center for Nonlinear Science and School of Physics ing laws of particles dynamics for hydrophobes of difference Georgia I sizes. Simulations of self-assembly of hydrophobic particles [email protected] will also be presented. Mu Xu Nikolaos Voulgarakis Department of Mechanical Engineering Washington State University Virginia Tech [email protected] [email protected]

MS83 MS83 Persistence Modules and their Applications to Ma- Reconstructing Manifolds and Functions from terial Sciences Point Samples

In this talk, we present several applications of persistence We will survey some fantastic work of Niyogi, Smale and modules to material sciences such as proteins and glasses. Weinberger which provides explicit bounds on the num- The types of persistence modules are given by represen- ber of sample points required to reconstruct an underly- tations on An-quiver (i.e., standard persistent homology) ing manifold up to homotopy type with high confidence. and on commutative triple ladder quivers. Furthermore, Next, we imagine the situation where an unknown func- we give a generalized notion of persistence diagrams which tion between two such manifolds must be inferred from is defined as a graph on Auslander-Reiten quivers. Some of point samples along with the ability to evaluate the func- the computational results applied to proteins and glasses tion at the domain-samples. Not only can such functions are also shown. be reconstructed up to homotopy from finite point samples with high confidence, but also that the entire process of re- Yasuaki Hiraoka construction is robust to certain models of sampling and Kyushu University evaluation noise. [email protected] Vidit Nanda Department of Mathematics MS83 University of Pennsylvania Analyzing the Dynamics of Pattern Formation in [email protected] the Space of Persistence Diagrams

Persistence diagrams are a relatively new topological tool MS83 for describing and quantifying complicated patterns in a Word Representations of Structurally Stable simple but meaningful way. We will demonstrate this Hamiltonian Flows in Multiply Connected Do- technique on patterns appearing inRayleigh-Benard con- mains and its Applications vection. This procedure allows us to transform experimental or numerical data from experiment or simulation into We consider Hamiltonian vector fields with a dipole sin- a point cloud in the space of persistence diagrams. There gularity that satisfy the slip boundary condition in two- are a variety of metrics that can be imposed on the space dimensional multiply connected domains. One example of persistence diagrams. By choosing different metrics one of such a Hamiltonian vector field is the incompressible 92 AN14 Abstracts

and inviscid flow in an exterior multiply connected domain PDEs in Water Wave Propagation in the presence of a uniform flow whose Hamiltonian is called the stream function. They are regarded as mathe- We consider numerical solutions for a fractional PDE aris- matical models of biofluids, rivers and coastal flows. Here, ing as a nonreflecting boundary condition in water wave we are interested in structurally stable Hamiltonian vector propagation. The fractional derivative is expressed as di- fields and their topological structures of contour lines of vergence of a singular integrable convolution. The equation the Hamiltonian, i.e. streamline patterns. We develop an is viewed as a linear conservation law with a nonlocal sin- encoding procedure to assign a unique sequence of words to gular flux. A semi-discrete finite volume scheme uses local every streamline pattern. Owing to this word representa- polynomial approximation of order p from solution cell av- tion, we not only determine all possible streamline patterns erages, followed by exact integration of the singular flux, in a combinatorial manner, but also describe the complex and yields a surprising convergence rate of p +3/2. Time evolution of fluid flows as a change of words. Moreover, integration uses Runge-Kutta methods of matching order. we can determine possible transitions between two differ- We discuss stability and convergence, and show numerical ent structurally stable streamline patterns. In the present results for uniform and nonuniform grids. talk, we introduce the theory of word representations for structurally stable Hamiltonian vector fields and demon- David Prigge strate how it is applicable to fluid flow problems with vor- University of Michigan tex structures. Department of Mathematics [email protected] Takashi Saka jo Kyoto University Sean Carney [email protected] University of Michigan [email protected] Tomoo Yokoyama Kyoto University of Education Smadar Karni [email protected] University of Michigan Department of Mathematics [email protected] MS85 High-Order Algorithms for Compressible Reacting Remi Abgrall Flow with Complex Chemistry INRIA Bordeaux Sud-Ouest Universite de Bordeaux We describe a numerical algorithm for integrating the mul- [email protected] ticomponent, reacting, compressible Navier-Stokes equations, targeted for direct numerical simulation of combus- tion phenomena. The algorithm addresses two shortcom- MS85 ings of previous methods. First, it incorporates an eighth- Semi-Lagrangian Discontinuous Galerkin Schemes order narrow stencil approximation of diffusive terms that for the 2+2 Vlasov-Poisson System on Unstruc- reduces the communication compared to existing methods tured Meshes and removes the need to use a filtering algorithm to remove Nyquist frequency oscillations that are not damped with traditional approaches. The methodology also incorporates The Vlasov-Poisson system is a set of equations that de- a multirate temporal integration strategy that provides an scribe collisionless plasma far from thermodynamic equilib- efficient mechanism for treating chemical mechanisms that rium. Numerical difficulties in solving the Vlasov-Poisson are stiff relative to fluid dynamical time scales. The over- system include the high-dimensionality and severe time all methodology is eighth order in space with option for step restrictions attributed to moderate to large veloci- fourth order to eighth order in time. The implementation ties in the system. Explicit Eulerian methods require ex- uses a hybrid programming model designed for effective uti- cessively small time steps, and implicit Eulerian methods lization of many-core architectures. We present numerical have matrices with large condition numbers. Particle in results demonstrating the convergence properties of the al- Cell methods together with their Lagrangian and semi- gorithm with realistic chemical kinetics and illustrating its Lagrangian counterparts relax this time step restriction performance characteristics. We also present a validation by solving for the characteristics in the system. We pro- example showing that the algorithm matches detailed re- pose a high-order operator split DG method for solving the sults obtained with an established low Mach number solver. Vlasov-Poisson system. Our hybrid method incorporates large time steps using semi-Lagrangian methods, and complicated geometries in configuration space with unstructured grids. We present 2D-2V results including the for- Matthew Emmett, Weiqun Zhang mation of a plasma sheath in the proximity of a cylindri- Lawrence Berkeley National Laboratory cal Langmuir probe, as well as the simulation of a single- Center for Computational Sciences and Engineering species charged particle beam in an accelerator. [email protected], [email protected] James A. Rossmanith John B. Bell Deparment of Mathematics CCSE Iowa State University Lawrence Berkeley Laboratory [email protected] [email protected] David C. Seal Department of Mathematics MS85 Michigan State University High-Order Numerical Methods for Fractional [email protected] AN14 Abstracts 93

Andrew J. Christlieb ples the computation of the linear and angular velocities. Michigan State Univerity Similarly, for the Rosensweig model we present the basic Department of Mathematics PDE results, together with an fully-discrete scheme com- [email protected] bining Continuous Galerkin and Discontinuous Galerkin techniques in order to guarantee discrete energy stability. Finally, we demonstrate the capabilities of the Rosensweig MS85 model and its numerical implementation with some numer- Evaluation of Discrete and Continuous Adjoint Ap- ical simulations in the context of ferrofluid pumping by proaches for Sensitivity Analysis and Error Estima- means of external magnetic fields. tions for Numerical Approximations of Hyperbolic Pdes with Shocks Ignacio Tomas University of Maryland, College Park The literature on adjoint methods for shock-hydrodynamic [email protected] applications is actually rather sparse and recent. Early investigations with continuous adjoint problems required accurate knowledge of the discontinuities. Recent work has MS86 shown that this issue may be mitigated by considering an alternative dual problem based on the concept of limiting Optimal Energy Norm Error Estimates for a Mixed viscocity. We compare and evaluate this approach using FEM for a Cahn-Hilliard-Stokes System either a discontinuous Galerkin approximation or a continuous Galerkin approximation with flux-corrected transport In this I talk describe a mixed finite element method for for shock-hydrodynamic applications. a modified Cahn-Hilliard equation coupled with a non- steady Darcy-Stokes flow that models phase separation and Tim Wildey coupled fluid flow in immiscible binary fluids and diblock Optimization and Uncertainty Quantification Dept. copolymer melts. The time discretization is based on a con- Sandia National Laboratories vex splitting of the energy of the equation. I show that the [email protected] scheme is unconditionally energy stable and unconditionally uniquely solvable and that the discrete phase variable ∞ ∞ John N. Shadid is bounded in L (0,T; L )andthediscretechemicalpo- ∞ 2 Sandia National Laboratories tential is bounded in L 0,T; L , for any time and space [email protected] step sizes, in two and three dimensions, and for any finite final time T . WiththisinhandIshowthatthese Eric C. Cyr variables converge with optimal rates in the appropriate Scalable Algorithms Department energy norms in both two and three dimensions. I will Sandia National Laboratotories describe how this analysis can be extended to two-phase [email protected] diffuse interface models with large density mismatch. This is joint work with Amanda Diegel and Xiaobing Feng.

MS86 Steven M. Wise Energetic Variational Approaches in Ion Transport Mathematics Department University of Tennessee Almost all biological activities involve transport of charged [email protected] ions in specific biological environments. In this talk, I will discuss a unified energetic variational approach developed specifically for these multiscale-multiphysics prob- MS87 lems. I will discuss the relevant classical theories and relevant physical approaches and methods. I will focus on Generalized Multiscale Finite Element Methods for the mathematics, in particular the analytical issues arising Wave Propagation in Heterogeneous Media from these studies. Numerical modeling of wave propagation in heterogeneous Chun Liu media is important in many applications. Due to the com- Department of Mathematics, Penn State University plex nature, direct numerical simulations on the fine grid University Park, PA 16802 are prohibitively expensive. It is therefore important to [email protected] develop efficient and accurate methods that allow the use of coarse grids. In this talk, we present a multiscale finite element method for wave propagation on a coarse grid. MS86 To construct multiscale basis functions, we start with two From Micropolar Navier Stokes to Ferrofluids, snapshot spaces in each coarse-grid block where one rep- Analysis and Numerics resents the degrees of freedom on the boundary and the other represents the degrees of freedom in the interior. We The Micropolar Navier-Stokes Equations (MNSE), is a sys- use local spectral problems to identify important modes tem of nonlinear parabolic partial differential equations in each snapshot space. To our best knowledge, this is coupling linear velocity, pressure and angular velocity, i.e.: the first time where multiple snapshot spaces and multiple material particles have both translational and rotational spectral problems are used and necessary for efficient com- degrees of freedom. The MNSE is a central component of putations. These multiscale basis functions are coupled via the Rosensweig model for ferrofluids, describing the linear the symmetric IPDG method which provides a block diag- velocity, angular velocity, and magnetization inside the fer- onal mass matrix, and, consequently, results in fast com- rofluids, while subject to distributed magnetic forces and putations in an explicit time discretization. Our methods’ torques. We present the basic PDE results for the MNSE stability and spectral convergence are rigorously analyzed. (energy estimates and existence theorems), together with a Numerical examples are presented to show our methods’ first order semi-implicit fully-discrete scheme which decou- performance. The research is supported by Hong Kong 94 AN14 Abstracts

RGC General Research Fund (Project number: 400411). under Grant GRF603011.

Eric Chung Wenbin Li The Chinese University of Hong Kong Department of Mathematics, Department of Mathematics Hong Kong University of Science and Technology [email protected] [email protected]

Yalchin Efendiev Shingyu Leung Dept of Mathematics Hong Kong University of Science and Technology Texas A&M University [email protected] [email protected] Jianliang Qian Wing Tat Leung Department of Mathematics Texas A&M University Michigan State University [email protected] [email protected]

MS87 MS87 Maximal Laplace-Beltrami Eigenvalues on Com- Fast Matrix-free Direct Solution and Selected In- pact Riemannian Surfaces version for Seismic Imaging Problems

Let (M,g) be a connected, compact Riemannian sur- Fast direct solvers have been shown very useful for mod- face and denote by λk(M,g)thek-th eigenvalue of the eling large inverse problems. In this talk, we show our Laplace-Beltrami eigenproblem. We consider the mapping recent development of matrix-free direct solvers for large (M,g) → λk(M,g). We propose computational methods dense or spare matrices based on rank structures and ran- for solving the eigenvalue optimization problem of maxi- domized sampling. Unlike existing direct or iterative meth- mizing λk(M,g)asg varies within a conformal class [g0] ods, these new solvers can quickly provide direct solutions of fixed volume and for the problem where M is addition- with controllable accuracies, using only a small number of ally allowed to vary over surfaces with fixed genus. Sev- matrix-vector multiplications. This is especially attractive eral properties are also studied computationally, including for problems which are ill-conditioned, where it is too ex- uniqueness, symmetry, and eigenvalue multiplicity. pensive to form the matrix, or where there are too many right-hand sides. The solvers are also useful for problems Chiu-Yen Kao with varying parameters (e.g., frequency). We then dis- Claremont McKenna College cuss the application of the methods to the extraction of [email protected] selected entries of the inverse of large sparse matrices. For discretized Helmholtz equations, we can quickly compute Rongjie Lai the diagonal blocks or any off-diagonal entries of the in- University of Southern California verse. Such information is useful for the preconditioning of [email protected] the problem. These methods can significantly improve the efficiency of the solution/inversion of the Hessian matrix Braxton Osting in Gauss-Newton iterations for FWI. University of California, Los Angeles Jianlin Xia [email protected] Department of Mathematics Purdue University MS87 [email protected] A Level Set-Adjoint State Method for the Joint Maarten de Hoop Transmission-Reflection First Arrival Traveltime Center for Computational & Applied Mathematics Tomography Purdue University We propose an efficient partial differential equation (PDE) [email protected] based approach to the joint transmission-reflection traveltime tomography using first arrivals. In particular, we Xiao Liu consider only the first arrivals from the transmission and Department of Mathematics reflection measurements at a series of receiver-source pairs. Purdue University Unlike typical reflection tomography where the location [email protected] of the reflector is assumed to be known by some migration techniques, we propose an efficient numerical approach Yuanzhe Xi based on the adjoint state method and the PDE based lo- Purdue University cal level set method to invert both the piecewise smooth [email protected] velocity within the computational domain and the location of a codimension-one reflector. Since we are using only first arrivals for tomography, we might not be able to obtain a MS88 perfect illumination of the reflector because the relevant The Scholarly Work of Reliable and Well-Designed information might be carried by the later arrivals. In this Mathematical Software work, we propose an easily computed quantity which can quantify the reliability of our reconstruction. Numerical Well-designed mathematical software has long been con- examples in both two- and three-dimensions will be given sidered a cornerstone of scholarly contributions in compu- to demonstrate the efficiency of the proposed approach. tational science. Forsythe, founder of Computer Science at The work is supported in part by the Hong Kong RGC Stanford and regarded by Knuth as the ”Martin Luther of AN14 Abstracts 95

the Computer Reformation,” is credited with inaugurating MCS Division the refereeing and editing of algorithms not just for their [email protected] theoretical content, but also for design, robustness, and us- ability. His vision extends to the current day, and this talk presents a modern perspective of academic software. The MS89 speaker’s academic software constitutes much of x=A\bin The Inverse Fast Multipole Method MATLAB when A is sparse, and is widely used in many other academic, government, and commercial applications, We present a fast direct solver for dense linear systems aris- because of its performance and its reliability. ing out of wide range of applications, integral equations, multivariate statistics, radial basis interpolation, etc., to Timothy A. Davis name a few. The highlight of this new fast direct solver is University of Florida that the solver scales linearly in the number of unknowns Computer and Information Science and Engineering in all dimensions. The solver, termed as the Inverse Fast [email protected] Multipole Method, works on the same data-structure as the Fast Multipole Method. More generally, the solver extends to the class of hierarchical matrices, denoted as H2 MS88 matrices with strong admissibility criteria, i.e., only the in- A Deterministic Guaranteed Automatic Algorithm teraction between particles corresponding to well-separated for Univariate Function Approximation clusters is represented as a low-rank matrix, and thereby the algorithm departs from the existing (HSS/ HODLR) Function recovery is a fundamental computational prob- approaches. We also present numerical benchmarks in 1D lem. It is desirable to have automatic algorithms for solv- and 2D validating the linear scaling of the algorithm. ing such problems, i.e., the algorithms decide adaptively how many and which pieces of function data are needed Sivaram Ambikasaran and then use those data to construct an approximate func- Department of Mathematics tion. The error of this approximation should be guaranteed Courant Institute of Mathematical Sciences not to exceed the prescribed tolerance. We provide a de- [email protected] terministic guaranteed automatic algorithm for univariate function approximation on a given finite interval and prove Eric F. Darve its reliability. Stanford University Yuhan Ding,FredJ.Hickernell Mechanical Engineering Department Illinois Institute of Technology [email protected] [email protected], [email protected] MS89 MS88 Hierarchical Interpolative Factorization A Survey of Issues in Reliable Computational Sci- ence We present some recent results on the efficient factorization of matrices associated with non-oscillatory integral op- Continuing developments in computing software and hard- erators in 2D and 3D. In contrast to the 1D case, such ware allow us to solve more complex problems than ever matrices exhibit considerable rank growth in their off- before. However, there remains the nagging question of diagonal blocks when compressed using standard hierar- how we can be sure that the answers are correct. This talk chical schemes. We combat this with explicit dimensional surveys the efforts that have been made to ensure that com- reductions via geometric reclustering and additional computational science is reliable and the work that still needs pression. The resulting ranks are much better behaved, to be done. yielding essentially linear costs to construct, apply, and invert the factorization. Our method is fully adaptive and Fred J. Hickernell can handle both boundary and volume problems. Illinois Institute of Technology Department of Applied Mathematics Kenneth L. Ho [email protected] Department of Mathematics Stanford University [email protected] MS88 Generation of Appropriate Publication Citations by Numerical Software Libraries MS89 Randomized Methods for Accelerating Structured Properly citing academic publications that describe soft- Matrix Computations ware libraries and algorithms is the way that open source scientific library users “pay” to use the free software. With Randomized methods have over the last several years large multifaceted libraries and applications that use sev- proven to be powerful tools for computing low-rank approx- eral such libraries, even the conscientious user may end up imations to matrices whose singular values exhibit appro- citing publications in error or missing relevant publications. priate decay. In this talk, we describe how such techniques Based on a feature recently added to the PETSc numerical can be extended to certain ”rank-structured” matrices, for software libraries, we suggest an alternative model where which only certain off-diagonal blocks (not the matrix it- the library itself generates the bibtex items based on ex- self) admit accurate low-rank approximations. Matrices actly what algorithms and portions of the code are used in of this type often arise in the construction of O(N) direct the application. solvers for elliptic PDEs.

Barry F. Smith Gunnar Martinsson Argonne National Lab Univ. of Colorado at Boulder 96 AN14 Abstracts

[email protected] will be discussed.

Bruce Palmer MS89 Pacific Northwest National Lab Parallel Structured Direct Solvers for Nonsymmet- [email protected] ric and Indefinite Sparse Matrices William Perkins Fast structured direct solvers have been extensively studied Pacific Northwest National Laboratory for matrices with a low-rank property. Most existing work [email protected] concentrates on symmetric and/or positive definite problems. Here, we exploit this structure in the direct solution Kevin Glass of nonsymmetric and indefinite matrices. Graph ordering Pacific Northwest National Laboratory and pivoting are performed. The pivoting strategy is de- Richland WA signed in a way so as to preserve both the sparsity and the [email protected] rank structure. A structured multifrontal LU factorization is then performed. To implement the method in parallel, Yousu Chen we use static mapping to preallocate tasks to processes. Pacific Northwest National Lab Under a certain switching level in the tree, factorizations [email protected] are done locally in each process. Beyond the switching level, processes of child nodes form a process grid on parent nodes where structured operations are performed among Shuangshuang Jin, Ruisheng Diao the processes. In such a way, both idling and communi- Pacific Northwest National Laboratory cations are reduced. All the frontal and update matrices [email protected], [email protected] are structured and their factorizations are done in parallel. In the numerical experiments, we show the applications of Mark Rice this method to seismic imaging and more general problems. Pacific Northwest National Lab This is joint work with Jianlin Xia. [email protected]

Zixing Xin David Callahan, Steve Elbert Department of Mathematics Paciﬁc Northwest National Laboratory Purdue University [email protected], [email protected] [email protected] Zenyu Huang Paciﬁc Northwest National Lab MS91 [email protected] A Fully Implicit Approach for the Solution of Temporal Multiscale Problems with Application to Power Grid MS91

In this talk, we present a fully implicit approach for tem- Power Grid Simulation: Needs, State of the Art, poral multiscale problems and discuss a power grid appli- Challenges cation that involves two time-scales. At each step of the slow time-scale, our approach involves solving equations for The complexity of Power Grid is increasing, due to the mas- one step of the slow time-scale along with several coupled- sive integration of intermittent generation far away from in-time equations for the fast time-scale. We will discuss load centers or dispersed in the distribution grids. The the formulation, preconditioning techniques, and parallel Power Grid is operated nearest to its limits; more and more implementation of our approach. closed loop controls are installed in the system. There is an urgent need to base decisions on a more accurate Shrirang Abhyankar description of the system including its dynamic behavior. Argonne National Laboratory The Power Grid simulation must now include time domain [email protected] simulation and not only static Power Flow. Most of the Power Grid Simulation tools use fixed time step methods Alexander J. Flueck, Xu Zhang and hard coded modeling of the components even if only Illinois Institute of Technology variable time step implicit method can offer a certain level fl[email protected], xu zhang ¡[email protected]¿ of confidence for the accuracy of the results in particular at the design stage when the dynamic behavior could be far away from a realistic and expected behavior. A tough MS91 requirement is that physical unstable Power Grid must be simulated as unstable. The ”over damping” intrinsically in- Gridpack Toolkit for Developing Power Grid Simu- duces by numerical methods which guarantees the damping lations on High Performance Computing Platforms of numerical errors, must be minimized as much as possible. This presentation describes the GridPACK framework, which is designed to help power grid engineers develop Patrick Panciatici modeling software capable of running on todays high per- RTE France formance computers. The framework contains modules for [email protected] managing power grid networks, distributed matrices and vectors, parallel linear and non-linear solvers, and mapping functionality to create matrices and vectors based on MS91 properties of the network. Examples of applications built with GridPACK will be presented and performance results Experiences with Time Integration Algorithms in AN14 Abstracts 97

a Time Domain Simulation Code [email protected]

Commercial power grid simulators often employ a standard Trapezoid time integration scheme along with con- MS92 stant time steps for their time evolution. In this talk we will Building Support, Building Budgets for the Math- discuss our experiences in incorporating a variable step in- ematical Sciences tegrator within a commercial time domain simulation code. The method used includes a second order predictor and I will provide some perspectives on how federal science bud- a time step selector based on controlling local truncation get requests are built; what kinds of arguments seem to error. Preliminary results show potential for signiﬁcant be eﬀective for increasing requests; and what actions the speedup in simulation runs. mathematical sciences community can take to justify and support such requests.

Carol S. Woodward Peter March Lawrence Livermore Nat’l Lab Ohio State University [email protected] Department of Mathematics [email protected] Chaoyang Jing eMIT [email protected] MS92 SIAM’s Initiatives and Activities in STEM Educa- Liang Min tion Lawrence Livermore National Laboratory [email protected] In this talk SIAM’s initiatives in STEM education, and their relations to science policy will be discussed. Impor- Steve G. Smith tant aspects of this are the Modeling across the Curricu- Lawrence Livermore National Lab lum, MaC, initiative. The two MaC workshops (August [email protected] 2012 and January 2014) and their outcomes will be presented. Other important recent activities include the IN- GenIOuS project which exemplified the way various math- MS92 ematical sciences professional societies can work together to enhance understanding of the issues and affect policy. Mathematics Research: Support, Stakeholders, Accountability Peter R. Turner Clarkson University The papers we publish and read are crucial to us as re- School of Arts & Sciences searchers. However, there are many other stakeholders of [email protected] mathematical publishing as well: our employers, organi- zations like SIAM, corporate publishers, funding agencies, MS93 and society, which ultimately pays for and benefits from the research. The diverse requirements of stakeholders, Crop Rotation Modeling and Optimization for Sus- together with rapidly advancing technology and economic tainable Water Use and social factors have created turmoil and sometimes con- flict in publishing, placing us in a time of both peril and We use a simulation-based optimization framework to opportunity. guide planting decisions with a constraint to account for sustainable water usage. The motivation is the berry farming region of the Pajaro Valley, CA, which is over- Douglas N. Arnold drawing from the aquifer, resulting in seawater intrusion. School of Mathematics MODFLOW-FMP is treated as a black-box with optimiza- University of Minnesota tion tools from DAKOTA. We compare modeling formula- [email protected] tions and optimization algorithms to understand trade-offs and identify challenges.

MS92 Kathleen Fowler Clarkson University Mathematics and Science Policy: Some Perspec- Department of Mathematics tives from SIAM’s President [email protected]

Mathematical sciences are a common denominator behind key scientific and technological advance, from robotics and MS93 genetics to Big Data, reminding us all of the vital impor- Estimating Uncertainty in Annual Energy Produc- tance of a well-trained STEM community to the future. tion Accordingly, SIAM plays a pivotal role promoting the visi- bility of mathematics in the halls of government, contribut- A primary quantity in the evaluation of a proposed solar ing to science policy discussions, all the while advocating power plant is the annual energy production (AEP). Un- for much-needed research dollars and resources to improve certainty in the AEP is often quantified by estimating the STEM education. 50th and 10th percentiles by means of a model. The ratio between these quantiles significantly affects the financial Irene Fonseca risk associated with the proposed power plant, and thus, Carnegie Mellon University uncertainty in AEP significantly impacts a proposals suc- Center for Nonlinear Analysis cess. We outline a method for estimating uncertainty in 98 AN14 Abstracts

annual energy accounting for the three primary contribu- computationally predict previously unknown physical, cel- tions to this uncertainty: inter-annual variability in the lular and evolutionary mechanisms that govern the activity weather; uncertainty in measurements of irradiance; and of DNA and RNA. We will present novel generalizations of modeling error in the translation from irradiance to power. the singular value decomposition as well as experimental We describe how this can be used to improve AEP uncer- veriﬁcation and validation of some of the computational tainty estimates in Arizona and Georgia. predictions.

Genetha Gray Orly Alter Sandia National Laboratories Sci Comp & Imaging (SCI) Inst, Bioeng & Human [email protected] Genetics Depts University of Utah [email protected] MS93 Analysis of a Managed Aquifer Recharge System MS94 Over the last few decades, groundwater resources have been Deconvolution of the Mammalian Cell Cycle depleted at a faster rate than the underlying aquifers have Metabolome been replenished. This imbalance has led water management agencies to consider managed aquifer recharge net- We have completed a comprehensive mass spectrometry works, where infiltration basins are used to replenish the analysis quantifying hundreds of small molecule metabo- aquifers using previously uncaptured storm water runoff. lites throughout the phases of the mammalian cell cy- In this work, we utilize optimization to evaluate the costs cle. Using singular value decomposition of the matrix of associated with constructing such a network while simul- metabolite abundance from a synchronized culture of HeLa taneously meeting demands placed on the aquifer. We cells, we have produced a map of metabolic changes by present results for a realistic subwatershed in the Pajaro phase of cycle, allowing the characterization of the coor- Valley region of California. We utilize existing computa- dinated metabolic changes occurring in the proliferating tional tools to determine limits for the constraint equa- human tumor cell. tions, to compute subwatershed drainage areas, and to compute the corresponding storm water runoff over a pre- Anneleen Daemen, Christopher Delnagro, Jonathan Choi, determined time period consisting of several rain events. Peter Jackson, Thomas O’Brien, Matthew Brauer We present results that may be used to suggest best prac- Bioinformatics & Computational Biology tices with regards to regional recharge basin design. Genentech, Inc. [email protected], [email protected], Lea Jenkins [email protected], [email protected], to- Department of Mathematical Sciences [email protected], [email protected] Clemson University [email protected] MS94 MS93 Tensor Completion Methods in Seismology: Re- Modeling Impacts of Water Level Control Proce- construction, Denoising and Un-Mixing Seismic dures on Water Quality of the St Lawrence River Sources

The St Lawrence River is the 13th largest river on the earth Seismic data can be stored in 5D tensors that depend on and the greatest single fluvial point source of freshwater to time (or frequency), x-y position of receivers, and x-y po- the North Atlantic. This river is faced with important sition of sources. This talk will discuss the development ecosystem management issues related to the interdepen- of algorithms, inspired by tensor algebra and recent work dence of environmental issues, e.g., the effect of climate on nuclear norm minimization, to de-noise and reconstruct change on invasive species, nutrient processing, and wa- large 5D volumes of seismic data. I will also discuss the ter budgets. Our work focus on development of integrated application of tensor algebra techniques to the problem of modeling techniques to explore the interplay of nutrient seismic source separation. The latter arises when seismic loading and population dynamics as modulated by the wa- data are acquired with sources that are triggered almost ter control procedures implement to maintain nearly neu- simultaneously in order to save acquisition time. tral levels. Our work seeks to understand the impact of more natural level excursions in the river that might be Mauricio D. Sacchi considered as a way to maintain the nearshore ecosystem. Deparment of Physics University of Alberta Joseph Skufca [email protected] Clarkson University [email protected] MS94 Coherent Pattern Detection in Tensor Data MS94 Discovery of Principles of Nature from Matrix and In real-world applications, multidimensional data may con- Tensor Modeling of Large-Scale Molecular Biolog- tain coherent patterns and we need to perform clustering ical Data simultaneously along all dimensions of the data to detect these patterns. In this talk, we will discuss how column- We will describe the use of matrix and tensor decomposi- pair based strategies we have developed for biclustering 2D tions in comparing and integrating different types of large- data can be extended to higher dimensions. We can use scale molecular biological data, from different studies of tensor decomposition algorithms to convert a complicated cell division and cancer and from different organisms, to coherent pattern detection problem in a high dimensional AN14 Abstracts 99

data space to simpler 2D data analysis problems. ﬁt, and security procedures such as canine detection create dependencies. This research presents an analytical model Hongya Zhao, Hong Yan of the border crossing process with an implementation of Department of Electronic Engineering Mixture of Generalized Erlang (MGE) distributions, also City University of Hong Kong known as Coxian k-phased distributions, as an improved [email protected], [email protected] inspection service time approximation.

Hiram Moya MS95 University of Texas-Pan American A Spectral Analysis for Regularization and Image [email protected] Processing Applications

Regularization incorporates prior information into math- MS96 ematical models to favor desired solutions. When com- A Fast Finite-Volume Eulerian-Lagrangian Lo- puting piecewise polynomial solutions whose derivatives of calized Adjoint Method for Space-Fractional certain order are sparse, a common regularizer is the L1- Advection-Diffusion Equations norm of the derivatives. Our interest evolved from the fact that approximations to the desired solution are often more Fractional advection-diffusion PDEs provide an adequate accurate, up to orders of magnitude, than approximations and accurate description of subsurface flow and trans- to the derivatives. We explain such a phenomenon by a port processes in porous media that exhibit anomalous spectral analysis of discrete derivatives and propose alter- diffusion, which can not be modeled properly by second- native regularizers. order advection-diffusion equations. However, fractional advection-diffusion PDEs raise mathematical and numeri- Jorge A. Castanon cal difficulties that have not been encountered in the con- Rice University text of second-order advection-diffusion PDEs. In this [email protected] talk we present a faithful and fast finite-volume Eulerian- Lagrangian localized adjoint method for space-fractional advection-diffusion equations, without resorting to any MS95 lossy compression, but rather by exploring the structure Exploiting Nonlinear Structure for Nonconvex Op- of the coefficient matrices. These methods have computa- timization tional cost of O(N log2 N) per time step and memory of O(N), while retaining the same accuracy and approxima- Many important design and operational planning problems tion property of the underlying numerical methods. give rise to nonconvex optimization problems. We review the reformulation-linearization technique (RLT) for solving Mohamed Al-Lawati certain polynomial optimization problems to global opti- Department of Mathematics and Statistics mality. We show how to exploit nonlinear structure in Sultan Qaboos University RLT, such as partial separability, and present numerical re- [email protected] sults that show that the resulting relaxation can be solved orders of magnitude faster. MS96 Sven Leyffer Argonne National Laboratory Variational Formulation of Problems Involving leyff[email protected] Fractional Order Differential Operators In this talk, we consider boundary value problems involv- MS95 ing either Caputo or Riemann-Liouville fractional derivatives of order α ∈ (1, 2) on the unit interval (0, 1). The Topology Control for Load Shed Recovery variational problem for the Riemann-Liouville case is co- α/2 We introduce the dc optimal load shed recovery with trans- ercive on the space H0 (0, 1) but the solutions are less mission switching model (DCOLSR-TS), which seeks to regular, whereas that for the Caputo case involves differ- reduce potential post-contingency load shedding by mod- ent test and trial spaces. We establish the regularity pickup ifying the system topology. Since solving DCOLSR-TS is of the solutions of the variational problem, which enables computationally difficult, we develop a heuristic (MIP-H), one to establish convergence rates of the finite element ap- which improves the system topology while specifying the proximations. The analytical theory is then applied to the sequence of switching operations. We argue the use of a Sturm-Liouville problem involving a fractional derivative parallelized version of MIP-H for on-line load shed recovery in the leading term. Finally, extensive numerical results and recurring contingency-response analysis. are presented to illustrate the error estimates.

Erick Moreno-Centeno Bangti Jin Texas A&M University-College Station Department of Mathematics [email protected] University of California, Riverside [email protected]

MS95 A Coxian-Phased Approximation for Border Cross- MS96 ing Service Times of Commercial Trucks High Order Scheme for Caputo Derivative and Its Application to Caputo Type Advection-Dispersion Since 2011, yearly combined trade exceeds $1 trillion within Equation North American nations, with 80% transported by commercial trucks. Previous analytical models assume Marko- In this paper, we derive a high order numerical scheme for vian distributions for service time. Yet, ﬁeld data lacks α(∈ (0, 1))-th order Caputo derivative of a given function 100 AN14 Abstracts

f(t), where the convergence order is 4 − α, which is higher subspace iteration technique using the approximate spec- than any reference available. Then we apply this scheme tral projector with a truncated series of expanding gener- to Caputo type advection-dispersion equation. The con- ated subspaces. This approach significantly improves the vergence, stability, and error estimate for the Caputo type current performance capabilities and convergence efficiency advection-dispersion equation are also given. of the solver. In particular, the approach allows to reduce considerably the number of linear systems to solve by Jianxiong Cao contour integration and then optimize the need in parallel Shanghai University computing power. [email protected] Eric Polizzi Changpin Li University of Massachusetts, Amherst, USA College of Sciences [email protected] Shanghai University, Shanghai, China [email protected] MS97 YangQuan Chen Compact Rational Krylov Methods for Solving University of California, Merced Nonlinear Eigenvalue Problems [email protected] We present a new framework of Compact Rational Krylov (CORK) methods for solving the nonlinear eigenvalue MS96 problem (NLEP): Fractional Sturm-Liouville Theory for Spectral and A(λ)x =0. Spectral Element Methods In this framework, we generalize the linearization based methods for solving NLEPs by writing the different linear We first introduce a new theory on fractional Sturm- pencils in a similar form and exploiting the corresponding Liouville problems, leading to the development of structure. The CORK family of rational Krylov methods exponentially-accurate spectral and spectral element meth- also uses a generalization of the compact Arnoldi decom- ods for time- and space-fractional PDEs. We introduce position. In this way, the extra memory cost due to the a new Discontinuous Petrov-Galerkin (DPG) method for linearization of the original NLEP is negligible. fractional hyperbolic problems. Next, we present a unified Petrov-Galerkin (PG) spectral method for low-to- Roel Van Beeumen high dimensional fractional advection, diffusion, and Pois- KU Leuven son/Helmholtz problems. We conclude the talk with a frac- [email protected] tional collocation spectral method for efficient treatment of nonlinear/multi-term FPDEs. Karl Meerbergen Mohsen Zayernouri, George E. Karniadakis K. U. Leuven Division of Applied Mathematics [email protected] Brown University mohsen [email protected], Wim Michiels george [email protected] KU Leuven [email protected]

MS97 z-Pares: A Complex Moment Based Hierarchical MS97 Parallel Eigensolver Package Preconditioning Subspace Iteration for Large Eigenvalue Problems with Automated Multi-Level We have developed a parallel software package for solving Sub-Structuring generalized eigenvalue problems which is named z-Pares. This software enables users to utilize a large amount of The subspace iteration method (SIM) is a numerical pro- computational resources because of its hierarchical par- cedure for normal mode analysis which has shown to be allel structure. z-Pares implements the Sakurai-Sugiura robust and reliable for solving very large general eigen- method proposed in 2003. This method computes an eigenvalue problems. Although its classical form as introduced subspace using complex moments that are obtained by by Bathe in the seventies of the last century is less effi- contour integral. Numerical experiments and performance cient than the Lanczos iteration method in terms of CPU evaluations using matrices from some practical applications time, it is beneficial in terms of storage use if a very large are shown. number (say hundreds) of eigenmodes are needed and good approximations to the wanted eigenvectors are at hand. In Yasunori Futamura,TetsuyaSakurai this paper we take advantage of the automated multi-level Department of Computer Science sub-structuring (AMLS) to construct an accurate initial University of Tsukuba subspace for SIM. Along with the AMLS reduction we de- [email protected], saku- rive a very efficient preconditioning method for SIM which [email protected] solves the linear systems for a transformed system with block diagonal system matrix whereas the multiplication with the mass matrix is executed in the original variables. MS97 The presentation is based on a joint paper with Pu Chen Improved Convergence and Parallel Performances and Jiacong Yin, Peking University. for the FEAST Eigensolver Heinrich Voss A new numerical scheme is introduced for the symmetric Hamburg Univ of Technology FEAST algorithm. The approach combines the FEAST Institute of Numerical Simulation AN14 Abstracts 101

[email protected] proaches to allow for the spatial pattern wavenumber to vary on the macroscale variables and to find how changes in microstructure geometry affect macroscopic properties MS98 and transport. To this end, we consider the thermal trans- Transport Properties of Periodic Metamaterials port of a fluid through nonuniformly spaced laminates, as a simple model for heat sinks in electronics. We find a cou- Periodic microstructures such as metamaterials may con- pled system of partial differential equations that describe tain arrays of nanowires, holes or metallic nanoparticles, the local microscale temperature and deviations from the whose material properties are complex-valued. Evaluation Darcy pressure. Microscale values of all of these quantities of their overall properties requires challenging computa- are known in terms of the solutions to these effective eqau- tions. In this talk I will present a new approach based on tions. Examples of optimal channel geometries are found, the construction of periodic harmonic functions, and derive which depend on the ability to transfer heat from the de- a formula for the effective tensor that excellently agrees vice to the enviornment, the orientation of the device with with numerical calculations. Results of the talk has ap- respect to gravity, and the available power needed to drive peared in the Journal of Mathematical Physics 54, 053505 the fluid motion. (2013). Burt S. Tilley Yuri Godin Worcester Polytechnic Institute University of North Carolina at Charlotte Mathematical Sciences Department [email protected] [email protected]

MS98 MS99 Homogenization for Sea Ice Deterministic Quantities for Understanding Stochastic Dynamics Sea ice is a leading indicator of climate change, and a key component of Earth’s climate system. As a material, To understand dynamics under uncertainty, it is desirable sea ice is a porous composite of pure ice with submillime- to examine the quantities that carry dynamical informa- ter scale brine inclusions whose volume fraction and con- tion. A quantity called escape probability is investigated nectedness vary significantly with temperature. Fluid flow in order to describe transitions between dynamical regimes. through the brine microstructure mediates a broad range of This leads to consideration of a deterministic nonlocal par- geophysical and biological processes. Sea ice also displays tial differential equation. The speaker will focus on under- composite structures over much larger scales. For exam- standing stochastic dynamics by examining escape proba- ple, the sea ice pack itself is a fractal composite of ice floes bility, in the context of prototypical examples in biophysi- and ocean, while surface ponds on melting Arctic sea ice cal and physical settings. Relevant theoretical results will exhibit complex dynamics and self-similar geometrical con- also be highlighted. figurations. I will discuss how methods of homogenization and statistical physics are being used to study the effective Jinqiao Duan properties of such systems. This work helps improve our Illinois Institute of Technology understanding of the role of sea ice in the climate system, [email protected] and the representation of sea ice in climate models.

Kenneth M. Golden MS99 University of Utah Department of Mathematics A Multi-Time-Scale Analysis of Stochastic Chemi- [email protected] cal Reaction Network We consider stochastic descriptions of reaction networks MS98 in which there are both fast and slow reactions, and the time scales are widely separated. We obtain a reduced Review of Network Methods for Study of Singular equation on a slow time scale by applying a state space Phenomena in Heterogeneous Media decomposition method to the full governing equation and This talk will provide a comprehensive overview of discrete describe our reduction method on the reaction simplex. We network approximation techniques that have been demon- illustrate the numerical accuracy of the approximation by strated to be an elegant and powerful approach for deriving simulating several motivating examples. and justifying asymptotic formulas for (1) eﬀective properties, (2) electric ﬁeld, and (3) Dirichlet to Neumann map of Xingye Kan high contrast disordered composites with inhomogeneities University of Minnesota close to touching. [email protected]

Yuliya Gorb Department of Mathematics MS99 University of Houston Fokker-Planck Equations for Stochastic Dynamical [email protected] Systems with Symmetric L´evy Motions

The Fokker-Planck equations for stochastic dynamical sys- MS98 tems, with non-Gaussian α−stable symmetric L´evy mo- On Global Microchannel Conﬁgurations for Liquid- tions, have a nonlocal or fractional Laplacian term. Tak- Cooled Electronics Applications with Large Power ing advantage of the Toeplitz matrix structure of the time- Densities space discretization, a fast and accurate numerical algorithm is proposed to simulate the nonlocal Fokker-Planck We are interested in extending classical asymptotic ap- equations, under either absorbing or natural conditions. 102 AN14 Abstracts

The scheme is shown to satisfy a discrete maximum prin- sions with spectral deferred correction methods in order to ciple and to be convergent. It is validated against a known achieve high-order accuracy. exact solution and the numerical solutions obtained by using other methods. The numerical results for two proto- Bryan D. Quaife typical stochastic systems, the Ornstein-Uhlenbeck system Institute for Computational Engineering and Sciences and the double-well system are shown. University of Texas at Austin [email protected] Xiaofan Li Illinois Institute of Technology [email protected] MS100 Boundary Integral Methods for General Elliptic Problems MS99 DiPaola-Falsone Formula and Marcus Integral for Elliptic problems such as Poisson, Yukawa, Helmholtz, Stochastic Dynamical Systems under non-Gaussian Maxwell, Stokes and elasticity equations are converted to White Noise a consistent overdetermined first-order form. We derive simple well-conditioned integral equations for this form, DiPaola-Falsone formula is widely used in engineering and analyze their solvability in Sobolev spaces, and build fast science. The equivalence between DiPaola-Falsone formula high-order solution methods with Ewald summation and and Marcus integral was first proved by Sun, Duan and Li the nonuniform fast Fourier transform. ( arXiv:1202.2565 , Feb. 2012, the published final version appeared on Probabilistic Engineering Mechanics, Vol 32, John A. Strain pp:1-4, Jan. 2013). This talk further explores the rela- Department of Mathematics tionship between DiPaola-Falsone formula and Marcus in- University of California at Berkeley tegral to solve some challenging problems associated with [email protected] stochastic dyanamcial systems such as deriving Fokker- Planck equations and moment equations . MS100 Xu Sun Volume Integral Equation Approaches for Fast Huazhong University of Science and Technology Field Analysis in Inhomogeneous Media, with ap- [email protected] plications to MR Imaging and Induction Power Couplers

MS100 Volume integral methods are an appealing choice for com- Stable, Accurate, and Efficient Schemes for puting electromagnetic fields in inhomogeneous media, Parabolic Problems using the Method of Lines such as a human head or an induction power coupler. Transpose These methods generates second-kind integral equations, so matrix-implicit iterative methods should convergence We present a numerical scheme suitable for solving rapidly, though convergence is often slow in practice. In parabolic partial differential equations using the Method this talk we show that the observed slow convergence can of Lines Transpose (MOLT ), and dimensional splitting. As be an artifact of mismatching the material and basis func- a result, several one-dimensional boundary value problems tion boundaries, and resolve the mismatch to generate canbesolvedinO(N) work, to high precision; and a multi- a fast FFT-accelerated iterative method suitable for MR dimensional solution is formed by dimensional sweeps. We imaging field computation. We also show an approach ef- prove that the scheme converges to prescribed orders in fective for induction power couplers, where proper bound- both time and space, and is L-stable. We demonstrate our aries allow the use of a numerically computed Toeplitz- solver on the Allen-Cahn equation, and discuss. Hankel decomposition.

Matthew F. Causley Athanasios Polimeridis, Richard Zhang Michigan State University MIT [email protected] thanos [email protected], [email protected]

Andrew J. Christlieb Jacob White Michigan State Univerity Dept. of Elec. Eng. and Comp. Sci and Res. Lab. Elec. Department of Mathematics MIT [email protected] [email protected]

MS100 MS101 Spectral Deferred Correction Methods for Vesicle Computing Singular and Nearly Singular Integrals Suspensions We will describe recent progress with J. Wilson and W. Many ﬂuid structure interaction problems have changing Ying in computing a singular or nearly singular integral, characteristic time scales throughout a simulation. For such as a harmonic function given by a single or double such problems, an adaptive high-order time integrator is layer potential on a smooth, closed curve surface in 3D. The important. Adaptive time stepping methods often require present approach is suited for use with moving interfaces forming multiple numerical solutions to estimate the lo- since the representation of the interface is simple and the cal truncation error. However, for vesicle suspensions, by value of the integral can be found at nearby points as well taking advantage of the underlying physics, we are able to as on the surface. The value of the integral is found using estimate the local truncation error with a single numerical a standard quadrature, with the singularity replaced by a solution. I will also show how we couple vesicle suspen- regularized version. Correction terms are then added for AN14 Abstracts 103

the errors due to regularization and discretization. They [email protected] are needed at points near the surface, since the integrals are nearly singular. Surface integrals can be computed in overlapping coordinate grids; however, in recent work, MS101 we improve this method and make it more practical. We use a technique of J. Wilson for surface integration which A Kernel-Free Boundary Integral Method for Mov- allows accurate representation without explicit reference to ing Interface and Free Boundary Problems the coordinate charts. For efficient summation, we use a treecode developed by Duan and Krasny for the Gaussian The kernel-free boundary integral method is a Cartesian regularization of the fundamental solution of Laplacian. grid-based boundary integral method for elliptic partial differential equations. The method avoids direct evalua- J. Thomas Beale tion of boundary integrals and does not need to know an Duke University analytical expression for kernels of boundary integrals or [email protected] the fundamental solution of the associated elliptic partial differential equation. To evaluate a boundary integral, the kernel-free boundary integral method first solves an equiv- Wenjun Ying alent interface problem on a Cartesian grid and then inter- Department of Mathematics and Institute of Natural polates the grid solution to get values of the corresponding Sciences boundary integral at discretization points of the boundary Shanghai Jiao Tong University or interface of the problem. The method is efficient as well [email protected] as accurate. Numerical experiments for some moving interface and free boundary problems such as the Hele-Shaw flow will be presented in this talk. MS101 An Interface Problem for Biomolecules Wenjun Ying Department of Mathematics and Institute of Natural A biomolecule placed in solvent can be viewed as gener- Sciences ating an interface separating the biomolecule and vacuum Shanghai Jiao Tong University from the surrounding solvent. The size and configuration of [email protected] this interface plays an important role in biomolecule functions such as protein folding and docking. We develop the setup and algorithms to capture such interfaces, using a MS102 variational framework and gradient descent flow for en- Elastic Structure Coupled with the Air/water In- ergy minimization; the level-set method to handle interfa- terface, Inspired by Diving Birds cial motion and topological changes; and a new finite difference compact stencil approach to compute electrostatic We investigate how a soft elastic body responds to water- contributions. entry impact analogous to a bird diving into water to catch prey. Experimentally, dumbbell shaped objects made of Li-Tien Cheng two acrylic spheres connected by an elastic rod are dropped University of California, San Diego into water. A buckling threshold was calculated using a Department of Mathematics linear Euler beam theory, which is expressed in terms of [email protected] body geometry, impact force, and elastic rod stiffness. This threshold may have implication as to how birds are able to Bo Li safely dive into water at high speeds and avoid any neck- Department of Mathematics, UC San Diego injury. [email protected] Sunghwan Jung Engineering Science and Mechanics MS101 Virginia Tech [email protected] An Overlapping Patch Boundary Integral Method for Dynamic Interface Problems MS102 A nonstiff boundary integral method for 3D interfacial flow with surface tension or elastic membrane stress is pre- Simulations of Pulsating Sessile Coral and the Re- sented. The stiffness is removed by developing a small-scale sulting Fluid Flow decomposition, based on a generalized isothermal parameterization of the interface. New applications of the method Soft coral of the family Xeniidae have a pulsating motion, to water waves and hydroelastic waves will be discussed. a behavior not observed in other immobile marine organ- We will also present preliminary work on a new version of isms. These pulsations consume a large amount of energy, the method which uses domain decomposition or overlap- and determining the benefits of this behavior is vital to un- ping coordinate patches to describe the interface. This is derstanding the evolution of such animals. We will present necessary to treat problems for which generalized isother- direct numerical simulations of the pulsations of the coral mal coordinates do not provide a global parameterization. and the resulting fluid flow by solving the Navier-Stokes It also provides a framework for significant spatial adaptiv- equations coupled with the immersed boundary method to ity of the method. This is joint work with David Ambrose model individual and interacting polyps. and Carlo Fazioli. Shilpa Khatri Michael Siegel Department of Mathematics New Jersey Institute of Technology University of North Carolina at Chapel Hill 104 AN14 Abstracts

[email protected] the wave propagation. The imaging functions are designed to visualize the location of the point scatterers and the shape of the extended obstacle scatterers. MS102 Performance of Vortex-Based Propulsion on a Kai Huang Jellyfish-Like Swimmer Department of Mathematics Florida International University This study develops a computational approach to inves- khuang@fiu.edu tigate the vortex wakes generated by an axisymmetric jellyfish-like swimmer. The parameter space of swimmer Peijun Li body kinematics is explored. The effects of these parame- Department of Mathematics ters on thrust, input power and circulation are quantified. Purdue University Two metrics, cruising speed and energy cost of locomo- [email protected] tion, are used to evaluate the propulsion performance. The knowledge from this study can be used for the design of Hongkai Zhao robotic swimmers that use vortex rings for propulsion. University of California, Irvine Department of Mathematics Jifeng Peng [email protected] Department of Mechanical Engineering University of Alaska [email protected] MS103 Fast Solver for Multi-Particle Scattering in a Lay- MS102 ered Medium Simulation of a 3D Viscous Flow Past a Deformable This talk is devoted to the scattering of multi-particle in Thin-Walled Circular Disk Tethered at Its Center a layered medium. Assume the medium has three layers by An IB Method and a large number of dielectric particles are randomly distributed and well separated in the middle layer. The Motived by animal locomotion in a fluid, we model and size of each particle is comparable to the wavelength and simulate the interaction of a viscous incompressible flow the shape of each particle is the same up to a rotation past a deformable circular thin-walled disk tethered at its but not restricted to be a disk. The field is excited by center. The thin-walled structure is modelled by a classic some external source. Direct evaluation for the scattered approach (shell as an assembly of plate elements) and a field is notoriously slow due to the large number of un- special finite element method (the corotational scheme) is knowns. We propose a method based on the combination used to solve numerically the partial differential equations of Sommerfeld integral, scattering matrix and fast multiple (PDE) governing the motion of the thin-walled structure. method(FMM), which can dramatically speed up the cal- The flow is modelled by the classic viscous incompress- culation. Numerical experiments will be shown to confirm ible Navier-Stokes equations and are solved numerically by the efficiency. This is a joint work with Leslie Greengard a popular lattice Boltzmann model (D3Q19). The inter- and Motoki Kobayashi. action between the structure and flow is handled by the immersed boundary (IB) method. Our simulations have Jun Lai identified three distinct deformation modes of the thin Courant Institute of Mathematical Science disk: circular, folding, and triple-petalled, depending on [email protected] the parameters of the flow and the structure. Our results are in very good agreement with laboratory experiments published very recently (L Schouveiler and C Eloy, Flow- MS103 induced drapping, Phys Rev Lett 111: 064301, 2013). The Factorization Method for a Cavity in An In- homogeneous Medium RuNan Hua Univ of Science and Technology of China We consider the inverse scattering problem for a cavity [email protected] that is bounded by a penetrable anisotropic inhomogeneous medium of compact support and seek to determine Xiyun Lu the shape of the cavity from internal measurements on a Univ of Science and Technology of China curve or surface inside the cavity. We derive a factorization PR China method which provides a rigorous characterization of the [email protected] support of the cavity in terms of the range of an operator which is computable from the measured data. The support Luoding Zhu of the cavity is determined without any a-priori knowledge Indiana Univ-Purdue Univ Indianapolis of the properties of the surrounding anisotropic medium. [email protected] Numerical examples are given showing the viability of our method.

MS103 Shixu Meng University of Delaware Multiple Scattering Using the Generalized Foldy- [email protected] Lax Formulation

Consider the scattering of a time-harmonic plane wave inci- Houssem Haddar dent on a two-scale heterogeneous medium, which consists CMAP, Ecole Polytechnique of scatterers that are much smaller than the wavelength [email protected] and extended scatterers that are comparable to the wavelength. This talk will present the computational study for Fioralba Cakoni AN14 Abstracts 105

University of Delaware complex data manipulation tasks, and large, and often dis- [email protected] tributed software stacks. The research paper, in its current text form, is only able to summarize the associated data and computation and not able to reproduce it computa- MS103 tionally. While papers corroborate descriptions through in- Surface Plasmon Enhancement in Nano Dielectric direct means, such as by building companion websites that Layer share data and software packages, these external websites continue to remain disconnected from the content within We consider the experiments done by Brian Cullum and his the paper, making it difficult to verify claims and repro- group at UMBC of multilayer silver film over nanostructure duce results. There is a critical need for systems that min- substrates that provide much greater surface-enhanced Ra- imize this disconnect. We describe Science Object Linking man scattering signal compared to single layer of silver with and Embedding (SOLE), a framework for creating verifi- the same thickness as multilayer. We are going to discuss able publications by linking them with associated science the multilayer and nano gap effects mathematically in an objects, such as source code, datasets, annotations, work- experimental related set up and compare the results with flows, re-playable packages, and virtual machine images. that of the experiments. SOLE provides a suite of tools that assist the authors to create and host science objects that can then be linked with Yannan Shen research papers for the purpose of assessment, repeatabil- University of Minnesota ity, and verification of research. The framework also cre- [email protected] ates a linkable representation of the science object with the publication and manages a bibliography-like specification of science objects. In this presentation, we will introduce MS104 SOLE through examples from climate science, chemistry, Improving Computing Skills of STEM Graduates biology, and computer science, and describe its use for aug- menting the content of computation-based scientific publi- Computing skills are today a requirement for any STEM cations. graduate, yet we still have not found a way to embed computing throughout the curriculum in engineering and math- Tanu Malik ematics. Many students only experience an ”introduction Computation Institute to programming” class in their freshman year, and then we University of Chicago expect them to teach themselves whatever they might need [email protected] to succeed in other courses, and in their careers. It’s no wonder that so many scientist and engineers don’t use best practices for scientific computing, including good software design and development, reproducibility, testing and ensur- MS104 ing the permanence of the scientific evidence they create. A What Is Worth Reproducing in Computational Sci- few trends are taking hold that have potential to improve ence? this situation. Efforts like Software Carpentry (Mozilla Foundation) are spreading best practices in software creation and curation: version control, testing, automation, What is driving the call for reproducible science? The provenance, sharing. Less commonly, some schools are re- sentiment is that the archival literature should have a re- vising their approach to computing in the curriculum. We producible basis and computational science is particularly are conducting a pilot study using just-in-time online mod- ephemeral due to the ever-changing landscape of compu- ules that teach context-based computing for engineers. The tation. Simultaneously, we see an explosion of papers that context-based approach has already demonstrated its effec- exceeds the ability of scientists to keep up with. Should we tiveness, e.g., in the media computing course introduced at add to this tsunami of data with reproducibility? Perhaps Georgia Tech some years back (which not only improved reproducibility will stem the tide and make the literature student success, but also reduced the gender achievement more compact and valuable. gap in computing). We are extending this approach with the just-in-time delivery of skills, as a ”performance sup- William J. Rider port” device. In this talk, we will present our theory of ac- Sandia National Laboratory tion for this educational intervention, the design concepts, [email protected] and the preliminary data from our evaluation.

Lorena A. Barba Department of Mechanical Engineering MS104 Boston University Constructing Guaranteed Automatic Numerical [email protected] Algorithms for Univariate Integration

MS104 The project establishes an automatic, adaptive algorithm for solving univariate integration problems using trape- Towards Veriﬁable Publications zoidal rule. The algorithm provides rigorous guarantees Research papers provide the primary mechanism for shar- of success and computational cost. The key idea is that ing novel methods and data. Papers describe experiments the error analysis should be done for cones of input func- involving small amount of data, derivations on that data, tions rather than balls. Theoretical and numerical results and associated methods and algorithms. Readers repro- are provided. duce the results by repeating physical experiments, performing hand calculations, and setting forth logical argu- Yizhi Zhang ments. The scientiﬁc method in this decade has become de- Department of Applied Mathematics cisively computational, involving large quantities of data, Illinois Institute of Technology 106 AN14 Abstracts

[email protected] tion for Groundwater Contaminant Transport

The movement of contaminant plumes in underground MS105 aquifers is highly dependent on many hydrogeological parameters. It is often prohibitively expensive or impossible A Practical Guide to Measure-Theoretic Inversion: to make accurate and reliable measurements of these pa- Algorithms and Error Estimation rameters in the field. We utilize a measure-theoretic inverse framework to perform uncertainty quantification and esti- We describe the practical elements of a measure-theoretic mation for these parameters. Forward problem calculations framework for solving stochastic inverse problems for de- of quantities of interest are improved using a posteriori er- terministic models with uncertain parameters. Theoretical ror estimates calculated by solving adjoint problems. results on the existence and uniqueness of solutions are presented that outline a basic computational algorithm for Steven Mattis approximation of solutions. We extend the algorithm for University of Texas at Austin estimating solutions in high dimensional parameter spaces [email protected] and explore an a posteriori error analysis on computed probabilities of events. Clint Dawson Institute for Computational Engineering and Sciences Troy Butler University of Texas at Austin University of Colorado Denver [email protected] [email protected] Troy Butler Don Estep, Simon Tavener Colorado State University Colorado State University [email protected] [email protected], [email protected] Donald Estep Department of Statistics MS105 Colorado State University Spatially Heterogeneous Parameter Estimation [email protected] Within the Advanced Circulation (ADCIRC) Model MS105 We describe a framework for estimating spatially heteroge- Advanced Coastal/Subsurface Models and a neous paramters critical to the accuracy of model forecasts Measure-Theoretic Uq Framework Using Real of storm surge. We use pixelated land cover data to de- Data termine the spatial distribtion of land cover classifications which we consider certain. We estimate the Manning’s n In this talk we’ll focus on advanced models for near shore (a bottom friction paramter) value associated with these flows and multiphase flows in the subsurface. In partic- land cover classifications. We solve an inverse problem for ular, the focus will be on identifying the computational these values using a measure-theoretic approach applied to issues that need to be addressed in estimating parameters the ADCIRC storm surge model. especially in highly heterogeneous materials in the case of subsurface flows. We will also describe methods of dealing Lindley Graham with real data to quantify uncertainties. University of Austin at Texas Institute for Computational Engineering and Sciences Nishant Panda (ICES) University of Texas at Austin [email protected] Colorado State University ¡[email protected] Troy Butler University of Colorado Denver MS106 [email protected] Novelty, Convention and Scientific Impact

Clint Dawson Analyzing all 17 million papers in the Web of Science Institute for Computational Engineering and Sciences database, we employ a methodology based on journal pair- University of Texas at Austin ings that characterizes each paper by the convention and [email protected] novelty of the prior work combined. We measure the relative conventionality and novelty of the prior work that a Donald Estep paper combines by examining the journals referenced. Colorado State University [email protected] or [email protected] Satyam Mukherjee Kellogg School of Management Joannes Westerink Northwestern Institute on Complex Systems Department of Civil Engineering and Geological Sciences satyam,[email protected] University of Notre Dame [email protected] MS106 Modeling the Dynamics of Vector-Host Interaction MS105 of Easter Equine Encephalitis Uncertainty Quantiﬁcation and Parameter Estima- Eastern equine encephalitis (EEE) virus is a highly AN14 Abstracts 107

pathogenic mosquito-borne infectious disease that is re- astrocytomas (LGAs). GSVD of LGA patient-matched sponsible for outbreaks in humans and equines, resulting in profiles uncovers molecular similarities and differences be- high mortality or severe neurological impairment in most tween glioblastoma and LGA that suggest drug targets. survivors. In the northeastern United States, EEE virus is maintained in an enzootic cycle involving the mosquito, Katherine A. Aiello Culiseta melanura, and perching birds in freshwater swamp Sci Comp & Imaging (SCI) Inst & Dept of Bioeng habitats. Utilizing the SIR model, we examine the influ- University of Utah ence of the different bird species and time of year in the [email protected] spread and survival of EEE. Orly Alter Timothy Muller Sci Comp & Imaging (SCI) Inst, Bioeng & Human Department of Mathematics Genetics Depts Oregon State University University of Utah [email protected] [email protected]

MS106 MS108 Controllability Of Infections In Models Exhibiting Multiple Endemic Equilibria Network-Based Methods for Understanding Dis- ease and Predicting Therapy In mathematical infectious disease epidemiology, reducing R0 to slightly below 1 is sufficient to control the infection Cellular processes are driven by complex interacting net- under consideration. This is true only if the model doesnt works comprised of diverse cellular components. Although show the existence of endemic equilibria for R0 < 1. How- we have seen a revolution in our ability to generate multi- ever, some models of infections exhibits backward bifurca- omic data, our ability to use these data to infer information or even hysteresis. In this case reducing R0 to below tive cellular networks has lagged. We will present data- 1 is necessary but not sufficient to eliminate the infection. driven methods that incorporate knowledge about poten- We show a family of models showing hysteresis and find the tial network structure that capture essential network fea- conditions on model parameters assuring the elimination of tures, leading to clinically-relevant insight into disease pro- the infection. cesses. Muntaser Safan Kimberly Glass, John Quackenbush Department of Mathematics, Faculty of Science, Dana-Farber Cancer Institute Mansoura Univ Harvard School of Public Health Mathematical Computational and Modeling Sciences [email protected], [email protected] Center, ASU [email protected] MS108 Variant Prioritization by Genomic Data Fusion MS106 Modeling the Transmission Dynamics of H7N9 Exome sequencing has revolutionized the discovery of mu- Avian Influenza Outbreak: Poultry Markets tations causing rare monogenic disorders. However, sequencing identifies many candidate mutations and we need The outbreak of H7N9 avian influenza in humans in Asia better methods to prioritize variants for validation. Our during 2013 and 2014 underlines the need for better un- methodology for genomic data fusion uses machine learn- derstanding of the mechanisms by which avian influenza ing to integrate multiple strategies to detect deleteriousness spreads among bird flocks in live markets. Here we employ of mutations. Our key innovation is the incorporation of a and susceptible, exposed, infected, recovered (SEIR) model computational method for gene prioritization, which scores and fit the parameters of the model to low-pathogenic avian mutated genes based on their similarity to known disease influenza prevalence data collected in in Hong Kong live genes. bird markets between 1999 to 2005. In conjunction with climate data from the Hong Kong observatory, we exam- Yves Moreau ine the dependence of model parameters on temperature, K.U. Leuven, Dept. of Electrical Engineering ESAT-SCD relative humidity, and absolute humidity. [email protected] Sherry Towers Mathematical and Computational Modeling Sciences MS108 Center, ASU [email protected] Discovery of Multidimensional Modules in Cancer Genomic Data

MS108 Recent technology has made it possible to simultaneously Comparison and Integration of Genomic Profiles perform multi-platform genomic profiling of biological sam- Predict Brain Cancer Survival and Drug Targets ples, resulting in so-called multidimensional genomic data. Such data provide unique opportunities to study the coor- Recently, we demonstrated the effectiveness of the GSVD dination between regulatory mechanisms on multiple lev- in comparing patient-matched genomic profiles and identi- els. However, integrative analysis of multidimensional ge- fying a pattern of DNA copy-number aberrations that cor- nomics data for the discovery of combinatorial patterns is relates with glioblastoma survival. Here, we show cross- currently lacking. Here, we develop a series of methods to platform validation of this signature, bringing it a step address this challenge. We applied this method to data closer to the clinic. Surprisingly, we also find that the prog- from The Cancer Genome Atlas, and prove its utilities in nostic value of the signature is maintained for lower-grade identifying subtly perturbed cancer pathways and distin- 108 AN14 Abstracts

guishing patients with diﬀerent survival time. to Ice Sheet Models

Xianghong J. Zhou Modeling the dynamics of polar ice sheets is critical for Biological Science and Computer Science projections of future sea level rise. Yet, there remain large University of Southern California uncertainties in the basal boundary conditions employed [email protected] within ice sheet models, which rely on the incompressible Stokes equations with shear thinning rheology to describe the behavior of ice sheets. We address the problem of quan- MS109 tifying uncertainties in the inference of basal boundary con- The Role of Numerical Boundary Procedures in the ditions for large-scale ice sheet inverse problems within the Stability of Perfectly Matched Layers framework of Bayesian inference.

We address the temporal energy growth associated with Noemi Petra numerical approximations of the perfectly matched layer Institute for Computational Engineering and Sciences (PML) for Maxwell’s equations in first order form. In (ICES) the literature, several studies have shown that a numer- The University of Texas at Austin ical method which is stable in the absence of the PML can [email protected] become unstable when the PML is introduced. We demonstrate in this talk that this instability can be directly re- Tobin Isaac, Georg Stadler lated to numerical treatment of boundary conditions in the University of Texas at Austin PML. At the continuous level, we establish the stability of [email protected], [email protected] the constant coefficient initial boundary value problem for the PML. To enable the construction of stable numerical Omar Ghattas boundary procedures, we derive energy estimates for the The University of Texas at Austin variable coefficient PML. Numerical experiments verify the [email protected] theoretical results

Kenneth Duru MS110 Department of Geophysics, Stanford University, Stanford CA Bio-inspired Wing Design for Flying Micro Robots Stanford University [email protected] Low Reynolds number aerodynamics is of great importance for the optimization of Micro Air Vehicles (MAV). A possibility to improve the flight performance of MAVs is to take MS109 inspiration from efficient flyers and swimmers in nature. Studies have shown that the scales on the wing of a but- A Fast Algorithm for 3D Azimuthally Anisotropic terfly as well as the ribs present on the dermal denticles of Velocity Scan sharkscanhaveapositiveeffectonthefluiddynamicper- formance, using different principles of flow boundary layer Conventional velocity scan can be computationally expen- control which increase the lift to drag ratio. In this talk, I sive for large-size seismic data, particularly when the pres- will present different fabrication methods for mimicking the ence of anisotropy requires multiparameter scanning. We scales on the wings of butterflies as well as the ribs present introduce a fast algorithm for 3D azimuthally anisotropic on the skin of sharks. Furthermore, I will present recent velocity scan by generalizing the previously proposed 2D work on high-performance butterfly-inspired wing shapes butterfly algorithm for hyperbolic Radon transform. To that can be used for MAVs and I will outline how optimized compute semblance in a two-parameter residual move- wing designs in robotics can give insights to questions in out domain, the numerical complexity of our algorithm is evolutionary biology. roughly O(N 3 log N)asopposedtoO(N 5)ofthestraight- forward velocity scan, with N being the representative of Mirko Kovac the number of points in either dimension of data space Faculty of Engineering, Department of Aeronautics or parameter space. Synthetic and field-data examples Imperial College London demonstrate the superior efficiency of the proposed algo- [email protected] rithm.

Jingwei Hu MS110 The University of Texas at Austin [email protected] Sharks and Butterflies: Micro-Sized Scales Have Macro Effects Sergey Fomel Sharks and butterflies swim and fly in two completely dif- University of Texas at Austin ferent flow regimes, yet the structure of their surfaces inter- [email protected] acting with the surrounding fluid look amazingly similar. Both are not smooth but have unique microgeometries that Lexing Ying potentially work to control the flow. Sharks have move- Stanford University able scales that appear to act as a passive, flow-actuated Department of Mathematics dynamic roughness for separation control. Alternatively, [email protected] butterfly scales appear to fundamentally alter the local skin friction drag depending on flow orientation.

MS109 Amy Lang Uncertainty Quantiﬁcation for Large-Scale Aerospace Engineering and Mechanics Bayesian Inverse Problems with Application University of Alabama AN14 Abstracts 109

[email protected] Ren-Cang Li University of Texas - Arlington [email protected] MS110 Friction Enhancement in Snake Locomotion MS111 Snakes are one of the worlds most versatile organisms, High-Performance Algorithms for Computing at ease slithering through rubble or climbing vertical tree Pseudospectra trunks. In this study, we elucidate the physics of snake interactions with its complex environment. We present a series of experiments and supporting mathematical models While numerous authors investigated parallel schemes for demonstrating how snakes optimize their speed and effi- computing pseudospectra over the past two decades, no ciency by adjusting their frictional properties as a function technique has yet emerged as a massively-parallel black- of position and time. We use this discovery to build two box replacement for Liu’s algorithm, which uses the shifted snake-robots with enhanced climbing capabilities. Schur factor to drive inverse iteration. This talk proposes and evaluates two classes of distributed-memory algorithms Hamidreza Marvi which interleave many Lanczos processes in order to greatly Carnegie Mellon University increase efficiency relative to traditional schemes: (1) Schur Robotics Institute and Department of Mechanical decomposition followed by simultaneous shifted triangu- Engineering lar solves, and (2) reduction to Hessenberg form followed [email protected] by simultaneous shifted Hessenberg solves. While the underlying high-performance computational kernels of these two inverse iteration procedures were proposed nearly two Jeffrey Streator, David Hu decades ago by Henry in the context of control theory, they Georgia Institute of Technology seem to be underappreciated by the pseudospectra commu- jeff[email protected], [email protected] nity.

MS110 Jack Poulson Georgia Institute of Technology Bioinspired Transformative Skins: From Funda- [email protected] mental Physics to Applications

As human beings age, our skins develop wrinkles and folds Greg Henry an undesirable feature that has fueled a multi-billion-dollar Intel Corporation skin care industry. Conversely, many animals such as [email protected] cephalopods can reversibly create skin patterns to match surrounding textures for active camouflage. This talk will present a unified model that can predict various modes MS111 of instabilities and patterns on skins. We will then dis- An Indefinite Variant of LOBPCG for Definite Ma- cuss novel transformative applications of surface instabil- trix Pencils ities such as tunable superhydrophobicity and on-demand stem-cell alignment by seeking bioinspirations. We propose a novel preconditioned solver for generalized Hermitian eigenvalue problems. More specifically, we ad- Xuanhe Zhao dress the case of a definite matrix pencil A − λB (i.e., A, Department of Mechanical Engineering & Materials B are Hermitian and there is a shift λ0 such that A − λ0B Science is definite). Our new method is a variant of the popular Duke University LOBPCG method operating in an indefinite inner product. [email protected] It also turns out to be a generalization of the recently proposed LOBP4DCG method for solving product eigenvalue MS111 problems. A Nonlinear QR Algorithm for Unstructurally Meiyue Shao Banded Nonlinear Eigenvalue Problems MATHICSE EPF Lausanne A variation of Kublanovskaya’s method for solving nonlin- meiyue.shao@epfl.ch ear eigenvalue problems will be presented for the case of unstructurally banded problems. The new method is iterative and specifically designed for problems too large to use dense linear algebra techniques. A new data structure will MS111 also be presented for storing the matrices to keep memory Preconditioned Locally Minimal Residual Methods and computational costs low. In addition, an algorithm for Large-Scale Eigenproblems will be presented for computing several nearby eigenvalues to already computed eigenvalues. We study the preconditioned locally minimal residual method (PLMR) for computing invariant pairs of non- Charles K. Garrett linear eigenproblems of the form T (λ)v =0.PLMRis Oak Ridge National Laboratory a newly-developed preconditioned eigensolver which does [email protected] not require the computation of shift-invert matrix vector products. It bears close connections to several well-known Zhaojun Bai algorithms, including LOPCG, Jacobi-Davidson and the Departments of Computer Science and Mathematics inverse-free preconditioned Krylov subspace method. Nu- University of California, Davis merical experiments show the flexibility and competitive- [email protected] ness of PLMR on large-scale benchmark nonlinear eigen- 110 AN14 Abstracts

problems. Michael Miksis Department of Engineering Science and Applied Fei Xue Mathematics Louisiana State University Northwestern University [email protected] [email protected]

MS112 MS112 Multiscale 3D Simulation of Whole Blood in Com- Extensional Dynamics of Vesicles: Asymmetric plex Geometry Rayleigh-Plateau, Burst, and Pearling A 3D multiscale immersed-boundary method is developed to simultaneously simulate major hemodynamics processes When deformable vesicles with an aspect ratio of at least in whole blood flowing in microvascular network. The 3.5 are subject to extensional flow, they undergo an elon- whole blood is represented as a suspension of red blood gational transition above a critical capillary number. We cells, white blood cells and platelets. The dynamics of each complete 3D boundary integral simulations and develop a cell is resolved using a front-tracking method. The vascu- multipole expansion spectral theory for vesicles with aspect lar network in 3D is modeled directly using a ghost-node ratios up to 10. We demonstrate that the critical conditions immersed-boundary method. The method simulates inter- can be predicted quantitatively. Moreover, a second burst action among blood cells, platelet adhesion, WBC rolling transition at higher Capillary number which is a prelude adhesion, and dispersion of drug-carriers in vascular net- to pearling is demonstrated. work. Eric S. Shaqfeh Prosenjit Bagchi, Koohyar Vahidkhah, Peter Balogh, Professor, Chemical Engineering & Mechanical Daniel Cordasco Engineering Rutgers University Stanford University, Stanford, CA [email protected], [email protected], pete- [email protected] [email protected], [email protected] MS113 MS112 A Difference Equations Approach to Studying Os- Simulation of Cellular Blood Flow in Microvessels cillations in a Suspension Bridge involving a Non- linear Cable Function The cellular character of blood leads to complex flow phe- nomenology in vessels of comparable size to the blood cells. In their 2000 paper ’Multiple Periodic Solutions to a We have designed a fast spectral boundary integral algo- Suspension Bridge Ordinary Differential Equation’, P. J. rithm that simultaneously solves for the dynamics of the McKenna and K. S. Moore studied oscillations in a suspen- highly deformable blood cells and their flow in such con- sion bridge by analyzing periodic solutions to the system figurations. The talk will include an outline this method of nonlinear ordinary differential equations and discussion of two applications: the transport of magnetic nanoparticles amongst the flow blood cells the flow 6K of red-blood cells through a model spleenic slit. θ = − cos θ sin θ − δ1 θ + f(t) m Jonathan B. Freund (3) 2K UIUC y = − y − δ2 y + g [email protected] m

where δ1, δ2 are damping constants, K, m are positive pa- MS112 rameters, g is the force due to gravity and f(t)isanexter- Long-Wave Dynamics of An Inextensible Plannar nal force at time t. They used Leray-Schauder Degree The- Membrane in An Electric Field ory along with numerical methods like the Runge-Kutta Method to do so. In this talk, I will analyze the periodic We investigate the long-wave nonlinear dynamics of an in- solutions of (1) using a slightly newer more nontraditional extensible capacitive elastic membrane under ac and dc method. More specifically, I will introduce a nonlinear ca- electric fields. In the lubrication framework we derive a ble function c(t)inthey-equation in (1), discretize the nonlinear evolution equation for the membrane height with resulting system into a system of two coupled second-order an integral constraint. Different membrane dynamics, such second-degree difference equations and then perform a lo- as undulation and flip-flop are found at different electric cal and global stability analysis of this new system using field strengths and membrane area. In particular an alter- the mathematical theory of difference equations. One of nating wave on the membrane is found as a response to an the biggest challenges of this study will be setting up the ac field in the perpendicular direction. global analysis framework for general second-order second- degree difference equations along the way since this topic Yuan-Nan Young is still largely an open research area. However if success- Department of Mathematical Sciences ful, this study will provide a way to analyze the local and NJIT global dynamics of periodic solutions of (1) for entire re- [email protected] gions of initial conditions and parameter values as opposed to a limited number of initial conditions and parameter Shravan Veerapaneni values as is generally possible using numerical methods. Department of Mathematics University of Michigan Sukanya Basu [email protected] Wentworth Institute of Technology AN14 Abstracts 111

[email protected] Electrolyte Media

In this talk, computation of the electrostatic potential aris- MS113 ing from the hybrid solvation model for ion channels will be From Billiard Dynamics to Thermodynamics discussed. The Poisson-Boltzmann (P-B) equation is considered. In order to model the cell membrane where the We develop a stochastic approach to thermodynamics usion channel is located, the layered media Green’s function ing a model of gas-surface interactions derived from a ran- of the P-B equation is used to develop a boundary integral domized version of billiard dynamical systems. We first equation for a finite hight hollow cylinder. Two fictitious recover some classical results from the kinetic theory of half spheres are attached top and bottom of the cylinder gases, specifically Knudsen’s Law for angle of reflection. to avoid edge singularities. Then, a body-fitted mesh is We then derive diffusion constants for particles moving in used to discretize the boundary of the cylinder. Several a channel with rough walls. Finally, we develop notions of numerical examples will be presented. temperature, heat flow, and entropy production, leading to Min Hyung Cho models of simple machines. Department of Mathematics Scott Cook Dartmouth College Swarthmore College [email protected] [email protected] MS114 Tim Chumley Life after Sweeping: Hopping for the Helmholtz Iowa State University Equation [email protected] The high-frequency 3D Helmholtz equation in a heteroge- Renato Feres neous medium is a difficult question in numerical analysis. Washington University in St. Louis Direct solvers are either unwieldy to set up for the prob- [email protected] lem as a whole, or are hard to link up in a domain decomposition framework. In this work we consider an upwind, incomplete form of Green’s identity as a high-quality trans- MS113 mission boundary condition, and use it to define polarized Predictor-Based Tracking for Neuromuscular Elec- waves at interfaces between subdomains. This approach is trical Stimulation attractive when local Green’s functions are precomputed, and a fast algorithm is available for their application: we Neuromuscular electrical stimulation is a technology that obtain an algorithm with complexity sublinear in the num- helps restore functionality to human limbs. We study neu- ber of unknowns normally needed to represent the solution romuscular electrical stimulation of the human knee, by in the volume. The new method can be seen as a gener- providing a tracking controller such that the tracking error alization of the sweeping preconditioner of Engquist-Ying globally asymptotically converges to zero, under any input to larger subdomains. Joint work with Leonardo Zepeda- delay, a state constraint on the knee position, and sampled Nunez. state measurements. We use a new method for constructing predictors. This work is joint with Iasson Karafyllis, Laurent Demanet Marcio de Queiroz, Miroslav Krstic, and Ruzhou Yang. Mathematics, MIT [email protected] Michael Malisoff Department of Mathematics Louisiana State University MS114 malisoff@math.lsu.edu A Robust Maxwell Solver in Axisymmetric Geome- tries

MS113 Several integral equations used for electromagnetic scattering problems suffer from instabilities at low frequencies. Solving Linear Differential Equations and Inverting Some instabilities occur from purely numerical consider- Matrices: Key Formulas ations, others from non-trivial topology of the scatterer. In this talk, we review an integral equation formulation In preparing a new textbook on Differential Equations and based on generalized Debye sources which addresses both Linear Algebra, one function and one formula took a cen- of these forms of low-frequency breakdown. We will present tral place: the solution g(t) with driving function δ(t)= a high-order solver based on this formulation for axisym- impulse response = Green’s function = fundamental solu- metric geometries, both for perfect conductor and dielectric tion. When the driving function is f(t), the solution is the problems. integral of g(t − s)f(s). The talk will connect the different ways to find this growth factor g(t). Separately we call at- −1 Michael O’Neil tentiontoanamazingexpressionforA when that matrix Courant Institute is tridiagonal. New York University [email protected] Gilbert Strang MIT [email protected] MS114 Scalable Quasi-direct Solvers for 3D Elliptic Prob- lems MS114 Boundary Integral Equation for an Ion Channel in While scalable distributed-memory techniques have re- 112 AN14 Abstracts

cently been proposed for the approximate factorization of bearing the normal jump of Maxwell stress on the inter- HSS/H 2/H-matrices deﬁned through a “weak” admissi- face. A series of numerical tests with diﬀerent permittivity bility condition, no scalable HSS/H2/H-matrix factoriza- and conductivity ratios are performed and compared with tion strategy is known which can handle the “strong” ad- the results obtained by the small deformation theory. missibility condition needed to represent Green’s functions of 3D elliptic problems. This talk evaluates two direc- Ming-Chih Lai tions for circumventing this problem: (1) an approximate NCTU, Taiwan Newton-Schulz iteration based upon a new parallelization Department of Applied Math of H-matrix/H-matrix multiplication and (2) the recently [email protected] introduced Hierarchical Interpolative Factorization.

Jack Poulson MS115 Institute for Computational Engineering and Sciences Electro-Hydrodynamics of Vesicle Suspensions The University of Texas at Austin [email protected] We investigate the mechanics of inextensible capacitive elastic membranes in applied electric fields. A new bound- Austin Benson ary integral formulation for the coupled electric and hydro- UC Berkeley dynamic governing equations will be presented. The mem- [email protected] brane evolution is characterized by a competition between elastic energy, inextensibility, non-local hydrodynamic interaction, electric potential and the a.c. field field fre- Kenneth L. Ho quency. We will discuss new insights gained via numerical Department of Mathematics simulations. Stanford University [email protected] Shravan Veerapaneni Department of Mathematics Yingzhou Li University of Michigan Stanford [email protected] [email protected]

Lexing Ying MS115 Stanford University Recent Developments of Grid Based Particle Department of Mathematics Method [email protected] Grid based particle method (GBPM) is a meshless point method for moving interface problems. GBPM has a par- MS115 ticle method nature which can capture a moving interface accurately and eﬃciently. At the same time these meshless A Treecode-Accelerated Boundary Integral particles carry both Lagrangian and Eulerian information Poisson-Boltzmann Solver for Solvated Proteins simultaneously with the help of a underlying grid which We present a treecode-accelerated boundary integral allows one to handle diﬀerent kind of topological changes (TABI) solver for electrostatics of solvated proteins de- easily. Also adaptivity can be incorporated into GBPM scribed by the linear Poisson-Boltzmann equation. The naturally. In this presentation, I will talk about some re- integral equations are discretized by centroid collocation. cent developments in GBPM and using it to model various The linear system is solved by GMRES and the matrix- moving interface problems. vector product is carried out by a treecode. We compute Hongkai Zhao the electrostatic solvation energy for a protein. We com- University of California, Irvine pare TABI results with those obtained using the grid-based Department of Mathematics APBS code and we present parallel TABI simulations. [email protected] Robert Krasny University of Michigan MS116 Department of Mathematics [email protected] Ten Good Reasons for using Kernel Reconstruc- tions in Adaptive Finite Volume Particle Methods

Weihua Geng This talk discusses the utility of meshfree kernel techniques Southern Methodist University in adaptive finite volume particle methods (FVPM). To [email protected] this end, we give ten good reasons in favour of using kernel- based reconstructions in the recovery step of FVPM, where our discussion addresses relevant computational aspects MS115 concerning numerical stability and accuracy, as well as A Hybrid Immersed Boundary and Immersed In- more specific points concerning efficient implementation. terface Method for Two-Phase Electrohydrody- Special emphasis is finally placed on more recent advances namic Simulations in the construction of adaptive FVPM, where WENO reconstructions by polyharmonic spline kernels are used in In this talk, we introduce a hybrid immersed boundary combination with ADER flux evaluations to obtain high (IB) and immersed interface method (IIM) to simulate the order methods for hyperbolic problems. dynamics of a drop under the influence of electric field in Navier-Stokes flows. Instead of applying the volume elec- Armin Iske tric force arising from the Maxwell stress tensor, we al- University of Hamburg ternatively treat the electric effect as an interfacial force Department of Mathematics AN14 Abstracts 113

[email protected] [email protected]

MS116 MS117 Denoising Simultaneously Structured Signals Model Selections for Polynomial Kernel Regres- sions Models or signals exhibiting low dimensional behavior (e.g., sparse signals, low rank matrices) arise in many applica- Polynomial kernel regression is one of the most commonly tions in signal processing and machine learning. We focus used methods in numerical analysis and statistics. How- on models that have multiple structures simultaneously; ever, in dealing with many real world problems, choosing e.g., matrices that are both low rank and sparse, arising in the right degree of a polynomial kernel is a challenging phase retrieval, quadratic compressed sensing, and cluster issue, as poor choices often lead to either “under-ﬁtting” detection in social networks. We consider the estimation of or “over-ﬁtting”. We propose and study criteria and new such models from direct observations corrupted by additive strategies especially designed for this purpose. We provide Gaussian noise. Our main result is to provide tight upper both theoretical analysis and numerical simulations to il- and lower bounds on the mean squared error (MSE) of a lustrate the performance of the new strategies. convex denoising program that uses a combination of regularizers to induce multiple structures. In the case of low rank and sparse matrices, we quantify the gap between the Xingping Sun MSE of the convex program and the best achievable error, Missouri State University and also compare it with a simple nonconvex thresholding [email protected] algorithm in a certain regime of signal-to-noise ratio.

Maryam Fazel MS116 University of Washington Electrical Engineering Multiscale Rbf Interpolation and Collocation [email protected]

The combination of compactly supported radial basis func- Samet Oymak tions with a residual correction scheme has proven to be nu- California Institute of Technology merically extremely efficient and accurate for solving both [email protected] scattered data interpolation and collocation problems. In this talk I will give a short survey of what is known so Amin Jalali far and address recent developments particularly when it University of Washington comes to solving partial differential equations. For exam- [email protected] ple, I will address adaptivity, boundary conditions and scaling. Babak Hassibi Electrical Eng. Dept Holger Wendland Caltech, Pasadena, CA Univ. Goettingen [email protected] Germany [email protected] MS117 Frontiers of Atomic Norm Minimization MS117 We often model signals from the physical world with Conjugate Gradient Iterative Hard Thesholding continuous parameterizations. Unfortunately, continuous models pose problems for the tools of sparse approxima- Conjugate Gradient Iterative Hard Thresholding is a tion, and popular discrete approximations are fraught with greedy algorithm for solving the compressed sensing and theoretical and algorithmic issues. In this talk, I will matrix completion problems combining the advantages propose a general, convex-optimization framework—called of the low per iteration complexity of Normalized Itera- atomic-norm minimization—-that obviates discretization tive Hard Thresholding and the effectiveness of projection and gridding by generalizing sparse approximation to con- based algorithms such as Hard Thresholding Pursuit and tinuous dictionaries. I will discuss recent theoretical and Compressive Sampling Matching Pursuit. This talk will algorithmic advances that demonstrate the utility of this also introduce the compressed sensing and matrix comple- framework in a diverse set of applications. tion problems as examples of low dimensional models. Ben Recht UC Berkeley Jeffrey D. Blanchard [email protected] Department of Mathematics and Statistics Grinnell College jeff@math.grinnell.edu MS117 Modal Analysis with Compressive Measurements Jared Tanner University of Oxford We consider the problem of determining the mode shapes [email protected] of a structure from a compressed collection of vibrational time series recordings, as might be collected by a network Ke Wei of wireless sensor nodes performing Compressive Sensing Mathematics Institute (CS). We consider three different CS strategies, analyze a University of Oxford simple SVD-based method for estimating the mode shapes 114 AN14 Abstracts

from compressive samples without performing CS recon- act, approximate, and heuristic solution methodologies are struction, and provide novel finite sample reconstruction proposed. Encouraging computational results including bounds. This work has potential applications in structural phased array antenna simulations are reported. health monitoring. Serdar Karademir Jae Young Park University of Florida EECS Department karademir@ufl.edu University of Michigan [email protected] Oleg A. Prokopyev University of Pittsburgh MichaelB.Wakin [email protected] Dept. of Electrical Engineering and Computer Science Colorado School of Mines [email protected] MS119 Accelerated Bregman Operator Splitting with Anna Gilbert Variable Stepsizes Department of Mathematics University of Michigan In this talk, we present a novel scheme, namely accel- [email protected] erated Bregman operator splitting with variable stepsize (ABOSVS), for solving problems of the type min{1/2||Au− 2 f||2 + φ(Bu)},whereφ may possibly be nonsmooth. Our MS118 proposed algorithm incorporates a multi-step acceleration Universe Geometry scheme into BOSVS to improve the convergence rate. ABOSVS is compared with other state-of-art algorithms This brief history will elucidate the role of supercomput- by using partially parallel magnetic image reconstruction. ers in enhancing progress in mathematics. Moving through The numerical results show that the proposed ABOSVS al- the exciting history of supercomputing, we will broach the gorithm performs more efficiently in terms of image quality top supercomputers of its time and its important applica- and CPU time. tions. This will be followed by a stimulating story about a supercomputer simulation that has proven the validity of Xianqi Li, Yunmei Chen a theory that was proposed 40 years ago for the evolution Department of Mathematics of the universe. University of Florida xianqili@ufl.edu, yun@ufl.edu Samar A. Aseeri Computational Scientist at the KAUST Supercomputing Yuyuan Ouyang Laboratory Department of Mathematics, University of Florida [email protected] ouyang@ufl.edu

MS118 MS119 Understanding the Universe with Petascale Simu- lations - the Enzo Cosmology Code Accelerated First-Order Method for Convex Com- posite Optimization and the Applications in Image Abstract not available at time of publication. Analysis Brian O’Shea We present an accelerated scheme for solving a class of con- Department of Physics and Astronomy vex composite optimization problems and its application in Michigan State University image analysis. The proposed AL-ADMM method, namely [email protected] accelerating linearized alternating direction method of multipliers, has accelerated rate of convergence in terms of its dependence on Lipschitz constant of the smooth com- MS118 ponent. A backtracking technique for searching Lipschitz Talk title: Creating a Virtual Universe constant is also proposed for practical performance. Abstract not available at time of publication. Yuyuan Ouyang Department of Mathematics, University of Florida Mark Vogelsberger ouyang@ufl.edu MIT address:[email protected] Yunmei Chen Department of Mathematics MS119 University of Florida yun@ufl.edu Irregular Polyomino Tiling via Integer Program- ming with Application in Phased Array Antenna Design Guanghui Lan Department of Industrial and Systems A polyomino is a generalization of the domino and is cre- University of Florida ated by connecting a fixed number of unit squares along [email protected]fl.edu edges. Tiling a region with a given set of polyominoes is a hard combinatorial optimization problem. This work Eduardo Pasiliao Jr. is motivated by a recent application of irregular poly- AFRL Munitions Directorate, Air Force Research omino tilings in the design of phased array antennas. Ex- Laboratory AN14 Abstracts 115

[email protected] disease-free equilibrium is found to be globally stable under certain conditions when R0 < 1. When R0 > 1, existence of an endemic equilibrium is proved (with uniqueness MS119 for the ODE case and local stability under stricter condi- Image Reconstruction for Dynamic Cone Beam tions) and uniform persistence of the disease is established. Computed Tomography The inclusion of reduction in susceptibility of vaccinated birds, reduction in infectiousness of asymptomatically in- Dynamic cone beam computed tomography (CBCT) has fected birds and vaccine waning can have important im- been developed to provide respiratory phase correlated plications for disease control. We analytically and numer- imaging in image guided therapy. The difficulty of acqui- ically demonstrate that vaccination can paradoxically in- sition of dynamic CBCT images is due to the fact that crease the total number of infected, resulting in the “silent multiple phase binning of CBCT scans leading to insuffi- spread’ of the disease. We also study the effects of vac- cient number of projections available for image reconstruc- cine efficacy on disease prevalence and the minimum criti- tion. By making use of the redundant information shared cal vaccination coverage, a threshold value for vaccination by constituent scans, we proposed a computational model coverage to avoid an increase in total disease prevalence to reconstruct dynamic CBCT images with relatively high due to asymptomatic infection. spatial resolution as well as utilizing the temporal coherence. Hayriye Gulbudak, Maia Martcheva University of Florida Hao Zhang hgulbudak@ufl.edu, maia@ufl.edu Department of Mathematics hza39@ufl.edu MS120 Yunmei Chen Modeling Avian Influenza and Implications for Department of Mathematics Control University of Florida yun@ufl.edu A mathematical model of avian influenza which involves human influenza is introduced to better understand the complex epidemiology of avian influenza. The model is MS120 used to rank the efficacy of the current control measures. Qualitative Assessment of the Role of Climate We find that culling without re-population and vaccination Change on Malaria Transmission Dynamics are the two most efficient control measures. Control measures applied to humans, such as wearing protective gear, A new model for assessing the impact of climate change on are not very efficient. Furthermore, we find that should malaria transmission dynamics is developed. The disease- a pandemic strain emerge, it will invade, possibly displac- free periodic solution of the resulting non-autonomous de- ing the human influenza virus in circulation at that time. terministic model is shown to be locally-asymptotically sta- Moreover, higher prevalence levels of human influenza will ble when the associated basic reproduction ratio is less than obstruct the invasion capabilities of the pandemic H5N1 unity. The disease persists in the community when the re- strain. This effect is not very pronounced, as we find that production ratio is greater than unity. The effect of un- 1% increase in human influenza prevalence will decrease the certainties of the estimates of the parameter values used in invasion capabilities of the pandemic strain with 0.006%. the numerical simulations of the model is analyzed. Nu- merical simulations of the model suggest that disease bur- Maia Martcheva den increases with increasing temperature (as measured in University of Florida terms of the cumulative number of new cases and malaria- maia@ufl.edu induced mortality) in the community. Furthermore, simulations of the autonomous version of the model suggest that MS120 personal protection measures (against mosquito bites) are marginally more effective than mosquito-reduction mea- Evaluation of Malaria Vaccines as a Control Strat- sures. As expected, the universal anti-malaria strategy egy in a Region with Naturally Acquired Immunity (which combines both mosquito-reduction and personal protection strategies) is the most effective means to combat The malaria vaccine RTS,S has reached the final stages of the spread of malaria in the population. vaccine trials, demonstrating an efficacy of roughly 50% in children. Regions with high prevalence tend to have Folashade Agusto high levels of naturally acquired immunity (NAI) to severe Austin Peay State University malaria. I will introduce a model developed to address [email protected] concerns about how these vaccines will perform in regions with existing NAI, discuss some analytic results and their public health implications, and reframe our question as an MS120 optimal control problem. A Structured Avian Influenza Model with Imper- Olivia Prosper fect Vaccination University of Florida We introduce a model of avian influenza in domestic birds [email protected] with imperfect vaccination and age-since-vaccination structure. The model has four components: susceptible birds, Nick Ruktanonchai vaccinated birds (stratified by vaccination-age), asymp- University of Florida tomatically infected birds, and infected birds. The model Department of Biology includes reduction of probability of infection, decreasing [email protected] severity of disease of vaccinated birds and vaccine waning. The basic reproduction number, R0,iscalculated.The Maia Martcheva 116 AN14 Abstracts

University of Florida [email protected] maia@uﬂ.edu

MS122 MS121 Fluid-Structure Interaction Decoupling by Opti- Undergraduate Modeling Curricula mization Simulating fluid-structure interactions is challenging due Abstract not available at time of publication. to the tight coupling between the fluid and solid substructures. An approach is presented that allows the problem Jeff Humpherys to be decoupled by reformulating it in an optimal control Department of Mathematics setting. A control is introduced to minimize the jump in ve- Brigham Young University locity and stress on the interface. An analytical framework jeff[email protected] is developed to show the well-posedness of the optimality system for the time dependent case.

MS121 Paul A. Kuberry Modeling in the Early Grades Clemson University [email protected] Abstract not available at time of publication. Hyesuk Lee Rachel Levy Clemson University Harvey Mudd College Dep. of Mathematical Sciences [email protected] [email protected]

MS121 MS122 Numerical Approximation of Non-Newtonian Fluid Mathematical Modeling in High School - Structure Interaction Problems

Abstract not available at time of publication. Fluid-structure interaction (FSI) problems governed by non-Newtonian fluid models are considered. For viscoelas- Katherine Socha tic and quasi-Newtonian fluid models variational formula- Math for America tions of the coupled FIS systems are developed based on [email protected] the Arbitrary Lagrangian-Eulerian (ALE) method. Stabil- ity of the time discretized systems and finite element error estimates are discussed, and numerical results will be pre- MS121 sented. SIAM-NSF Modeling across the Curriculum initia- Hyesuk Lee tive and Workshops: Introduction Clemson University Dep. of Mathematical Sciences Abstract not available at time of publication. [email protected] Peter R. Turner Clarkson University Shuhan Xu School of Arts & Sciences Clemson Univeristy [email protected] [email protected]

MS122 MS122 Greenland Ice-sheet Initialization: Optimal Con- Reduced Order Modeling of the Quasi-Geostrophic trol and Bayesian Calibration Approaches Equations Greenland ice sheet plays a significant role in climatology This talk surveys some recent developments in the mod- and, in particular, in sea-level rise. In order to simulate eling, analysis and numerical simulation of the quasi- the evolution of the ice sheets we need to know the current geostrophic equations, which describe the wind-driven thermomechanical state of the system. In this talk, we large scale ocean circulation. A new large eddy simula- seek an initial state for the Greenland ice sheet via the tion model, which is based on approximate deconvolution, estimation of the basal sliding coefficient and the bedrock is proposed for the numerical simulation of the one-layer topography. We consider both a deterministic approach and two-layer quasi-geostrophic equations. A reduced or- (PDE constrained optimization) and a Bayesian calibration der model based on the proper orthogonal decomposition is approach. also proposed as an accurate and computationally efficient tool for the numerical simulation of the quasi-geostrophic MichaelS.Eldred equations. The error analysis for the finite element dis- Sandia National Laboratories cretization and the numerical investigation of the new mod- Optimization and Uncertainty Quantification Dept. els are also presented. [email protected]

Traian Iliescu John D. Jakeman Department of Mathematics Sandia National Labs Virginia Tech [email protected] AN14 Abstracts 117

Irina Kalashnikova [email protected] Sandia National Laboratories [email protected] MS123 Mauro Perego Pattern Discovery and Cancer Gene Identiﬁcation CSRI Sandia National Laboratories in Integrated Cancer Genomic Data [email protected] We propose a latent variable approach for joint clustering of discrete and continuous variables that arise from inte- Stephen Price grated genomic, epigenomic, and transcriptomic proﬁling Los Alamos National Laboratory in large-scale genome characterization studies. A penalized [email protected] likelihood approach is implemented for variable selection. We show application of the method to The Cancer Genome Andrew Salinger Atlas (TCGA) pan-cancer cohort with whole-exome DNA CSRI sequencing, SNP 6.0 array, and mRNA sequencing data in Sandia National Labs 3,000 patient samples spanning 12 cancer types. [email protected] Ronglai Shen Georg Stadler Department of Epidemiology & Biostatistics University of Texas at Austin Memorial Sloan-Kettering Cancer Center [email protected] [email protected]

MS123 MS123 Optimal Shrinkage of Singular Values Breaking the Curse of Dimensionality Using De- compositions of Incomplete Tensors It is common practice in multivariate statistical analysis to reduce dimensionality by performing SVD or PCA, and The number of elements in higher-order tensors scales ex- keeping only r singular values. For white noise and ap- ponentially in the number of dimensions as do the compu- propriate asymptotic frameworks, random matrix theory tation and memory costs. Because of this, working with describes the random behavior of the singular values and very large full tensors becomes infeasible. To alleviate or vectors of Y. It delivers simple, convincing answers to a break this curse of dimensionality, tensor decompositions range of fundamental questions, such as the location of the can be used instead. We discuss such decompositions and optimal singular value threshold and the shape of the op- structure-exploiting, compressed sensing-type algorithms timal singular value shrinker. to compute these decompositions of large tensors while using only a small fraction of known elements. Matan Gavish Department of Statistics Nico Vervliet, Otto Debals Stanford University Department of Electrical Engineering (ESAT) [email protected] KU Leuven [email protected], [email protected] David L. Donoho Stanford University Department of Statistics Laurent Sorber, Lieven De Lathauwer [email protected] Katholieke Universiteit Leuven [email protected], [email protected] MS123 Tensor GSVD for Comparison of Two Column- MS124 Matched and Row-Independent Large-Scale Biomedical Datasets Div First-Order System LL* for Elliptic Systems The first-order system LL* (FOSLL*) approach was in- There exists a fundamental need for frameworks that can 2 simultaneously compare and contrast large-scale data ten- troduced in order to retain the full efficiency of the L sors, e.g., biomedical datasets recording multiple aspects norm first-order system least-squares (FOSLS) approach of a disease across a set of patients. We describe a novel while exhibiting the generality of the inverse-norm FOSLS exact and unique simultaneous decomposition for two ten- approach. In this talk, we will present the div FOSLL* sors that generalizes the GSVD to a tensor GSVD. We approach to the Stokes and linear elasticity equations and show that tensor GSVD comparisons of two ovarian cancer the a priori and a posteriori error estimations. patient- and platform-matched genomic datasets from The Zhiqiang Cai Cancer Genome Atlas predict survival and drug targets. Purdue University Department of Mathematics Theodore E. Schomay, Preethi Sankaranarayanan [email protected] Sci Comp & Imaging (SCI) Inst & Dept of Bioeng University of Utah [email protected], [email protected] MS124 What Kinds of Singularities can we Deduce from Orly Alter the Corner Singularity Theory of the Compressible Sci Comp & Imaging (SCI) Inst, Bioeng & Human Viscous Stokes Flows? Genetics Depts University of Utah Based on some known corner singularity and regularity re- 118 AN14 Abstracts

sults for the compressible viscous Stokes equations, I will [email protected] describe certain singularities of solutions in the domain, for instance, interior layer, jump discontinuities of the density solution across the streamline emanating from the non- MS125 convex vertex or grazing vertex. Recent Progress in MatCont Development

Jae Ryong Kweon MatCont is an interactive MATLAB software for numeri- POSTECH(Pohang University of Science and Technology) cal analysis of ODEs in Rn. It allows to simulate ODEs, Korea continue equlibria and cycles in one parameter, and study [email protected] bifurcations of equilibria, cycles, and homoclinic orbits in two-parameter ODEs. Recent features of MatCont will be presented, including normal form computations for codim MS124 2 bifurcations of cycles and initialization of homoclinic or- Compact Implicit Integration Factor Method for bits. Decisions made during the development and future High Order Diﬀerential Equations of the software will be discussed.

When developing efficient numerical methods for solving Iourii Kouznetsov parabolic types of equations, severe temporal stability con- Department of Mathematics, Utrecht University straints on the time step are often required due to the high- The Netherlands order spatial derivatives and/or stiff reactions. The im- [email protected] plicit integration factor (IIF) method, which treats spatial derivative terms explicitly and reaction terms implicitly, can provide excellent stability properties in time with nice MS125 accuracy. One major challenge for the IIF is the storage Numerical Analysis of Travelling Waves in Neural and calculation of the dense exponentials of the sparse dis- Fields cretization matrices resulted from the linear differential operators. The compact representation of the IIF (cIIF) can We consider waves in integro-differential systems modelling overcome this shortcoming and greatly save computational neural activity. For special cases of spatial coupling a suit- cost and storage. On the other hand, the cIIF is often able ODE can be derived whose solutions correspond to hard to be directly applied to deal with problems involving patterns of the original system. We exploit the numerical cross derivatives. In this talk, by treating the discretiza- toolbox MATCONT to construct a complete bifurcation tion matrices in diagonalized forms, we present an efficient diagram for smooth nonlinearities. For more general, but cIIF method for solving a family of semilinear fourth-order translationally invariant connectivity including transmis- parabolic equations, in which the bi-Laplace operator is ex- sion delays, we propose novel numerical schemes to com- plicitly handled and the computational cost and storage re- pute travelling waves and discuss its implementation. main the same as to the classic cIIF for second-order problems. In particular, the proposed method can deal with not Hil Meijer only stiff nonlinear reaction terms but also various types of Twente University, NL homogeneous or inhomogeneous boundary conditions. Nu- [email protected] merical experiments are finally presented to demonstrate effectiveness and accuracy of the proposed method. MS125 Xingfeng Liu (Parallel) Auto and Applications: Past, Present University of South Carolina and Future xfl[email protected] We show how the numerical continuation package AUTO- 07p can effectively run in parallel using MPI on modern MS124 HPC clusters, and explain its algorithms. Much larger An Asymptotic Splitting Approximation for Highly problems can now be continued than was reasonably pos- Accurate Numerical Solutions of Differential Equa- sible in the past. Combining with the method of continua- tions tion of orbit segments we can investigate how certain ODE and PDE solutions suddenly change as parameters cross This talk explores applications of the asymptotic splitting critical values. Several examples illustrate this technique. method for approximating highly oscillatory solutions of Lastly, possible future directions for AUTO are given. the systems of paraxial Helmholtz equations. An eikonal transformation is introduced for oscillation-free platforms Bart E. Oldeman and matrix operator decompositions. It is found that the CLUMEQ (McGill, ETS) sequential, parallel and combined exponential splitting for- [email protected] mulas possess not only anticipated algorithmic simplicity and efficiency, but also the accuracy and asymptotic stability required for highly oscillatory wave computations via MS125 systems of partial differential equations. Analysis of Nonsmooth Systems: Perspectives and Directions Qin Sheng Department of Mathematics The realisation that many real-world systems possess nons- Baylor University mooth characteristics has opened up a plethora of different Qin [email protected] directions for the analysis of such systems. In this presentation I will give a background to nonsmooth systems, de- Hai-Wei Sun scribe a few of the analysis techniques employed, and also Department of Mathematics discuss where the field is heading. Open problems that will University of Macau keep the dynamical systems community busy for years to AN14 Abstracts 119

come will be highlighted through a couple of examples. spectra exhibit exotic properties that are more challenging to analyze than periodic or random potentials; often these Petri T. Piiroinen spectra are Cantor sets. Quasiperiodic potentials can be School of Mathematics, Statistics and Applied approximated by periodic potentials, whose spectrum can Mathematics be computed by solving ﬁnite dimensional eigenvalue prob- National University of Ireland, Galway lems. Accurate estimates require long periods. We show [email protected] how to compute such approximations quickly and address the need for high accuracy.

MS126 Mark Embree,CharlesPuelz A Locally Accelerated Block Preconditioned Steep- Department of Computational and Applied Mathematics est Descent Method for Ill-conditioned Generalized Rice University Hermitian Eigenvalue Problems [email protected], [email protected]

In this talk, we first present a locally accelerated block preconditioned steepest descent (LABPSD) algorithm for solv- MS126 ing ill-conditioned generalized Hermitian eigenvalue prob- Eigenvalue Problems in Electron Excitation lems, such as arising in orbital based ab initio methods for electronic structure calculations. We then revisit the classi- Single-electron excitation can be described by a nonlin- cal convergence analysis of steepest descent algorithms and ear eigenvalue known as Dyson’s equation in which the provide a new analysis to justify the efficiency of LABPSD. Hamiltonian operator is a function of an eigenvalue to be determined. We will describe the nonlinear structure of the eigenvalue problem and examine numerical methods Zhaojun Bai for solving this type of problem. Departments of Computer Science and Mathematics University of California, Davis Chao Yang [email protected] Lawrence Berkeley National Lab chao yang [email protected] Yunfeng Cai Peking University, P. R. China Fang Liu [email protected] Central Univerisity of Finance and Economics Peking, China John Pask cufe.fl[email protected] Lawrence Livemore National Lab [email protected] Lin Lin Lawrence Berkeley Lab N. Sukumar [email protected] University of California, Davis [email protected] Alexander Kemper Lawrence Berkeley National Lab Berkeley, CA MS126 [email protected] Structured Eigensolvers for the Analysis of Symmetry-Breaking in Next Generation Gyro- scopes MS127 Rheology of Sickle Cell Anemia: Effects of Hetero- In 1890, G. H. Bryan demonstrated that when a ring- geneous RBC Shapes ing wine glass rotates, the shape of the vibration pattern precesses. This effect is the basis for a family of high- Sickle cell anemia (SCA) is a a highly complex, inherited precision gyroscopes. Mathematically, the precession can blood disorder exhibiting heterogeneous cell morphology be described in terms of a symmetry-breaking perturbation and abnormal rheology. To better understand the rela- due to gyroscopic effects of a geometrically degenerate pair tionship between rheological behavior and cell morpholog- of vibration modes. Unfortunately, current attempts to ical characteristics of blood in SCA, we present a multi- miniaturize these gyroscope designs are subject to fabrica- scale sickle red blood cell (SS-RBC) model, accounting for tion imperfections that also break the device symmetry. In diversity in both cell shape and rigidity. The proposed this talk, we describe the structure of the eigenvalue prob- model provides a systematical approach to quantify the lems that arise in simulation of both ideal and imperfect rheological behavior and hemodynamics of SS-RBC sus- geometries, and show how to use this structure in accurate pensions. We quantify the heterogeneous shear viscosity of and efficient simulations. SS-RBC suspensions with different cell morphologies, i.e., the SS-RBC suspensions with granular shapes are the most David Bindel, Erdal Yilmaz viscous; while the shear viscosity of SS-RBC suspensions Cornell University containing elongated cells show a dramatic decrease. In [email protected], [email protected] combination with the experimental data of SS-RBCs from patients treated with and without hydroxyurea, we also predict the shear viscosity of SS-RBC suspensions under MS126 different conditions. These findings lead to useful insights Fast Spectral Computations for Quasiperiodic into the abnormal rheological behavior of blood in SCA. Schroedinger Operators Xuejin Li Discrete Schrödinger operators with quasiperiodic poten- Brown University tials arise as mathematical models of quasicrystals. Their xuejin [email protected] 120 AN14 Abstracts

Huan Lei layer to develop a fast and accurate ‘hybrid’ or multiscale Paciﬁc Northwest National Laboratory numerical method. The method incorporates an asymp- [email protected] totic analysis of the electric potential and ﬂuid dynamics in the Debye layer into a boundary integral numerical so- E Du, Ming Dao lution of the full moving boundary problem. Massachusetts Institute of Technology [email protected], [email protected] Michael Siegel New Jersey Institute of Technology [email protected] George E. Karniadakis Brown University Division of Applied Mathematics MS128 george [email protected] Integral Equations on Domains with Edges

We will discuss the discretization of integral equations on MS127 surfaces with edges and corner points. Although achieving Lipid Bilayer and Cytoskeletal Interactions in a high accuracy in this setting is not that difficult, there are Red Blood Cell a number of issues (such as the need for highly anisotropic meshes) which make the construction of efficient discretiza- We developed a two-component model of red blood cell tion procedures challenging. We will discuss our progress (RBC) membranes to study interactions between the lipid on addressing these issues. bilayer and the cytoskeleton for healthy and diseased RBCs. We modeled the bilayer and the cytoskeleton as James Bremer two distinct components and consider the normal elastic UC Davis interaction and tangential viscous friction between them. [email protected] We implemented this model using both a three-level multiscale continuum approach and Dissipative Particle Dynam- ics, and investigated RBC-related diseases such as malaria MS128 and sickle cell disease. Integral Equation Techniques for Solving Elliptic Problems with Mixed Boundary Conditions Zhangli Peng MIT This talk describes integral equation techniques for solving [email protected] elliptic problems with mixed boundary conditions (i.e. a portion of the obstacle has Dirichlet boundary conditions while the remainder has Neumann boundary conditions.) MS127 The proposed approach avoids using a hypersingular ker- Three-Dimensional Vesicle Electrohydrodynamics: nel as a result the system is better conditioned than exist- A Level Set Method ing integral equation based methods. For many problems, the discretized system is amenable linear scaling solvers. The electrohydrodynamics of three-dimensional vesicles is Numerical experiments illustrate the performance of the investigated using a combined Jet level set/continuum force solution technique. method. The electric field in the domain is obtained by an immersed interface method, for which the necessary jump Adrianna Gillman conditions have been developed. Numerical results match Dartmouth College well with the dynamics observed experimentally. A investi- Department of Mathematics gation of parameters influencing the vesicles dynamics will [email protected] also be presented.

David Salac MS128 University at Buffalo - SUNY Practical and Efficient Direct Solvers for BIEs davidsal@buffalo.edu The last several years have seen rapid progress on con- Mohammad Kolahdouz structing direct solvers for the dense linear systems arising University at Buffalo, SUNY upon discretization of BIEs. The goal is to build direct mkolahdo@buffalo.edu solvers with O(N p) complexity, where p is one, or close to one, and with high practical efficiency. This talk will describe techniques aimed at improving performance and MS127 simplifying coding by using randomized methods to accel- A Hybrid Numerical Method for Electro-Kinetic erate certain structured matrix computations. Flow with Deformable Membranes Gunnar Martinsson We consider two-phase flow of ionic fluids whose motion Univ. of Colorado at Boulder is driven by an imposed electric field. At a fluid-fluid in- [email protected] terface, a screening cloud of ions develops and forms an electro-chemical double layer or ‘Debye layer’. The applied electric field acts on the ionic cloud it induces, result- MS128 ing in a strong slip flow near the interface. This is known Updating Techniques for Hierarchical Factoriza- as ‘induced-charge electro-kinetic flow’, and is an impor- tions tant phenomenon in microfluidic applications and in the manipulation of biological cells. We address a significant Many fast direct algorithms for solving linear systems aris- challenge in the numerical computation of such flows in ing from discretized partial differential equations or bound- the thin-double-layer limit, by using the slenderness of the ary integral equations rely on a hierarchical tree decompo- AN14 Abstracts 121

sition of the domain, e.g., methods based on nested dis- the form of defects – such as vacancies, grain boundaries, section for PDEs or recursive skeletonization for integral and dislocations – and controlling, or at least predicting, equations. In this talk we will show that, given a factor- the formation and evolution of such imperfections is a ma- ization corresponding to a given problem, we can update jor challenge. The phase field crystal (PFC) methodology the factorization to solve problems related by local changes has emerged as a important, increasingly-preferred mod- such as localized modification of the PDE coefficients or eling framework for investigating materials with atomic- perturbation of the problem geometry. In cases where the scale structures on diffusive time scales. In essence, the computational cost per tree node is the same across all fast atomic vibrational time-scale phenomena are averaged nodes, updating is both asymptotically and practically less out, but the atomic spatial resolution is preserved. In this expensive than re-doing the complete factorization. talk, I describe some efficient, stable, and convergent numerical methods for some PFC and PFC-type equations, a Victor Minden family of highly nonlinear hyperbolic-parabolic PDE and Stanford integro-PDE. I will also discuss a new PFC framework for [email protected] multi-spatial-scale modeling based on the recent method of amplitude expansions.

MS129 Steven M. Wise Diﬀusion-Limited Growth and Decay of 2D Epitax- Mathematics Department ial Nanoclusters: Atomistic and Coarse-Grained University of Tennessee Modeling [email protected]

Random deposition onto isotropic or anisotropic crystalline surfaces leads to diffusion-mediated formation of an en- MS129 semble of epitaxial 2D islands or nanoclusters. The pro- Continuum Framework for Dislocation Structure, cess might be described by stochastic fully atomistic-level Energy and Dynamics of Dislocation Arrays and models or by coarse-grained 2D continuum descriptions Low Angle Grain Boundaries of surface diffusion and aggregation. However, the latter must retain the stochastic aspects of nucleation, and We present a continuum framework for dislocation struc- an open challenge is to capture far-from equilibrium is- ture, energy and dynamics of dislocation arrays and low an- land growth shapes (as this requires precise treatment of gle grain boundaries which may be nonplanar and nonequi- non-equilibrium diffusion around island edges). After de- librium. In our continuum framework, we define a dislo- position, these island ensembles coarsen usually by Ost- cation density potential function on the dislocation array wald ripening. Again atomistic or continuum-level treat- surface or grain boundary to describe the orientation de- ment is possible, the latter being more common. How- pendent continuous distribution of dislocation in a very ever, recent experiments reveal shortcomings of standard simple and accurate way. The continuum formulations of continuum formulations for strongly anisotropic systems, a energy and dynamics include the long-range interaction of feature which we address. constituent dislocations, local line tension effect of dislocations and the cooperative motion of dislocations, which Jim W. Evans are derived from the discrete dislocation model. We also Ames Laboratory USDOE and Iowa State University present numerical simulations using this continuum model [email protected] including applications to dislocation structures of low angle grain boundaries and interfaces with misfitting spherical Yong Han inclusions. IOwa State University [email protected] Yang Xiang Hong Kong University of Science and Technology [email protected] MS129 Efficient Numerical Methods for Molecular Beam Xiaohong Zhu Epitaxial Growth Jinan University [email protected] This work is concerned with efficient numerical methods for the simulation of the dynamics of molecular beam epitaxial (MBE) growth. Numerical simulations of MBE mod- MS130 els require long time computations, and therefore large An Adaptive RBF-WENO Method for Hyperbolic time-stepping methods become necessary. In this work, Problems we present some unconditionally energy stable finite difference schemes for MBE models. We will also discuss on An adaptive RBF-WENO method is proposed. The RBF- some time adaptive strategies. WENO hybrid method is to use the radial basis function interpolation replacing the polynomial interpolation. We Zhonghua Qiao show that the locally adapted shape parameters can el- Applied Math Dept. evate the regular WENO order resulting better accuracy The Hong Kong Polytechnic University Hong Kong and convergence. Numerical examples are provided. [email protected] Jae-Hun Jung SUNY at Buffalo MS129 jaehun@buffalo.edu Stable and Convergent Numerical Schemes for Phase Field Crystal Models MS130 Crystalline materials have atomic-scale imperfections in Matrix-Valued Kernels Associated to Vector- 122 AN14 Abstracts

Valued Random Fields with Correlated Compo- the Sphere nents One approach for simulation of stationary random fields in We propose a class of nonseparable space-time compactly the Euclidean space is based on Matheron’s turning bands supported correlation functions, termed here quasi-tapers, methods. The idea behind this method is to relate positive to mean that such correlations can be dynamically com- definite radial functions in the Rd to corresponing ones on pactly supported over space or time. An important feature the circle using averaging. The explicit form of the turning of the quasi-taper is given by a spatial (temporal) compact bands operator turns out to be a special case of a well- support being a decreasing function of the temporal lag known recurrence relation for Bessel functions. Aiming at (spatial distance), so that the spatial (temporal) compact similar recurrences for zonal basis functions on the sphere, support becomes smaller when the temporal (spatial) de- we can use relations between Gegenbauer polynomials of pendence becomes weaker. We propose general classes as different parameters. Interestingly, there is a set of opera- well as some examples that generalize the Wendland tapers tors which can be used to derive analogous relations. We to the space-time setting. Then a non separable space-time will discuss some of these operators and their interrelations. taper with spatial and temporal compact support is obtained as tensor product of quasi-tapers. Our space-time taper includes all the known constructions as special cases Wolfgang zu Castell and will be shown to have great exibility. Covariance ta- Helmholtz Zentrum Muenchen, German Research Center pering is then explored as an alternative to maximum like- for Envir lihood when estimating the covariance model of a space- Ingolstaedter Landstrasse 1, 85764 Neuherberg, Germany time Gaussian random field in the case of large datasets. [email protected] The proposed quasi and space-time tapers allows to perform covariance tapering when dealing with data that are densely observed in time (space) but sparse in space (time) MS131 or densely observed both in time and space. The statistical and computational properties of the space-time covari- Tracking a Low-Dimensional Vector Via Quantized ance tapering is addressed under increasing domain asymp- Measurements Or Pairwise Comparisons totics. A simulation study and two real data examples k illustrate the statistical and computational performances Suppose that we wish to track a point xt ∈ R as its posi- of the covariance tapering with respect to the maximum tion changes in time. In this talk I will describe approaches likelihood method using the space-time tapers proposed. to this problem in two practical settings. First, I will consider the case where the observations consist of highly Emilio Porcu quantized linear measurements. Next I will describe the re- Institute for Mathematical Stochastics lated case where our data is given by pairwise comparisons k Georg-August-Universitaet, Goettingen, Germany between between xt and various points x1,...,xn ∈ R [email protected] with known position. I will describe practical algorithms for handling both cases. MS130 Mark Davenport Improved Exponential Convergence Rates for Reg- Georgia Institute of Technology ularized Approximation by Oversampling Near the [email protected] Boundary

We discuss convergence rates for kernel based approximation in smooth settings. Typical examples range from clas- MS131 sical function approximation to the approximate solution Intrinsic Volumes of Convex Cones: Theory and of partial differential equations. In smooth settings one Applications expects exponential convergence orders, but the numerical schemes are notoriously ill conditioned, which enforces some kind of regularization. Further, in smooth settings Spherical intrinsic volumes are fundamental statistics of one often observes boundary effects, i.e., the determinis- convex cones, and occupy a central role in integral geom- tic approximation rates for scattered data approximation etry. They also appear in various guises in statistics, con- are improved globally if the data sets are distributed more vex optimization, compressed sensing (polytope angles), densely near the boundary. In this talk, such boundary algebraic combinatorics, and differential geometry, among effects for regularized approximation schemes are analyzed other fields. In particular, they are the main ingredients by means of sampling inequalities for smooth functions. of the classical kinematic formulas, which describe the ex- The latter provide a bound on a continuous norm in terms act intersection probabilities of randomly oriented cones. of a discrete norm and an error term that tends to zero Combining the kinematic formula with another pillar of exponentially as the discrete data set becomes dense. We integral geometry, the spherical Steiner formula, and con- show that the exponential convergence rates are improved centration of measure arguments, gives rise to a complete by oversampling near the boundary. explanation of phase transition phenomena for general ran- This is partly based on joint works with Christian Rieger dom convex optimization problems. This talk surveys the (Bonn) and Robert Schaback (Göttingen). theory of intrinsic volumes, present methods of computation, and highlights connections to problems in statistics, Barbara Zwicknagl convex regularization, and to the theory of condition num- University of Bonn bers for convex optimization. Based on joint work with [email protected] Dennis Amelunxen, Mike McCoy and Joel Tropp

Martin Lotz MS130 School of Mathematics Recurrence Operators for Zonal Basis Functions on The University of Manchester AN14 Abstracts 123

[email protected] kinetics of the bio-molecule.

Hee Sun Lee, Surl-Hee Ahn MS131 Stanford University The Achievable Performance of Demixing [email protected], [email protected]

Demixing is the problem of disentangling multiple informative signals from a single observation. These problems ap- MS132 pear frequently in image processing, wireless communica- The Reduction of Molecular Dynamics Models Us- tions, machine learning, statistics, and other data-intensive ing Mori-Zwanzig Projection Formalism fields. Convex optimization provides a powerful framework for creating tractable demixing procedures that work right Molecular dynamics models find applications in many ar- out of the box. In this talk, we describe a geometric the- eas of applied sciences. One often needs to restrict the ory that precisely characterizes the performance of convex simulations to localized regions to minimize the computa- demixing methods under a generic model. This theory pre- tional cost. I will present the Mori-Zwanzig formalism as cisely identifies when demixing can succeed, and when it a systematic approach to coarse-grain molecular dynamics cannot, and further indicates that a sharp phase transi- models. In particular, I will discuss how to approximate tion between success and failure is a ubiquitous feature of the memory functions, and how to sample random noises. these programs. Our results admit an elegant interpre- As example, simulations of crack propagation, dislocation tation: Each signal has an intrinsic dimensionality, and dynamics, and protein dynamics will be presented. demixing can succeed if (and only if) the number of measurements exceeds the total dimensionality in the signal. Xiantao Li Joint work with Joel A. Tropp. Department of Mathematics MichaelB.McCoy,JoelA.Tropp Pennsylvania State University Caltech CMS [email protected] [email protected], [email protected] MS132 MS131 Stochastic Modeling Through the Mori-Zwanzig Adaptively Sensing in Compressive Sensing Appli- Formalism cations The Mori-Zwanzig formalism tells us that if we project a In this talk we will present new results in compressive sens- dynamical system onto a subset of its degrees of freedom, ing using adaptive sampling. Compressive sensing is a new the resulting process will generally exhibit memory effects. signal acquisition technology which reconstructs a high di- Unfortunately, the associated memory kernels, which are mensional signal from a small number of linear measure- needed for dimension reduction, are typically difficult to ments. In the typical setting, these measurements are de- obtain directly from the formalism itself. In this talk, we termined a priori. However, in some cases selecting these propose an empirical approach based on statistical estima- measurements adaptively can lead to improvements both tion and apply it to certain prototypical models of spa- in error and in the number of samples required. We discuss tiotemporal chaos. some fundamental limitations of this sampling scheme, as well as some new encouraging results which show compres- Alexander J. Chorin sive sensing can benefit from adaptivity. University of California, Berkeley Mathematics Department Deanna Needell [email protected] Department of Mathematics Claremont McKenna College Kevin K. Lin [email protected] Department of Mathematics University of Arizona MS132 [email protected] Building Meso-Scale Stochastic Models Using the Mori-Zwanzig Formalism MS132 We present a meso-scale model built from the Mori- MZ-PDF Methods for Stochastic Analysis in Non- Zwanzig (MZ) formalism. The meso-scale model is built linear Dynamical Systems with the projection operator that is applied on the discretized MZ equation in time. The projection operator is We propose a new framework for stochastic analysis in non- used to calculate the memory function with a simple re- linear dynamical systems based on goal-oriented probabil- currence without having to compute orthogonal dynamics, ity density function (PDF) methods. The key idea stems or esQL. Assuming that the memory function can be well- from techniques of irreversible statistical mechanics, and it approximated by exponentials, we can generate the cor- relies on deriving reduced-order PDF equations for quanti- responding fluctuation using Ornstein-Ulenbeck process. ties of interest, e.g., functionals of the solution to systems of Then we can obtain the generalized Langevin equation. stochastic ordinary and partial differential equations. The Our approach was validated by the simple heat bath model, proposed approach is useful to many disciplines as it leads in which the analytical solution is known. The Dissipative to new and more efficient computational algorithms. Particle Dynamics (DPD) system with one tagged particle was also used as a numerical test case. Finally, we apply Daniele Venturi our framework to generate the meso-scale model of alanine Division of Applied Mathematics dipeptide (in Φ and Ψ dihedral angle) to correctly predict Brown University 124 AN14 Abstracts

daniele [email protected] PTC is achievable.

Jessica M. Conway MS133 Los Alamos National Laboratory A Predator-prey-disease Model with Immune Re- [email protected] sponse in Infected-prey Alan S. Perelson This talk presents a predator-prey-disease model with im- Theoretical Biology and Biophysics mune response in the infected prey. The basic repro- LosAlamosNationalLab duction number of the within-host model will be defined n/a and it is found that there are three equilibria: extinc- tion equilibrium, infection-free equilibrium and infection- persistent equilibrium. The stabilities of these equilibria MS133 are completely determined by the reproduction number of Dyanamics of Low and High Pathogenic Avian In- the within-host model. Furthermore, a basic reproduction fluenza in Wild and Domestic Bird Populations number of the between-host model and two predator invasion numbers exists along with a predator invasion number An earlier infection with low pathogenic avian influenza in the absence of disease and predator invasion number (LPAI) provides a partial immunity towards infection with in the presence of disease. There also exists a predator high pathogenic avian influenza (HPAI). We consider a and infection-free equilibrium, infection-free equilibrium, time-since recovery structured model to study the dynam- predator-free equilibrium and a coexistence equilibrium. ics of LPAI and HPAI in wild and domestic bird popula- The local stabilities of these equilibria under certain con- tions. The system has a unique disease-free equilibrium ditions depending on the basic reproduction and invasion which is locally and globally stable when the reproduc- reproduction numbers shall be explained in this talk. Fi- tion number is less than one. There are unique LPAI-only nally the global stability of the predator-free equilibrium and HPAI-only equlibria, which are locally asymptotically will be explained in this talk. stable as long as the other pathogen can not invade the equilibrium. There exist a coexistence equilibirum when Souvik Bhattacharya the invasion number of both pathogens are greater than North Dakota State University one. We show that both pathogen can coexist in the form Visiting Assistant Professor of sustained oscillations. [email protected] Necibe Tuncer University of Tulsa MS133 [email protected] Modeling the Spread of Bacterial Infections in a Hospital with Environmental Contamination Maia Martcheva, Juan Torres University of Florida Nosocomial infections, i.e. hospital-acquired infections, maia@ufl.edu, gatorcha@ufl.edu have become a major concern for public health officials as the amount of antibiotic-resistant bacterial infections increases. One important mechanism for bacterial persis- MS134 tence is the ability of bacteria to contaminate hospital sur- Inverting for Maritime Environments Using Em- faces and survive in this environment for extended periods pirical Eigenfunction Bases from Radar Imagery of time. In this talk, I discuss a differential equation model of bacterial infections in a hospital with environmental con- Radar wave front arrival times and spatial energy depo- tamination. The basic reproduction number of the model sition, associated with propagation through a given ma- is proved to be a global threshold under certain conditions. rine atmospheric boundary layer, may be described using In addition, simulations of the deterministic model and a proper orthogonal modes, and subsequently represented as stochastic version of the model provide insight into an out- points on the compact Stiefel manifold. By exploiting the break of bacterial infections in a hospital. This is joint Riemannian structure of Stiefel, interpolation within the work with Glenn Webb. cloud of manifold points is possible when solving inverse problems aimed at uncovering in situ maritime conditions Cameron Browne affecting radar propagation on a given day. Vanderbilt University [email protected] Vasileios Fountoulakis, Christopher J. Earls Cornell University [email protected], [email protected] MS133 Model of Spontaneous HIV Infection Control Fol- lowing Cessation of Antiretroviral Therapy MS134 Optimal Filters for General-Form Tikhonov Regu- Reports suggest that HIV antiretroviral therapy initiated larization early may permit post-treatment control (PTC) of HIV (undetectable viral load) after treatment termination. We In this work, we use training data in an empirical Bayes hypothesize that early treatment induces PTC by restrict- risk framework to estimate optimal regularization parame- ing the latent reservoir size, allowing immune responses to ters for the general-form Tikhonov problem and the multi- control infection post-treatment. ODE model analysis re- parameter Tikhonov problem. We will show how estimates veals a range in immune response-strengths where a patient of the optimal regularization parameters can be efficiently may show viral rebound or PTC. In this bistable regime, obtained and present several numerical examples from sig- we predict a latent reservoir size threshold below which nal and image deconvolution to demonstrate their perfor- AN14 Abstracts 125

mance. view the classical staggering-grid techniques proposed by Arakawa et al almost forty years ago. Some recent devel- Julianne Chung opments will be presented, and ideas for future work will Virginia Tech also be discussed. [email protected] Qingshan Chen Malena I. Espanol Clemson University Department of Mathematics [email protected] University of Akron [email protected] MS135 MS134 Finite Volume Approximation of the Inviscid Prim- itive Equations in a Complex Domain Reproducible Kernel Hilbert Space Modeling and Computing in Imaging We construct the cell-centered Finite Volume discretization Regularization ensures uniqueness and smoothness in var- of the two-dimensional inviscid primitive equations in a do- ious inverse problems arisen in imaging science. Most of main with topography. To compute the numerical fluxes, the existing regularization methods can not efficiently in- the so-called Upwind Scheme (US) and the Central-Upwind terpolate or extrapolate image intensity. They are thus Scheme (CUS) are introduced. We verify, with our numer- not effective in solving image super-resolution and inpaint- ical simulations, that the US (or CUS) is a robust first (or ing problems that both need to extend intensity informa- second) order scheme, regardless of the shape or size of tion at one region to another. We use reproducible kernel the topography and without any mesh refinement near the Hilbert space (RKHS) to model these two problems. RKHS topography. method is more flexible, adaptive to data and involves simple computation. Gung-Min Gie Indiana University Weihong Guo USA Department of Mathematics, Case Western Reserve [email protected] University [email protected] MS135 Liangjian Deng, Si Wang Approximation of the Singularly Perturbed Equa- University of Electronic Science and Technology of China tions of Parabolic Type in a Circular Domain [email protected], [email protected] In this talk, I will present convergence results of singularly perturbed problems in a circular domain and provide as MS134 well approximation schemes, error estimates and numerical Improved Image Reconstruction by Statistically simulations. To resolve the oscillations of classical numer- Estimating Near-Optimal Parameters for Spectral ical solutions due to the stiffness of our problem, we con- Filters struct, via boundary layer analysis, the so-called boundary layer elements which absorb the boundary layer singular- Spectral Filters improve the reconstruction of images cor- ities. Using a P1 classical finite element space enriched rupted by blur and unknown noise. We compute in this with the boundary layer elements, we obtain an accurate work the near-optimal parameters for general filters such numerical scheme in a quasi-uniform mesh. as a hybrid method that combines the Tikhonov filter and the truncated SVD. Using the discrete Picard condition, YoungJoon Hong we provide an algorithm for computing a Picard parame- Indiana University ter, a cut-off for the singular values beyond which the ob- [email protected] servations are predominantly noise. The method compares favorably against other reconstruction methods.

Victoria Taroudaki MS135 University of Maryland POD Reduced-order Models of Complex Fluid [email protected] Flows

Dianne P. O’Leary The proper orthogonal decomposition (POD) method has University of Maryland, College Park been commonly applied to generate reduced-order mod- Department of Computer Science els for turbulent flows. However, to achieve a balance be- [email protected] tween the low computational cost required by a reduced- order model and the complexity of the targeted turbulent flows, appropriate closure modeling strategies are needed. MS135 In this talk, we present several new nonlinear closure meth- Considerations in the Design of Numerical Schemes ods for the POD reduced-order models, which synthesize for Geophysical Flows ideas originating from large eddy simulation. We design efficient discretization algorithms for the new models and Long-term simulations of geophysical flows, e.g. in pre- perform the numerical validation and verification in chal- dicting the climate change for the next century, require lenging computational settings. numerical schemes that conserve key quantities and accurately represent internal wave propagations, all at reason- Zhu Wang able computational costs. In this talk, we will briefly re- IMA, University of Minnesota 126 AN14 Abstracts

[email protected] Frederic Chavane CNRS Institut de Neurosciences de la Timone MS136 [email protected] Distribution of Directional Change as a Signature of Complex Dynamics Alain Destexhe CNRS UNIC Analyses of random walks traditionally use the mean [email protected] square displacement (MSD) as an order parameter characterizing dynamics. We show that the distribution of relative angles of motion between successive time intervals of MS137 random walks in two or more dimensions provides infor- A Novel Higher Order ETD Scheme for System of mation about stochastic processes beyond the MSD. We Coupled Semi-linear PDEs illustrate the behavior of this measure for common models and apply it to experimental particle tracking data. For We introduce a novel version of the ETD3RK scheme based a colloidal system, the distribution of relative angles re- on (1, 2)−Padé approximation to exponential function. In ports sensitively on caging as the density varies. For trans- addition, we develop its extrapolation form to improve tem- port mediated by molecular motors on filament networks in poral accuracy to the fourth order. The scheme and its ex- vitro and in vivo, we discover self-similar properties that trapolation are seen to be strongly stable and have ability cannot be described by existing models and discuss pos- to damp spurious oscillations. We demonstrate the perfor- sible scenarios that can lead to the elucidated statistical mance of the schemes on system of nonlinear Schrödinger features. equations and problem from biochemistry which contains Stas Burov discontinuity between initial and boundary condition. University of Chicago Harish Bhatt tba Middle Tennessee State University [email protected] MS136 Honeybee Nest Bentilation: A Bio-robotic Study MS137 of Collective Flapping Wing Fluid Mechanics Local Discontinuous Galerkin Method with a Honeybee workers ventilate their hive by collectively fan- Fourth Order Exponential Time Differencing ning their wings. The fluid mechanics of this phenomena— Scheme for System of Nonlinear Schrodinger Equa- in which wings continuously operate in unsteady oncoming tions flows (i.e. the wake of neighboring worker bees) and near the ground—are unstudied and may play an important role This paper studies a local discontinuous Galerkin (LDG) in the physiology of colony life. We perform field and lab- approximation combined with fourth order exponential oratory observations of nest ventilation wing kinematics. time differencing Runge-Kutta (ETDRK4) method for Through recent advances in micro-robotics we construct solving the N-coupled nonlinear Schrödinger equation at scale micro-mechanical models of honeybee ventilation (NLSE). The numerical method is proven to be highly effi- swarms to explore the fluid mechanics of collective ventila- cient and stable for long-range soliton computations. Nu- tion. merical examples with periodic boundary conditions are provided to illustrate the accuracy, efficiency and reliabil- Nick Gravish ity of the proposed method. Harvard University [email protected] Xiao Liang Middle Tennessee State University [email protected] MS136 Propagating Waves Structure Spatiotemporal Ac- tivity in Visual Cortex of the Awake Monkey MS137 A New Family of Discontinuous Galerkin Methods Propagating waves have recently been found in the neocor- for Linear and Nonlinear Partial Differential Equa- tex of anesthetized animals. Whether propagating waves tions appear during awake and conscious states, however, remains unclear. To address this, we apply a phase-based In this talk, we discuss a discontinuous Galerkin (DG) fi- analysis to single-trial voltage-sensitive dye imaging data, nite element differential calculus theory for approximat- which captures the average membrane potential of neu- ing weak derivatives of Sobolev functions and piecewise ronal populations over large cortical areas with high spa- Sobolev functions. By introducing numerical one-sided tiotemporal resolution. With this approach, we detect and derivatives as building blocks, various first and second or- characterize spontaneous and stimulus-evoked propagating der numerical operators such as the gradient, divergence, waves in visual cortex of the awake monkey. Hessian, and Laplacian operator are defined, and their corresponding calculus rules are established. We show that Lyle Muller several existing DG methods can be rewritten compactly CNRS UNIC using the proposed DG framework, and that new DG meth- [email protected] ods for linear and nonlinear PDEs are also obtained.

Alexandre Reynaud Michael J. Neilan CNRS & Aix-Marseille Universit´e, Marseille, France University of Pittsburgh tba Department of Mathematics AN14 Abstracts 127

[email protected] 2013, students explored agent-based models (ABMs) with NetLogo. Initially, they completed tutorials to develop models on unconstrained growth and average distance cov- MS137 ered by random walkers. Besides revealing their utility, Application of the Laplace Transform Method to these models provided an opportunity to compare agent- Solving Evolution Problems based modeling with previously considered techniquessys- tem dynamics modeling, empirical modeling, and cellular We are interested in the highest-possible order time dis- automaton simulations. Improved test scores and positive cretization for solving parabolic problems. Recently the questionnaire results support the success of this approach. method of Laplace transform has been drawing an increasing attention. Instead of solving parabolic problems using time-marching algorithms, we attempt to solve the Angela B. Shiflet Laplace-transformed complex-valued elliptic equations in McCalla Professor of Math. & CS, Dir. of Computational parallel. The inverse Laplace transform then gives the Sci. time-domain solutions by using exponentional convergent Wofford College quadrature rules on carefully-chosen contours. We will give shifletab@wofford.edu a short review on this approach and generalize the method to solving parabolic equations with time-dependent coef- George W. Shiflet ficients. The method will be shown to converge exponen- Wofford College tially under suitable assumptions. We will discuss a couple shifletgw@wofford.edu of directions to generalize this approach.

Dongwoo Sheen Seoul National University MS138 Department of Mathematics The Ingenious Project and Other Initiatives [email protected] This talk will focus on aspects of the INGenIOuS Mathe- MS138 matical Sciences Workforce Development project that relate especially to computational applied mathematics ed- Uncover Deep Learning: Assess Online Learners ucation. The NSF-funded project was a joint venture of Cognitive Presence in Mooc all the main professional societies (ASA, AMS, MAA and SIAM). The focus on workforce development led to a strong The study will investigate learners cognitive presence level role for applied mathematical science education. This in a ﬁve-week MOOC data science course. Transcript anal- theme continues for the upcoming CBMS forum, which will ysis, social network analysis, learning records (i.e. fre- focus on the ﬁrst two years of college education. quency of views, grades), survey of perceived learning and satisfaction will be used to assess the learning process and outcomes. The results will reveal the levels of cognitive Peter R. Turner presence exhibited by learners, how their cognitive pres- Clarkson University ence evolves overtime, and how their levels of cognitive School of Arts & Sciences presence correlate with their online behaviors and satisfac- [email protected] tions.

Ye Chin MS139 Syracuse University Mathematical Modeling and Discretization for Ex- [email protected] ascale Simulation

MS138 In simulations, the choices of mathematical models and their discretization significantly influence the properties of Coalition for Undergraduate Computational Sci- the resulting discrete systems. The advent of exascale com- ence and Engineering Education - Proof of Concept puting is an opportunity to re-think the formulation and This talk will present the project funded by NSF TUES implementation of mathematical models and discretiza- to create a cluster of collaborating institutions that com- tions in ways that are more favorable for numerical in- bine students into common classes and use cyberlearning tegration on exascale machines. We will survey several technologies to deliver and manage instruction. As an idea promising research topics and the fundamental constraints of scale-up project, we will discuss how to advance Under- involved in the process of expressing physical phenomena graduate Computational Science Education through learn- as fully discrete models. ing analytics, deep learning assessment and massive open online courses. Luis Chacon Los Alamos National Laboratory Hong Liu [email protected] Department of Mathematics Embry-Riddle Aeronautical University [email protected] MS139 Resilient Algorithms and Computing Models MS138 Undergraduate Exploration of Agent-Based Mod- Abstract not available at time of publication. eling MichaelA.Heroux The final week of a modeling and simulation course in fall, Sandia National Laboratories 128 AN14 Abstracts

[email protected] Department of Engineering Sciences and Applied Mathematics Northwestern University MS139 [email protected] Discrete Solvers at the Exascale

Discrete solvers are crucial in scientific simulations. Mov- MS140 ing to the exascale will put heavier demands on these ker- Electrohydrodynamics of Lipid Bilayer Vesicles in nels due to the need for increasing amounts of data locality AC and DC Fields and to obtain much higher factors of fine-grained parallelism. Thus, parallel solvers must adapt to this environ- Vesicles are closed, fluid-filled lipid bilayers which exhibit ment, and new algorithms and implementations must be shape transitions in the presence of electric fields. Here developed to capitalize on the capabilities of future hard- we model the vesicle membrane as an infinitely thin, ca- ware. We will discuss several key topics that are potentially pacitive, area-incompressible interface with the surround- relevant in the exacale era. ing fluids acting as charge-advecting leaky dielectrics, then use the boundary integral method to numerically investi- Esmond G. Ng gate the dynamics of a vesicle in various electric field pro- Lawrence Berkeley National Laboratory files. Finally, we present a comparison of our numerical [email protected] results with recent small deformation theory and experimental data.

MS139 Lane McConnell University of New Mexico Hierarchical Multilevel Methods for Exascale Un- [email protected] certainty Quantiﬁcation and Optimization

The sustained increase in computational capabilities will MS140 enable new possibilities at the intersection of optimization and uncertainty quantification (UQ), including model Field Theoretic Approaches for Non-Spontaneous calibration, robust control and design under uncertainty. Deformation of Bilayers under Surface Director However, numerous changes in scientific computing at Energies extreme scales are expected to challenge the current The shapes of membranes are continually changing in their UQ/optimization paradigm, wherein theses techniques are aqueous environment. Often, these shape changes involve typically wrapped around a black-box simulation. This proteins but the mechanistic coupling between proteins and talk will focus on several multi-fidelity, hierarchical approx- bilayers is poorly understood. In this talk, we will discuss imations for UQ/optimization that exploit greater levels of some classical and field theoretic calculations which have parallelism provided by emerging many-core architectures. given insight into membrane shape changes away from equi- Clayton G. Webster librium and allowed us to evaluate a path of deformations Oak Ridge National Laboratory leading to a least energy barrier between quasi-static mem- [email protected] brane configurations. Rolf Ryham Stefan Wild Fordham University Argonne National Laboratory [email protected] [email protected] Fredric Cohen MS140 Department of Molecular Biophysics and Physiolog Rush University The Behavior of a Quasi-Circular Vesicle During fredric [email protected] Drying Processes Bob Eisenberg A proposed method for the preservation of biological cells Department of Molecular Biophysics and Physiology is through desiccation. We consider a two-dimensional, Rush University Medical Center quasi-circular vesicle, whose boundary is an inextensible [email protected] bilipid membrane wall but whose enclosed area varies owing to the osmotic transport of water through the membrane. The evolution of the vesicle’s shape is computed MS140 and the effects of advection, diffusion and the membrane’s permeability are analyzed and compared with conclusions Deformation and Stability of Vesicles in Dc Electric drawn from recent level-set simulations. Pulses Electrohydrodynamics of vesicles are investigated under Maurice J. Blount strong DC pulses. In an applied field, the membrane acts Cardiff University as a capacitor and the vesicle deforms into an oblate or blountmj@cardiff.ac.uk prolate ellipsoid. If poration occurs, the membrane capacitor becomes short-circuited and leads to non-ellipsoidal Stephen H. Davis shape and vesicle collapse. The evolution of vesicle shape Dept. of Engineering Sciences and Applied Math is studied for DC pulses of different strength and duration. Northwestern University Membrane composition is varied to observe the effect of [email protected] membrane viscosity, capacitance, and poration threshold.

MichaelJ.Miksis Paul Salipante AN14 Abstracts 129

Max Plank Institute University of California, Berkeley [email protected] Mathematics Department [email protected] Petia Vlahovska Brown University petia [email protected] MS142 Fast Algorithms for the Evaluation of Layer Poten- tials using ’Quadrature by Expansion’ MS142 Fast Iterative Methods for The Variable Diffusion Quadrature by Expansion, or ’QBX’, is a systematic, high- Coefficient Equation in a Disk order approach to singular quadrature that applies to layer potential integrals with general kernels on curves and sur- Variable coefficient diffusion equation has widespread ap- faces. This talk discusses algorithmic options for using plications in many areas of Physics, Engineering and Indus- QBX within a variant of the Fast Multipole Method. A trial research like the flow in porous media, tomography in method is presented that preserves accuracy, generality and image processing to mention a few. We present here fast, close evaluation capability while only requiring a relatively efficient iterative methods to solve this equation in a disk modest increase in computational cost in comparison to a with applications to the Ginzburg Landau equation. Our point-to-point FMM. technique is based on the solution of the Poisson equation in a disk using fast Fourier transform and recursive rela- Andreas Kloeckner tions. The method takes advantage of scaling the original Courant Institute of Mathematical Sciences problem and using shifted iteration. This is an ongoing New York University work and our focus is to develop a fast solution for this non- [email protected] seperable elliptic equation in arbitrary two-dimensional domains by the help of domain embedding method using the optimal distributed control algorithm. The performance of MS142 this fast method is illustrated with some numerical exam- Stability and Accuracy of Structured Direct ples. Solvers

Aditi Ghosh, JoungDong Kim Structured direct solvers are known to be very efficient in Texas A&M University solving some integral equations and PDEs. Here, we show [email protected], [email protected] that they are not only faster than standard direct solvers, but can also have much better stability.Inparticular, Prabir Daripa for hierarchically semiseparable (HSS) matrices, we first Texas A&M University show how the approximation errors can be controlled by Department of Mathematics the tolerance in either classical or randomized compression. [email protected] We further demonstrate the backward stability of the direct solution. In fact, the growth of the numerical error in the direct factorization is significantly slower than that MS142 in standard LU factorization with pivoting. The growth Subspace Iteration Randomization and Low-rank factors are derived. Approximation Jianlin Xia A classical problem in matrix computations is the efficient Department of Mathematics and reliable approximation of a given matrix by a matrix Purdue University of lower rank. The truncated singular value decomposi- [email protected] tion (SVD) is known to provide the best such approximation for any given fixed rank. However, the SVD is also Yuanzhe Xi known to be very costly to compute. Among the differ- Purdue University ent approaches in the literature for computing low-rank [email protected] approximations, randomized algorithms have attracted researchers’ recent attention due to their surprising reliability and computational efficiency in different application areas. MS143 Typically, such algorithms are shown to compute with very Fictitious Domain Method with a Hybrid Cell high probability low-rank approximations that are within Model for Simulating Motion of Cells in Fluid Flow a constant factor from optimal, and are known to perform even better in many practical situations. In this paper, we This talk will consider a hybrid model to represent biologi- present a novel error analysis that considers randomized cal cells and the distributed-Lagrange-multiplier/fictitious- algorithms within the subspace iteration framework and domain (DLM/FD) formulation for simulating the show with very high probability that highly accurate low- fluid/cell interactions. The hybrid model to represent the rank approximations as well as singular values can indeed cellular structure consists of a continuum representation be computed quickly for matrices with rapidly decaying of the lipid bilayer, from which the bending force is cal- singular values. Furthermore, we show that the low-rank culated through energetic variational approach, a discrete approximations computed by these randomized algorithms cytoskeleton model utilizing the worm-like chain to repre- are actually rank-revealing approximations, and the spe- sent network filament, and area/volume constraints. For cial case of a rank-1 approximation can also be used to our computational scheme, a formally second-order accu- correctly estimate matrix 2-norms with very high proba- rate fractional step scheme is employed to decouple the en- bility. Our numerical experiments are in full support of tire system, and is solved by the projection method, level our conclusions. set method, ENO reconstruction, and the Newton method. Numerical results compare favorably with previously re- Ming Gu ported numerical and experimental results, and show that 130 AN14 Abstracts

our method is suited to the simulation of the cell motion Pseudospectral Mode in flow. We numerically investigate radial basis function (RBF) col- Wenrui Hao location method in block pseudospectral (BPS) mode, a Dept. of Applied and Comp. Mathematics and Statistics method popularized by Driscoll and Fornberg for pseu- University of Notre Dame dospectral collocation method. The RBF implementation [email protected] allows us to deal with irregular domain whereas matching solution and derivatives continuities are done in similar ways as in BPS. Numerical experiments in solving simple MS143 collocation problems will be shown. Modeling and Computation of a Precipitate in In- homogeneous Elastic Media Alfa Heryudono University of Massachusetts Dartmouth We present linear theory and nonlinear simulations to Department of Mathematics study the self-similar growth/shrinkage of a precipitate in [email protected] a 2D elastic media. For given applied stress boundary conditions, we show that depending on the mass flux enter- ing/exiting the system, there exist critical flux and elastic- MS144 ity at which compact self-similar growth/shrinkage occurs Adaptive Trial Subspace Selection for Ill- in the linear regime. Numerical results reveal that at long Conditioned Kernel Collocation times there exists nonlinear stabilization that leads the precipitate to evolve to compact limiting shape. Choosing data points is a common problem for researchers who employ various meshless methods for solving partial Shuwang Li differential equations. On the one hand, high accuracy Department of Applied Mathematics is always desired; on the other, ill-conditioning problems Illinois Institute of Technology of the resultant matrices, which may lead to unstable al- [email protected] gorithms, prevent some researchers from using meshless methods. In this talk, we will go over some adaptive trial subspace selection algorithms that select basis to approxi- MS143 mate the true solution of the full problem. A Boundary Integral Method for Particles Moving in Viscoelastic Fluids Ling Leevan Hong Kong Baptist University We present a boundary integral method for computing Department of Mathematics forces on interacting particles in an unsteady viscoelastic [email protected] flow. Using a correspondence principle between Stokes flow and linear viscoelasticity in the Fourier domain, we provide a simple boundary integral formulation for solid particles MS144 moving in a linear viscoelastic fluid. We present an ac- Reproducing Kernel Hilbert Spaces Related to curate numerical method for finding the particle surface Parametric Partial Differential Equations forces when the velocities are given or vice versa. Our numerical methods are validated against a known exact solu- Parametric partial differential equations often arise in com- tion and an existing asymptotic solution. The comparisons plicated physical simulations. A recent source for high- and are in excellent agreement. even infinite dimensional problems is the modeling of uncertainties. For the efficient numerical treatment of those Xiaofan Li problems it is crucial to have a decay in importance of Illinois Institute of Technology the input parameters. Such a decaying ordering can be [email protected] formally stated in terms of reproducing kernels. Such a point of view also indicates numerical schemes which are well-known in the kernel-based literature. We will provide MS143 some non-standard examples and discuss the resulting ap- Solving Interface Problems to High-order on a Reg- proximation properties. This is partly based on joint work ular Cartesian Grid with M. Griebel and B. Zwicknagl (both Bonn University).

In this talk I will present a regular Cartesian grid framework for solving two problem of central importance to in- Christian Rieger terfacial dynamics. The first one is the solution of Poisson’s Universität Bonn equation with interface jump conditions and the second one Haussdorff Center for Mathematics is the evolution of the interface. The methods presented [email protected] are high order (4th order accurate), optimally local (compact stencil sizes), and easy to implement. I will present applications of these methods to solve the incompressible MS144 two-phase Navier Stokes equations for flows involving the A Novel Radial Basis Function (RBF) Method for interaction of droplets with a membrane. Solving Partial Differential Equations (PDEs) on Large Point Clouds Jean-Christophe Nave McGill University Radial Basis Function (RBF) methods, with advantages [email protected] such as mesh-free, simplicity of implementation, and dimension-independence, have been broadly employed for reconstructing arbitrary surfaces. However, there are still MS144 many challenge problems in the numerical solution of Par- Radial Basis Function Collocation Method in Block tial Differential Equations (PDEs) on large point clouds. In AN14 Abstracts 131

this talk, a novel RBF method will be brieﬂy introduced. mathematical theory that shows that a random projection Several related topics, such as fast algorithms, treecode, embeds a collection of K-dimensional spaces if the num- will also be discussed. Numerical examples demonstrate ber of samples is on the order of K times a constant that that this method yields promising results. describes the geometry of the collection. We also show how this embedding results in a guarantee on our ability Lei Wang to choose the a subspace which is (almost) as good as the Argonne National Laboratory one computed from a full observation of the signal. This is [email protected] joint work with William Mantzel.

Zeyun Yu Justin Romberg University of Wisconsin, Milwaukee School of ECE ”zeyun yu” ¡[email protected]¿ Georgia Tech [email protected] Emmanuel O. Asante-Asamani Department of Mathematical Sciences MS145 University of Wisconsin-Milwaukee [email protected] Constructing Matrices with Optimal Block Coher- ence

MS145 Block coherence of matrices plays an important role in analyzing the performance of block compressed sensing re- Exponentially Decaying Error Rate in One-Bit covery algorithms (Bajwa and Mixon, 2012). We present Compressive Sensing bounds on worst-case block coherence and Kronecker prod- In one-bit compressive sensing, s-sparse vectors x ∈ Rn uct constructions which achieve these bounds. We also are acquired via extremely quantized linear measurements show that random subspaces have optimal-order worst-case block coherence asymptotically. Finally, we present a flip- yi =sgn ai, x , i =1,...,m. Several procedures to reconstruct these sparse vectors have been shown to be ef- ping algorithm that can improve the average block coherence of a matrix, while maintaining the worst-case block fective when a1,...,am are independent random vectors. They typically yield an error decaying polynomially in coherence of the original matrix. λ := m/(s log(n/s)). This rate cannot be improved in Andrew J. Thompson, Robert Calderbank the measurement framework described above. However, we Mathematics show that a reconstruction error decaying exponentially in Duke University λ is achievable when thresholds τ1,...,τm are chosen adap- [email protected], [email protected] tively in the quantized measurements yi =sgn( ai, x −τi), i =1,...,m. Our procedure, which is robust to measurement error, is based on a simple recursive scheme involving Yao Xie either hard-thresholding or linear programming. Industrial and Systems Engineering Georgia Institute of Technology Richard G. Baraniuk [email protected] Rice University Electrical and Computer Engineering Department [email protected] MS145 Compressed Sensing and Sigma-Delta Quantiza- Simon Foucart tion: Decoding Via Convex Optimization Mathematics University of Georgia We introduce an alternative reconstruction method for sig- [email protected] nals whose compressed samples are quantized via a Sigma- Delta quantizer. The method is based on solving a convex optimization problem, and unlike the previous approaches, Deanna Needell it yields a stable and robust estimate of the original sig- Department of Mathematics nal. Consequently, we can use Sigma-Delta quantizers for Claremont McKenna College compressible signals and when the measurements are noisy. [email protected] Finally, our theory applies to ”fine” Sigma-Delta quantizers and ”coarse” Sigma-Delta quantizers, e.g., 1-bit per Yaniv Plan measurement. Deaprtment of Mathematics University of Michigan Ozgur Yilmaz [email protected] Mathematics University of British Columbia Mary Wootters [email protected] University of Michigan [email protected] Rongrong Wang University of British Columbia [email protected] MS145 Compressed Subspace Matching on the Continuum MS146 We consider the general problem of matching a subspace Mori-Zwanzig Analysis of Brownian Motion in a to a set of (compressed) samples. We are interested in the Confined Molecular System case where the collection of subspaces is continuously parameterized, i.e. uncountably infinite. We present some Brownian motion in molecular systems is one of the orig- 132 AN14 Abstracts

inal examples for which Mori-Zwanzig projection method [email protected] was developed. Compared to the unbounded case, Brown- ian motion in a confined fluid exhibits interesting features, which are reflected on its memory kernel. By calculating PP1 the memory kernel from molecular dynamics simulations A Mesh Free Method for Numerical Simulation of and obtaining analytic results for the Rayleigh gas model, Calcium Dynamics In Ventricular Myocytes we investigate the effects of confinement. We consider a coupled system of non-linear reaction- Changho Kim, George E. Karniadakis diffusion equations that model the spatio-temporal vari- Brown University ation of intracellular calcium concentration in ventricular Division of Applied Mathematics myocytes. We introduce a modified mesh free method and changho [email protected], george [email protected] utilize exponential time differencing, to significantly reduce the simulation time. At the end we present numerical results demonstrating the stability of the method when used MS146 on uneven distribution of nodes. Mori-Zwanzig and Adaptive Mesh Refinement for Emmanuel O. Asante-Asamani Uncertainty Quantification Department of Mathematical Sciences University of Wisconsin-Milwaukee We employ the Multi-element generalized Polynomial [email protected] Chaos method to deal with stochastic equations involving discontinuities in random space. We develop a new crite- Bruce Wade rion through the model reduction and study the connection Department of Mathematical Sciences, UW-Milwaukee between the variances of the outputs and the quantities Milwaukee, Wisconsin 53201-0413 which are selected as the accuracy control parameters to [email protected] determine when to carry out the mesh refinement. The Kraichnan-Orszag three mode problem is used to illustrate Zeyun Yu the effectiveness of the algorithm for ODEs. University of Wisconsin-Milwaukee [email protected] Jing Li University of Minnesota [email protected] PP1 Gene Selection from Microarray Data : An Ex- ploratory Approach MS146 The goal of microarray data analyses is often to identify the Scale Dependence and Renormalization in Model smallest set of genes that can distinguish between classes of Reduction samples (e.g., from unhealthy samples to healthy ones). In this work, we explore current statistical learning techniques The problem of model reduction for complex systems is on the discovery of informative genes from microarray ex- an active area of research. In this talk I want to discuss periments. In particular, several gene selection algorithms how the physics inspired concepts of scale dependence and are tested on a microarray data sets from samples in a renormalization can be used to facilitate the construction type-1-diabetes (T1D) study. The results are compared of accurate reduced models for complex problems. and discussed.

Panos Stinis Sami Cheong University of Minnesota, Twin Cities University of Wisconsin-Milwaukee [email protected] [email protected]

PP1 PP1 AWM Workshop: Confidence Sets for Geometric A New Test for Exclusion Algorithm to Find the and Topological Distances Optimum Value of Function in Rn Distance measures arise in many contexts. Unfortunately, The problem of finding the global minimum of a vector the most interesting distance is the one between an un- function is very common in science, economics and engi- known ground truth object and an object created from neering. One of the most notable approaches to find the sampling. In this talk, we introduce the statistical boot- global minimum of a function is that based on interval strap for the purpose of bounding the distance between a analysis. In this area, the exclusion algorithms (EAs) are reconstructed object and the original object. In particular, a well-known tool for finding the global minimum of a func- we derive confidence sets for persistence diagrams, persis- tion over a compact domain. There are several choices for tence landscapes, road networks, and Reeb graphs. the minimization condition In this paper, we introduce a new exclusion test and analyze the efficiency and compu- Brittany Fasy tational complexity of exclusion algorithms based on this Tulane University approach.We consider Lipschitz functions and give a new [email protected] minimization condition for the exclusion algorithm. Then we study the convergence and complexity of the method. PP1 Ibraheem Alolyan AWM Workshop: Fast Iterative Methods for The King Saud University Variable Diffusion Coefficient Equation in a Unit AN14 Abstracts 133

Disk ble method for synthesizing realistic ensembles of networks starting from a known network, through a series of map- Variable coefficient diffusion equation has widespread ap- pings that coarsen and later refine the network structure plications in many areas of Engineering and Industrial re- by randomized editing. The method, MUSKETEER, pre- search like the flow in porous media and Tomography. We serves structural properties with minimal bias, including present here fast, iterative methods to solve this equation unknown or unspecified features, while introducing realis- with applications to the Ginzburg Landau equation. Our tic variability at multiple scales. technique is based on solution of Poisson and Helmholtz equation in a unit disc using fast FFT and recursive rela- Alexander Gutfraind tions. The performance of this fast method is illustrated Cornell University with some numerical examples. [email protected]

Aditi Ghosh Ilya Safro Texas A&M University Clemson University [email protected] [email protected]

PP1 Lauren A. Meyers The University of Texas at Austin Spatiotemporal Pattern of Temperature Change Section of Integrative Biology over US Using Bounded-Variation Segmentation [email protected] In order to analyze low frequency variability of climate, the method of bounded-variation segmentation is applied PP1 for modeling temperature time series of US from 1184 sta- tions during 1900-2012. The method finds multiple lin- Pathways to Type 2 Diabetes with a Mathematical ear trends and locate times of significant changes. Im- Model portant attribute of this method is that it is not depen- We develop a mathematical model of how pancreatic beta dent on Gaussian or Markovian assumptions. Also multi- cells fail in the progression to type 2 diabetes. Insulin re- dimensional analysis used in this method eliminate the ef- sistance by itself does not generally lead to diabetes unless fect of sensors relocation on the detected trends. it is extreme. In contrast, typical degrees of insulin resis- Mohammad Gorji Sefidmazgi tance do lead to disease if accompanied by an increased PhD Student propensity to apoptosis, which impairs the ability to ex- North Carolina A&T State University pand beta-cell mass or function in response to insulin re- [email protected] sistance. We have incorporated the dynamics of exocytosis of insulin granules. These enhancements allow us to look at the mechanistic defects that underlie observed patholo- Abdollah Homaifar gies such as impaired fasting glucose (IFG) and impaired North Carolina A&T State University glucose tolerance (IGT). The model supports associations [email protected] in experiments between IFG and excess HGP and between IGT and peripheral insulin resistance. Mina Moradi Kordmahalleh North Carolina A&T State Unviersity Joon Ha, Arthur S. Sherman [email protected] National Institutes of Health [email protected], [email protected] PP1 AWM Workshop: The Asymptotic Analysis of a PP1 Thixotropic Yield Stress Fluid in Squeeze Flow Bayesian Statistics and Uncertainty Quantification for Safety Boundary Analysis in Complex Systems The partially extending strand convection model, combined with a Newtonian solvent, is investigated for a vis- The analysis of a safety-critical system often requires de- coelastic fluid in biaxial extensional (squeeze) flow. For a tailed knowledge of safe regions and their high-dimensional prescribed tensile stress, the asymptotic analysis, while not non-linear boundaries. We present a statistical approach to simple, is an essential tool for the physical interpretation iteratively detect and characterize the boundaries, which of the distinct stages in evolution. The overall picture that are provided as parameterized shape candidates. Using emerges captures a number of features that are associated methods from uncertainty quantification and active learn- with thixotropic yield stress fluids, such as delayed yielding ing, we incrementally construct a statistical model from and hysteresis for up-and-down stress ramping. only few simulation runs and obtain statistically sound estimates of the shape parameters for safety boundaries. Holly Grant Virginia Tech Yuning He [email protected] UC Santa Cruz [email protected]

PP1 Multiscale Decomposition and Modeling of Com- PP1 plex Networks AWM Workshop: Traveling Fronts to the Combus- tion and the Generalized Fisher-Kpp Models Statistical analyses of networks can provide critical insights into the structure, function, dynamics, and evolu- We show the nonexistence of traveling fronts in the com- s tion of many complex systems. Here, we introduce a ﬂexi- bustion model with fractional Laplacian (−Δ) when s ∈ 134 AN14 Abstracts

(0, 1/2].Ourmethodcanbeusedtogiveadirectand Variables simple proof of the nonexistence of traveling fronts for the usual Fisher-KPP nonlinearity. Also we prove the existence We modify the method suggested earlier by us and over- and nonexistence of traveling fronts for different ranges of come its main deficiency. The method enables the approx- the fractional power s for the generalized Fisher-KPP type imation of the singularity curve of a piecewise constant model. function of two variables by means of its Fourier-Jacobi coefficients. The method is based on the technique sug- Tingting Huan gested by the author for recovering the locations of dis- University of Connecticut continuities of a piecewise smooth function of one variable. [email protected] The method could be generalized for functions of three or more variables. In addition, some numerical examples are presented. PP1 Which Conical Ant Mound is Optimal in Collection George Kvernadze of Solar Beams From Transient Sun Weber State University [email protected] We optimize domes of ant nests, receiving energy from solar heating and losing it to a cold night air. Sun completes the daily sky cycle with beams of radiation continuously PP1 changing their altitude and azimuthal angles. We calcu- Stable Implementation of Complete Radiation late the incoming radiation at each exposed point of a con- Boundary Conditions in Finite Difference Time ical dome surface and at each instance from dawn to sun- Domain Solvers for Maxwell’s Equations set. The daily energy serves as a criterion and the surface area of the cone, through which heat is lost during night Complete Radiation Boundary Conditions (CRBCs) allow time, serves as an isoperimetric constraint in the sense of for the efficient truncation of unbounded domains in wave Polya-Szego, with the height to cones base ratio chosen as a propagation problems. Unlike standard Perfectly Matched control variable. For the simplest case, the instantaneous Layer (PML) approaches, CRBCs allow for a weakly time flux of the terrestrial solar power is explicitly expressed dependent error estimate for both propagating and decay- through the altitude Sun angle. Time-integration over the ing waves. We demonstrate the how the CRBC can be azimuthal angle and areal-integration over the illuminated implemented in a Finite Difference Time Domain (FDTD) half-cone give the total solar day energy. This functional is scheme and obtain an energy estimate using a summation then optimized with respect to the size of the anthill that by parts (SBP) argument to prove stability. answers the question stated in the title. John Lagrone, Fritz Juhnke Rouzalia Kasimova Southern Methodist University German University of Technology in Oman [email protected], [email protected] [email protected] Thomas Hagstrom Denis Tishin, Yurii Obnosov Department of Mathematics Kazan Federal University, Russia Southern Methodist University [email protected], [email protected] [email protected]

Anvar Kacimov PP1 Sultan Qaboos University Regression in High Dimensions Via Geometric [email protected] Multi Resolution Analysis

We present a framework for high-dimensional regression PP1 using the GMRA data structure. In analogy to classi- AWM Workshop: Competitive Geometric Flow Of cal wavelet decompositions of function spaces, GMRA is Network Morphologies Under The Functionalized a tree-based decomposition of data sets into local affine Cahn-Hilliard (fch) Free Energy projections. Moreover, GMRA admits a fast algorithm for computing the projection coefficients on the already- The FCH is a higher order free energy which balances solo- learned dictionary. Within each node of the tree one can vation energy of ionic groups against elastic energy of the also assign regression coefficients in any manner; here we underlying polymer backbone, and describes the formation study the simple case of weighted linear regression. of solvent network structures which are essential to ionic conduction in polymer membranes. For the H -1 gradi- David Lawlor ent flow of the FCH energy, using functional analysis and Department of Mathematics asymptotic methods, we drive a sharp-interface geometric Duke University motion which couples the flow of co-dimennsion 1 and 2 [email protected] network morphologies, through the far-field chemical potential. PP1 Noa Kraitzman Two Projection Methods for Regularized Total Michigan State University Least Squares Approximation [email protected] We consider the Total Least Squares problems with Tikhonov Regularization. Since the problem of finding the PP1 Total Least Squares solution is equivalent to the solution of On a Method for Approximation of the Singularity the two parameter linear system, our method derives two Curve of a Piecewise Constant Function of Two nonlinear equations from the two parameter linear system, AN14 Abstracts 135

applied a Newton method with a nonlinear Jacobian matrix pothesis, where we link a females propensity to cannibalize that is computed inexpensively. For large-scale problems, a mate to her aggression towards prey. Higher levels of ag- this is further combined with two projection methods, one gression lead to higher food consumption and lower mating based on bidiagonal reduction, the other projecting onto a rates, a trade-off in fitness. We find an optimal aggression generalized Krylov space. level and analyze its effects on the frequency and type of sexual cannibalism. We then compare our results to exist- Geunseop Lee ing models of sexual cannibalism. The Pennsylvania State University [email protected] Sara Reynolds University of Nebraska-Lincoln Jesse L. Barlow [email protected] Penn State University Dept of Computer Science & Eng [email protected] PP1 AWM Workshop: Time-Delayed Pdes with Stochastic Boundary in Mathematical Modeling of PP1 Kidney Theoretical Analysis of Low-Energy Electron Diffraction: New Results for Real Systems and We consider nonlinear time-delayed transport equations New Understanding for Model Ones with stochastic boundary to study the stability of feedback systems in the kidney. We prove the existence and We describe our novel, first-principles approach to theoret- uniqueness of the steady- state solution for deterministic ical calculations of low-energy electron diffraction (LEED) and stochastic boundary cases with small delay, based on spectra, and especially its expansion to off-normal inci- the contraction mapping theorem. Model results revealed dence diffraction from few-layer-graphene systems. We that the system admits the stationary solution for small compare our calculated off-normal incidence reflection in- delay despite stochastic influences, whereas it exhibits os- tensities to conventional LEED calculations. We also cillatory solutions for large delay, resembling irregular os- present an asymptotic investigation of electron scattering cillations in spontaneously hypertensive rats. in model systems, e.g., 2D square well potential, to better understand the anomalous solutions that create difficulties Hwayeon Ryu for our wave-matching approach to this boundary value Duke University problem. [email protected]

John F. Mcclain University of New Hampshire PP1 jfi[email protected] Analysis of a Camera-Based Model of Bar Code Decoding Jiebing Sun Michigan State University This work addresses the issue of the limited capability of a [email protected] camera-based bar code decoding method. The question we wish to address is “What is the resolution needed in the Karsten Pohl, Jian-Ming Tang captured image to unambiguously decode a bar code?” For University of New Hampshire simplicity, we consider the UPC bar code which consists of [email protected], [email protected] black and white bars of different widths. The width of the black and white bars encode a 12-digit number according to a look-up table. The smallest element in the bar code PP1 is assumed to be of width h. We further assume that the A Viscoelastic Model That Displays Thixotropic camera pixels are lined up along the bars and they are of Yield Stress Fluid Behavior size d. The question now amounts to unique determination of the digits for a fixed ratio of d to h. We show that the There are biological fluids such as the slime excreted by digits are uniquely determined if the pixel size is no greater slugs, which are yield stress fluids. Among them, some are than twice the smallest element. Moreover, we show that thixotropic. Typically, a model for yield stress fluids be- this determination is stable. A decoding algorithm is pre- gins with inputting a measured value for the yield stress. sented, along with numerical examples that illustrate the On the other hand, our model does not assume any yield main ideas behind this work. stress behavior a priori. The relaxation time of the material is taken as a large parameter, and asymptotic solu- Madeline J. Schrier, Fadil Santosa tions are obtained. These display some observed features University of Minnesota-Twin Cities of thixotropic yield stress fluids. [email protected], [email protected]

Yuriko Renardy Virginia Tech PP1 Department of Mathematics Fully Nonlinear Model for Dispersive Wave Turbu- [email protected] lence

The Majda-McLaughlin-Tabak (MMT) model describes a PP1 one-dimensional system exhibiting dispersive wave turbu- AWM Workshop: Sexual Cannibalism As An Op- lence, and includes linear and nonlinear terms. I consider timal Strategy in Fishing Spiders a modiﬁed version of the model where the linear term is absent. I discuss symmetry-based arguments, perturbative We consider a model, based on the aggressive spillover hy- solutions, and other methods for predicting the dispersion 136 AN14 Abstracts

relation and waveaction spectrum, and compare with nu- [email protected] merical results. I consider both the case where driving and damping are present and the case where they are absent. PP1 Michael Schwarz A Mathematical Model of Moisture Movement and Rensselaer Polytechnic Institute Bacterial Growth in a Two-Dimensional Porous [email protected] Medium

David Cai Bacterialgrowthinsandisofconcerninregardtothe New York University health of beaches. A mathematical model is presented that Courant institute represents the movement of moisture and the growth of [email protected] bacteria through a beach. Simulations were run by numerically solving Richard’s Equation using a Finite Volume Method. These simulations show that elevated bacteria Gregor Kovacic counts following rain events do not necessarily result from Rensselaer Polytechnic Inst bacteria in the body of water, but can also be sourced from Dept of Mathematical Sciences the sand. [email protected] Rachel E. Tewinkel Peter R. Kramer University of Wisconsin - Milwaukee Rensselaer Polytechnic Institute [email protected] Department of Mathematical Sciences [email protected] PP1 A Guaranteed, Adaptive, Automatic Algorithm PP1 For Univariate Function Minimization Ritz-Augmented Extended Krylov Subspaces for Sequences of Lyapunov Equations This algorithm attempts to provide an approximate minimum value of a one-dimensional function that diﬀers from We consider the numerical solution of generalized Lya- exact minimum value by no more than an error tolerance. punov equations occurring in bilinear model order reduc- Besides guaranteed the error tolerance, this algorithm also tion. We proceed by splitting the operator and use a clas- considers the lengths tolerance of the subset containing sical stationary iteration, performing standard Lyapunov point(s) where the minimum occurs. solves with the extended Krylov subspace method. This enables reuse of computation via the use of augmented Xin Tong Krylov subspaces. The resulting algorithm appears com- Department of Applied Mathematics petitive with the existing state of the art on two benchmark Illinois Institute of Technology problems. [email protected]

Stephen D. Shank PP1 Temple University [email protected] Iterative Functional Modiﬁcation Method for Solv- ing a Transportation Problem

PP1 New method for solving transportation problems based on decomposing the original problem into a number of two- Numerical Investigation of Microfluidic Droplet dimensional optimization problems is proposed. Since the Breakup Using T-Junction Geometry solution procedure is integer-valued and monotonic in the objective function, the required computation is finite. As A critical analysis on the breakup of Microfluidic droplet in a result, we get not only a single optimal solution of the a T-junction is presented. A way by which droplets can be original transportation problem but a system of constraints evenly distributed over multiple micro channels is to break that can yield all optimal solutions. We give numerical them into many smaller droplets. Hence it is essential to examples illustrating the constructions of our algorithm. understand the behavior of the breakup of droplet in a micro channel. Available theoretical and numerical data Vladimir I. Tsurkov are compared with simulations obtained using a modified Computing Centre of RAS version of the interFoam solver of the OpenFOAM CFD [email protected] package.

Olabanji Y. Shonibare Alexander Tizik Department of Mathematical Sciences CC RAS Michigan Technological University [email protected] [email protected] PP1 Kathleen Feigl A Multiscale Implementation for the Peridynamic Michigan Technological University Model of Mechanics Dept. of Mathematical Sciences [email protected] An investigation in continuous and discontinuous ﬁnite element methods for a peridynamics model of mechanics gives Franz Tanner us a new view of the peridynamic model when dealing with Department of Mathematical Sciences solutions with jump discontinuities. Peridyanmics can be Michigan Technological University transit between nonlocal and local models depending on AN14 Abstracts 137

the size of horizon compared to the grid size. Therefore, a Alexander Alexeev mesh of good quality and an appropriate quadrature rule George W. Woodruff School of Mechanical Engineering to conform the multiscale setting need to be concerned. We Georgia Institute of Technology developed a local grid refinement method that can be suit- [email protected] able for the multiscale peridynamic model and also found a quadrature rule to estimate the weak formulation with high accuarcy. PP1 Inverse Modeling and Prediction Uncertainty Feifei Xu Analysis of a Co2 Injection Pilot Test, Cranfield, Florida State University Mississippi winterfl[email protected] The ensemble-based filtering algorithms and the null-space Monte Carlo approach are applied for characterizing the PP1 heterogeneity and quantifying model prediction uncer- AWM Workshop: Three Model Problems for 1-D tainty of a CO2 injection test, Cranfield, Mississippi. An Particle Motion with the History Force in Viscous ensemble of reservoir model conditioned to the observed Fluids data is retained from both approaches and models prediction results are analyzed to evaluate the trade-off between Abstract. We consider various model problems that de- model efficiency and model complexity to provide a com- scribe rectilinear particle motion in a viscous fluid under putationally efficient and practically useful framework for the influence of the history force. These problems include predictive uncertainty analysis of CO2 sequestration. sedimentation, impulsive motion, and oscillatory sliding motion. The equations of motion are integrodifferential Hongkyu Yoon equations with a weakly singular kernel. We provide ana- Geoscience Research and Applications lytical solutions using Laplace transforms and discuss the Sandia National Laboratories mathematical relation between the sedimentation and im- [email protected] pulsive start problems. We also compare several numerical schemes and benchmark them against the analytical re- Reza Tavakoli sults. UT-Austin [email protected] Shujing Xu CLAREMONT GRADUATE UNIVERSITY Bill Arnold fl[email protected] Sandia National Laboratories [email protected] PP1 AWM Workshop: A Local Grid Mesh Reinement PP1 for a Nonlocal Model of Mechanics A Spatio-Temporal Point Process Model for Am- bulance Demand Nonlocal problems are based on integro-diferential equations, which do not involve spatial derivatives. This makes We model spatio-temporal point processes as a time se- it possible to deal with discontinuous solutions. We are ries of spatial densities using finite mixture models. We most interested in the numerical results for piecewise so- fix the mixture component distributions across time while lutions with a jump discontinuity. A local grid reinement letting the mixture weights evolve over time. We capture method is then investigated for two-dimensional nonlocal seasonality by constraining mixture weights; we represent model, which would be suitable for the curve discontin- location-specific temporal dependence by applying autore- uous path. With the reine meshes, optimal convergence gressive priors on mixture weights. To illustrate, we esti- behaviors are achieved. mate ambulance demand in Toronto, Canada. Our method accurately captures the complex spatial and temporal dy- Feifei Xu namics present in this large-scale dataset. Florida State University winterfl[email protected] Zhengyi Zhou Center for Applied Mathematics Cornell University PP1 [email protected] Designing a Self-Propelled Hydrogel Microswim- mer David Matteson Department of Statistical Science We use dissipative particle dynamics to design a new self- Cornell University propelling bi-layered gel microswimmer. The gel consists [email protected] of one layer that swells in response to an external stimulus and one passive layer. When a periodic stimulus is applied, the microswimmer undergoes a sequential expansion, Dawn Woodard bending, contraction, and straightening motions leading to School of Operations Research and Information net propulsion at low Reynolds number. We probe how Engineering the swimming speed can be enhanced by selecting mate- Cornell University rial properties and geometry of the gel swimmer. [email protected]

Peter Yeh, Svetoslav Nikolov Shane Henderson Georgia Institute of Technology Cornell University [email protected], [email protected] School of Operations Research and Industrial Engineering 138 AN14 Abstracts

[email protected]

Athanasios Micheas Department of Statistics University of Missouri-Columbia [email protected]