4 AN10 Abstracts

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4 AN10 Abstracts

IC1 IC4 On Dispersive Equations and Their Importance in Kinematics and Numerical Algebraic Geometry Mathematics Kinematics underlies applications ranging from the design Dispersive equations, like the Schrödinger equation for ex- and control of mechanical devices, especially robots, to the ample, have been used to model several wave phenom- biomechanical modelling of human motion. The major- ena with the distinct property that if no boundary con- ity of kinematic problems can be formulated as systems ditions are imposed then in time the wave spreads out of polynomial equations to be solved and so fall within spatially. In the last fifteen years this field has seen an the domain of algebraic geometry. While symbolic meth- incredible amount of new and sophisticated results proved ods from computer algebra have a role to play, numerical with the aid of mathematics coming from different fields: methods such as polynomial continuation that make strong Fourier analysis, differential and symplectic geometry, an- use of algebraic-geometric properties offer advantages in alytic number theory, and now also probability and a bit of efficiency and parallelizability. Although these methods, dynamical systems. In this talk it is my intention to present collectively called Numerical Algebraic Geometry, are ap- few simple, but still representative examples in which one plicable wherever polynomials arise, e.g., chemistry, biol- can see how these different kinds of mathematics are used ogy, statistics, and economics, this talk will concentrate on in this context. applications in mechanical engineering. A brief review of the main algorithms of the field will indicate their broad Gigliola Staffilani applicability. MIT [email protected] Charles Wampler General Motors Research Laboratories, Enterprise Systems Lab IC2 30500 Mound Road, Warren, MI 48090-9055, USA On the Role of Error and Uncertainty in the Nu- [email protected] merical Simulation of Complex Fluid Flows

The failure of numerical simulation to predict physical real- IC5 ity is often a direct consequence of the compounding effects Cloaking and Transformation Optics of numerical error arising from finite-dimensional approximation and physical model uncertainty resulting from in- We describe recent theoretical and experimental progress exact knowledge and/or statistical representation. In this on making objects invisible to detection by electromagnetic topical lecture, we briefly review systematic theories for waves, acoustic waves and matter waves. For the case of quantifying numerical errors and restricted forms of model electromagnetic waves, Maxwell’s equations have transfor- uncertainty occurring in simulations of fluid flow. A goal mation laws that allow for design of electromagnetic ma- of this lecture is to elucidate both positive and negative terials that steer light around a hidden region, returning aspects of applying these theories to practical fluid flow it to its original path on the far side. Not only would ob- problems. Finite-element and finite-volume calculations of servers be unaware of the contents of the hidden region, subsonic and hypersonic fluid flow are presented to contrast they would not even be aware that something was being the differing roles of numerical error and model uncertainty hidden. The object, which would have no shadow, is said for these problems. to be cloaked. We recount some of the history of the subject and discuss some of the mathematical issues involved. Timothy J. Barth NASA Ames Research Center [email protected] Gunther Uhlmann University of Washington Department of Mathematics IC3 [email protected] Communication Complexity of Algorithms Algorithms have two kinds of costs: arithmetic and com- IC6 munication, which means either moving data between lev- Algebraic Geometric Algorithms in Discrete Opti- els of a memory hierarchy (in the sequential case) or over a mization network connecting processors (in the parallel case). The costs of communication often dominate the cost of arith- It is common knowledge that the understanding of the ge- metic. Thus, minimizing communication is often highly de- ometry of convex bodies has helped speed up algorithms sirable. The main goal of this talk is to describe a general in discrete optimization. For example, cutting planes and method for deriving upper and lower bounds on the amount facet-description of polyhedra have been crucial in the suc- of data moved (also known as bandwidth) for a very gen- cess of branch-and-bound algorithms for mixed integer lin- eral class of algorithms, including most dense and sparse ear programming. Another example is how the ellipsoid linear algebra algorithms. The method involves combinato- method can be used to prove polynomiality results in com- rial analysis of computation graphs, in particular, of their binatorial optimization. For the future, the importance expansion properties. This is joint work with Grey Ballard, of algebra and geometry in optimization is even greater James Demmel, and Oded Schwartz. since applications now demand non-linearity constraints together with discrete variables. In the past 5 years two Olga Holtz beautiful algebraic geometric algorithms on polyhedra have University of California, Berkeley been used to prove unexpected new results on the compu- Technische Universitat Berlin tation of integer programs with non-linearly objective func- [email protected] tions. The first is Barvinok’s algorithm for polytopes, and the second is Graver’s bases method on polyhedral cones. I will describe these two algorithms and explain why we AN10 Abstracts 5

can now prove theorems that were beyond our reach be- understanding of the options available to reduce energy fore. I will also describe attempts to turn these two al- use in buildings and will highlight the role of mathematics gorithms into practical computation, not just theoretical and particularly computational science in delivering low results. This is a nice story collecting results contained energy buildings to the market in cost-effective ways. A in several papers, joint work with various subsets of the systems approach to designing and operating low energy following people: R. Hemmecke, M. Koeppe, S. Onn, U. buildings will be described and the opportunities to de- Rothblum, and R. Weismantel. velop and deploy methods for uncertainty quantification, dynamical systems and embedded systems will be high- Jesus De Loera lighted. University of California, Davis [email protected] Clas Jacobson United Technologies Research Center IC7 [email protected] Scalable Tensor Factorizations with Incomplete Data IC10 Incomplete data is ubiquitous in biomedical signal pro- Semidefinite Programming: Algorithms and Appli- cessing, network traffic analysis, bibliometrics, social net- cations work analysis, chemometrics, computer vision, communication networks, etc. We explain how factor analysis can The last two decades have seen dramatic advances in the identify the underlying latent structure even when signif- theory and practice of semidefinite programming (SDP), icant portions of data are missing and the remainder is stimulated in part by the realization that SDP is an ex- contaminated with noise. Though much of what we will tremely powerful modeling tool. Applications of SDP in- say is also applicable to matrix factorizations, we focus clude signal processing, relaxations of combinatorial and on the CANDECOMP/PARAFAC (CP) tensor decompo- polynomial optimization problems, covariance matrix es- sition. We demonstrate that it is possible to factorize in- timation, and sensor network localization. The first part complete tensors that have an underlying low-rank struc- of the talk will describe several applications, such as ma- ture. Further, there are approaches that can scale to sparse trix completion, that have attracted recent interest in large-scale data, e.g., 1000 x 1000 x 1000 with 99.5% miss- large scale SDP. The second part will focus on algorithms ing data. Real-world applicability is demonstrated in two for SDP. First, we present interior-point methods (IPMs) examples: EEG (electroencephalogram) applications and for medium scale SDP, follow by inexact IPMs (with lin- network traffic data. ear systems solved by iterative solvers) for large scale SDP and discuss their inherent limitations. Finally, we Tamara G. Kolda present recent algorithmic advances for large scale SDP Sandia National Laboratories and demonstrate that semismooth Newton-CG augmented [email protected] Lagrangian methods can be very efficient. Kim-Chuan Toh IC8 National University of Singapore Factorization-based Sparse Solvers and Precondi- Department of Mathematics tioners [email protected]

Efficient solution of large-scale, ill-conditioned and highly- indefinite algebraic equations often relies on high quality IP0 preconditioners together with iterative solvers. Because W. T. and Idalia Reid Prize in Mathematics Lec- of their robustness, factorization-based algorithms often ture: William T. and Idalia Reid: His Mathematics play a significant role in developing scalable solvers. We and Her Mathematical Family present our recent work of using state-of-the-art sparse factorization techniques to build domain-decomposition type The W. T. and Idelia Reid Prize in Mathematics was es- direct/iterative hybrid solvers and efficient incomplete fac- tablished in 1993 by SIAM and is funded by an endowment torization preconditioners. In addition to algorithmic prin- from the late Mrs. Idalia Reid to honor the memory of her ciples, we also address many practical aspects that need to husband Dr. W. T. Reid and his love of mathematics. Over be taken into consideration in order to deliver high speed time we often forget the people whose names are attached and robustness to the users of today’s sophisticated high to the prizes that are periodically awarded for outstanding performance computers. research or other contributions to our profession. Since I am the first of Professor Reid’s students to be honored by Xiaoye S. Li this Prize, it is only fitting that I take this opportunity to Computational Research Division review some of Dr. Reid’s contributions to mathematics Lawrence Berkeley National Laboratory and Mrs. Reid’s support of his mathematical colleagues [email protected] and students.

John A. Burns IC9 Interdisciplinary Center for Applied Mathematics Energy Eﬃciency in the Built Environment: Sys- Virginia Tech tems Approaches and Mathematical Challenges [email protected] Buildings consume nearly 40% of the world’s energy, sig- niﬁcantly more than either the transportation or industrial IP0 sectors. Any comprehensive plan to reduce atmospheric Julian Cole Prize Lecture: Mathematical Mod- carbon must include actions to reduce energy consumption in the building sector. This talk will focus on the current 6 AN10 Abstracts

elling of Tissue Growth models that allow us to see and hear music simultaneously.

Approaches to the continuum modelling of biological tissue growth will be described, with specific emphasis on (i) Dmitri Tymoczko novel aspects of the resulting PDE formulations that arise Princeton University from the biological contexts to which they are intended [email protected] to apply and (ii) the role of singular-perturbation methods in elucidating model properties. The talk will focus on recent developments in the application of multiphase IP1 continuum-mechanics descriptions, particularly in describ- Mathematical Challenges in Climate Change Sci- ing the growth of engineered tissue within a porous scaffold. ence John King Climate models solve the equations for the conservation University of Nottingham of momentum, mass and energy in the atmosphere and School of Mathematical Science oceans, the equations of state of air and for sea water, as [email protected];[email protected] well as equations for energy and water exchange with the land and cryosphere. This talk will present a brief review of the progress of climate modeling and will emphasis new IP0 challenges in projecting future climate change. Examples The AWM-SIAM Sonia Kovalevsky Lecture: Mix- will include prediction of co-evolution of atmospheric CO2 ing It Up: Discrete and Continuous Optimal Con- and climate, carbon data assimilation, and chaotic transi- trol for Biological Models tions. This presentation will illustrate optimal control methods Inez Fung applied to several types of models, including a mixture of University of California, Berkeley discrete and continuous features. The applications range [email protected] from a discrete model for cardiopulmonary resuscitation to partial differential equation models for rabies in raccoons. Detailed results will be given for harvesting in a PDE fish- IP2 ery model that answer the question: Does a marine reserve Compressed Sensing: Survey and Applications occur when maximizing harvest yield? Compressed sensing is a very active area of recent research Suzanne M. Lenhart attracting researchers from approximation theory, informa- University of Tennessee tion theory, harmonic analysis, statistics and signal pro- Department of Mathematics cessing. It has applications in areas ranging from speed- [email protected] ing up medical imaging to enabling more ambitious deep- sky astronomy. In addition the topic combines a bit of paradox – seeming to show that traditional ’barriers’ such IP0 as the Shannon-Nyquist sampling theorem don’t apply – The John von Neumann Lecture - Algebra: From while also involving some pretty advanced ideas from high- Linear to Non-Linear dimensional geometry and even statistical physics. In my talk I will try to engage newcomers with a survey some This lecture will discuss recent applications of methods of the excitement of this area, while also mentioning the from abstract algebra in modeling and solving non-linear sophisticated new ideas appearing almost daily. I will also problems across the mathematical sciences. Techniques try to bridge my talk to the associated minisymposia on that are familiar from linear algebra have natural exten- Compressed Sensing. sions in the non-linear world of algebraic geometry, whose recent advances are now transforming our thinking about David L. Donoho problems arising in domains such as convex optimization, Stanford University statistical inference and computational molecular biology. Department of Statistics [email protected]

Bernd Sturmfels University of California , Berkeley IP3 [email protected] Closing the Loop: Computational Physics and the Industrial Design Process IP0 Over the last two decades, improvements in computer hard- I.E. Block Community Lecture: The Geometry of ware and the development of nearly linear scaling methods Music have brought a variety of large-scale calculations within practical reach. While these methods have had substantial In my talk, I show how to translate the language of elemen- impact in industry, a number of improvements are needed tary music theory into that of contemporary geometry. It in order for these methods to be fully integrated into acous- turns out that concepts such as ”chord” and ”chord type” tic, electromagnetic, thermal and mechanical design envi- are naturally represented by points in geometrical spaces ronments. In this talk, we will describe the current state known as ”orbifolds.” Understanding these spaces can help of the art, as well as some recent ideas that may lead to a us to understand general constraints on musical style, as new generation of fast solvers, enabling robust, automatic well as the inner workings of speciﬁc pieces. For example, and geometrically ﬂexible design by simulation. we will see that Mozart, Chopin, and Schubert made very sophisticated use of a necklace of four-dimensional cubes Leslie Greengard representing four-note chords. The talk will be accessible Courant Institute to non-musicians and will exploit interactive 3D computer New York University AN10 Abstracts 7

[email protected] sumes a narrow plume of hot gas rising and entraining the surrounding air. The surrounding air is assumed to have constant density and is irrotational far from the fire line. IP4 Then the flow outside the plume is described by a Biot- Transaction Costs Savart integral with jump conditions across the position of the plume. The plume model describes the unsteady Stochastic calculus models for financial markets have evolution of the mass, momentum and energy inside the played a fundamental role in finance in the past 30 years. plume, with sources derived to model mixing in the style The first application of these models is to determine the of Morton, et al. [1956]. The model is implemented in the price of a derivative security by working out the strategy same manner as structure-fluid interaction models [Alben by which the security payoff can be replicated by trading and Shelley 2008], except that we include a sink term in in primary assets. The second application is to solve the the Biot-Savart integral to couple the entrainment into the stochastic control problem of maximizing the utility of in- plume to the potential flow around the plume. The results vestment. If there are no transaction costs for trading in show that this model is capable of capturing a complicated assets, these problems have elegant solutions. This talk interaction of the plume with the surrounding air. Morton, is discusses what can be done when transaction costs are B. R., Taylor, Sir G. I., and Turner, J. S., Proc. Roy. Soc. present. The principal tool for analysis is a variational in- London, A 234, 1-23 (1956). Alben, S. and Shelley, M. J., equality version of the Hamilton-Jacobi-Bellman equation. Phys. Rev. Letters, 100, 074301, (2008). Although this equation does not have an analytical solution, the initial terms in an asymptotic expansion of the Donald A. Drew solution can be obtained. Rensselaer Polytech Institute Dept of Mathematical Sciences Steven E. Shreve [email protected] Carnegie Mellon University Dept of Mathematical Sciences Kevin DelBene [email protected] Rensselaer Polytech Institute Department of Mathematical Sciences IP5 [email protected] Extension of Functions and Interpolation of Data CP1 We discuss the problem of finding a Cm extension of a given real-valued function defined on an arbitrary given subset E Asymptotic Structure of Diffusion Flames at High of Rn. If E is infinite, then we ask how to decide whether Pressure with Soret Transport an extension exists. If E is finite, then we ask for efficient Mathematical models of nonpremixed flames usually as- algorithms to compute an extension with close-to-minimal m sume Fick’s law applies to the molecular diffusivities. How- C norm. ever, at elevated pressures, it is known that the Soret ef- Charles Fefferman fects, i.e. mass transport via temperature gradients, be- Princeton University, USA come important. Moreover, at very high pressures, includ- [email protected] ing supercritical conditions, Soret effects may become dominant. We investigate the asymptotic structure of diffusion flames with Soret mass transport. Our theory provides ex- JP1 plicit expressions for flame temperature, location and ex- The Dynamics of Obesity tinction conditions in terms of physico-thermal parameters affecting combustion. The past two decades have seen a surge in the incidence of obesity in the developed world. Changes in body weight Daniel Fong,JohnK.Bechtold that can lead to obesity are known to result from imbal- New Jersey Institute of Technology ances between the energy derived from food and the en- [email protected], [email protected] ergy expended to maintain life and perform physical work. However, quantifying this relationship has proved difficult. CP1 Here, I will show how simple concepts from dynamical systems can be used to provide a general quantitative descrip- Modes of Buckling of Viscous Fluid Threads tion of how body weight will change over time. The model The ‘coiling’ of a thin thread of viscous fluid falling onto a can then be used to answer open questions (and dispel surface is a familiar example of a buckling instability. Us- some myths) regarding weight loss and gain and provide ing an asymptotic ‘slender thread’ model embedded in a an explanation for the American obesity epidemic. numerical continuation procedure, we show that the onset Carson C. Chow of coiling can occur in three distinct modes involving dif- National Institutes of Health ferent balances of viscous forces, gravity, and inertia. We [email protected] confirm these numerical predictions using laboratory experiments, which also reveal a previously unobserved ‘ro- tatory folding’ mode of finite-amplitude buckling. Hydro- CP1 dynamic stability; turbulence (1704) Computational fluid Mathematical Model for the Behavior of Wildfires dynamics (1707) Incompressible fluids (1701)

Wildfires have been a long-standing problem in today’s so- Neil Ribe ciety. In this paper, we derive and solve a fluid dynam- Laboratoire FAST, France ics model to study a specific type of wildfire, namely, a [email protected] two dimensional flow around rising plume above a concentrated heat source modeling a fire line. This flow as- 8 AN10 Abstracts

CP1 terials Bifurcation and Chaos in Rotating Driven Cavity Flow Ostwald ripening is the self-organization of components of two phase mixtures through a diffusive mechanism. This Numerical simulations of the incompressible Navier Stokes phenomenon has been modeled using stochastic partial equations in a two-dimensional driven cavity are performed differential equations derived from the underlying micro- using high-order numerical methods. The effect of solid physics. In this talk, results from simulations using spec- body rotation rate and Reynolds on flow stability is stud- tral schemes for stochastic partial differential equations are ied. The results show that the flow converged to a station- described and new results for improving the efficiency of ary state up to a certain rotation rate for a given Reynolds such schemes will be described. These simulation results number. Above this critical value periodic oscillations in- are compared with theoretical results such as the Lifshitz- dicative of Hopf bifurcation and eventually chaos are ob- Slyozov growth law. served and analyzed. David J. Horntrop Dinesh A. Shetty Dept of Mathematical Sciences, Center for Applied Math School of Mechanical Engineering New Jersey Institute of Technology Purdue University [email protected] [email protected] CP2 Steven Frankel School of Mechanical Engineering A Highly Effective Finite Difference Approach for Purdue University Oscillatory Optical Beam Equations [email protected] This talk discusses a class of efficient and effective finite difference schemes for solving highly oscillated optical CP2 wave equations. To achieve the computational efficiency, mathematical transformations are used to map the com- Weak-Material Approximations of Natural Bound- plex model equations to coupled real differential equations. ary Conditions Then operator splitting strategies are introduced to de- The technique of Topology Optimization using the material compose the acquired nonlinear differential equations. An distribution approach is increasingly used in the design of Crank-Nicolson type discretization incorporates with par- advanced mechanical components. This approach approx- allel computation architectures is finally implemented un- imates natural boundary conditions at material interfaces der proper adaptations. The finite difference schemes con- by a fictitious-domain approach: a very weak material re- structed are numerically stable. Simulation experiments places regions of non-material (“void’). The energy-norm are given to illustrate our results, conclusions and expec- error associated with this approximation is shown to scale tations. linearly with the weak-material density and with the norm Qin Sheng of the boundary flux of a continuously extended solution Department of Mathematics to the original problem. Baylor University Martin Berggren Qin [email protected] Department of Computing Science, Umea University [email protected] Shekhar Guha U.S. Air Force Research Laboratory Fotios Kasolis [email protected] Department of Computing Science Umea University, Sweden Leonel Gonzalez [email protected] Air Force Research Laboratory Wright-Patterson AFB, OH 45433-7702 [email protected] CP2 The Effective Nonlinear Schrodinger Equation for Dark Spatial Plasmon-Polariton Solitons CP2 Shocks Versus Kinks in a Discrete Model of Dis- We derive an effective Nonlinear Schrodinger Equation for placive Phase Transitions propagation an optical dark spatial soliton at the subwave- length with surface plasmonic interaction. Starting with We consider dynamics of phase boundaries in a bistable Maxwell’s Equations we derive TM polarized type spatial one-dimensional lattice with harmonic long-range inter- solitons on a metal dielectric interface in which the dielec- actions. Using Fourier transform and Wiener-Hopf tech- tric is a Kerr medium that has self-defocusing. We numer- nique, we construct traveling wave solutions that represent ically and theoretically study the beam dynamics of this both subsonic phase boundaries (kinks) and intersonic ones nano-waveguide. (shocks). We derive the kinetic relation for kinks that provides a needed closure for the continuum theory. We show Sihon H. Crutcher that the different structure of the roots of the dispersion U. S. Army, Research, Development,& Engineering Center relation in the case of shocks introduces an additional free Redstone Arsenal, Alabama parameter in these solutions, which thus do not require [email protected] a kinetic relation on the macroscopic level. The case of ferromagnetic second-neighbor interactions is analyzed in detail. We show that the model parameters have a signif- CP2 icant effect on the existence, structure and stability of the Stochastic Simulation of Self-Organization in Ma- traveling waves, as well as their behavior near the sonic AN10 Abstracts 9

limit. case there is measurement error, the Tikhonov regularization method is still convergent. The study is motivated by Evgeni Troﬁmov physical considerations. Department of Mathematics University of Pittburgh Xinfu Chen [email protected] Mathematics University of Pittsburgh Anna Vainchtein [email protected] Department of Mathematics University of Pittsburgh Yan-Hsiou Cheng [email protected] nsysu [email protected]

CP2 C.K. Law Structure Preserving Tau Methods for Stochastic NSYSU Chemical Systems [email protected] Tau leaping methods can efficiently simulate models of stiff stochastic chemical systems. However, most existing meth- CP3 ods do not naturally preserve some chemical structures, ASolutiontoAnAmbarzumyanProblemonTrees such as integer-valued and nonnegative molecular population states. In this talk, we present structure preserving We consider the Neumann Sturm-Liouville problem defined tau methods for simulating stochastic chemical systems. on trees such that the ratios of lengths of edges are not nec- We illustrate the new methods through a number of bio- essarily rational. It is shown that the potential function of chemically motivated examples, and provide comparisons the operator must be zero if the spectrum is equal to that with existing implicit tau methods. for zero potential. This extends a previous result which states that if the edgelengths of a tree are in rational ra- Yushu Yang tio and the spectrum contains {(nπ)2}, then the potential University of Maryland Baltimore County function is zero. Our result gives a complete solution to this [email protected] Ambarzumyan problem. For a proof, we compute approximated eigenvalues for zero potential by using a generalized Muruhan Rathinam pigeon hole argument, and make use of a recursive formula University of Maryland, Baltimore County for characteristic functions. [email protected] Chun-Kong Law Jinglai Shen Dept of Applied Mathematics University of Maryland Baltimore County National Sun Yat-sen University [email protected] [email protected]

Eiji Yanagida CP3 Mathematical Institute Hopf Bifurcation of a Ratio-Dependent Predator Tohoku University Prey System with Time Delay [email protected]

In this study, we consider a predator-prey system with time delay where the predator dynamics is logistic with the car- CP3 rying capacity proportional to prey population. We study Existence of Solutions and Asymptotic Analysis of the impact of the time delay on the stability of the model a Singularly Perturbed BVP and by choosing the delay time t as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay I will outline a proof of the existence of two solutions of time t passes some critical values. Using normal form the- a singularly perturbed BVP εy +2y + ey =0,y(0) = ory and central manifold argument, we also establish the 0,y(1) = 0 for 0 <ε<1/10. Both the solutions have direction and the stability of Hopf bifurcation. Finally, we the same outer solution on (0, 1], but different boundary perform numerical simulations to support our theoretical behavior near x = 0. One of them is bounded, the other results. unbounded as ε → 0. If time permits, I will briefly discuss a rigorous proof that the conjectured formal asymptotic Canan Celik expansion for the smaller solution is correct. Bahcesehir University, Turkey [email protected] Susmita Sadhu University Of Pittsburgh [email protected] CP3 Reconstructing Potentials from Zeros of One Eigenfunction CP3 Value Functions and Transversality Conditions for We study an inverse nodal problem, concerning the re- Infinite-Horizon Optimal Control Problems construction of a potential of a Sturm-Liouville operator by using zeros of one eigenfunction as input. We pro- The purpose of this paper is to establish the transversality pose three methods for the reconstruction, one of which condition at infinity as necessary and sufficient conditions is the Tikhonov regularization method. The explicit er- for optimality in optimal control problems with an infi- ror bounds are calculated for all the three methods. In nite horizon under nonsmoothness assumptions, dispens- 10 AN10 Abstracts

ing with any controllability condition on the velocity. We CP4 introduce the coercivity of the integrand, which plays a sig- A Mixed Implicit-Explicit Multirate Numerical nificant role in verifying the sufficiency of the transversality Scheme for Time-Dependent Equations condition at infinity together with convexity assumptions. Consequently, it is possible to derive a new characteriza- We develop a multirate time integration method for sys- tion of optimality in terms of the adjoint inclusions for tems of time-dependent equations that present two signif- the value function and the Hamiltonian, without using any icantly different scales within the model. We use an it- transversality condition at infinity. eration scheme to decouple the two time scales. At each iteration, we use an implicit Galerkin method to solve for Nobusumi Sagara the fast scale variable and an explicit method to solve for Faculty of Economics, Hosei University the slow variable. The error equation consists of a com- [email protected] putable leading order term and a provably higher order expression. CP3 Brandon Chabaud The Inverse Nodal Problem and Ambarzumyan Pennsylvania State University Problem for the p-Laplacian with Various Bound- [email protected] ary Conditions Qiang Du We study the issues of the reconstruction and stability Penn State University of the inverse nodal problem for the one-dimentional p- Department of Mathematics Laplacain eigenvalue problem. A key step is the appli- [email protected] cation of a modified Prufer substitution. Two associated Ambarzumyan problems are also solved. We consider the 1 case of C potentials with the Dirichlet boundary condi- CP4 tion and extend to the case of integrable potentials with Domain Decomposition Methods for Coupled the periodic or anti-periodic boundary conditions. Stokes-Darcy Model C.K. Law The Stokes-Darcy model arises in many applications such NSYSU as surface water flows, groundwater flows in karst aquifers, [email protected] and petroleum extraction. It has higher fidelity than either the Darcy or Stokes systems on their own. However, cou- W.C. Lian pling the two constituent models leads to a very complex NKMU system. This presentation discusses the domain decompo- [email protected] sition methods for solving the coupled Stokes-Darcy system. Convergence of these algorithms is demonstrated and Wei-Chuan Wang the results of computational experiments are presented to [email protected] illustrate their features. [email protected] Xiaoming He Y.H. Cheng Department of Scientific Computing NSYSU Florida State University [email protected] [email protected]

CP4 CP4 Effect Of Abrupt Expansion On Nanofluid Flow Solving High Speed Flow Problems with An Im- And Heat Transfer Characteristics: A Numerical proved Version of Ice. Study The Implicit Continuous-fluid Eulerian(ICE), a semi- Using the standard k-e turbulence model, incompressible implicit finite-volume solver, is used for simulating prob- nanofluid flow is simulated. Effect of alumina volume lems in multiphase flow which span a wide area of science concentration in water flow and heat transfer character- and engineering. ICE is utilized by the C-SAFE code Uin- istics downstream of an axisymmetric sudden expansion tah at the University of Utah to simulate explosions, fires is investigated. Assuming homogenous nanofluid, different and other fluid and fluid-structure interaction phenomena. alumina volume fractions in water, ranging from 0.01 to The implementation of ICE used in Uintah is given in many 0.05 are considered. The simulation revealed recirculation papers by Kashiwa at Los Alamos and extended to solve downstream of the expansion. Wall shear stress and heat multifield cases by Harman at Utah. In its original form transfer coefficient are shown to increase linearly with in- the ICE algorithm does not perform as well as the best creasing alumina volume fraction, up to 14% for alumina current methods for compressible flow problems. An im- volume fraction of 0.05. It is shown that the boundary proved version of ICE method using limiters is discussed layer reattachment length is insensitive to alumina volume and the obtained numerical results for several test prob- fraction under the assumptions invoked. lems are shown.

Khalid N. Alammar Lethuy T. Tran,MartinBerzins Department of Mechanical Engineering University of Utah King Saud University, Riyadh, SA [email protected], [email protected] [email protected] CP4 A Particle-in-Cell Method with Remapping and AN10 Abstracts 11

Local Mesh Refinement for Plasma Physics equations arising from motion within a sphere with a small gate for escape. Computational methods will be used to The Vlasov-Poisson equation describes the kinetic behavior compare via statistical analysis with the theoretical results of a collisionless plasma. We present an accurate and sta- to determine whether they are consistent, and also to ex- ble particle-in-cell based algorithm for solving the Vlasov- plore the limitations of the theory. Poisson equation. The method overcomes the numerical noise inherent in the usual particle-in-cell methods by pe- Carey Caginalp riodically remapping the distribution function on a hier- University of Pittsburgh archical of regularized grids. Positivity can be preserved [email protected] through the novel use of a limiter. The method has successfully been applied to a set of one-dimensional problems, e.g., strong Landau damping, two stream instability. Sec- CP5 ond order accuracy is observed over short times. Over long Predictability in Stochastic Dynamical Systems times, the test problems gradually evolve into a weakly collisional domain. There, filamentation in velocity space This talk presents sensitivity and predictability analysis of develops which leads to instability and loss of accuracy. stochastic reaction networks. Polynomial chaos expansions We solve this issue by introducing a collisional term to the are used to efficiently perform non-intrusive parametric un- Vlasov-Poisson equation. The collision equation is solved certainty propagation in the presence of intrinsic noise. on the remapping grids periodically, and coupled to the The effects of strong nonlinearities and bimodalities in the system using operator splitting. Second order accuracy is forward model are relieved with an adaptive, dimension- obtained for the coupled system. specific domain decomposition technique. The curse of dimensionality is addressed using sparse quadrature methods Bei Wang for orthogonal projections. Department of Applied Science University of California at Davis Bert J. Debusschere [email protected] Energy Transportation Center Sandia National Laboratories, Livermore CA Greg Miller [email protected] University of California Department of Applied Science Khachik Sargsyan [email protected] Sandia National Laboratories [email protected] Phillip Colella Lawrence Berkeley National Laboratory Habib N. Najm [email protected] Sandia National Laboratories Livermore, CA, USA [email protected] CP4 A Lagrangian Vortex Method for Barotropic Vor- ticity Equation on a Rotating Sphere CP5 On the Maximum Entropy Solution to PDE-Based We present a Lagrangian vortex method for the barotropic Inverse Problems vorticity equation on a rotating sphere. The method tracks the flow map and absolute vorticity using Lagrangian par- We present a novel approach, based on the principle of ticles and panels. The velocity is computed from the Biot- maximum entropy, to statistical inverse problems con- Savart integral on the sphere. An adaptive refinement strained by partial differential equations (PDEs). Indi- strategy is implemented to resolve small-scale features and rectly observable parameters are estimated by a probabil- a treecode is used for efficient computation. Results are ity distribution that best represents our current state of presented for Rossby-Haurwitz waves and vortex interac- knowledge and does not impose additional synthetic con- tions. straints. Uncertainty is quantified naturally by information entropy, a by-product of our inversion method. Results are Lei Wang compared to the standard Bayesian approach for a thermal University of Michigan conduction problem. [email protected] Chad E. Lieberman John P. Boyd MIT University of Michigan [email protected] Ann Arbor, MI 48109-2143 USAUSA [email protected] Karen Willcox Massachusetts Institute of Technology Robert Krasny [email protected] University of Michigan Department of Mathematics CP5 [email protected] Multiscale Methods for Statistical Inference in El- liptic Problems CP5 Estimating the coefficients of an elliptic or parabolic PDE Asymptotics and Computation on Brownian Mo- from observations of the solution is typically an ill-posed tion Escape problem. Finite data resolution and the smoothing char- This talk will focus on asymptotics of partial differential acter of the forward operator limit one’s ability to recover 12 AN10 Abstracts

fine-scale information. We use the multiscale finite ele- models and numerical methods. We treat American opment method (MsFEM) to formulate a low-dimensional tion models as a special class of obstacle problems. Fi- and computationally efficient inference problem in this con- nite element formulation is introduced together with error text. A fully Bayesian treatment of the problem conditions analysis of numerical solutions. Some interesting arbitrage both small-scale and large-scale variability in the coeffi- properties about sensitivity of the option price to the pay- cients on available data. off function are proved. We also give a criterion for the convergence of numerical free boundaries (optimal exercise Youssef M. Marzouk, Matthew Parno boundaries) under mesh refinement. Some future research Massachusetts Institute of Technology plans will be discussed. [email protected], [email protected] Yongmin Zhang Xi’an Jiaotong - Liverpool University CP5 [email protected] A Multi-Scale Random Basis Method for Stochas- tic PDEs CP6 Uncertainty quantification is important in the field of engi- The Two-Machine Flowshop Scheduling Problem neering and applied mathematics. In this talk I will intro- to Minimize Maximum Lateness duce a multi-scale random basis method for elliptic PDE with random coefficients. We first derive the multi-scale This study addresses a two-machine flowshop scheduling random basis offline based on the Karhunen-Loève decom- problem to minimize maximum lateness where processing position using Monte-Carlo simulations for one particular times are random variables with lower and upper bounds. non-zero force term. Then we use the multi-scale random Given that the problem is NP-hard, we propose several basis to solve the elliptic PDE for a general force term. algorithms and heuristics. The proposed algorithms and One important advantage of this method is that only very heuristics are compared through randomly generated data. small number of random bases is required to accurately The computational analysis has shown that one of the pro- represent the stochastic solution, thus providing significant posed heuristics performs very well with an overall average saving in the on-line computational effort compared with percentage error of less than one. existing methods. Numerical results will be provided to demonstrate the effectiveness of the method. Ali Allahverdi Kuwait University Mike Yan [email protected] Applied and computational mathematics California Institute of Technology Harun Aydilek [email protected] Gulf University for Science and Technology [email protected] Tom Hou California Institute of Technology [email protected] CP6 Matrix Splitting Method Combined with the Gra- Mulin Chen dient Projection Method for Support Vector Ma- Caltech chines [email protected] We propose the matrix splitting method combined with the gradient projection method can be applied for the CP5 quadratic programming problem with a single linear equal- A Stochastic Heterogeneous Multiscale Method for ity constraint and box constraints arising in training sup- Porous Media Flow port vector machines. The support vector machine problem has a dense Hessian matrix. The matrix splitting al- A stochastic heterogeneous multiscale method is intro- gorithm transforms the problem into a sequence of approx- duced for modeling flows in heterogeneous media. To ac- imate subproblems which have a diagonal Hessian matrix count for the high stochastic dimensionality of the perme- and can be solved by the efficient pegging algorithm. The ability field, we employ the recently developed stochastic gradient projection method is combined with the matrix high dimensional model representation (HDMR) technique splitting method to reduce its sensitiveness. Some tech- for the solution of stochastic PDEs. HDMR decomposes niques for calculating the stepsize and non-monotone line the original high-dimensional problem into several lower search are applied for the proposed method to compare dimensional sub-problems which are efficiently solved us- their performances. In addition, we use the incomplete ing adaptive sparse grid collocation. The methodology is Cholesky decomposition method for large scale problems. demonstrated through a number of benchmark examples Our experimental results show the viability of the proposed of flows in porous media. algorithm.

Nicholas Zabaras,XiangMa Gitae Kim, Chih-Hang Wu Cornell University Kansas State University [email protected], [email protected] [email protected], [email protected]

CP5 CP6 American Option Pricing Models and Obstacle On the Extremal Problem of Polya Problems The notion of transﬁnite diameter of planar sets was in- We ﬁrst give a brief overview of American option pricing troduced by M. Fekete around 1920s. This concept plays AN10 Abstracts 13

an important role in the classical complex analysis and is constrained problems. Compared to traditional SQP algo- related to other well-known concepts such as the logarith- rithms, this algorithm does not require the exact evaluation mic capacity and Chebyshev polynomials. The transﬁnite of constraint Jacobian in each optimization step but uses diameter of a compact set in the complex plain is the limit an approximation of the ﬁrst-order derivative information. of n-diameters of the set. For each n ≥ 3, the n-diameter Hence the proposed algorithm is well suited to solve opti- dn(E)ofE is given by mization problems where the constraint Jacobian is dense i.e. the time required for the computation of the Jaco- 2 bian and its factorization dominates the overall optimiza- dn(E)=max /zi − zj / n(n−1) , (1) tion process. The quality of the approximated constraint 1≤i

1 Carnegie Mellon University dn(E) ≤ n n−1 (2) [email protected] and the equality holds for n-tuples of equally spaced points on the boundary of D. While investigating the transfinite Biegler Lorenz diameter of sets of constant width, Prof. Zair Ibragimov Carnegie Mellon University was led to the following weaker version of Polya’s problem: [email protected] among all n-tuples E = {z1,z2, ···,zn} with |zi − zj |≤2, find one with the largest n-diameter. He conjectured that Walther Andrea the extremal configuration will also be the vertices of a Institute of Mathematics regular n-gon, at least when n is odd. In this paper, I will University of Paderborn present my solution of Ibragimov’s problem for the case [email protected] n = 5 and approach for n = 7. I will also discuss why other cases can not be proved using the same method as for n =5. CP6 Image Space Analysis and Scalarization for Opti- Tuan N. Le mization of Multifunctions Fairmont High School [email protected] Using a new method based on generalized sections of feasible sets, we obtain optimality conditions for vector optimization of objective multifunction with multifunction CP6 constraints. In particular, necessary and sufficient condi- A Binary Tree Based Search Algorithm for Global tions for scalarization of ε-optimization for multifunctions Optimization are deduced. We describe a binary tree based search method for solving Jafar Zafarani global optimization problems in the framework of a recently Dept of Maths. , Sheikhbahaee University developed memoryless interval-based optimization method. University of Isfahan, Isfahan, 81745-163, Iran It attempts to improve the reliability of the memoryless al- [email protected] gorithm while sacrificing little both in memory space usage and in overall speed of convergence. A binary tree data structure is introduced as a means of memory that would CP7 guide the algorithm to locate a new approximate solution, Mortar Mixed Finite Element Method for Curved while the overall algorithm employs the memoryless algo- Domains rithm iteratively. We present a mortaring (or a domain decomposition) Min Sun method for the Darcy problem that can handle curved do- Univ. of Alabama mains. The meshes are allowed to be non-matching over Math Dept the subdomain interfaces and the continuity is enforced [email protected] weakly via mortars, i.e. Lagrange multipliers. We show error estimates and confirm the results with numerical ex- Laura Ingram amples. The University of Alabama Mika Juntunen [email protected] University of Texas at Austin, ICES / CSM [email protected] CP6 An Inexact Trust-Region Based SQP Method Mary F. Wheeler for Nonlinear Programming Problems with Dense Center for Subsurface Modeling Constraint Jacobians University of Texas at Austin [email protected] We present a trust-region based SQP algorithm for the solution of optimization problems with general non-linear 14 AN10 Abstracts

CP7 includedintwospacedimensions(d = 1 or 2). By applying Numerical Solution of Nonlinear Two-Dimensional the interpolated postprocessing technique, similar results Parabolic Partial Differential Equations by Branch- are also obtained on the error between the interpolation of ing Stochastic Processes the approximate solution and the exact solution. A new parallel numerical algorithm based on generating Kening Wang suitable random trees by Monte Carlo has been developed University of North Florida for solving nonlinear parabolic partial differential equa- [email protected] tions. While classical techniques based on a deterministic domain decomposition exhibits strong limitations, proba- Shuang Li bilistic methods are capable of exploit massively parallel Ernst & Young LLP architectures since the problem can be fully decoupled. [email protected] New examples of nonlinear equations have been run on a high performance supercomputer, showing a remarkable scalability and performance. CP7 Numerical Methods for Elliptic and Parabolic Angel Rodriguez-Rozas Equations in Perforated Domains Center for Mathematics and its Applications Department of Mathematics - Instituto Superior Técnico Let denote the size ratio of the holes of some perforated [email protected] domain to the whole domain. As closes to 0, a direct numerical simulation of the solutions of elliptic equations Juan Acebron in perforated domains can be very expensive. It is known Center for Mathematics and its Applications that the elliptic solutions approach a solution of some ho- Department of Mathematics - Instituto Superior Tecnico mogenized equation when is very small. It is reasonable [email protected] to expect that the numerical approximation of the solution of the homogenized equation is a good approximation for Renato Spigler the elliptic solutions in perforated domains when is small Dipartimento di Matematica, Universita Roma tre. enough. We use standard numerical methods to obtain the approximation for the homogenized elliptic solution and to Rome (Italy) ∞ 2 [email protected] derive the L estimate, L gradient estimate, and Lips- chitz estimate for the difference between the exact elliptic solutions and the numerical approximation of the homoge- CP7 nized solution. Counterpart results for parabolic equations Multiple Scattering from Complexly Shaped are also obtained. Coated Obstacles Li-Ming Yeh A numerical technique consisting of the Helmholtz equa- Department of Applied Mathematics tion in curvilinear coordinates coupled with an almost ex- National Chiao Tung University, Taiwan act Dirichlet-to-Neumann boundary condition is applied [email protected] to multiple scattering from coated obstacles of arbitrary shape. Novel elliptic grids conforming to complex geomet- CP7 rical configurations of several two-dimensional coated obstacles are constructed and approximations of the scattered New Immersed Finite Element Methods For Planar field supported by them are obtained. The numerical re- Elasticity Interface Problem sults illustrate the ability of the proposed technique to deal We will discuss immersed finite element (IFE) methods for with heterogeneous media. solving the planar elasticity interface problems with Carte- Vianey R. Villamizar sian meshes. The new IFE functions are formed on Carte- Department of Mathematics, Brigham Young University, sian meshes independent of the interface between different Provo, Utah 84602-6539 elastic materials. Some basic properties of the IFE func- [email protected] tions will be presented including the optimal approximation capability of these IFE functions spaces. Furthermore, numerical examples indicate that these IFE methods con- Sebastian Acosta verge optimally in both L2 and semi-H 1 norms. Department of Mathematics, Brigham Young University [email protected] Xu Zhang Virginia Tech [email protected] CP7 Strong Superconvergence of Finite Element Meth- Tao Lin ods for Linear Parabolic Problems Department of Mathematics We study the strong superconvergence of a semi-discrete Virginia Tech finite element scheme for linear parabolic problems on Q = [email protected] Ω×(0,T], where Ω is a bounded domain in R(≤)with piecewise smooth boundary. We establish the global two CP8 order superconvergence results for the error between the Improved Bounds on Restricted Isometry Con- approximate solution and the Ritz projection of the exact 1,p stants for Gaussian Matrices solution of our model problem in W (Ω) and Lp(Q)with ≤ ∞ 2 p< and the almost two order superconvergence in The Restricted Isometry Constants (RIC) of a matrix A 1,∞ ∞ W (Ω) and L∞(Q). Results of the p = case are also measures how close to an isometry is the action of A on AN10 Abstracts 15

vectors with few nonzero entries, measured in the 2 norm. Networks Using Slime Mold Specifically, the upper and lower RIC of a matrix A of size n × N is the maximum and the minimum deviation from We present a new protocol for wireless sensor networks unity (one) of the largest and smallest, respectively, square (WSNs) based on models of network self-assembly in N Physarum polycephalum, a true slime mold. Slime mold of singular values of all k matrices formed by taking k columns from A. Calculation of the RIC is intractable assembles and modifies networks of tubes to distribute refor most matrices due to its combinatorial nature; how- sources throughout its cell body. This system offers an ever, many random matrices typically have bounded RIC elegant solution to resource allocation problems similar to in some range of problem sizes (k, n, N). We provide the extracting data from WSNs. We present modeling, anal- best known bound on the RIC for Gaussian matrices, which ysis and simulation of this protocol for WSNs based on is also the smallest known bound on the RIC for any large models of Physarum polycephalum. rectangular matrix. Improvements over prior bounds are Louis F. Rossi achieved by exploiting similarity of singular values for ma- University of Delaware trices which share a substantial number of columns. [email protected] Bubacarr Bah, Jared Tanner University of Edinburgh Ke Li [email protected], [email protected] University of Delaware Computer and Information Sci. [email protected] CP8 A Mathematical Model of Communications Net- Claudio Torres works University of Delaware [email protected] The behavior of a communication network can be modeled at the node/link scale as traffic units flowing along Kyle Thomas the links connected by nodes. We present an approach to University of Delaware packet flow that derives the node/link network model and Chemical Engineering connects it to a fluid-like model of traffic flow. The discrete [email protected] node/link model describes packet queuing and the flow of packets from spatial point to spatial point. The model as- Chien-Chung Shen sumes that packets reside in buffers at each node, and are University of Delaware identified by their destination and the length of time they Computer and Information Sci. have resided in the buffer. An algorithm was created for [email protected] packets to exit the buffer at each node according to their age (“first in, first out”) and travel to the next node along a predetermined path to their destination. This algorithm CP8 calculates the rate at which packets distribute themselves An Iterative Thresholding Algorithm Using En- to the next link in the route to their destination, assumes hanced Sparsity a source of packets originating at the node, and subtracts packets arriving at their destination. A continuum model In this paper we propose a variation of the iterative soft- is derived from this discrete flow model by associating each thresholding algorithm that is used to find sparse (approx- node with a spatial area defined by Voronoi polygons. The imate) solutions to the equation Ax = b. In this variation, association with spatial areas leads to a flow continuity the sparsity of the iterate vector xn is used to redefine the equation. The continuity equation describes the density regularizing penalty function. Minimization of the newly of packets as a function of time and space, so that we are defined penalty function, then leads to the next iterate. able to predict changes in global flow patterns on a macro- Numerical data showing effectiveness of this approach will scopic scale due to aberrant flow behavior, such as outages be presented as well. or heavy traffic. Exact (non-classical) solutions are derived for one dimensional flows using the method of character- Hugo J. Woerdeman istics. These solutions show that if a combination of the Drexel University packet sources and network flow saturate the network flow hugo @ math.drexel.edu capacity, the packet density grows at the nearest upstream node. When the source strength is reduced, or when flow Ingrid Daubechies is restored, the buffered packets flow at capacity until the Princeton University density has been reduced. Multiple sources and destina- Department of Mathematics tions and multidimensional effects are discussed [email protected] Donald A. Drew Rensselaer Polytech Institute CP9 Dept of Mathematical Sciences A-Posteriori Estimator for Parabolic Coupled Sys- [email protected] tems of Pdes

James R. Gatewood We present an extension of recent results by [Bernardi et al] Rensselear Polytechnic Institute and [Verfurth] on residual a-posteriori estimators for scalar [email protected] parabolic PDEs. Our results concern multilevel discretization of parabolic systems in which each component can be computed on a diﬀerent grid. We analyze contribution of CP8 each term and show convergence results. The estimator is Modeling Adaptive Protocols for Wireless Sensor robust i.e. the eﬃciency index remains essentially constant 16 AN10 Abstracts

when the coefficients of the system vary even by several or- refining a mesh locally. We present a residual-based a pos- ders of magnitude. teriori error estimate for the finite element discretization of elliptic equations using PHT-splines basis functions. Then Viviane Klein numerical experiments are presented to verify the theoret- Oregon State University ical results and demonstrate the robustness of the error [email protected] estimate.

Malgorzata Peszynska Li Tian Department of Mathematics Penn State University Oregon State University [email protected] [email protected] Falai Chen Department of Mathematics CP9 University of Science and Technology of China Preconditioning for Implicit Ocean Models chenﬂ@ustc.edu.cn

One challenge in ocean modeling is the spin-up problem, Qiang Du which requires integrations over centuries of time. Using Penn State University implicit methods to take large timesteps requires effective Department of Mathematics preconditioners. We examine thin stratified fluid problems [email protected] as modeled by the Parallel Ocean Program(POP), considering multilevel preconditioners for the velocity-salinity- temperature subproblem and block preconditioners fully CP9 coupled system. We present theoretical results to guide Robust Multigrid Preconditioners for the High- the choice of preconditioners as well as numerical results Contrast Diffusion and Biharmonic-Plate Equa- illustrating the effect of those choices in practice. tions Chris Siefert, Andy Salinger We study finite volume discretization of high-contrast dif- Sandia National Laboratories fusion equation and HCT and Morley discretizations of [email protected], [email protected] high-contrast plate equation. We construct preconditioners that are robust with respect to the magnitude of the CP9 coefficient contrast and mesh size simultaneously. For that, we prove robustness of the preconditioner proposed by Ak- ADI As Preconditioner for Krylov Subspace Meth- soylu et al. (2008) by extending the devised singular per- ods in Serial and Parallel turbation analysis to the above discretizations leading to The alternating directions implicit (ADI) method is a a same family of preconditioners used for different PDEs classical iterative method for numerically solving linear and discretizations. systems arising from discretizations of partial differential Zuhal Yeter equations. We use ADI as a preconditioner for Krylov sub- Department of Mathematics, Louisiana State University space methods for a linear system from a finite difference [email protected] approximation of an elliptic test problem in three dimensions. The method is attractive because it allows highly efficient matrix-free implementations both in serial Matlab Burak Aksoylu and in parallel C with MPI. Louisiana State University, Department of Mathematics Center for Computation & Technology Kyle Stern [email protected] University of Maryland, Baltimore County [email protected] CP10 \√ Matthias K. Gobbert New Upper Bounds on the Complexity of - University of Maryland, Baltimore County Complete Algorithms Department of Mathematics and Statistics [email protected] In this talk we derive some new upper bounds on the complexity of algorithms which can solve NP-Complete prob- Andrei Draganescu lems. Also upper bounds on the complexity of algorithms University of Maryland, Baltimore County which have a high likelihood of solving NP-Complete prob- [email protected] lems within the given complexity bounds will be discussed. Emphasis will be placed on one or two NP-Complete problems. CP9 Adaptive Finite Element Method for Elliptic Equa- Michael Laidacker tions over Hierarchical T-Meshes Lamar University Beaumont, Texas Isogeometric analysis based on NURBS (Non-Uniform Ra- [email protected] tional B-Splines) as basis functions preserves the exact geometry but suffers from the inconvenience of a purely local refinement. In this paper, we use the so called polyno- CP10 mial splines over hierarchical T-meshes (PHT-splines) to Production Lot Sizing with a Secondary Outsourc- construct basis functions which share the similar properties as B-splines, and allow us to overcome the difficulty of AN10 Abstracts 17

ing Facility lem instances quickly on a PC.

An extended Economic Production Quantity (EPQ) model Hossein M. Soroush is investigated in this paper where a fixed lot sizing pol- Kuwait University icy is implemented to reduce the complexity of produc- P.O. Box 5969 tion planning and inventory control, and outsourcing with [email protected] a secondary facility is used to supplement the lot sizing policy and to cope with the random demand. The considered cost includes: set up cost for the batch production, CP10 inventory carrying cost, backorder cost when the demand A Polynomial Arc-Search Path-Following Algo- cannot be met during the production period, and outsourc- rithm for Linear Programming ing cost when the total demand is greater than the lot size in one production cycle. Under some mild conditions, the A simple analytic arc is proposed to approximate the cen- expected cost per unit time can be shown to be convex tral path of the linear programming. A primal-dual path- with respect to the lot size. The average cost reduction of following interior-point algorithm is developed to search the proposed model is 57.5%, when compared with that of the optimal solution along the analytic curve. The algorithm is proved to be polynomial with complexity bound the classical lot sizing policy. Outsourcing in the produc- 1 tion lot sizing policy contributes to a significant portion O(n 2 log(1/)). Numerical test is conducted for prob- of this cost savings when the mean demand rate is high. lems in Netlib. The result shows that the new algo- The numerical results also demonstrate that randomness rithm is promising compared to Matlab optimization tool- of demand has significant impact on the lot sizing policy. box linprog which implements the state-of-art Mehrotra’s predictor-corrector algorithm. Shine-Der Lee National Cheng Kung University Yaguang Yang Dept. of Industrial & Information Management NRC [email protected] [email protected]

Shu-Chuan Lan, Chin-Ming Yang National Cheng Kung University CP11 Dept. of Industrial & Inform Management Nonlinear Asymptotic Stability in the Semi-Strong [email protected], [email protected] Pulse Regime for the Gierer-Meinhardt Equation with N-Pulse Positions

CP10 This paper shows the nonlinear asymptotic stability of an Static Vertex Reordering Schemes for Local Mesh N-pulse solution to the Gierer-Meinhardt equation. Us- Quality Improvement ing semigroup and resolvent estimates, we are able to prove stability with renormalization group methods. In Vertex reordering can be performed within the context of the semi-strong limit the localized activator pulses interact local mesh quality improvement with the goal of decreas- strongly through the slowly varying inhibitor. The interac- ing the amount of time required for the mesh optimization. tion causes pulse amplitudes and speeds to change as the In this talk, we investigate various static vertex reordering pulse separation evolves. In addition the point spectrum schemes, based on mesh quality and the performance of the of the associated linearized operator evolves with the pulse optimization algorithm, and the trade-offs between order- dynamics. ing and overall performance of the optimization algorithm. The study uses the Laplace smoother within the Mesquite Thomas Bellsky package to optimize hexahedral meshes. Michigan State University Department of Mathematics Jeonghyung Park, Suzanne M. Shontz [email protected] The Pennsylvania State University [email protected], [email protected] Keith Promislow Michigan State University Patrick M. Knupp [email protected] Sandia National Laboratories [email protected] CP11 Nonsmooth Systems and Their Application CP10 Minimizing Weighted Quadratic Functions of Job For many years, nonsmooth systems have been used as Lateness in the Single Machine Scheduling System simplifications for certain types of smooth systems. In this with Inserted Idle Time talk we will show how this approach can lead to significant differences between solutions of both systems. We will il- This paper studies the problem of finding optimal sched- lustrate the talk using the example of a genetic regulatory ules that minimize the weighted sum of some quadratic network. functions of job lateness on a single processor where an idle time is inserted before the processing of the first job John Hogan begins. We introduce a novel exact two-stage algorithm Bristol Centre for Applied Nonlinear Mathematics for this NP-hard problem based on a precedence relation Department of Engineering Mathematics, University of structure among adjacent jobs. Our computational results Bristol demonstrate that the algorithm can solve very large prob- [email protected] 18 AN10 Abstracts

CP11 Cornell University Traveling Waves Driven by Spatio-Temporally [email protected] Varying Stimuli in Neural Field Equations Bernd Krauskopf We examine the existence of traveling waves for continuum University of Bristol neuronal networks modeled by integro-differential equa- Department of Engineering Mathematics tions. For a scalar field model with a general firing rate [email protected] function and spatio-temporally varying stimulus, we show stimulus-locked fronts exist for a certain interval of stim- Hinke M. Osinga ulus speeds. We also add a slow adaptation equation and University of Bristol obtain a formula, involving an adjoint solution, for stimu- Department of Engineering Mathematics lus speeds that induce locked pulses and perform a singular [email protected] perturbation analysis to approximate the adjoint. Jozsi Z. Jalics Martin Wechselberger Department of Mathematics and Statistics University of Sydney Youngstown State Univeristy [email protected] [email protected] CP11 G. Bard Ermentrout, Jonathan E. Rubin University of Pittsburgh Parallel Time Integration for a Membrane Problem Department of Mathematics A Ratio-based Parallel Time Integration method is applied [email protected], [email protected] to a membrane second order initial value problem, given by y −b|y |q−1y +|y|p−1y =0,wherep ≤ q ≤ 2p/(p+1). The CP11 solution y(t) exhibits an oscillatory behavior and blows- On the Stability of An Operator-Difference Scheme up as t tends to infinity. After transforming the initial for Non-Linear Hyperbolic Differential Equation value problem into a first order system of ordinary differential equations, we use a method that automatically We study the stability of second-order of accuracy differ- generates time-slices and rescales the time variable over ence scheme for the nonlinear hyperbolic equation u (t)+ every slice. Theoretically, in the case when q =2p/(p +1), A(t)u(t)=f (t, u, u)(0≤ t ≤ T ),u(0) = ϕ, u(0) = ψ in a such method leads to invariance with respect to the time Hilbert space H with the self-adjoint positive-definite oper- slices in the sense that the computation of y(t) is reduced ator A(t) with the domain of D (A (t)) . A new second-order to its finding over one slice. Whereas in the case when of accuracy difference scheme with operator coefficient in p ≤ q<2p/(p + 1), the method yields asymptotic simi- a Hilbert space for the approximate solution of the initial- larity to a limit model, in the sense that the the rescaled value problem is contracted. The stability estimates for systems admit a limit system. In both cases, this leads to the solution of this difference scheme are established. an interesting Ratio based Parallel Time Integration algorithm - RaPTI. Its implementation on a cluster of 2 to 8 Mehmet Emir Koksal,RaviP.Agarwal processors proves to be extremely efficient (decreasing ex- Florida Institute of Technology ecution time when increasing the number of processors). mkoksal@fit.edu, agarwal@fit.edu

ALLABEREN Ashyralyev Nabil R. Nassif Fatih University Mathematics Department [email protected] American University of Beirut [email protected]

CP11 CP12 Mixed-Mode Oscillations in the Koper Model Shift-Invert Arnoldi Approximation to the Toeplitz Mixed-mode oscillations (MMOs) appear in a wide variety Matrix Exponential of applied dynamical systems arising in chemistry, biology and physics. The model investigated by Koper in 1995 pro- The shift-invert Arnoldi method is employed to generate an vides an illustration how fast-slow system mechanisms can orthonormal basis from the Krylov subspace corresponding explain the complicated MMO patterns. We shall illustrate to a real Toeplitz matrix and an initial vector. The vec- the techniques required for the analysis which include ana- tors and recurrence coefficients produced by this method lytical as well as numerical ideas. An outlook on a possible are exploited to approximate the Toeplitz matrix exponen- general classification of MMOs will be given as well. tial. Toeplitz matrix inversion formula and rapid Toeplitz matrix-vector multiplications are utilized to lower the com- Christian Kuehn putational costs. For convergence analysis, a sufficient con- Center for Applied Mathematics dition is established to guarantee that the error bound is Cornell University independent of the norm of the matrix. Numerical results [email protected] are given to demonstrate the efficiency of the method. Spike T. Lee, Hong-Kui Pang, Hai-Wei Sun Mathieu Desroches Department of Mathematics University of Bristol University of Macau Engineering Mathematics [email protected], [email protected] [email protected], [email protected], [email protected]

John Guckenheimer AN10 Abstracts 19

CP12 method. Inexact Newton and Krylov Methods for Riccati Equations Hai-Wei Sun Department of Mathematics We explore the use of Inexact Newton methods to obtain a University of Macau low-rank solution of the Continuous-time algebraic Riccati [email protected] T equation. That is, we are looking for X∗ = YY ,withY ∈ n×p R , p n, such that F (X∗)=0whereF (X)=AX + T T T n×n n×m CP12 AX − XBB XA + C C, A ∈ R ,B ∈ R ,C ∈ Rq×n,andm, q n. The standard formulation of the Interpreting IDR As a Petrov-Galerkin Method Newton method for this problem implies the solution of a In this talk, we show that the IDR method of Sonn- (different) Lyapunov equation at each iteration. We use a eveld and van Gijzen [SIAM J. Sci. Comput., 31:1035– Krylov projection method to find an approximate low-rank 1062, 2008] can be interpreted as a Petrov-Galerkin (pro- solution of this Lyapunov equation. As is well known,the jection) method with a particular choice of left Krylov sub- accuracy of these approximations do not need to be too spaces; these left subspaces are rational Krylov spaces. precise at first, but need to improve as the (outer) Newton Consequently, other methods, such as BiCGStab and method proceeds. We also explore the use of some recycling ML(s)BiCG, which are mathematically equivalent to some strategies to reduce the computational cost. versions of IDR, can also be interpreted as Petrov-Galerkin Marlliny Monsalve methods. The connection with rational Krylov spaces in- Department of Mathematics spired a new version of IDR, called Ritz-IDR, where the Temple University poles of the rational function are chosen as certain Ritz [email protected] values. Experiments are presented illustrating the effectiveness of this new version.

CP12 Valeria Simoncini Univeristy of Bologna The Iterative Solution of General Finite Linear Sys- and IMATI-CNR, Pavia tems Via Flexible New Dual Variational Principles [email protected] These principles provide promising new approaches to numerically solving general systems of linear equations Daniel B. Szyld and/or linear inequalities – including general linear opti- Temple University mization problems. The resulting methodologies require Department of Mathematics only the numerical computation of a critical solution for [email protected] an unconstrained objective function – carefully chosen for each individual problem from an infinite number of candi- date functions, with the intent of employing parallel proces- CP13 sors and/or exploiting any special system structure (such Charge Retrieval Analysis for Lightning Flashes in as sparsity). This infinite flexibility makes these new it- a Mountain Thunderstorm erative solution methodologies competitive with, as well as much more general than, the previously developed iter- On 24 August 2007, a balloon was launched from Langmuir ative solution methodologies for solving large-scale linear Laboratory, NM. An electric field sonde (Esonde) measured systems – including both the conjugate-gradient method the electric field during the flight, while simultaneously for symmetric positive-definite systems of linear equations Lightning Mapping Array recorded the location of VHF and the interior-point methodologies for linear optimiza- pulses generated during lightning. The Esonde and LMA tion. Finally, this presentation provides an introduction data are the basis for an inverse problem whose solution to the basic ideas and fundamental theory of generalized yields the charge transport due to a lightning stroke. The geometric programming, within the familiar context of el- analysis of several interesting flashes provides new insight ementary linear algebra, using only elementary convexity into charge transport processes in a thunderstorm. theory and multi-variable differential calculus. Beyza C. Aslan Elmor L. Peterson University of North Florida Systems Science Consulting [email protected] [email protected] CP13 CP12 An Adaptive Mesh Refinement Strategy for Finite Fast Exponential Time Integration for Pricing Op- Volume Methods tions in Jump-Diffusion Models In this talk we will present a goal-oriented adaptive mesh We consider pricing options in jump-diffusion models which refinement strategy for finite volume methods. The strat- require solving partial integro-differential equations. Dis- egy is based on the a posteriori error analysis of the numer- cretizing by the central spatial finite difference scheme ical solution using the duality between the primal equation leads to linear systems of ordinary differential equations and the adjoint equation. This approach has two major with Toeplitz structure. A fast exponential time integra- advantages: one is that it does not require the numerical tion scheme, where the shift-invert Arnoldi method is em- method to be in a variational form, for which most FVMs ployed for the Toeplitz matrix exponential, is proposed to are not; the other is that the well-posedness of the ad- approximate the solutions of those systems. Numerical re- joint problem can be studied using standard PDE theories. sults are given to demonstrate the efficiency of the proposed Examples in 1D and 2D will be shown. When time permitting, the application of such strategy to regional modeling 20 AN10 Abstracts

will be discussed. consider how they behave in the ADI iteration and connect this to projection methods for solving Lyapunov equations. Qingshan Chen Florida State University [email protected] Garret M. Flagg, Serkan Gugercin, Chris Beattie Virginia Tech Max Gunzburger [email protected], [email protected], [email protected] Dept. of Scientific Computing Florida State University CP14 [email protected] 2 A Characterizaton of Dn(q) by Order of Normal- izer of Sylow Subgroups CP13 Equilibrium Conditions and Sound Velocities in Let (V,f) be a orthogonal space, where V = V2n(q), f is a nondegenerate orthogonal form and there are maximum Two-Phase Flows − (n − 1) distinct hyperplanes in V. Define SO2n(q)={A ∈ We consider a hierarchy of hyperbolic models describing SL2n(q) | f(Av, Aw)=f(v, w) for all v, w ∈ V } and 2 − − − single-component two-phase flows in pipelines, with ap- Dn(q)=Ω2n(q)/Z,whereΩ2n(q)=(SO2n(q)) and Z − plications to CO2 capture and storage. The hierarchy is is the center of Ω2n(q). In this paper, we characterize the 2 characterized by the number of equilibrium assumptions simple group Dn(q) by the order of normalizer of its Sylow made. We present a formal proof that every additional level subgroups. of enforced equilibrium lowers the propagation velocity of pressure waves. This subcharacteristic condition holds for A. Iranmanesh arbitrary thermodynamic state equations. We present nu- Modares University, Iran merical examples relevant for CO2 transport, and argue [email protected] the importance for pipeline integrity simulations.

Halvor Lund,ToreFl˚atten CP14 SINTEF Energy Research Measuring the Connectedness of Geographically [email protected], tore.fl[email protected] Embedded Graphs Many networks surround us share the property that there CP13 exists underlying metric space in which the nodes are em- Nonlinear Homogenization Problem in the Acous- bedded in. For example, neurons in the brain, or flight tics of a Two-Phase Medium connections. To measure the efficiency one can navigate in such networks with only local information, we introduce Effective equations modeling the acoustics of a two-phase the concept of greedy connectivity for such geographical medium with periodic microstucture are derived. The networks. By using a chemical potential like parameter, medium (such as cancellous bone) is composed of a linear the greedy connectivity accounts also for imperfect trans- viscoelastic matrix filled with non-Newtonian fluid. Non- mission across established links. linear governing equations are obtained via two-scale homogenization and other weak convergence techniques. The Jie Sun effective model is a two-velocity system for the effective ve- Clarkson University locity v and a corrector velocity w. The effective stress is [email protected] explicitly dependent on the sum of the strain rates. Ana Vasilic CP14 UAE University On the Largest Eigenvalue of Distance Matrix of [email protected] Some Nanotubes

Robert Gilbert Let G be a connected simple graph with set of vertices { } Department of Mathematical Sciences V (G)= v1,...,vn . The distance matrix D(G)ofG is University of Delaware a square matrix of order n,whoseentrydij the between [email protected] the vertices vi and vj in G. The eigenvalues of D(G)are denoted by μ1(G),μ2(G),...,μn(G). Since the distance matrix is symmetric, its eigenvalues are real numbers and Alexander Panchenko can be ordered as μ1(G) ≥ μ2(G) ≥ ...≥ μn(G). Washington State University [email protected] A. Tehranian Science and Research Branch, Islamic Azad University, Tehran CP14 [email protected] H2-Optimal Interpolation: New Properties and Applications CP14 H2-optimal interpolation points have received great atten- You Can’t Beat Gibbs and Runge tion recently due to their success in producing accurate reduced-order models in a numerically efficient way. In Suppose you sample an analytic function f in n equispaced this talk, first, we will show how H2 optimal interpola- points in [−1, 1]. Can you use this data to approximate f in tion points can be applied to optimal H∞ model reduction. a manner that converges exponentially as n →∞?Many Second we consider their potential-theoretic properties and algorithms have been proposed that are effective for prac- connection to the rational Zolotarev problem. Thirdly, we tical values of n, but we prove that they must all fail in the AN10 Abstracts 21

limit n →∞: exponential convergence implies exponential measure theoretic approach to approximate a probability ill-conditioning. measure on the input space.

Nick Trefethen Troy Butler Computing Laboratory Institute for Computational Engineering and Sciences University of Oxford University of Texas at Austin [email protected] [email protected]

CP14 CP15 Application of Fractional Calculus to the Analysis Large Deviation of Quantum Markov Semigroups. of Laplace Transformed Data It has been found recently in a series of papers by F. Fag- This paper describes a novel method using fractional cal- nola and R. Rebolledo that the time averages of a Markov culus to estimate non-integer moments of a random vari- semigroup of completely positive linear maps acting on a able from the measured Laplace transform of its probability von Neumann algebra converges in weak* topology to a density function. We demonstrate that the ω-th moment stationary quantum state and that necessary and sufficient (ω ∈ R) of the random variable can be directly obtained conditions have been established for the faithfulness of the by a linear transformation of the data. When ω>0, com- stationary state. In this paper we obtain a large deviation putation of moments corresponds to fractional integration principle for this convergent sequence. The rate function of the data. When ω ≤ 0, computation of moments corre- for large deviation is also established. sponds to fractional differentiation. Mou-Hsiung Chang Lalitha Venkataramanan, Tarek Habashy, Denise Freed U. S. Army Research Office Schlumberger Mathematics Division [email protected], [email protected], [email protected] [email protected]

CP15 CP15 Analysis of Centralized Sequential Probability Ra- Optimal Control of a Stochastic Volterra Integral tio Test (SPRT)-Based Models for Group Decision- Equation in Hilbert Space with Fractional Brown- Making ian Motion Input Centralized group decision-making models are of interest This paper investigates stochastic Volterra integral equa- because important decisions are frequently made by a com- tions in Hilbert spaces. The existence and uniqueness of mittee. Our goal is to analyze the relative benefits of differ- their adapted solutions is established. The regularity of the ent group decision rules, in terms of speed and accuracy. adapted solutions to these equations is proved by means of We model the individuals in our group with the SPRT, Malliavin calculus. For an application, we study an optimal an optimal and biologically-relevant method, then combine control problem for a stochastic Volterra integral equation the individual decisions to arrive at the group decision. We with Hilbert space-valued fractional Brownian motion in- will present both analytical and computational results. put. A Pontryagin-type maximum principle is formulated for the problem, and an example is presented. Margot Kimura, Jeffrey Moehlis UCSB Vo V. Anh [email protected], [email protected] Discipline of Mathematical Sciences Queensland University of Technology, Brisbane, Qld. 4001, Au CP15 [email protected] Evaluating Expectations of Functionals of Brown- ian Motions: a Multilevel Idea Wilfried Grecksch Pricing a path-dependent financial derivative, such as an Institute of Mathematics, Martin-Luther-University · Halle-Wittenberg 06099 Halle (Saale), Germany Asian option, requires the computation of E[g(B( ))], the expectation of a payoff functional, g, that depends on a [email protected] T Brownian motion, (B(t))t=0. This problem turns out to be an infinite dimensional problem. A multilevel algorithm Jiongmin Yong with low discrepancy designs is introduced to approximate University of Central Florida the infinite dimensional integral. The worst case error as a [email protected] functional of each level’s sample size and truncated dimension is minimized. Numerical examples in computational CP15 finance will be presented. A Computational Measure Theoretic Approach to Ben Niu Inverse Sensitivity Analysis Department of Applied Mathematics Illinois Institute of Technology We consider the inverse sensitivity analysis problem of [email protected] quantifying the uncertainty of inputs to a finite dimensional map given specified uncertainty in a linear functional of the output of the map. Our formulation is based on the Law of Fred J. Hickernell Total Probability that represents a direct inversion of the Illinois Institute of Technology forward stochastic sensitivity problem for a deterministic Department of Applied Mathematics model. We derive and analyze an efficient computational [email protected] 22 AN10 Abstracts

Thomas Muller-Gronbach tem in order to enhance detection of faults. Unlike previous U Passau studies where it is usually assumed that there is only one [email protected] fault occurring at a time, we allow for multiple faults to occur simultaneously which is a natural assumption in the Klaus Ritter incipient case. A computational method for the construc- TU Darmstadt tion of an optimal input signal for achieving guaranteed Fachbereich Mathematik detection with speciﬁed precision is presented. This work [email protected] is an extension of the multi-model approach used for the construction of auxiliary signals for incipient failure detection. There are both discrete time and continuous time CP15 versions of this problem. The discrete time case with a Benchmark Approach for Defaultable Claims modiﬁed noise bound is examined. The continuous time case with a similar model that requires solving a linear We study the benchmark approach for defaultable claims. quadratic regulator problem is also studied. Both models The local risk minimizing strategy is derived in the case involve only additive uncertainty. when the agent information takes into account the possibility of a default event. Here we do the pricing and hedging Martene L. Fair of the defaultable claim under the real world probability North Carolina State University measure only. martene [email protected]

Indukuri Raju Stephen L. Campbell Indian Institure of Tehcnology Guwahati North Carolina State Univ [email protected] Department of Mathematics [email protected] CP15 Convergence of Tau Leaping Schemes for Markov CP16 Jump Systems on a Lattice PageRank Optimization Through Ergodic Control Tau leaping methods provide an efficient way to simulate We study a general class of pagerank optimization prob- Markov jump systems on a lattice. Existing convergence lems, which consist in finding an optimal outlink strategy results on tau leap methods apply only to systems that refor a web site subject to design constraints. We model main in a bounded region and/or are specific to the explicit these problems by constrained Markov decision processes, and the implicit tau leap schemes with Poisson random in which the webmaster determines the transition probabil- variates. We present new convergence results that deal ities of websurfers. We identify assumptions under which with fairly general tau leap schemes applied to unbounded there exists a “master’ page to which all controlled pages systems that possess certain moment growth bounds. should point. We report numerical results exploiting dynamic programming and convex programming techniques. Muruhan Rathinam University of Maryland, Baltimore County [email protected] Olivier Fercoq INRIA Saclay and CMAP Ecole Polytechnique [email protected] CP16 Convergence of Discontinuous Time-Stepping Marianne Akian Schemes for the Gradient Minimization Boundary INRIA Saclay–Ile-de-France and CMAP, Ecole Control Problem Polytechnique The minimization of the energy functional having states [email protected] constrained to semi-linear parabolic PDE’s is considered. The controls act on the boundary and are of Robin type. Mustapha Bouhtou The discrete schemes under consideration are discontinu- France Télécom R & D ous in time but conforming in space. Stability estimates [email protected] are presented at the energy norm and at arbitrary times for the state, and adjoint variables. The estimates are de- Stéphane Gaubert rived under minimal regularity assumptions and allow us INRIA Saclay – Ile-de-France & to prove onvergence of the discrete solutions. Centre de Mathématiques appliquées, Ecole Polytechnique Konstantinos Chrysafinos [email protected] Department of Mathematics National Technical University of Athens, Greece chrysafi[email protected] CP16 Adaptive and Higher Order Numerical Solution for Optimal Control of Monodomain Equations in Car- CP16 diac Electrophysiology Active Incipient Fault Detection With Multiple Si- multaneous Faults The focus of this work is on the development and implementation of an efficient numerical technique to solve The problem of detecting small parameter variations in an optimal control problem related to a reaction-diffusions linear uncertain systems due to incipient (slowly develop- system arising in cardiac electrophysiology. A Newton-type ing) faults is considered. Using an active fault detection method for the monodomain model, which is a well estab- approach, an input signal is injected into the observed sys- AN10 Abstracts 23

lished model for describing wave propagation of the action Ume{ potential in the heart, is developed. The numerical treat- aa} Univsersity ment is enhanced by using a second order time stepping [email protected] method, adaptive grid reﬁnement techniques and receding horizon methods. A super linear convergence is achieved Martin Berggren for Newton’s optimization algorithm. Department of Computing Science, Umea University [email protected] Chamakuri Nagaiah Institute of Mathematics and Scientiﬁc Computing, University of Graz, Austria CP17 [email protected] Modeling Complex Fluid Flows in Porous Media

Karl Kunisch Flow of complex fluids in porous media occurs in many Universitat Graz processes, some naturally occurring and some by design. Institut fuer Mathematik Modeling of such flows accurately and efficiently is a non- [email protected] trivial task. We will discuss in this talk many non-trivial issues that come up in the context of setting the correct Gernot Plank mathematical model that includes myriad effects that play Institute of Biophysics a role. In this context we may take some simple model Medical University of Graz, Austria problems and show some exact and computational results. [email protected] This is an ongoing work. Prabir Daripa CP16 Texas A&M University Why Walk and Run: Towards a Predictive Theory Department of Mathematics of Legged Locomotion Based on Energy Optimality [email protected] Healthy human legs are capable of great behavioral complexity – some human legs are capable of even ”break- CP17 dancing”. But mostly, people use stereotypical gaits – Multiscale Modeling of Heterogenous Flow with ”walking” at low speeds and ”running” at high speeds. Non-Newtonian Behavior Why these particular gaits from among the millions our legs are capable of? Using optimal control calculations us- A new multiscale approach to modeling non-Newtonian ing a simple mathematical model and classic prior experi- /heterogenous flow will be discussed. The computations ments, I will show evidence that the patterns of movement are carried out by combining an Immersed-Boundary- that we use roughly minimize energy cost of locomotion. I Method with Brownian Dynamics. The exchange of in- will show how to extend this simple theory to obtain better formation between both computational techniques is done quantitative predictions of people walk and run. through the velocity gradient and stress state tensors. Sev- eral examples will be presented including the response of Manoj Srinivasan a Newtonian drop suspended in a viscoelastic fluid and Movement Lab, Mechanical Engineering the dynamics of Newtonian bubbles rising in a viscoelastic Ohio State University fluid. [email protected] Arturo Fernandez Department of Mechanical Engineering CP16 Worcester Polytechnic Institute Efficient Loudspeaker Horn Design: from Mathe- [email protected] matical Model to Experimental Validation During the last few years, we have designed numerous CP17 acoustic devices using gradient-based boundary shape and Three-Dimensional Multispecies Nonlinear Tumor topology optimization. This talk outlines strategies to op- Growth: Tumor Invasion and Angiogenesis timize acoustic devises with respect to efficiency and di- rectivity properties. The acoustical properties are calcu- We study 3D non-linear tumor growth by tracking multiple lated through numerical solutions of the Helmholtz equa- viable cell species populations, discrete angiogenesis vessels tion. Recently, we manufactured one of our designs and an- and individual cell movement using a hybrid continuum- alyzed it in an anechoic chamber. In the design frequency discrete approach. We investigate disease progression as band, the acoustic impedance is close to ideal. a function of cellular-scale parameters such as prolifera- tion and nutrient uptake rates in both avascular and vas- Eddie Wadbro cular regimes. We find that heterogeneity in the physio- Department of Computing Science logically complex tumor microenvironment can be quanti- Ume˚aUniversity tatively linked to the tumor macro-scale as a mechanism [email protected] that promotes morphological instability. Fang Jin Rajitha Udawalpola University of California, Irvine Department of Information Technology [email protected] Uppsala University [email protected] Herman Frieboes, Yaoli Chuang School of Health Information Science Daniel Noreland The University of Texas Health Science Center, Houston, Department of Computing Science 24 AN10 Abstracts

TX resolved by introducing a singular perturbation reduction [email protected], [email protected] of the transition layer into full numerical solution of the free boundary problem. Numerical results are presented Steven Wise for two-phase flows in the Stokes flow limit. Department of Mathematics University of Tennessee, Knoxville, TN Kuan Xu [email protected] Department of Mathematical Sciences New Jersey Institute of Technology [email protected] John Lowengrub Department of Mathematics University of California at Irvine Michael R. Booty [email protected] Department of Mathematical Sciences, NJIT [email protected] Vittorio Cristini School of Health Information Science Michael Siegel The University of Texas Health Science Center, Houston, New Jersey Institute of Technology TX [email protected] [email protected] CP18 CP17 On Accurate Reduced-Order Modeling Using Eulerian Formulation of Fluid/structure Interac- Proper Orthogonal Decomposition tion Reduced-order models based on the proper orthogonal de- The interaction of an elastic structure and a fluid occurs in composition (POD) are often used to represent a complex many phenomena in physics. To avoid the difficulty of cou- dynamical system in fluid flows. However, for Navier- pling lagrangian elasticity and eulerian fluid we consider a Stokes equations, these models have been successfully de- whole eulerian formulation. The elasticity of the structure veloped mainly for 2-D flows and are limited to a reference is computed with retrograde caracteristics which satisfy a simulation. We present improvements in the reduced-order transport equation and a level set function is introduced to model to expand its applicability and encounter various capture the interface between the fluid and the structure. stability issues in the model. We then compare results of In application, we will present some numerical simulation reduced-order models with direct numerical simulations. relative to biolocomotion. Imran Akhtar Thomas M. Milcent Virginia Tech University of Bordeaux 1, INRIA [email protected] [email protected] Jeff Borggaard Virginia Tech CP17 Department of Mathematics A Parallel Monolithic Approach for Blood Flow [email protected] Modeling Traian Iliescu, Zhu Wang We study a parallel algorithm for the simulation of blood Department of Mathematics flows in arteries using a coupled system of PDEs consist- Virginia Tech ing of incompressible Navier-Stokes equations and a linear [email protected], [email protected] elastic equation. The coupled nonlinear system is solved by a Newton-Krylov algorithm preconditioned by an overlapping Schwarz method. We focus on the investigation CP18 of the algorithm for different outflow boundary conditions, Semiclassical Asymptotics in Norm for Non- and also on the scalability of the software on computers Smooth and for Nonlinear Problems with a large number of processors. Quantum problems, formulated appropriately, are well Yuqi Wu known to converge to their classical counterparts as Dept. of Applied Math., University of Colorado Planck’s constant ¯h tends to zero. On a mathematical level, [email protected] this is traditionally seen as a weak-∗ proximity between the solutions of the quantum and classical phase-space kinetic Xiao-Chuan Cai equations (Wigner and Liouville respectively). Indeed a University of Colorado, Boulder lot is known for the weak-∗ convergence to the semiclas- Dept. of Computer Science sical limit, both for linear and nonlinear problems with [email protected] sufficient smoothness. However, much less is known for strong topology approximations; the first systematic exploration of H s convergence, for linear problems, appeared CP17 in 2006. In this work we show semiclassical approximation A Hybrid Numerical Method for Two-Phase Flow results, for the linear case (for pure and mixed states), in with Soluble Surfactant the Hs, s ∈ Z, norms, with weaker assumptions than the state of the art. Moreover, in certain cases we can lower the We present a hybrid numerical method for computation of smoothness assumptions enough for our results to be appli- fluid interfaces with soluble surfactant at large bulk Peclet cable to C1 \ C1,1 potentials. In such problems the weak-∗ number. A narrow transition layer adjacent to the interface approximation is known to hold, but the limit Liouville which is important in controlling the interface dynamics is AN10 Abstracts 25

equation has multiple solutions: the semiclassical limit is known to be a(weak)solution of the Liouville equation, but which one is not known. In a family of such problems, Anita Mareno we can choose the solution of the Liouville equation which Mathematics corresponds to the limit of the Wigner equation. Moreover, Penn State University for the first time to the best of our knowledge, we show an [email protected] L2 semiclassical limit for mixed states evolving under the Hartree equation, i.e. we show that the solutions of the Wigner-Poisson equation and the nonlinear Vlasov equa- CP18 tion are close in L2 as ¯h tends to zero. These results are The Effect of Upscaling on Seismic Inversion joint with T. Paul, M. Pulvirenti and F. Pezzoti, and use heavily the technique of the smoothed Wigner transform. Small-scale geologic features may have a large impact on estimates of material parameters determined by seismic Agisilaos G. Athanasoulis inversion. Unfortunately there is no magic scale known CMLS a priori on which the important features of the subsur- Ecole Polytechnique face reside. Two-scale forward modeling leads to interest- [email protected] ing questions about model parameter estimation. In the case of constant density acoustics, studies indicate the estimated sound velocity should correspond to an average, CP18 but numerical experimentation is required in the case of On the Right Hand Side Identification Problem for variable-density acoustics. a Parabolic Equation with Nonlocal Conditions Susan E. Minkoff We consider the inverse problem of reconstructing the right University of Maryland, Baltimore County ∂u(t,x) ∂u(t,x) side of a parabolic equation = ∂ k (x) − Dept of Mathematics and Statistics ∂t ∂x ∂x sminkoff@umbc.edu σu (t, x)+η (t) ψ (x) , 0 0andσ>0. Under the applicability con- [email protected] ditions, well-posedness of this problem is investigated. A numerical algorithm for the approximate solution of the John Burghardt problem is presented. Dept. of Mathematics and Statistics University of Maryland, Baltimore County Abdullah S. Erdogan, Allaberen Ashyralyev [email protected] Department of Mathematics, Fatih University [email protected], [email protected] CP19 Stability Results on Multi-Layer Hele-Shaw Flows CP18 An Extended State Approach to Online Parameter We will present stability results on multi-layer Hele-Shaw Identification in Parabolic Pdes flows in cases where layers may have either uniform or non- uniform properties. These results can be harnessed for sta- Existing techniques for estimating model parameters in bilization purposes. Theoretical and numerical studies re- time-dependent partial differential equations simultane- veal some interesting properties about instability transfer ously to the time evolution of the physical state exclude mechanism between different interfaces. the case of partial state observations or require to solve online Ricatti type operator evolution equations. We suggest Prabir Daripa and analyze an extended state approach to online parame- Texas A&M University ter identification in a class of possibly nonlinear parabolic Department of Mathematics PDEs that avoids Ricatti type equations but still allows for [email protected] partial state observations. Numerical examples underline the feasibility of our method. CP19 Philipp Kuegler Century-Timescale Rossby Waves in the Arctic RICAM, Austrian Academy of Sciences Ocean Austria [email protected] A number of co-existing oceanographic and atmospheric systems interact with quite different timescales in the evolution of the global climate. It has been suggested that CP18 the approximately circular arctic ocean might support a Maximum Principles and Bounds for Some Semi- century-timescale, ocean-layer Rossby (planetary) wave, linear Fourth Order Partial Differential Equations which could interact with the north Atlantic circulation. We investigate the modeling, dynamics and spectral prop- We consider several classes of elliptic, semilinear fourth or- erties of such a wave. Joint with T. Schmidt (Danish Me- der partial differential equations from plate theory. We use terological Institute), and M. Petersen, (DTU Mathemat- classical maximum principles to deduce that certain func- ics). tionals defined for the solution of these equations achieve their maximum value on the boundary of the domain. Poul G. Hjorth Bounds on various quantities of interest are then deduced. Technical Univ of Denmark Department of Mathematics 26 AN10 Abstracts

[email protected] MATLAB for sparse rectangular matrices.

Timothy A. Davis CP19 University of Florida Storm Surge Simulations Using Adaptive Mesh Re- Computer and Information Science and Engineering ﬁnement [email protected]

We present preliminary results of storm surge simulations with idealized bathymetry and hurricane model data with CP20 adaptive mesh refinement. The goal of this study is to Fast Computation of Schur Complements of Large gain an understanding of how adaptive mesh refinement Finite Difference Matrices could provide greater computational efficiency and higher resolution than traditional methods used to model these It is well-known that the linear equations associated with phenomena. Multi-layer methods are also investigated in finite difference operators on structured grids admit very order to include basic three dimensional affects in the sim- fast solution techniques. Recently developed fast direct ulation. solvers require much less memory than FFT for constant coefficient operators, and are more robust than iterative Kyle T. Mandli techniques in the general case. The direct solvers are also University of Washington extremely fast for problems with multiple right-hand sides. Dept. of Applied Mathematics We will present fast methods for computing Schur comple- [email protected] ments of a finite difference matrix.

Randall J. LeVeque Adrianna Gillman Applied Mathematics University of Colorado at Boulder University of Washington (Seattle) Department of Applied Mathematics [email protected] [email protected]

Per-Gunnar Martinsson CP19 University of Colorado at Boulder Accuracy of Tail Regions in Uncertain Climate [email protected] Model Predictions

Conventional spectral methods for uncertainty quantifica- CP20 tion are generally challenged in the “tails” of input distri- Parallel Solution of Large Symmetric Eigenvalue butions. Extensive sampling in the tail regions is especially Problems Via Trace Minimization costly in climate models. We will illustrate how the usage of non-conventional basis functions and surrogate model The Trace Minimization algorithm (TraceMIN) is a sym- analysis improves the convergence of the spectral expan- metric eigenvalue problem solver that minimizes the trace sions in the tail regions. Preliminary results will be shown over a subspace. TraceMIN requires the solution of a set for the Atlantic meridional overturning circulation shut- of linear systems with modest accuracy. In this talk we off case as a result of abnormally high climate sensitivity present the convergence properties and the parallel scal- values. ability of a new version of TraceMIN. In addition, we compare the parallel performance of our algorithm with Khachik Sargsyan, Cosmin Safta PARPACK for solving eigenvalue problems that arise in Sandia National Laboratories MEMS device simulation and other applications. [email protected], [email protected] Murat Manguoglu Habib N. Najm Purdue University Department of Computer Science Sandia National Laboratories [email protected] Livermore, CA, USA [email protected] Faisal Saied Purdue University Bert J. Debusschere [email protected] Energy Transportation Center Sandia National Laboratories, Livermore CA Ahmed Sameh [email protected] Department of Computer Science Purdue University [email protected] CP20 Multifrontal Multithreaded Rank-Revealing Sparse QR Factorization CP20 New Results in Numerically Solving Large-Scale SuiteSparseQR is a sparse QR factorization package based Algebraic Sylvester Equations on the multifrontal method. LAPACK and the multithreaded BLAS are used within each frontal matrix. Par- Two approaches are investigated for constructing numer- allelism across different frontal matrices is handled with ical solutions of large-scale Sylvester equations. The first Intel’s Threading Building Blocks library. Rank-detection is to transform the Sylvester equation into an invariant is performed within each frontal matrix using Heath’s subspace problem, which can be solved efficiently in real method. The resulting sparse QR factorization obtains a arithmetic. Optimal shift selection is presented to enhance substantial fraction of the theoretical peak performance of convergence of iterative eigensolvers. This optimal shift se- a multicore computer. The method is used in backslash in lection analysis is then generalized for the computation of AN10 Abstracts 27

multiple optimal real shifts for the ADI approach, resulting CP21 in a more compact search region for the optimal shifts. System Identification in Tumor Growth Modeling Hung Nong Several theoretical efforts were devoted to setting up Sandia National Laboratories phenomenological models describing cancer propagation. [email protected] Among them models based on partial differential equations describe macroscopic and mechanical features of tu- Danny C. Sorensen mor propagation on the basis of mixture theory. Such mod- Rice University els are parametric but parameters cannot be fixed apri- [email protected] ori because they do not derive from first principles. Also, they cannot be measured directly because they represent mesoscale properties. In order to approach realistic appli- CP20 cations, i.e., provide a prognosis or a therapy evaluation Piro sky: Pipelined Rotations for Sparse Skyline tool, realistic values for these parameters must be found. Svd The aim of this work is to present an efficient procedure to solve data assimilation problems, the data coming from PIRO SKY is a library for computing all the singular val- medical imagery. Several realistic cases are analyzed, show- ues of a sparse matrix efficiently. PIRO SKY uses sparse ing that the prognosis can be accurate on a significant time data structures and blocked algorithms to compute the scale. singular values. The impact of various profile reduction ordering strategies on computing the sparse SVD will be Angelo Iollo, Thierry Colin, Damiano Lombardi, Olivier discussed. We show PIRO SKY is competitive against it- Saut erative methods even when only a reasonable number of Institut de Mathématiques de Bordeaux singular values are required. We also present the software [email protected], [email protected] engineering aspects of PIRO SKY’s design. bordeaux1.fr, [email protected], [email protected] Sivasankaran Rajamanickam Sandia National Laboratories [email protected] CP21 A Lagrangian Scheme to Solve the Monge- Timothy Davis Kantorovich Problem University of Florida Dept of CISE The Monge-Kantorovich problem was recently re- [email protected]fl.edu discovered and studied, having applications in statistics, meteorology, numerical optimization, physics, medical imagery. In the literature three family of solution methods CP21 were proposed: the first class is based on the Kantorovich Numerical Tests of An Algorithm for Seismic Imag- duality, the second one on the continuous formulation and ing and Inversion the third one on the critical points of a dynamical flow (AHT). In this work we propose a different approach: we We present numerical tests for an acoustic inverse scat- implicitly satisfy the transport equation by propagating tering algorithm for simultaneous geophysical imaging and mass particles on rays. Particle discretization makes the amplitude correction from measured data. No knowledge integration simpler and the parallelization efficient. Sev- about the medium under investigation is assumed. We eral 2D and 3D cases are presented. model the data from several one-dimensional earth configurations and show how the algorithm can find the precise Damiano Lombardi, Angelo Iollo location and a good estimate of the layers’ parameters from Institut de Mathématiques de Bordeaux data only. Our tests will include different number of layers, [email protected], high/low contrasts, velocity inversions and noisy data. [email protected]

Ashley Ciesla, Bogdan G. Nita Montclair State University CP21 [email protected], [email protected] Simultaneous Imaging and Inversion Using An In- verse Scattering Algorithm CP21 We present a method, derived from inverse scattering the- Reduced Order Modeling to Enhance Thermal ory, for geophysical imaging and amplitude correction from Imaging for Crack Detection measured data. No knowledge about the medium under investigation is assumed. Although derived as a series, the Proper orthogonal decomposition is employed as part of an algorithm is shown to converge to a closed form indepen- algorithmic means to identify micro-cracks in metal plates. dent of the parameters involved in the problem. Analytic As model-updating approaches are used to solve the re- and numerical one dimensional examples show excellent sulting inverse problem, POD offers relief from the ensuing results in finding both the location of interfaces and the computational challenges. A new approach to incorporat- amplitude of acoustic reflections. ing POD modes, as an enrichment to the finite element basis functions used in the forward models, will be treated. Bogdan G. Nita, Ashley Ciesla Montclair State University [email protected], [email protected] Christopher J. Earls Cornell University [email protected] 28 AN10 Abstracts

CP21 CGS2 algorithm. Semi-Blind Deconvolution in 4Pi-Microscopy Jesse L. Barlow 4Pi-microscopy has been invented by Stefan Hell to im- Penn State University prove the resolution of confocal fluorescence microscopy Dept of Computer Science & Eng along the optical axis. The convolution kernel (or point [email protected] spread function, short psf) of a 4Pi-microscope differs from the psf of a corresponding confocal microscope approxi- Alicja Smoktunowicz mately by a squared cosine factor resulting in a main peak Warsaw University of Technology of much smaller band-width and several (typically at least Warsaw, 00-0661 Poland two) side lobes. The size and position of the main peak [email protected] and the side lobes of the 4Pi-psf depend on a phase parameter, which has been assumed to be space-invariant so far, yielding standard deconvolution problems with posi- CP22 tivity constraint. However, this assumption is violated e.g. Polynomial Transform Decomposition Using Mod- for inhomogeneous refractive indices, and the space depen- ule Induction dence of the psf is considered as one of the main problems in 4Pi-microscopy. In this project the joint recovery of the Polynomial transforms, or generalized Vandermonde ma- three-dimensional density of fluorescent markers and the trices, are an important class of matrix-vector products slowly varying phase function is considered as a nonlinear used in mathematics and engineering. Important exam- inverse problem, which is tackled by a variant of the it- ples include the discrete Fourier transform, discrete cosine eratively regularized Gauss-Newton method (IRGNM) re- and sine transforms, and transforms related to orthogonal specting the positivity constraint. We present a conver- polynomials. We present a novel method to derive fast gence proof for this constraint IRGNM and reconstruction transform algorithms by decomposing the associated poly- results for artificial and real data. nomial algebra using a technique from representation theory called induction. The method algebraically character- Robert Stück, Thorsten Hohage izes and generalizes transform algorithms reported in the Georg-August-Universität Göttingen literature. [email protected], [email protected] Aliaksei Sandryhaila, Markus Pueschel Carnegie Mellon University [email protected], [email protected] CP21 Attenuation Compensation and Boundary Segmen- tation in Ultrasound Images CP22 A Schur Complement Approach for Solving a Spatial variations of attenuation across tissue can result Nearly Hermitian System in shadowing and enhancement in ultrasound B-scan images. These artifacts affect the underlying signal backscat- We discuss an approach for solving an n × n linear system ter which is the main component of ultrasound images and with rank s skew-Hermitian part (s n). This can be has clinical significance in detecting diseases and tumors. interpreted as the Schur complement of a larger (n + s) × We present a joint estimation method based on the varia- (n+s) system. We can solve the original system by solving tional principle to compensate for attenuation artifacts via s + 1 Hermitian systems, e.g., using MINRES, and directly functional minimization and regularization. Pair of patho- solving one s × s system. We present a bound for the logical useful backscatter and attenuation fields is recon- outer residual norm in terms of residuals of the Hermitian structed along with segmented anatomic structures. systems and develop a suitable stopping criteria.

Jue Wang Kirk M. Soodhalter,DanielB.Szyld Union College Temple University [email protected] Department of Mathematics [email protected], [email protected] Yongjian Yu InfiMed Inc. Mark Embree yuy@infimed.com Department of Computational and Applied Mathematics Rice University [email protected] CP22 The Numerical Stability of Reorthogonalized Block Josef Sifuentes Classical Gram-Schmidt Rice University [email protected] A reorthogonalized block classical Gram–Schmidt algorithm is given that factorizes a full column rank matrix A into A = QR where Q is left orthogonal (has orthonor- CP22 mal columns) and R is upper triangular and nonsingular. Numerical Stability of a Complete CS Decomposi- With appropriate assumptions on the diagonal blocks of R, tion Algorithm the algorithm, when implemented in floating point arithmetic with machine unit εM , produces Q and R such that A proof of backward stability for the simultaneous bidiago- T I − Q Q F = O(εM )and A − QR F = O(εM A F ). nalization of all four blocks of a partitioned unitary matrix The resulting bounds also improve a previous bound by will be outlined. The reduction serves as the first phase in Giraud et al. [Numer. Math. 101:87–100,2005] on their AN10 Abstracts 29

an algorithm for the complete CS decomposition. Northwestern University [email protected] Brian D. Sutton Randolph-Macon College Michael Miksis [email protected] Department of Engineering Science and Applied Mathematics CP22 Northwestern University [email protected] Fast Inexact Implicitly Restarted Arnoldi Method for Generalized Eigenvalue Problems with Spectral Transformation Stephen H. Davis Dept. of Engineering Sciences and Applied Math We study an inexact implicitly restarted Arnoldi (IRA) Northwestern University method for computing a few eigenpairs of generalized non- [email protected] Hermitian eigenvalue problems with spectral transformation, where in each Arnoldi step (outer iteration) the matrix-vector product involving the transformed operator CP23 is performed by iterative solution (inner iteration) of the A Singularly Perturbed Formulation of the corresponding linear system of equations. We provide new Quantum-Corrected Energy Transport Model perspectives and analysis of two major strategies that help reduce the inner iteration cost: a special type of precon- A scaling reformulation of the quantum-corrected energy ditioner with “tuning’, and gradually relaxed tolerances transport model is presented. We find that the scaled De- for the solution of the linear systems. The effectiveness of bye length as the standard singular perturbation parameter these strategies is demonstrated by numerical experiments. for the classical models is no longer valid for the nano-scale semiconductor devices and that the scaled Planck constant Fei Xue is moderately small. We introduce here a new parame- Temple University ter called the scaled thermal conductivity and modify the [email protected] standard scaled intrinsic density to include a dependence on potentials. It is numerically shown that the modified intrinsic density and the scaled thermal conductivity are CP23 strongly singular for the continuity and energy transport Uzawa Algorithms for Non-Symmetric Saddle equations, respectively. Point Problems Jinn-Liang Liu This is joint work with Brendan McCracken (REU -2009), National Hsinchu University of Education and Lu Shu (GEMS-UDEL 2009). We introduce and ana- Dept. of Applied Mathematics lyze new Uzawa algorithms for non-symmetric saddle point [email protected] systems. Typical problems where such systems appear are, for example, in finite element or finite difference discretization of steady state Navier-Stokes systems. Convergence CP23 for the algorithms are established based on new spectral A Gradient-Augmented Level Set Approach with results about Schur complements. A new Uzawa type al- Subgrid Resolution gorithm with variable relaxation parameters is introduced and analyzed in a general framework. Numerical results Level set methods are versatile interface tracking ap- supporting the efficiency of the algorithms are presented for proaches. Common difficulties are the loss of small struc- finite element discretization of the the steady state Navier- tures, an accurate approximation of curvature, and the Stokes equations. Thanks to NSF. combination with adaptive mesh refinement. We present a gradient-augmented approach, which advects interfaces Constantin Bacuta with third order accuracy, and admits a second order ac- University of Delaware curate approximation of curvature, both with optimally Department of Mathematics local stencils. In addition, the presence of gradient infor- [email protected] mation yields a certain level of subgrid resolution, which is beneficial in the tracking of thin films or droplets. We demonstrate this advantage in fluid dynamics simulations. CP23 Self-Similar Solutions and Their Instability for Benjamin Seibold Liquid-to-Glass Phase Transitions in Vitrification Temple University [email protected] Some theoretical aspects of vitrification phase transitions are addressed by modeling the process as an isothermal Jean-Christophe Nave moving-boundary problem in which the two phases have Massachusetts Institute of Technology differing diffusivities. A similarity solution is obtained, [email protected] its linear stability is examined, and an analytic dispersion relation is investigated, yielding the stability boundaries. Rodolfo Ruben Rosales Extensions of this work in which the vitrified phase demon- Department of Mathematics strates subdiffusive behavior also will be discussed and the Massachusetts Institute of Technology dynamics and instabilities of this adjusted problem exam- [email protected] ined.

Christopher A. Gruber CP23 Department of Engineering Sciences and Applied The Immersed Interface Method for Two-Fluid Mathematics 30 AN10 Abstracts

Problems The osmotic effect is modeled by the relative sliding between fluid and membrane normal to the membrane, which Many problems of fluid mechanics involve the interaction of is mediated by the interaction between solute and mem- two immiscible fluids. It is generally difficult or inefficient brane through immersed chemical potentials. The influ- to simulate each fluid separately using an interface-fitted ence of internal versus external ion concentration in deter- grid method. In the immersed interface method, a two- mining the volume of an elastic semi-permeable vesicle is fluid problem is formulated as one set of governing equa- studied with and without electrical effects and/or exchange tions and simulated on a fixed Cartesian grid. The effect of pumping. the two-fluid interface enters the formulation as a singular force and a numerical scheme as jump conditions. In this Pilhwa Lee talk, we will present the principal jump conditions, discuss University of Connecticut Health Center the difficulties in implementing them, and provide a few [email protected] options to overcome the difficulties. We will use the two- fluid circular Couette flow to demonstrate the accuracy and efficiency of these options. CP24 Mathematical Model of Self-sustained Firing in Miguel A. Uh Motoneurons After Spinal Cord Injury Southern Methodist University [email protected] The self-sustained firing in motoneurons caused by plateau potentials provide a mechanism to translate short lasting synaptic inputs into long lasting motor output. During the CP24 acute stage of spinal cord injury the endogenous ability to Transport Effects on Surface Reaction Arrays: Ap- generate plateaus is lost; however, during the chronic stage plications to Biosensors the plateau potentials reappear. Using two-compartment conductance based differential equation model we investi- The ubiquity of surface-volume reactions makes knowledge gate mechanisms that might contribute to spasticity due of their kinetics critical. Several biosensors designed to to the self-sustained firing. measure rate constants, such as the Flexchip and the dot- Lab, have multiple reacting zones in a single flow chan- Mini P. Kurian nel. A basic unidirectional flow model is developed and School of Mathematical and Statistical Sciences solved for typical experimental parameters using perturba- Arizona State University tion methods. The effect of zone placement along the chan- [email protected] nel can be quantified in terms of an effective Damköhler number based upon position. Moreover, it is established Sharon M. Crook that zone placement across the channel does not affect the Dept of Mathematics and Statistics & School of Life measurements. Sciences Arizona State University David A. Edwards [email protected] University of Delaware Newark, DE [email protected] CP24 Mathematical Modeling of Cell Biopreservation by CP24 Desiccation Learning-Rate-Dependent Clustering and Self- We consider the model of a cell with an incompressible Development in a Network of Coupled Oscillators water-sugar mixture inside and outside the cell. The cell membrane has resistance to bending and local incompress- We investigate the role of the learning rate in a Kuramoto ibility. As water leaves through the surface, a glassy state model of coupled phase oscillators in which the coupling co- can be formed inside the cell, whose volume decreases while efficients dynamically vary according to the Hebbian learn- local area of the membrane is fixed. The hydrodynamics ing rule; here synapses between neurons are strengthened is governed by the Stokes equation. We investigate linear when they fire in synchrony. We show that either one or stability and dynamics of an initial spherical membrane. two synchronized clusters form, depending on the learning rate relative to a critical value. We also comment on the Alla Podolny possibility of self-development of neural networks within Northwestern University this model. [email protected] Lars English Dickinson College, Pennsylvania Michael Miksis USA Department of Engineering Science and Applied [email protected] Mathematics Northwestern University [email protected] Ritwik Niyogi Dickinson College [email protected] Stephen H. Davis Dept. of Engineering Sciences and Applied Math Northwestern University CP24 [email protected] On the Cellular Volume Regulation in 2-D The electrical and osmotic effects with ion exchange trans- CP24 port mechanism for the volume regulation are investigated. Frequency Modulation of the Excitable Fitzhugh- AN10 Abstracts 31

Nagumo System phase. The continuous phase is determined by large-eddy simulation in the Eulerian frame of reference whereas the Using a generalized Fitzhugh-Nagumo model we studied dispersed phase is simulated in a Lagrangian frame of ref- how temporal characteristics of an external signal affect the erence. dynamics of excitable systems. In particular, we choose a subset of parameters for the Fitzhugh-Nagumo system so Marcel Ilie that the solution contains (1) no limit cycle or (2) a unique University of Central Florida limit cycle. For this set of parameters, we investigate the Department of Mechanical, Material and Aerospace dynamic consequences of injecting the system a variable Engineering current I(t,w) with different frequency w. [email protected] Xujing Wang University of Alabama at Birmingham CP25 [email protected] Cluster Computing with Intel Nehalem and Infini- Band Interconnect

CP25 High performance parallel computing depends on the in- Finite Difference Method for Smoothed Gradually teraction of a number of factors including the proces- Varied Surfaces sors, the architecture of the compute nodes, their interconnect network, and the numerical code. In this talk,we A digital method for obtaining continuous functions with present performance and scalability studies on a new 86- (n) smoothness to a certain order (C ) from sample data node distributed-memory cluster with two quad-core Intel is designed. This method is based on gradually varied Nehalem processors per node and a quad-data rate Infini- functions discovered by Chen in 1989 and finite difference Band interconnect. These components are currently the method. This new method has been applied to real ground- most popular for general-purpose clusters and they exhibit water data and the results have validated the method. This excellent performance. method is independent from existing popular methods such as the cubic spline method and the finite element method. David Trott The new digital-discrete method has considerable advan- University of Maryland, Baltimore County tages for a large amount of real data applications. This [email protected] digital method differs from the classical discrete method that usually uses triangulations. Matthias K. Gobbert University of Maryland, Baltimore County Li Chen Department of Mathematics and Statistics University of the District of Columbia [email protected] [email protected]

CP25 CP25 Nonlinear Evolution of Electrified Liquid Threads Lime: Lightweight Integrated Multiphysics Envi- and Annular Layers ronemnt The nonlinear dynamics of an electrified liquid thread in a LIME is a multiphysics coupling environment that enables cylindrical tube (electrode) which is concentrically placed coupling of both legacy application codes as well as novel is studied. The radial electric field is generated by the po- codes. It is lightweight by requiring application codes to tential difference between the fluid interface and the outer only provide a response given requisite inputs. It provides electrode. We solve the system in the zero Reynolds num- value-added coupling by incorporating any additional in- ber limit by the boundary-integral method. Pinch-off so- formation to effect more robust coupling algorithms based lutions and satellite formation are discussed. In addition, on variations of Jacobian-Free Newton-Krylov. LIME is different breakup behaviors are found at other parameter currently implemented as extensions to the Trilinos Solver values. Framework thereby leveraging state-of-the-art solution algorithms to drive multiphysics coupling. Qiming Wang Department of Mathematical Sciences Russell W. Hooper, Rodney Schmidt, Kenneth Belcourt New Jersey Institute of Technology Sandia National Laboratories [email protected] [email protected], [email protected], [email protected] Demetrios Papageorgiou Department of Mathematics CP25 Imperial College London, UK [email protected] Numerical Computations of Particle-Laden Turbu- lent Flows CP25 An efficient Eulerian-Lagrangian particle dispersion algorithm for the prediction of particle-laden flows is proposed. Mathematical and Numerical Analysis of Peridy- The volume fraction of the dispersed phase is assumed to namic Models with Nonlocal Boundary Conditions be small enough such that particle-particle collisions are We study the linear bond-based peridynamic models with a negligible and properties of the carrier flow are not modi- particular focus on problems associated with nonstandard fied. With the examination of dilute systems only the effect nonlocal displacement loading conditions. Both stationary of turbulence on particle motion has to be taken into ac- and time dependent problems are considered for a one di- count (one-way coupling). With this assumption the con- mensional scalar equation defined on a finite bar and for a tinuous phase can be treated separate from the particulate 32 AN10 Abstracts

two dimensional system defined on a square. The related Dept of Chemistry and Mathematics peridynamic operators and associated functional spaces are [email protected] analyzed. Applications to the analysis of the finite dimensional approximations to peridynamic models are also illustrated. CP26 A Spatiotemporal Model of Barley Yellow Dwarf Qiang Du Virus in Competing Plant Species with Seasonality Penn State University and Age Structure Department of Mathematics [email protected] Barley yellow dwarf virus infects over 100 grass species in agricultural and natural systems, mitigating success of in- Kun Zhou vasive species. We model BYDV transmission within a Penn State University metapopulation framework incorporating the movement of [email protected] aphid vectors between discrete host patches. We examine BYDV persistence and alteration of pathogen-mediated interactions between perennial and annual competitors CP26 across a range of host community configurations. Sensi- A Differential Equation/agent-Based Hy- tivity analysis of the basic reproduction number for two brid Model of Antibiotic-Resistant Infection in a simplified models identifies how key parameters influence Hospital Ward pathogen invasion. When modeling the spread of bacterial infections in a popu- Carrie A. Manore, Sean Moore, Vrushali A. Bokil lation, dynamics occur on two levels: Interaction between Oregon State University the people in the ward, and the bacterial growth taking [email protected], place inside infected ward members. We propose a method [email protected], for combining both into a single model, where each person [email protected] is treated as an agent in an agent-based system, with the agent-specific dynamic parameters driven by a differential Elizabeth Borer equations system that models the within-host bacterial dy- University of Minnesota namics for that agent. Ecology, Evolution, and Behavior [email protected] Lester Caudill University of Richmond [email protected] CP26 Control of Mosquito Populations Through the In- troduction of Sterile Mosquitoes CP26 Optimal Efficacy of Ribavirin in the Treatment of We construct an ODE model for the release of sterile Hepatitis C mosquitoes into a population of wild mosquitoes. Assum- ing Holling-II dynamics, we examine the optimal control A mathematical model to represent hepatitis C is pre- of the wild mosquito population through several objec- sented. An objective functional keeping biomedical goals in tive function formulations. Numerical simulations are dis- mind is formulated. The optimal control problem is solved cussed. numerically to obtain an optimal efficacy of ribavirin in a combination treatment of ribavirin with interferon, where Maeve L. McCarthy, K. Renee Fister the efficacy of the latter has a clinically validated functional Murray State University form [email protected], renee.fi[email protected] Siddhartha P. Chakrabarty Dept. of Mathematics Seth F. Oppenheimer Indian Institute of Technology Guwahati Mississippi State University [email protected] [email protected]

CP26 CP26 Drug Resistance Effects on Weighted Optimal Con- PhaseLockingBetweentheExpressionProfilesof trol for Chemotherapy Transcription Factors and Their Target Genes Dur- A differential equations model for cancer and its treatment ing the Yeast Cell Cycle is examined. The governing equations are developed from Increasing evidence now suggest the role of frequency mod- a four-compartmental model that shows the development ulation in gene expression. We examined this question of resistance over time. Optimal control techniques are using the time course gene expression data of yeast cell then used to investigate the effects of drug resistance (both cycle. We found that between transcription factors and natural and induced) on cell-cycle specific chemotherapy their binding targets, the expressions are significantly more regimes. Optimal strategies are suggested that take into likely to be phase locked than random gene pairs. In ad- account factors such as toxicity level. Once the existence of dition, ∼ 5–10% show higher order, more than 1 : 1, phase the optimal control is established, the control is then char- locking. acterized through the Hamiltonian and the adjoint system to governing equations. Xujing Wang University of Alabama at Birmingham Daniel L. Kern [email protected] Florida Gulf Coast University AN10 Abstracts 33

CP27 pose a generic model of a reaction-diffusion system in the Quantitative Dynamics of Spiral Waves in Active presence of a morphogen gradient. This morphogen gra- Media. dient is established independently of the reaction-diffusion system and acts by increasing the production of the acti- If perturbed, spiral waves in active media slowly move their vator proportional to the morphogen concentration. The core. In linear approximation, the drift velocity is pro- model is motivated by several existing models in develop- portional to convolution of perturbation with translational mental biology in which a Turing patterning mechanism response function (RF), the eigenfunction of adjoint lin- is proposed and various chemical gradients are known to earized operator corresponding to translational symmetry. exist. We investigate how the Turing pattern is affected, For variety of perturbations, we compute drift velocities if it exists. We also apply our results to a model of bone using RFs in Barkley and FitzHugh-Nagumo models and pattern formation in vertebrate limbs and show how they show good quantitative agreement with direct numerical may shed light on some experimental findings. simulations. We also demonstrate orbital movement of spiral due to interaction with localized inhomogeneities. Tilmann Glimm Western Washington University Irina V. Biktasheva [email protected] University of Liverpool [email protected] CP27 Dwight Barkley Spatial Modeling of Bacterial Antibiotic Tolerance Mathematics Institute, The University of Warwick, UK Persisters are phenotypic bacterial variants which exhibit [email protected] ”antibiotic tolerance”: persisters survive when exposed to bactericidal antibiotics, but the bacterial colonies regrown from persister cells remain susceptible to killing by Vadim N. Biktashev further antibiotic treatments.Persister formation has been Dept of Applied Maths, University of Liverpool, linked to quorum sensing, the ability of bacteria to deter- UK mine their local population density, and with the formation [email protected] of biofilms, surface-growing bacterial communities particularly difficult to eradicate with antibiotic treatments. Ex- Andrew J. Foulkes tending a previous model of bacterial colony pattern for- Dept of Computer Science, mation, we present a reaction-diffusion model of bacterial University of Liverpool, UK growth which includes density-dependent persister forma- [email protected] tion. The model also exhibits separation of temporal and spatial scales between persister and regular bacteria. We investigate the pattern formation properties of the model CP27 as a number of experimentally accesible parameters are Complex Media, Complex Fluids and Complex varied. Flows William E. Sherwood Flows involving simple fluids are relatively well understood Center for Biodynamics in comparison to complex fluids such as blood, petroleum, Boston University jam, honey, just to cite a few. In fact, many of the biologic, [email protected] edible, and chemical fluids are complex in nature. Many such fluids are product of nature and many are man made John Burke by design in order to achieve some specific objectives. For Boston University example, complex fluid such as aqueous solution containing [email protected] polymer and surfactants are used in improved oil recovery processes.It is necessary to understand at the fundamental level the origin of many physical phenomena that can CP27 be triggered by the complex rheological properties of these Mathematical Analysis of a System of Pde Arising complex fluids, in particular in complex media. Such un- From Epidermal Wound Healing derstanding can lead to better design of many processes and better numerical methods to simulate these processes. Systems of reaction-diffusion equations have been proposed to study cell migration across the surface of an epidermal Prabir Daripa wound. Approximation of traveling waves which describe Texas A&M University the cell migration into the wound has been studied by a Department of Mathematics number of researchers. We will investigate asymptotic be- [email protected] havior and speed of the travel wave solutions. Analysis of the model system reveals biological interactions in the CP27 wound healing process and the role of the model parameters in determining the speed. Turing Patterns with External Morphogen Gradi- ents Haiyan Wang Arizona State University In embryonic development, cells self-organize into complex [email protected] distributions giving rise to tissues and organs. The basic mechanisms of how this happens are still not very well understood. One experimentally verified mechanism is the action of gradients of signalling molecules. Another one is the Turing mechanism in reaction-diffusion systems. To investigate how these two mechanisms may interact, we pro- 34 AN10 Abstracts

CP27 tors Analysis of Equations with Nonlinear Dispersion Anetworkofn coupled spherical-cap droplet oscillators is At this time, there is little existence theory for equations considered. The coupling by inviscid flow between droplets in which the mechanism which generates dispersion is itself is modeled as a system of n − 1 second-order differential nonlinear. In this talk, I will present a new equation which equations under a constant-volume constraint. For Sn sym- possesses compactly supported traveling wave solutions (a metric coupling, analytic stability and bifurcation results hallmark of degenerate dispersive equations) and for which are obtained for an arbitrary number of droplets. Nonlin- the Cauchy problem has a weak solution. This work is joint ear dynamics are explored numerically in both undamped with D. Ambrose. and weakly-damped cases. In addition, the influence of a variety of coupling laws is analyzed. J. Douglas Wright Drexel University David M. Slater Department of Mathematics Cornell University [email protected] [email protected]

Paul Steen CP28 School of Chemical Engineering Mathematical Analysis of Swarming: Integrat- Cornell University ing Agent-Based Simulation with Population-Level [email protected] Modeling and Analysis

An agent-based model is used to inform the design of a CP28 biologically relevant continuum model for swarming. Lin- Robustness and Efficiency of Ant-Based Routing ear stability analysis reveals the existence of low-frequency and Forwarding Protocols. instabilities as key behavioral parameters are varied. The results of the stability analysis are verified via numerical Ant-based protocols provide elegant solutions to routing simulation of the continuum model. Simulations of the and forwarding problems. These protocols use control agent-based model demonstrate a correspondence for finite packets or ”ants” to discover new routes and reinforce ef- swarms and are used to evaluate the effects of noise and ficient routes by adjusting pheromone values. We revisit changes in communication on stability. the new nonlinear stochastic models and compare them to network simulations with high-fidelity protocol, and phys- Allison Kolpas ical layer models. Through analysis of the models, we can Department of Mathematical Sciences understand how network behavior depends upon routing University of Delaware exponents and pheromone deposition/evaporation param- [email protected] eters.

Jennifer Miller, Joao Juchem Neto, Louis F. Rossi Claudio Torres, Louis F. Rossi, Chien-Chung Shen, Ke Li, University of Delaware Jeremy Keffer, Rui Fang [email protected], [email protected], University of Delaware [email protected] [email protected], [email protected], [email protected], [email protected], jeremy@yekeffer.net, [email protected] CP28 Mathematical Modeling and Analysis of a Contin- uum Model for Three-Zone Swarming Behavior CP28 Dynamics of Light Beam Switching at the Interface Swarms in nature have been modeled with individuals but of Two Nonlinear Optical Media a continuum model, in which individuals are replaced with fields, may be better suited to theoretical analysis and scal- The dynamics of two light beams interacting at an interface ing up to larger swarms. Models including zones of repul- separating tow nonlinear optical media is studied numeri- sion, orientation, and attraction are popular in ecological cally and analytically. The beam dynamics is simulated by modeling. Our integro-differential equations describe the the beam propagation method. The numerical simulations reactions to the varying density in these three zones. We agree with the results of analytical model. The trapped use linear stability analysis to explore first and second or- beam at the interface acts as a power controllable switch der models of constant density swarms. to reflect or transmit the incident beam at the interface. Some new results will be presented in this talk. Jennifer Miller, Louis F. Rossi University of Delaware Rajah P. Varatharajah [email protected], [email protected] North Carolina A &T State University Allison Kolpas [email protected] Department of Mathematical Sciences University of Delaware CP28 [email protected] High-Order Bisection Method for Computing In- variant Manifolds of 2-D Maps CP28 We describe an efficient and accurate numerical method for Nonlinear Dynamics of Coupled Droplet Oscilla- computing smooth approximations to invariant manifolds of planar maps, based on geometric modeling ideas from Computer Aided Geometric Design (CAGD). The unstable AN10 Abstracts 35

manifold of a hyperbolic fixed point is modeled by Bézier we explore both novel and traditional supporting compo- interpolant (a Catmull-Rom spline) and properties of such nents of high-order linear and nonlinear wave solvers for curves are used to define a rule for adaptively adding points their suitability for modern massively parallel computer ar- to ensure that the approximation resolves the manifold to chitectures. Components examined range from time step- within a specified tolerance. Numerical tests on a variety pers to preconditioners, linear solvers and shock capturing of example mappings demonstrate that the new method schemes, for which we examine design considerations, al- produces a manifold of a given accuracy with far fewer gorithms, and performance data. calls to the map, compared with previous methods. A brief introduction to the relevant ideas from CAGD is provided. Andreas Kloeckner Additionally, we will discuss the difficulties of extending Brown University these ideas to higher dimensions. [email protected] Jacek Wrobel, Roy H. Goodman New Jersey Institute of Technology MS1 Department of Mathematical Sciences An Accelerated Discontinuous Galerkin Method [email protected], [email protected] for Time-Domain Wave Propagation on Curvilin- ear Domains

MS1 We will introduce the low storage curvilinear discontinu- Absorbing Boundary Condition Taking into Ac- ous Galerkin (DG) method for solving time-dependent par- count the Grazing Modes tial differential equations on curvilinear domains. We will present a proof of stability and show results that indicate We propose a new Absorbing Boundary Condition for the the method is typically as accurate as standard DG dis- wave equation, which is adapted to arbitrarily-shaped con- cretizations on curvilinear domains. Finally we will discuss vex boundary. After having decomposed the exact solution how this approach has enabled three dimensional electro- into propagating, evanescent and grazing fields, this con- magnetic scattering and also fluid flows to be computed on dition is obtained by combining the approximations of the a workstation using commodity graphics processing units. transparent condition in the three corresponding regions. The absorption of the grazing field involves a fractional derivative in space which requires a specific discretization Tim Warburton in order to implement the condition in a finite element Computational and Applied Mathematics scheme. Rice University [email protected] Hélène Barucq, Julien Diaz Team-Project Magique-3D INRIA Bordeaux Sud-Ouest MS2 [email protected], [email protected] Model Reduction of Large Scale System in Oil In- dustries Véronique Duprat LMA, CNRS UMR 5142 Large-scale numerical models for suburface hydrocarbon Universit flow are frequently used during the design phase of oil ’e de Pau et des Pays de l’Adou fields. Moreover, an emerging technique is the use of such [email protected] models during the operational phase. To speed-up simulation of these models there appears to be a large scope for simplifying them using model-order reduction techniques. MS1 In particular we present an example of the use of Proper A Orthogonal Decomposition applied to a simple reservoir High Order Runge-Kutta Discontinuous Galerkin model for two-phase (oil-water) flow. Scheme with Time Accurate Local Time Stepping Patricia Astrid A new explicit RK based method for the time integration Shell Projects & Technology of the DG scheme is presented. The considered class of RK The Netherlands schemes have the property that a time polynomial of the [email protected] solution is available, which can be used to introduce local time stepping. Despite the local time steps, the scheme is Jan-Dirk Jansen high order accurate in time, conservative and ideally suited Delft University of Technology for massively parallel computations, allowing an efficient The Netherlands discretization of large scale time dependent problems. [email protected] Gregor Gassner Institut fuer Aerodynamik und Gasdynamik MS2 [email protected] Structure-preserving Model Reduction for MEMS Modeling

MS1 Abstract unavailable at time of publication. Machine-adapted Methods: High-order Wave Propagation on GPUs David Bindel Cornell University Having recently shown that high-order unstructured dis- [email protected] continuous Galerkin methods are a spatial discretization that is well-matched to execution on GPUs, in this talk 36 AN10 Abstracts

MS2 methods. Balanced Truncation for Switched Dynamical Sys- tems Amit Hochman, Jacob White Research Lab. of Electronics A hybrid dynamical system is a system described by MIT both differential equations (continuous flows) and differ- [email protected], [email protected] ence equations (discrete transitions). It has the benefit of allowing more flexible modeling of dynamic phenomena, including physical systems with impact such as a bouncing MS3 ball, switched systems such as a thermostat, and even in- Stochastic and Kinetic Approaches in Mesoscale ternet congestion. Hybrid dynamical systems pose a chal- Modeling of Grain Growth in Polycrystalline Ma- lenge since almost all reduction methods cannot be di- terials rectly applied. Here we introduce a balanced truncation- like method for switched linear dynamical systems. For Microstructure evolution is a problem of central impor- this we define the controllability and observability Grami- tance in materials science. Grain boundary engineering ans for either time-transmission switching or time-invariant techniques allow to design and manufacture materials pre- switching. For the first case, the Gramians are only the disposed to certain behavior under external conditions. sum of the Gramians of the subsystems, and so the bal- This type of work relies heavily on statistical analysis anced truncated switched system is the sum of the balanced of grain boundary evolution and of an interplay between truncated subsystems. For the second case the method is micro- and macroscopic properties. We present an account tricky as a notion of uncertainty should be added in order of recent developments in mesoscale theory of texture evo- to deal with the special structure of the switched system. lution in polycrystalline materials. The talk will demon- We also introduce two new definitions of the Gramians, strate how a carefully chosen combination of simulation, solutions of either special LMIs or Lyapunov equations to theory and modeling techniques can bring a deeper under- come up with the balanced truncated-like reduced model. standing to coarsening processes governed by the motion With this approach we will preserve the stability for the of triple junctions. By means of modulated stochastic pro- reduced model. Here one should notice that we supposed cess characterization and kinetic evolution equations, we implicitly that each subsystem is stable. aim at quantifying the rates of grain boundary disappear- ance events and predicting the influence of these events on Younes Chahlaoui macro-level materials properties. Comparison with large- CICADA scale 2D and 3D simulations will provide the necessary vali- The University of Manchester, UK dation and reveal similarities and differences between these [email protected] approaches. Maria Emelianenko MS2 George Mason University Interpolatory Projection Methods for Optimal [email protected] Model Reduction of Large-scale Dynamical Sys- tems MS3 We investigate interpolatory optimal model reduction of Predictive Theory for the Grain Boundary Char- large-scale dynamical systems. First, we present a trust- acter Distribution region approach for optimal H∈ approximation of MIMO systems. The approach generates a sequence of reduced or- Most technologically useful materials are polycrystalline microstructures composed of a myriad of small grains sepa- der models producing monotone improving H∈ error norms and is globally convergent to a reduced order model guar- rated by grain boundaries. The energetics and connectivity anteed to satisfy first-order optimality conditions. Then, of the grain boundary network plays a crucial role in deter- we extend this approach to optimal model reduction of pa- mining the properties of a material across a wide range of scales. A central problem is to develop technologies capable rameterized systems using an H∈ ⊗L∈ joint error measure. of producing an arrangement of grains—a texture—that provides for a desired set of material properties. Since the Serkan Gugercin dawn of man, coarsening has been the principal feature of Virginia Tech. these technologies. Cellular structures coarsen according to Department of Mathematics a local evolution law, a gradient flow or curvature driven [email protected] growth, for example, limited by space filling constraints, which give rise to changes in the configuration. There are two aspects of coarsening, geometric growth and texture MS2 development. The main objective of this presentation is Stability Issues and DEIM-based Nonlinear Model to show that they may be decoupled and characterized by Reduction different types of evolution processes, leading to statistically different types of coarsening rates. We consider the Reduced order model stability is examined for the discrete grain boundary character distribution, the GBCD, a ba- empirical interpolation based model reduction method sic texture measure, and establish an entropy based theory (DEIM). A micro-electromechanical and a circuit exam- for it which suggests that GBCD satisfies Fokker-Planck ple are used to demonstrate the stability issue, and type kinetics. For this, a simplified critical event model is stability-enhancing modifications of the algorithm are de- introduced and studied. scribed. We show that extracting an equilibrium point Jacobian guarantees local DIEM stability, and that multi- Yekaterina Epshteyn, David Kinderlehrer, Katayun point methods for extracting stabilizing projection matri- Barmak ces yields superior global stability. The examples are also Carnegie Mellon University used to demonstrate the failure characteristics of DEIM [email protected], [email protected], AN10 Abstracts 37

[email protected] [email protected]

Maria Emelianenko George Mason University MS4 [email protected] Modularity and Graph Algorithms A number of graph partitioning algorithms are based on Eva Eggeling the concept of modularity. In particular Clauset, Newman Fraunhofer InstitutComputer Graphics Research IGD and Moore (CNM) have developed a greedy agglomerative [email protected] graph partitioning algorithm that scales well but is known to have several flaws. Fortunato and Barthelemy have per- Shlomo Ta’asan formed a rigorous analysis of the CNM algorithm that elu- Department of Mathematical Sciences cidates it problems. More recently Berry, Hendrickson, Carnegie Mellon University Laviolette, and Phillips have derived a weighted variant of [email protected] CNM that performs much better in practice. This talk will focus on a different version of the parent CNM algorithm based on a statistical re-interpretation of CNM that also MS3 addresses some of the issues with the original algorithm. The Janossy Effect and Hybrid Variational Princi- ples Joe McCloskey National Security Agency Light changes the orientation of a liquid crystal. This is the [email protected] optical Freeder- icksz transition. In the Janossy effect, the threshold intensity for the optical Freedericksz transition David A. Bader is dramatically reduced by the additon of a small amount College of Computing of dye to the sample. This has been interpreted as an Georgia Institute of Technology optically pumped orientational rachet mechanism, similar [email protected] to the rachet mechanism in biological molecular motors and requires an innovative hybrid gradient flow. Joint work with Michal Kowalczyk. MS4 David Kinderlehrer Scalable Methods for Representing, Characteriz- Carnegie Mellon University ing, and Generating Large Graphs [email protected] Abstract unavailable at time of publication. Ali Pinar MS3 Sandia National Labs Kinetic Theory and Lax Equations for Shock Clus- [email protected] tering and Burgers Turbulence

We study shock statistics in scalar conservation laws with MS4 random initial data by deriving kinetic equations, which Exploiting Sparsity in the Statistical Analysis of have the form of a Lax pair. This, in addition to some Gene Expression Data exact solutions to the equation, suggest that the model is a completely integrable system in 2+1 dimensions. Abstract unavailable at time of publication. Ravi Srinivasan Padma Raghavan University of Texas at Austin The Pennsylvania State Univ. [email protected] Dept of Computer Science Engr. [email protected] Govind Menon Brown University Anirban Chatterjee, Francesca Chiaromonte [email protected] Pennsylvania State University [email protected], [email protected] MS4 People You May Know MS5 Multiscale Simulation Techniques for Fluid Struc- Facebook’s friend recommendation system helps people ture Interaction connect with their friends. Our system, called People You May Know, uses a combination of results from sociology In this talk, I will discuss multiscale simulation techniques and machine learning to make the best suggestions pos- for fluid-structure interaction. Our goal is to develop simu- sible. We will look at some of the challenges involved in lation techniques for solving fluid-structure problems with building a system that can handle the scale of Facebook complex microgeometries on a coarse grid. A particular ap- and provide high quality recommendations. In this talk plication is fluid flows in deformable fracture porous media. I will discuss both the algorithmic and machine learning Due to changes in pore pressure, the deformation can sig- challenges that we have faced and overcome in building nificantly alter pore geometry and change permeabilities. this system. Coarse-scale models will be discussed and numerical results will be presented. This is a joint work with Peter Popov, Lars Backstrom Yuliya Gorb, and Donald Brown. Facebook Palo Alto, CA Yalchin Efendiev 38 AN10 Abstracts

Dept of Mathematics tracts key nonlinearities, thereby providing a basis for un- Texas A&M University derstanding competing motivations that drive investor de- [email protected] cisions. One of the motivations involved is trend, or momentum, a key component of the system of ordinary diﬀer- ential equations modeling price dynamics developed since MS5 1990 (see www.pitt.edu/∼caginalp). We show equilibrium On a Nonlinear Problem Arising in Poroelasticity and stability results for this system.

In this work we study a model for steady fluid flow in a Mark DeSantis saturated deformable (elastic) porous medium. The model Mathematics which was developed in the context of modeling one of the Univ of Pittsburgh processes in paper production is distinguished in its use of [email protected] a Kozeny-Carman type relation for the fluid’s permeability, resulting in a quasilinear elliptic system. We describe and analyze a finite element method for approximating so- MS6 lutions of this nonlinear problem. TheDynamicsofaDurableConsumptionGood: Modeling for Experimental Design and Testing Yanzhao Cao Department of Mathematics & Statistics An unprecedented housing bubble, 1997 to 2007 subse- Auburn University quently engulfed the economy from 2007 to the present. [email protected] Economic theory and experiments have modeled the two polar extremes: (1) Services and other non-durables that A. J. Meir perish on consumption, and (2) Durable goods with infinite Auburn University life. We build on the previous literature to model a simple [email protected] consumer durable asset, that has a finite expected life, with agent producers who can vary their output of the durable asset depending on its market price and production cost. MS5 We characterize the long run stationary equilibrium of the Coupling of Elastic and Electromagnetic Waves and system, and show how it can be combined with existing Related Mathematical Problems models of asset pricing to enable the study of short-term dynamic behavior. Part 2. There are considered theoretical and numerical aspects of the interaction of elastic and electromagnetic waves in com- Steven Gjerstad plex media. The models considered are different combina- Chapman University tions of the Lamé and Maxwell equations. The coupling [email protected] mechanism is based on the seismomagnetic and electroki- netic effects. Theoretical results of the analytical solution are discussed for various direct and inverse problems. Fi- MS6 nally, we give some results of the numerical solution of some On the Specialization and Division of Exchange, direct and inverse problems describing linear processes of Durability and Market Performance interaction of elastic and electromagnetic waves. Robust laboratory studies have long established contrast- Viatcheslav I. Priimenko, Mikhail Vishnevsky ingly different behavior depending whether the items ex- North Fluminense State University Darcy Ribeiro changed are final use goods, with specialized buyers, and [email protected], [email protected], sellers, or assets that can be re-traded over multiple peri- [email protected] ods. The former perform with high efficiency, the latter poorly, tending to bubble and crash. New experiments combine these features in simple markets where durability, MS5 and specialization, is varied by imposing or relaxing a re- Fluid Flows in Karst Aquifer striction on re-trade within each period. Since about 60 percent of national output is consumer non-durable goods We discuss two types of models for flows in karst aquifer. and services, a component that resists change in good times The first is the coupled Navier-Stokes-Darcy model and its or recessions, while economic troubles originate in asset variants. The second is the so-called coupled continuum markets, the results illuminate the much greater stability pipe flow model (CCPF) or conduit flow process model of expenditure patterns in perishable final goods markets (CFP). Mathematical well-posedness of the models, their relative to durable goods, credit and financial markets. numerical approximation, calibration of key physical parameters will be discussed. David Porter Economics and Mathematics Xiaoming Wang Chapman University Department of Mathematics [email protected] Florida State University [email protected] MS6 Housing Bubbles and the Economy: Challenge to MS6 Modeling Nonlinearity and Instability in the Dynamics of Fi- nancial Markets An unprecedented housing bubble, 1997 to 2007 subse- quently engulfed the economy from 2007 to the present. Two recent studies in collaboration with Prof. Caginalp are Economic theory and experiments have modeled the two presented. A large-scale statistical methodology demon- polar extremes: (1) Services and other non-durables that strates a significant role for numerous variables, and ex- perish on consumption, and (2) Durable goods with infinite AN10 Abstracts 39

life. We build on the previous literature to model a simple MS7 consumer durable asset, that has a ﬁnite expected life, with Topics in Kinetic Simulation: A Brief Look at the agent producers who can vary their output of the durable Landscape asset depending on its market price and production cost. We characterize the long run stationary equilibrium of the This talk will be a brief survey of numerical methods used system, and show how it can be combined with existing to solve kinetic equations and the current challenges faced models of asset pricing to enable the study of short-term by computational scientists in various applications. This dynamic behavior. Part 1. includes an overview of topics to be addressed in more detail during the symposium. Vernon Smith Economics and Law Cory Hauck Chapman University Oak Ridge National Laboratory [email protected] [email protected]

MS6 MS7 A Proﬁt Keeping and Loss Protection Strategy in A Nonlinear Spatial Closure for the 2-D Sn Equa- Portfolio Management tions

The widely studied power-utility-maximization strategy is We present a strictly positive non-linear Petrov-Galerkin optimal only in the sense of ensemble averaging. However, method that reduces to the standard linear-discontinuous in reality, only one random path will be realized and the Galerkin spatial discretization when that method produces value of the portfolio at the end of the investment horizon a positive solution. In addition to strictly positive angu- could be dramatically lower than its historical high. This lar flux solutions, our method offers preservation of the P1 is evident in the recent financial crisis. We will present a spatial moments of the transport equation. Computational new strategy to overcome this problem. results for several test problemsinbothslabandrectan- gular geometries are presented. Qiang Zhang Mathematics Jim Morel, Peter Maginot City Univ of Hong Kong Texas A&M [email protected] [email protected], [email protected]

Jean Ragusa MS7 Department of Nuclear Engineering Positivity-preserving Discontinu- Texas A&M University ous Galerkin Schemes for Linear Vlasov-Boltzmann [email protected] Transport Equations

We develop a high-order positivity-preserving discontinu- MS7 ous Galerkin (DG) schemes for linear Vlasov-Boltzmann Conservative High Order Semi-Lagrangian Finite transport equations (BTE) under the action of quadrati- Difference Weno Methods for Advection in Incom- cally confined electrostatic potentials. The solutions of the pressible Flow and Kinetic Equations BTEs are positive probability distribution functions. It is very challenging to have a mass-conservative, high-order We propose a novel semi-Lagrangian finite difference for- accurate scheme that preserves positivity of the numeri- mulation for approximating conservative form of advec- cal solutions in high dimensions. Our work extends the tion equations with general variable coefficients. Com- maximum-principle-satisfying scheme for scalar conserva- pared with the traditional semi-Lagrangian finite differ- tion laws by Zhang and Shu (2010) to include the linear ence schemes, which are designed by approximating the Boltzmann collision term. The DG schemes we developed advective form of equation via direct characteristics trac- conserve mass and preserve the positivity of the solution ing, the scheme we proposed approximates the conservative without sacrificing accuracy. A discussion of the standard form of equation. This essential difference makes the pro- semi-discrete DG schemes for the BTE are included as a posed scheme conservative by nature, and extendable to foundation for the stability and error estimates for this equations with variable coefficients. The proposed semi- new scheme. Potential applications of this solver include Lagrangian finite difference framework is coupled with high the modeling of charge transport in nano-scale semiconduc- order essentially non-oscillatory (ENO) or weighted ENO tor and solar devices and Vlasov-Poisson, Vlasov-Maxwell (WENO) reconstructions to achieve high order accuracy in systems in plasma physics. smooth parts of the solution and capture sharp interfaces without introducing oscillations. The scheme is extended Yingda Cheng to high dimensional problem by Strang splitting. The per- Dept. of Math and ICES formance of the proposed schemes is demonstrated by lin- University of Texas at Austin ear advection, several challenging examples of rigid body [email protected] rotation and swirling deformation in multi-dimensions. As the information is propagating along characteristics, the Irene M. Gamba semi-Lagrangian scheme does not have CFL time step re- Department of Mathematics and ICES striction, allowing for a cheaper and more flexible numeri- University of Texas cal realization than the regular finite difference scheme for [email protected] some problems.

Jennifer Proft Jing-Mei Qiu University of Texas at Austin Mathematical and Computer Sciences [email protected] Colorado School of Mines 40 AN10 Abstracts

[email protected] ties of the method, as well as numerical examples illustrating its high-order convergence properties. Chi-Wang Shu Division of Applied Mathematics Jia Li, Dongbin Xiu Brown University Purdue University [email protected] [email protected], [email protected]

MS8 MS8 Anchor Point in ANOVA Decomposition with Ap- A Stochastic Heterogeneous Multiscale Method for plications to Stochastic Problems Porous Media Flow

Analysis of variance (ANOVA) is presented to lift the curse Abstract not available at time of publication. of dimensionality for high dimensional problems. We focus Nicholas Zabaras,XiangMa on anchored-ANOVA representation employing the Dirac Cornell University measure that converges exponentially for certain classes [email protected], [email protected] of functions. However, the error depends on the anchor points. We investigate which anchor points give the best approximation. We then present examples of a function ap- MS9 proximation as well as numerical solutions of the stochas- Krylov Subspace Enhanced Parareal Algorithms tic advection equation using a combination of anchored- ANOVA and polynomial chaos expansions. We are interested in a variant of the parareal algorithm introduced by Farhat et al., which uses previous iterations in Minseok Choi, Zhongqiang Zhang, George Karniadakis order to create a subspace in which a more accurate coarse Brown University approximation of the solution is sought at each iteration. minseok [email protected], zhongqiang [email protected], We show that this approach can be interpreted as a Krylov george [email protected] subspace method with an incomplete subspace: there are missing powers of the iteration matrix. This leads to a new MS8 and interesting polynomial approximation problem. A Sparse Approximation of Partial Differential Stefan Guettel Equations with Random Inputs Mathematics University of Geneva In this work, using techniques based on concentration of [email protected] measure theory we derive a method for approximation of sparse solution of stochastic PDEs. The proposed method is: Martin Gander Department of Mathematics • Non-intrusive: It is based on the direct solution sam- Universite’ de Geneve, Switzerland pling, [email protected] • Provably convergent: We obtain probabilistic bounds on the approximation error proving the convergence MS9 of the method, Parallel Deferred Corrections and Parareal • Well suited for high dimensional problems. A method for temporal parallelization which combines fea- Several numerical experiments will be presented to explore tures of the parareal algorithm and spectral deferred cor- different aspects of the proposed method. rection methods will be presented. This approach can be viewed either as a way to parallelize deferred corrections, or Alireza Doostan as a technique for improving the efficiency of the parareal Department of Aerospace Engineering Sciences algorithm. University of Colorado, Boulder [email protected] Michael Minion University of North Carolina-Chapel Hill Houman Owhadi Mathematics Department Applied Mathematics [email protected] Caltech [email protected] Jan Prins University of North Carolina Computer Science MS8 [email protected] Stochastic Collocation Methods on Arbitrary Nodes Alex Keng Computer Science We present a stochastic collocation strategy based on mul- University of North Carolina tivariate interpolation theory. The key feature of the [email protected] method is that it allows simulations on collocation nodes (sampling points) of arbitrary number and at arbitrary locations in arbitrary dimensional spaces. Therefore the method results in great flexibility for practical stochastic simulations, particularly in high dimensions. We present mathematical analysis on the well-posedness and proper- AN10 Abstracts 41

MS9 in studying colloids is that there are very few rigorous re- Parallel Implicit Deferred Corrections sults and it even appears difficult to efficiently simulate these systems to test hypotheses experimentally. We study We present an extension of revisionist integral deferred cor- several discrete models of colloids with large squares sus- rection, a parallel high order time integrator, to solve stiff pended in a sea of small diamonds and rigorously show that systems implicitly. Based on the corrector-predictor model, the squares will cluster together beyond a certain density, the main idea is to decouple the prediction and correction extending a result of Frenkel and Louis. We also study steps so that they can be run in parallel. Time permitting, heuristics due to Buhat, Dress and Krauth for sampling we apply our algorithms to stiff rate equations. configurations of colloids and show that their algorithms are provably efficient in certain settings and inefficient in Andrew J. Christlieb others. (This is joint work with Sarah Miracle and Amanda Michigan State Univerity Pascoe.) Department of Mathematics [email protected] Dana Randall Georgia Institute of Technology Ben Ong [email protected] michigan state university [email protected] MS10 Phase Transitions for Random Graph Processes MS9 A Parallel in Time Solver for Optimal Control The classic random graph evolution of Paul Erd˝os and Al- fred Rényi undergoes a phase transition. Parametrizing the Problems n number of edges as t 2 there is a critical point tcr =1.For In this talk, we present a general methodology that cou- ttcr a “gi- ples optimization algorithms and time parallelization tech- ant component” has emerged. The Bohman-Frieze process niques to tackle optimal control issues. Our approach con- places more weight on joining isolated vertices. We define sists in defining two sets of N initial intermediate values the susceptibility of a graph, give a differential equation and N intermediate targets, so that the initial problem for its value, and and show that tcr is that t at which is split into N independent smaller problems. To illus- the value explodes. We examine the fine behavior near trate the efficiency of our strategy, we apply it to quantum criticality, particularly the growth of the “baby giant” at (bilinear) control setting and to the control of parabolic tcr + . We discuss other processes, including the Product equation. Rule process for which simulations indicate very different behavior near criticality. (Joint work with Svante Janson, Julien Salomon Milyun Kang, Will Perkins and others.) CEREMADE, Universite Paris-Dauphine [email protected] Joel Spencer Department of Mathematics, Courant Institute New York University, New York, NY 10012, U.S.A. MS10 [email protected] Random Vectors, Random Matrices, and Diagram- matic Fun MS10 If x, y,andz are random vectors, what is the expecta- Spectral Sparsification of Graphs tion of the product of their inner products, < y,z >< z,x >?IfU and V are random unitary matrices, A sparsifier of a graph G is a sparse graph that is a good what is the expected trace of their commutator? Diagram- approximation of G. We consider the problem induced by matic methods for evaluating integrals like these, which measuring quality of approximation in a spectral sense. transform them into combinatorial problems, are starting We describe deterministic polynomial-time algorithms that to show up in computer science. I will describe two appli- produce excellent sparsifiers, and fast randomized algo- cations: showing that a simple ”product of inner products” rithms that produce cruder sparsifiers. function of directed graphs is #P-complete, and showing that certain estimators for the permanent, based on deter- Daniel Spielman minants over nonabelian algebras, have exponentially large Yale University variance.ThisisjointworkwithAlexRussell. [email protected] Cris Moore Santa Fe Institute MS11 [email protected] Subdomain Radial Basis Collocation Method for Fracture Mechanics

MS10 This work attempts to apply radial basis collocation Discrete Models of Colloids method to fracture mechanics by introducing a domain decomposition technique with proper interface conditions. Colloids are mixtures of substances that tend to separate The proposed method allows (1) natural representation of so that like particles are clustered together. Unlike re- discontinuity across the crack surfaces and (2) enrichment lated models with enthalpic forces causing like particles to of crack-tip solution in a local subdomain. Exponential attract or disparate particles to repel, colloids are driven convergence rate can be achieved while keeping the dis- solely by entropic forces. It seems that in these models crete system well-conditioned. The analytical prediction clustering occurs above a certain density if conﬁgurations and numerical results demonstrate that an optimal dimen- are chosen from the uniform distribution. The challenge 42 AN10 Abstracts

sion of the near-tip subdomain exists. time dependent expansion coefficients. Using rotational and translational transformations, the Euler equations are Jiun-Shyan Chen solved as exact time dependent differential equations in a University of California, Los Angeles (UCLA) moving frame. Riemann solvers are used to calculate vari- Dept. of Civil & Environmental Eng. ous wave interactions. The eigenvalues of the time amplifi- [email protected] cation matrix are all unity. No artificial viscosity, upwind- ing or entropy violating methods were needed. Lihua Wang Tongji University, China Edward Kansa [email protected] University of California, Davis (UC Davis) [email protected] or [email protected] Hsin-Yun Hu Tunghai University, Taiwan MS12 [email protected] On the Stochastic Navier-Stokes Equations

Abstract unavailable at time of publication. MS11 The Gibbs Phenomenon for Radial Basis Functions Alexander Labovsky Department of Scientific Computing The Gibbs phenomenon was first observed in the con- Florida State University text of truncated Fourier expansions, but it arises also in [email protected] cases such as truncated integral transforms and different interpolation methods. Radial basis functions (RBFs) include both splines and trigonometric interpolation as spe- MS12 cial cases in 1-D, and they generalize these methodologies Filter Based Stabilization for Evolution Equations to scattered node layouts in any number of dimensions. We investigate here the Gibbs phenomenon in the case of RBF This project, which describes joint work with Vince Ervin interpolation on an equispaced grid in 1-D. (Clemson) and Monika Neda (UNLV), considers the following idea: Step 1: Take one step of any numerical method for Bengt Fornberg advancing an evolution equation in time, Step 2: take the University of Colorado result of Step 1, Filter it and use that for the following step. Boulder We show how this process Evolve then Filter can overdif- [email protected] fuse an approximate solution. We then show how to fix it to produce a highly accurate, stable and non-overdiffused Natasha Flyer approximation. One advantage of this approach to stabi- National Center for Atmospheric Research lization is that Steps 1 and 2 can be performed by calls to Division of Scientific Computing independent, black box programs. fl[email protected] William Layton University of Pittsburgh MS11 [email protected] An RBF-Gegenbauer Method for Time Dependent Discontinuous Problems MS12 Radial basis function(RBF) methods have been actively Analysis of Generalized Alpha-models of Turbu- developed in the last decades. The advantages of RBF lence methods are that these methods are mesh-free and yield high order accuracy if the function is smooth enough. The In this talk I will discuss the global existence and unique- RBF approximation for discontinuous problems, however, ness results for the general family of regularized Navier- deteriorates its high order accuracy due to the Gibbs phe- Stokes and Magnetohydrodynamics (MHD) models . This nomenon. In this talk we will show that high order accu- family captures most of the specific regularized models racy can be recovered from the RBF approximation con- that have been proposed and analyzed in the literature, in- taminated with the Gibbs phenomenon if a proper recon- cluding the Navier-Stokes equations, the Navier-Stokes-α struction method is applied. In this work, the Gegenbauer model, the Leray-α model, the Modified Leray-α model, reconstruction method is used to reconstruct the RBF ap- the Simplified Bardina model, the Navier-Stokes-Voight proximation for the recovery of high order accuracy. Nu- model, the Navier-Stokes-α-like models, and certain MHD merical examples including the linear and nonlinear hyper- models, in addition to representing a larger 3-parameter bolic partial differential equations are presented. family of models not previously analyzed. We give a unified analysis of the entire three-parameter family of models us- Sigal Gottlieb ing only abstract mapping properties of the principal dissi- Department of Mathematics pation and smoothing operators, and then use assumptions University of Massachusetts at Dartmouth about the specific form of the parameterizations, leading to [email protected] specific models, only when necessary to obtain the sharpest results.

MS11 Evelyn Lunasin Meshfree Solutions of One-dimensional Inviscid University of California San Diego Euler Equations [email protected]

The inviscid Euler equations are solved by expanding any dependent variable in terms of radial basis functions and AN10 Abstracts 43

MS12 Oscar Bruno Drag and Lift Computations of High Order Accu- Division of Engineering and Applied Science racy Fluid Flow Models California Institute of Technology [email protected] Numerical studies based on finite element discretizations of a higher order time relaxation models of fluid motion will be presented. The family of models is based on filtering MS13 and deconvolution techniques for driving the unresolved Complete Radiation Boundary Conditions: Theory fluctuations to zero. Optimal error estimates for velocity and Application convergence analysis are derived. The family of models is tested on a benchmark problem where drag and lift esti- Complete radiation boundary conditions (CRBCs) are ge- mates and pressure drop on a body immersed in a fluid ometrically flexible, applicable to all standard wave equa- were investigated. tions in homogeneous, isotropic media as well as to a limited class of anisotropic models, and satisfy optimal com- Monika Neda plexity estimates. They provide provably accurate long- University of Nevada Las Vegas time results on small domains using parameters which are [email protected] determinable a priori. We review the CRBC theory and describe our ongoing efforts to develop a generally usable implementation and to extend their applicability to more MS12 complex models. Solving the Navier-Stokes Equations for Velocity, Vorticity and Helicity Thomas M. Hagstrom Southern Methodist University For the three-dimensional incompressible Navier-Stokes Department of Mathematics equations, we present a formulation featuring velocity, vor- [email protected] ticity and helical density as independent variables. We show that mathematically the helical density can be observed as a Lagrange multiplier corresponding to the MS13 divergence-free constraint on the vorticity variable. As one Stable Fourier Based Embedding Methods for possible practical application of this formulation, we con- Wave Propagation on Complex Domains sider a time-splitting numerical scheme based on a simple alternating procedure between vorticity - helical density The FC-AD methodology provides efficient new PDE and velocity - Bernoulli pressure systems of equations. We solvers based on the use of a certain “Fourier continua- discuss the relation of the numerical method to some well tion’ (FC) method in conjunction with alternating direc- known turbulence models. tion (AD) strategies and can be applied directly to complex computational domains with unconditional stability Maxim Olshanskii and high-order accuracy. FC-AD techniques are uniquely Department of Mechanics and Mathematics suited for wave propagation problems as the Fourier basis Moscow State M.V.Lomonosov University, Moscow, essentially eliminates pollution error. New extensions in- Russia cluding those to handle Neumann- and mixed-type bound- [email protected] ary conditions will be presented.

Mark Lyon MS13 University of New Hampshire High Order Accurate Discretization of the Wave [email protected] Equation on Structured Grids Enforcement of boundary conditions in high-order MS13 embedded-boundary methods that removes small-cell stiff- Boundary and Interface Conditions for Non-Linear ness for both Dirichlet and Neumann b.c. and guarantee Wave Propagation Problems single valued solutions for slender bodies is presented. The b.c. enforcement is paired with Taylor-series-time-stepping Most wave propagation problems are linear and the re- and a high-order spatial discretization to accurately solve lated boundary and interface conditions that lead to well- the wave equation. Three spatial discretizations are consid- posedness and stability are relatively well known. For ered: Pade (implicit), summation by parts finite difference non-linear problems that is not the case. We will discuss and Fourier continuation. Numerical experiments illustrat- boundary treatments where the non-linearity adds addi- ing the properties of the methods are presented. tional complications. Typical applications that will be dis- ussed are related to shocks in fluid flow, propagation of Daniel Appelo discontinuities in stochastic PDE’s and earthquake prob- Division of Engineering and Applied Science lems. California Institute of Technology [email protected] Jan Nordstrom University of Witwatersrand Anders Petersson South Africa Center for Applied Scientific Computing [email protected] Lawrence Livermore National Lab [email protected] MS14 Randomization in the Default Boundary Problem Nathan Albin California Institute of Technology We consider an inverse problem for the first hitting time [email protected] distribution of a Wiener process and its application for 44 AN10 Abstracts

credit risk pricing. We demonstrate that randomization of transparent and robust methods for valuing and hedging the initial state of the process lead to analytically tractable structured credit portfolios. First-generation models, such solution. as the Gaussian copula-based methods have well docu- mented practical and theoretical limitations. In this paper, Alexander Kreinin we demonstrate the practical application of the weighted University of Toronto and Monte Carlo methodology to value and compute sensitivi- Algorithmics Inc. ties and risk statistics for ABS and CLO structures. The [email protected] model extends the full bottom-up approach of Rosen and Saunders (2009) for pricing bespoke CDOs to include can- Sebastian Jaimungal, Angel Valov cellability and stochastic LGDs in a natural way. The University of Toronto performance of the model is analyzed throughout a three- [email protected], [email protected] month period during the credit crisis in 2008. The model calibrates very well to observed prices for the CDXHY and LCDX indices, and provides stable implied distributions MS14 for the systematic factor. Furthermore, it gives robust, Modeling Default Correlation and Clustering: A consistent prices and sensitivities , even during this very Time Change Approach volatile period. We present a novel framework for modeling correlated de- Dan Rosen faults where it is possible to capture the so-called “con- R2 Financial Technologies tagion effect’. Time changing multi-parameter Markov dan.rosen@r2-financial.com processes with multivariate subordinators leads to jump- diffusion processes that are correlated through their jump measures. When unpredictable shocks arrive, the default MS15 intensity of multiple firms will shift simultaneously, which Linear Feedback Control Strategies for the Navier- can trigger multiple defaults. Stokes Equations

Rafael Mendoza-Arriaga One systematic control strategy often proposed for fluid University of Texas at Austin flows is optimal feedback control of the linearized system. [email protected] If the linearized portion of the Navier-Stokes equations are stabilized, then the full nonlinear system is stabilized. The Vadim Linetsky natural questions are practical-how does this strategy per- Northwestern University form in practice. This talk will focus on a numerical proce- [email protected] dure for solving the LQR control problem associated with the Oseen equations and numerical experiments to determine the effectiveness of the feedback control strategy. MS14 Pricing Counterpary Risk at the Trade Level and Imran Akhtar CVA Allocation Virginia Tech [email protected] We address the problem of allocating the counterparty- level credit valuation adjustment (CVA) to the individual Jeff Borggaard trades composing the portfolio. We show that this problem Virginia Tech can be reduced to calculating contributions of the trades to Department of Mathematics the counterparty-level expected exposure (EE) conditional [email protected] on the counterparty’s default. We propose a methodology for calculating conditional EE contributions for both col- Miroslav Stoyanov lateralized and non-collateralized counterparties. Calcu- Florida State University lation of EE contributions can be easily incorporated into Department of Scientific Computing exposure simulation processes that already exist in a finan- [email protected] cial institution. We also derive closed-form expressions for EE contributions under the assumption that trade values are normally distributed. Analytical results are obtained MS15 for the case when the trade values and the counterparty’s Bridging the Boussinesq and Primitive Equations credit quality are independent as well as when there is a Through Spatio-Temporal Filtering dependence between them (wrong-way risk). We propose a novel approach for bridging the Boussinesq Michael Pykhtin equations and the primitive equations. This approach uses Federal Reserve Board spatio-temporal filtering as an alternative to traditional [email protected] scaling arguments used in the derivation of simplified models for the ocean and atmosphere. Dan Rosen R2 Financial Technologies Traian Iliescu dan.rosen@r2-financial.com Department of Mathematics Virginia Tech [email protected] MS14 Pricing Structured Credit Products with Implied Jinqiao Duan Factor Models Illinois Institute of Technology [email protected] The current financial crisis has underscored the need for AN10 Abstracts 45

Paul F. Fischer ing Models Argonne National Laboratory fi[email protected] In this talk I’ll focus on fundamental properties of two specific car-following (CF) models of highway traffic; namely Tamay Ozgokmen he Intelligent Driver Model, IDM, and the Aw-Rascle- University of Miami/RSMAS Greenberg Model, ARG. I shall show that for both of these [email protected] models there are no car crashes and no velocity rever- sals. These results concern well-posedness of the underlying ODE system and are addressed by a-priori estimates MS15 which are independent of the number of cars in the system. Improving Mass Conservation in FE Computations I shall also establish that both the IDM and ARG models of NSE with C0 Velocities support large amplitude Stop and Go waves; these waves are traveling wave solutions of the underlying systems. This talk will begin by introducing the Scott-Vogelius element pair, then show a connection between it and the James M. Greenberg grad-div stabilized Taylor-Hood element. Implications of Carnegie Mellon University this connection will be discussed, and numerical experi- Dept of Mathematical Sciences ments will also be given. [email protected] Michael Case Dept. of Mathematical Sciences MS16 Clemson University Impact of Protein and Lipid Binding on Drug Dis- [email protected] position Abstract unavailable at time of publication. Leo Rebholz Clemson University L. Peletier Department of Mathematical Sciences Mathematical Institute [email protected] Leiden University [email protected] Vince Ervin Department of Mathematical Sciences Clemson University MS16 [email protected] Solutions of Semilinear Equations

Alexander Linke We study solutions of a second order semilinear pde, with WIAS Berlin particular focus on singular solutions. For both the fo- [email protected] cussing and non-focussing versions of the equation we ﬁnd new singular solutions.

MS15 William Troy University of Pittsburgh Two-Level Strategies for Large Eddy Simulation Department of Mathematics Proper Orthogonal Decomposition Models [email protected] One of the main hurdles in the development of modern closure models in Proper Orthogonal Decomposition of tur- MS16 bulent flows has been the lack of efficient computational strategies for the discretization of the associated nonlinear- A Weak KAM Theorem for the Nonlinear Vlasov ities. We introduce a two-level discretization methodology System that reduces dramatically the computational cost without The space L2(0, 1) has a natural Riemannian structure on compromising the accuracy of the closure model. This is the basis of which we introduce an L2(0, 1)–infinite dimen- demonstrated numerically in the 3D simulation of a flow sional torus T. For a class of Hamiltonians defined on its past a cylinder at Re=1,000. cotangent bundle we establish existence of a viscosity so- Zhu Wang, Traian Iliescu lution for the cell problem on T or, equivalently, we prove Department of Mathematics a Weak KAM theorem. As an application, we obtain exis- Virginia Tech tence of absolute action-minimizing solutions of prescribed [email protected], [email protected] rotation number for the one-dimensional nonlinear Vlasov system with periodic potential.

Imran Akhtar Wilfrid Gangbo Virginia Tech Georgia Institute of Technology [email protected] [email protected]

Jeﬀ Borggaard Adrian Tudorascu Virginia Tech Department of Mathematics Department of Mathematics University of Wisconsin, Madison [email protected] [email protected]

MS16 MS17 Collective Behavior of Two Classes of Car Follow- Practical Heuristics for Inexact Subgraph Isomor- 46 AN10 Abstracts

phism MS18 Taking the Road Not [Usually] Taken Abstract unavailable at time of publication. There are commonalities among research career paths; Jon Berry however, internally motivated and externally mandated Sandia Natinal Laboratories transitions help mold each experience into our own unique [email protected] journey. I will discuss major transition points in my professional career ranging from graduate school to early career MS17 and personal as well as externally motivated events that brought me to career crossroads. My experience and pos- Spectral Methods for Subgraph Detection sible lessons learned in taking less traveled paths will be We describe a statistical test for subgraph detection and examined. localization using spectral properties of the so-called mod- Elebeoba May ularity matrix, a type of residual under the Chung-Lu ran- Sandia National Laboratories dom graph model. We show that the resultant algorith- [email protected] mic procedure can be applied to very large graphs (< 106 vertices), with complexity dominated by that of standard sparse eigensolver methods, and can successfully isolate MS18 anomalous vertices in real data examples. Panel Discussion: Success through Transitions

Nadya Bliss, Benjamin A. Miller This panel session provides an opportunity for AWM work- MIT Lincoln Laboratory shop members to ask questions and discuss issues with pro- [email protected], [email protected] fessional development speakers. Patrick J. Wolfe Elebeoba May Harvard University Sandia National Laboratories [email protected] [email protected]

Gigliola Staﬃlani MS17 MIT Tools and Primitives for High-performance Graph [email protected] Computation

Abstract unavailable at time of publication. Mary Ann Horn National Science Foundaton John Gilbert [email protected] U. California at Santa Barbara [email protected] MS18 Title Not Available at Time of Publication MS17 Hybrid Parallel Programming for Massive Graph Abstract unavailable at time of publication. Analysis Gigliola Staffilani Abstract unavailable at time of publication. MIT [email protected] Kamesh Madduri Lawrence Berkeley National Lab [email protected] MS19 FETI Methods for Mortar Coupling of Stokes- Darcy Systems MS18 Deciding to Give Up Tenure: Surprising Decisions Abstract unavailable at time of publication. Along the Path Juan Galvis In a world where a successful research program and tenure Texas A&M University often seem to be the main goals of a Ph.D. scientist, one [email protected] may find it hard to see the other options available. After receiving my degree, my choices were not unusual and I MS19 spent three years as a postdoc before accepting a tenure- track position and, later, receiving tenure. But life some- An Efficient Method for Solving Multiscale Elliptic times throws unexpected opportunities in your path and Problems with Randomly Perturbed Data I will describe a number of my own experiences, includ- We propose a method for efficient solution of elliptic prob- ing how I eventually reached a decision to resign a tenured lems with multiscale features and randomly perturbed co- position. efficients. We use the multiscale finite element method Mary Ann Horn (MsFEM) as a starting point and derive an algorithm for National Science Foundaton solving a large number of problems with randomly per- [email protected] turbed coefficients. We show that the method converges to the multiscale finite element solution in the limit. A set of numerical examples is presented to illustrate theoretical AN10 Abstracts 47

findings. tested on both single-machine and multi-machine system with various random disturbances. Our numerical results Victor E. Ginting demonstrate the validity and performance of the proposed Department of Mathematics dynamic state estimation approach with different random University of Wyoming disturbance. The numerical results also indicate the pro- [email protected] posed approach can include the full dynamics of power systems and ensure an accurate representation of the changing Axel Malqvist states in the power system. Department of Information Technology Uppsala University Guang Lin [email protected] Pacific Northwest National Laboratory [email protected] Michael Presho Department of Mathematics MS20 University of Wyoming [email protected] Capturing All Scales of Random Modes in Stochas- tic Pdes Based on Polynomial Chaos and a Dynam- ically Adaptive Wavelet Method MS19 We consider the numerical solution of stochastic partial dif- Some Computational Issues in the Modeling and ferential equations based on polynomial chaos expansion Simulation of Coupled Surface and Subsurface exemplified by the convection-diffusion equation model. Fluid Flow This typically produces a coupled system of determinis- Abstract unavailable at time of publication. tic equations for the coefficients of the expansion whose size can become very large with an increasing number of Junping Wang independent random variables and/or order of polynomial National Science Foundation chaos expansion (dubbed the dimensionality curse). We [email protected] tackle this challenge using a dynamically adaptive wavelet- based methodology utilizing space-refinement that allows capturing all scales of each random/unceretainty mode on MS20 indepenent grids. We present numerical results illustrating Adaptive Strategies for Uncertain Hyperbolic Sys- the salient features of the proposed method. tems Xiaoan Ren Abstract not available at time of publication. University of Shanghai for Science and Technology [email protected] Olivier Le Maitre LIMSI-CNRS Wenquan Wu [email protected] Univ of Shanghai Sci & Technology, Shanghai 200093, PR China Julie Tryoen xiao ann [email protected] UniversitéParis-Est CERMICS - ENPC Leonidas S. Xanthis [email protected] Department of Aeronautics, Imperial College [email protected] Alexandre Ern Universite Paris-Est CERMICS, Ecole des Ponts MS20 [email protected] Multi-element Uncertainty Quantification Based on Simplex Elements Stochastic Collocation MS20 A Simplex Elements Stochastic Collocation (SESC) A Multi-element Probabilistic Collocation Based method is presented for robust and efficient multi-element Kalman Filter for Power System Dynamic State uncertainty quantification. The method is equally robust Estimation as Monte Carlo simulation in terms of the Extremum Di- minishing (ED) robustness concept extended to probabil- In this talk, we propose an efficient multi-element proba- ity space. Its efficient extension to multiple uncertainties bilistic collocation method (MEPCM) based Kalman filter is considered based on higher degree polynomial interpola- (KF) to include dynamic state variables in the power sys- tion, randomized refinement sampling, and Essentially Ex- tem dynamic state estimation process. Comparing with tremum Diminishing (EED) extrapolation. These strate- Monte Carlo (MC) based KF approach, the proposed gies employ the flexibility of simplex elements for han- MEPCM based KF implementation can solve the system dling randomized samples and non-hypercube probability of stochastic state equations much more efficient. Ad- spaces. ditionally, the proposed approach can sample the generalized polynomial chaos approximation of the stochastic Jeroen Witteveen solution with an arbitrarily large number of samples, at Stanford University virtually no additional computational cost. The proposed Center for Turbulence Research algorithm thus can drastically reduce the sampling errors [email protected] and achieve a high accuracy at reduced computational cost, compared to the classical MC implementations of KF. The Gianluca Iaccarino proposed MEPCM-KF based dynamic state estimation is Stanford University 48 AN10 Abstracts

[email protected] [email protected]

MS21 MS21 Anatomy of a Young Giant Component in the Ran- Structure of Random r-SAT below the Pure Literal dom Graph Threshold

In this talk, we will completely describe the structures of gi- It is well known that there is a sharp density threshold for ant components in random graphs G(n, p)withn−1/3 << a random r-SAT formula to be resolved by the pure literal pn − 1 << n−1/4. The description can be made by us- rule, and a higher threshold for satisfiability. We analyze ing random 3-regular graphs and Galton-Watson Poisson the structure of the (rare) unsatisfiable instances below the branching processes. The proof uses the Poisson cloning pure literal threshold, contrasting this with the situation model and interesting computation arguments. We will above the satisfiability threshold. It remains open what also present some results regarding the diameter and the happens between the two thresholds. mixing time of the giant component. Gregory Sorkin Jeong Han Kim IBM Research Yonsei University Mathematical Sciences National Institute for Mathematical Sciences [email protected] [email protected] MS21 Jian Ding Phase Transition for the Mixing Time of the University of California, Berkeley Glauber Dynamics for Coloring Regular Trees [email protected] We prove that the mixing time of the Glauber dynamics Eyal Lubetzky, Yuval Peres for random k-colorings of the complete tree with branch- Microsoft Research ing factor b undergoes a phase transition at k = b(1 + [email protected], [email protected] ob(1))/ ln b. Our main result shows nearly sharp bounds on the mixing time of the dynamics on the complete tree with n vertices for k = Cb/ln b colors with constant C.ForC ≥ MS21 1+o (1) 2 1 we prove the mixing time is O(n b ln n). On the How Frequently is a System of 2-linear Boolean other side, for C<1 the mixing time experiences a slowing Equations Solvable? down, in particular, we prove it is O(n1/C+ob(1) ln2 n)and 1/C−ob(1) We consider a random system of equations xi + xj = Ω(n ). The critical point C=1 is interesting since it b(i,j)(mod2), (xu ∈{0, 1},b(u,v) = b(v,u) ∈{0, 1}), with coincides (at least up to first order) to the so-called recon- the pairs (i, j)fromE, a symmetric subset of [n] × [n]. E struction threshold which was recently established by Sly. is chosen uniformly at random among all such subsets of a The reconstruction threshold has been of considerable in- given cardinality m; alternatively (i, j) ∈ E with a given terest recently since it appears to have close connections to probability p, independently of all other pairs. Also, given the efficiency of certain local algorithms, and this work was E, Pr{be =0} = Pr{be =1} for each e ∈ E, indepen- inspired by our attempt to understand these connections dently of all other be .Itiswellknownthat,asm passes in this particular setting. This is joint work with Prasad through n/2(p passes through 1/n, resp.), the underlying Tetali, Juan C. Vera, and Linji Yang which appeared at random graph G(n, #edges = m), (G(n, P r(edge) = p), SODA’10. resp.) undergoes a rapid transition, from essentially a forest of many small trees to a graph with one large, mul- Eric Vigoda ticyclic, component in a sea of small tree components. Georgia Institute of Technology We should expect then that the solvability probability de- [email protected] creases precipitously in the vicinity of m ∼ n/2(p ∼ 1/n), 1/4 and indeed this probability is of order (1 − 2m/n) , MS22 1/4 for m 0. Mike Molloy noticed neutral- and delayed differential equations based on multiquadrics (MQ) collocation is presented. Furthermore, we that the Boolean system with be ≡ 1 is solvable iff the underlying graph is 2-colorable, and asked whether this report on our progress to extend the method to deal with connection might be used to determine an order of proba- state-dependent neutral differential equations. This kind bility of 2-colorability in the near-critical case. We answer of nonlinear problem may be numerically elusive due to its Mike’s question affirmatively and show that probability of ability to form and propagate discontinuities and low-order −1/4 1/8 −1/12 singularities in the solution, which may take place at times 2-colorability is ≤∼ 2 e c(λ)n , and asymptotic −1/4 1/8 −1/12 not known in advance. The ultimate goal is to infer the to 2 e c(λ)n at a critical phase λ = O(1), and for singularity locations in computing time by monitoring the →−∞ λ . In part, this study was inspired by the work of MQ weights in the interpolant and then partition the time HervéDaudé and Vlady Ravelomanana who analyzed the domain into smooth subintervals. case of a random multigraph MG(n, #edges = m). This is ajointworkwithDr.Ji-AYeum. Francisco Bernal UT Dresden Boris Pittel [email protected] The Ohio State University AN10 Abstracts 49

Jae-Hun Jung Department of Mathematics Department of Mathematics University of Massachusetts at Dartmouth SUNY at Buﬀalo [email protected] jaehun@buﬀalo.edu

MS23 MS22 Regulatory Network Analysis and Approximation Anti-Gibbs and Anti-Runge Strategies in Spectral Using Tensor Products Methods We consider the problem of recovering a system of func- We discuss the relationship between the Gibbs and Runge tions governing a regulatory network using time course Phenomena and compare and contrast single-interval and data, such as that obtained from microarrays. The num- three-interval strategies for combating them. RBF, Fourier ber of components in the regulatory networks and the cost and polynomial bases are analyzed. The limitations of of data collection yield an ugly showing of the curse of these tactics in both accuracy and ill-conditioning and the dimensionality. In [Gregory Beylkin, Jochen Garcke, and trade-offs are discussed. Martin J. Mohlenkamp. ’Multivariate regression and Ma- chine Learning with Sums of Separable Functions,” SIAM John P. Boyd Journal on Scientific Computing (2009)] it was shown that University of Michigan regression with tensor products provides a way to effec- Ann Arbor, MI 48109-2143 USAUSA tively overcome this and obtain good approximations. We [email protected] will incorporate time derivatives into a novel ALS algorithm for approximating time course data. We will then consider the benefits of using tensor product in the analy- MS22 sis of the approximated network. Kernel-based Approximation for Ill-posed and Dis- continuous Problems Ryan Botts Ohio University In this talk we present the idea of meshless computational Department of Mathematics methods based on the use of kernel-based functions for solv- [email protected] ing various ill-posed problems and problems with discontinuity. In particular, the recent development of the method Martin J. Mohlenkamp of fundamental solutions combined with various regular- Ohio University ization techniques to solve Cauchy problems and inverse [email protected] heat conduction/source identification problems will be discussed. The main idea is to approximate the unknown solution by a linear combination of fundamental solutions MS23 whose singularities are located outside the solution domain. Solution of High-Dimensional Uncertain Systems More recent works on using the particular solutions and Using Separated Tensor Decomposition Green’s functions will be highlighted. Separated representations have proven efficient to relax the Benny Hon curse-of-dimensionality associated with approximation of City University of Hong Kong high-dimensional functions and tensors. In this talk, we [email protected] will demonstrate how such techniques can be employed to efficiently compute the solution to linear elliptic PDEs with MS22 high-dimensional random inputs. In particular, we illustrate the existence of an approximate low-rank separated Detecting Edges in Two Dimensional Functions solution to this class of stochastic PDEs and further explore with Radial Basis Functions the efficiency and accuracy of alternating least-squares and We extend the iterative adaptive multiquadric radial Rayleigh-Ritz methods in computing the solution. basis function (RBF) method for the detection of lo- Alireza Doostan cal jump discontinuities in one-dimensional problems to Department of Aerospace Engineering Sciences two-dimensional problems. The iterative edge detection University of Colorado, Boulder method is based on the observations that the absolute val- [email protected] ues of the expansion coefficients of RBF approximation have different growth rates. We consider two approaches: the dimension-by-dimension technique and the global ex- Gianluca Iaccarinno tension approach. Numerical examples demonstrate that Stanford University the two-dimensional iterative adaptive RBF method yields Mechanical Engineering accurate results. [email protected] Saeja Kim University of Massachusetts Dartmouth MS23 [email protected] Source Apportionment of Particulate Matter Based on Segregated Composition Size Data Jae-Hun Jung Source apportionment on bulk airborne particle composi- Department of Mathematics tion data resolves the data into a product of two matrices, SUNY at Buffalo source profiles and source contributions. However, size- jaehun@buffalo.edu segregated data requires a higher dimension model since source emissions are size dependent. Source profiles are Sigal Gottlieb a composition matrix as a function of size. The model 50 AN10 Abstracts

sums outer products of matrices times vectors. The ap- have implemented this scheme to model hot electron-hole plication of this model to data collected using a multiple transport on Kane and full energy bands in the simulation stage DRUM impactor analyzed by synchrotron XRF will of one and two-physical and three-phase space dimensional be presented. nano meter devices with a base channels of the order of 50 nm. The energy bands (conduction and valence) are Philip Hopke, Jihong Wang, Punith Nallathamby computed by eingenvalue solvers for electronic structures Clarkson University and coupled to the Boltzmann Poisson solver. Center for Air Resources Engineering and Science [email protected], [email protected], James R. Chelikowsky [email protected] University of Texas at Austin Institute for Computational Engineering and Sciences [email protected] MS23 Convergence Results of a Regularized Tensor Al- Yingda Cheng ternating Least-Squares Dept. of Math and ICES University of Texas at Austin The Alternating Least-Squares (ALS) for tensor decom- [email protected] position has been widely applied to many applications, for example, in signal processing, chemometrics, and data mining. However, ALS can be prohibitively slow for some data. Irene M. Gamba We improved ALS with a regularization term. Our regu- Department of Mathematics and ICES larized method dramatically accelerates ALS. In addition University of Texas to providing numerical results for several data sets, we also [email protected] analyze the convergence of the regularized ALS. Armando Majorana Na Li Dipartimento di Matematica e Informatica Clarkson University University of Catania - Italy Dept. of Mathematics [email protected] [email protected] Chi-Wang Shu Stefan Kindermann Division of Applied Mathematics RICAM Institute, Linz Brown University Austria [email protected] [email protected]

Carmeliza Navasca MS24 Clarkson University New Models of Chemotaxis: Analysis and Numer- [email protected] ics Patlak-Keller-Segel (PKS) system is a classical PDE model MS24 of the chemotaxis. The system admits solutions that de- Diffeomorphic Deformation of Textured Shapes velop delta-type singularities within a finite time. Even though such blowing up solutions model a concentration This work proposes a new method to match shapes with in- phenomenon, they are not realistic since biological cells terior textures through the large deformation diffeomorphic do not converge to one point (while the cell density grows metric mapping, resulting in optimizing for geodesics on sharply, it must remain bounded at all times). I will present the space of diffeomorphisms connecting textured shapes. a new chemotaxis model, which can be viewed as a regular- This study is to address the problems caused by boundary ized PKS system. The proposed regularization is based on conditions and response to the need of matching regions of a basic physical principle: boundedness of the chemotac- interest directly in medical applications. The new method tic convective flux, which should depend on the gradient is illustrated by numerical experiments on MRI images. of the chemoattractant concentration in a nonlinear way. Solutions of the new system may develop spiky structures Yan Cao that model the concentration phenomenon. However, both The University of Texas at Dallas cell density and chemotattractant concentration remain Department of Mathematical Sciences bounded. The proposed model is studied both analytically [email protected] and numerically. I will first prove a global existence result and then use the bifurcation theory to investigate existence of nontrivial steady states and their stability properties. MS24 Finally, I will persent one- and two-dimensional numerical Discontinuous Galerkin Solvers for Boltzmann- examples that support the analytical findings and demon- Poisson Systems in Semiconductor Device Simu- strate the formation and stability of the spiky solutions. lations

The Boltzmann transport equation (BTE) is an integro- Alina Chertock differential model describing the evolution of a single point North Carolina State University probability distribution function. The mathematical and Department of Mathematics computational difficulties associated to this equation is due [email protected] to the balance of a first order transport term to an integral operator accounting for their interactions and the coupling Alexander Kurganov to the Poisson equation. We will present a discontinuous Tulane University Galerkin solver for the Boltzmann Poisson systems. We Department of Mathematics AN10 Abstracts 51

[email protected] Enhanced heavy oil recovery methods are an intensive research area in the oil industry, and have recently generated Xuefeng Wang a battery of recovery methodsinwhatisthelargestgrow- Tulane University ing sector of this industry, such as steam assisted grav- [email protected] ity drainage (SAGD) and cyclic steam stimulation (CSS). However, the environmental impacts of these processes and Yaping Wu the use of a high volume of water and natural gas suggest Department of Mathematics that extensive research is required for economic and en- Capital Normal University, Beijing vironmentally friendly development of heavy oil reserves. [email protected] This presentation will give an overview on current research in heavy oil modeling, and the presenter will also describe his current research program. MS24 Zhangxin Chen Well-Balanced University of Calgary Positivity Preserving Central-Upwind Scheme on [email protected] Triangular Grids for the Saint-Venant System

We introduce a new second-order central-upwind scheme MS25 for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves Rate and Interfacial Tension Dependent CO2 Rel- stationary steady states (lake at rest) and guarantees the ative Permeability positivity of the computed fluid depth. Moreover, it can We must develop models that better quantify and predict be applied to models with discontinuous bottom topogra- the influence of important processes and small-scale fea- phy and irregular channel widths. We demonstrate these tures on fluid behavior and CO2 containment potential. features of the new scheme, as well as its high resolution Recent relative permeability experiments indicate the de- and robustness in a number of numerical examples. pendency of supercritical CO2 on interfacial tension as re- Yekaterina Epshteyn sults of changes in insitu pressure and temperature. We Carnegie Mellon University investigate the roles of capillary and gravitational forces on [email protected] trapped CO2 taking into the account the density, viscosity, and interfacial tension computed from the compositional phase behavior model. The combined capillary number Alexander Kurganov and bond number referred to as trapping number is suc- Tulane University cessfully implemented in IPARS simulator. Carbon storage Department of Mathematics simulation results with this new modeling capability will be [email protected] presented. Steve Bryson Mojdeh Delshad NASA Ames Research Center Department of Petroleum and Geosystems Engineering [email protected] The University of Texas at Austin [email protected] Guergana Petrova Texas A&M University X. Kong, M.F. Wheeler [email protected] The University of Texas at Austin [email protected], [email protected]

MS24 Stencil Choosing Sensitivity in WENO MS25 Towards Accurate and Efficient Computational The weighted essentially non-oscillatory method is used to Modeling of Compositional Multi-Phase Flow approximate the numerical flux in hyperbolic PDEs. It automatically centers the stencil in the case of a smooth Compositional multiphase flow modeling is demanded in solution, but places larger weights on the smoother stencils a number of important reservoir applications. One im- when the solution has a discontinuity pr sharp gradient. A portant application is the injection of CO2 in hydrocarbon significant parameter in determining the WENO weights, reservoirs, which is becoming increasingly attractive due to epsilon, is examined in this talk. issues related to global warming, and urgent need for improved hydrocarbon recovery. CO2 injection may be one of Sigal Gottlieb the most attractive options for water-flooded reservoirs ei- Department of Mathematics ther from natural water drive or from external water injec- University of Massachusetts at Dartmouth tion. Coinjection of water with CO2 for improved mobility [email protected] and increased sweep is also another process of high interest. To evaluate the efficiency of CO2 injection in water-flooded reservoirs, three-phase compositional numerical models are MS25 required. Such simulators have to be equipped with unique Mathematical and Computational Techniques for capabilities due to special features of CO2 mixing in hydro- Modeling Heavy Oil Reservoirs carbon liquids and gases for CO2 applications. Specifically, when dissolved in liquids, CO2 generally increases the den- While mathematical modeling has been successful in the sity. The density increase may have a significant effect on recovery of conventional oil, it is still in the early stage flow path and may result in convective mixing. Moreover, of heavy oil modeling. As conventional oil reserves dwin- CO2 mixing may also lower the viscosity; it may also in- dle and oil prices rise, heavy oil is now the center stage. crease the viscosity when there is substantial vaporization 52 AN10 Abstracts

of liquid components in the gas phase. In this talk, we MS26 present three-phase compositional flow using higher-order On the Geometry of Discrete Exponential Families finite element methods. Our numerical model is based on with Application to Exponential Random Graph an iterative IMPEC coupling of the pressure equation and Models species transport equations, which are solved by mixed finite element (MFE) and discontinuous Galerkin (DG) There has been an explosion of interest in statistical models methods, respectively. Compared with lower order finite for analyzing network data, and considerable interest in the volume methods, the proposed MFE-DG method has low class of exponential random graph (ERG) models. In this numerical diffusion and can capture the solution discon- talk I will relate the properties of ERG models to the prop- tinuities and yield accurate prediction of shock locations erties of the broader class of discrete exponential families. arising in computational three-phase flow. I will describe a general geometric result about discrete exponential families with polyhedral support. Specifically, I Shuyu Sun will show how the statistical properties of these families can Clemson University and KAUST be well captured by the normal fan of the convex support. [email protected] I will discuss the relevance of such results to maximum likelihood estimation and apply them to the analysis of ERG models. By means of a detailed example, I will provide MS25 some characterization and a partial explanation of certain Compositional Flow Modeling in Porous Media pathological features of ERG models known as degeneracy. Joint work with S.E. Fienberg and Y. Zhou. Abstract unavailable at time of publication. Alessandro Rinaldo Mary F. Wheeler Carnegie Mellon University Center for Subsurface Modeling [email protected] University of Texas at Austin [email protected] MS26 MS26 Introduction to Algebraic Statistics Methods and Extensions for Parametric Inference I will provide an introduction to one of the main principles of algebraic statistics– that statistical models are semial- In computational biology, many dynamic programming algebraic sets– and illustrate this idea with examples. gorithms can be interpreted as sum-product algorithms. Examples include Needleman–Wunsch and Viterbi algo- Seth Sullivant rithms. Equivalently, these algorithms find the leading North Carolina State University term of a given multivariate polynomial F presented by a [email protected] short and structured factorization. The term-order is part of the input to the sum-product algorithm – and usually depends on biological parameters which are estimated or MS27 guessed. Given this unavoidable uncertainty in the term- Improved Accuracy and Efficiency in Leray-alpha order, it is desirable to compute all leading terms of F Computations under all term-orders – or equivalently, compute the New- ton polytope NP(F ). This is called parametric inference. In this talk I will discuss how some simple, yet fundamen- In this talk, we discuss a general framework for parametric tally important changes can be made to numerical algo- inference, and review existing results. Then, motivated by rithms for the Leray-alpha model, which lead to significant biological applications, we propose two key extensions: 1) improvements in accuracy and efficiency. parametric k-best inference, and 2) constrained parametric inference. We finish by presenting recent results for these Abigail Bowers extensions. Department of Mathematical Sciences Clemson University Peter Huggins [email protected] Carnegie Mellon University [email protected] Leo Rebholz Clemson University Department of Mathematical Sciences MS26 [email protected] Hermite Polynomial Aliasing

A representation of Hermite polynomials of degree 2n +1, MS27 as sum of an element in the polynomial ideal generated by Uncertainty Quantification for a Two Domain Nat- the roots of the Hermite polynomial of degree n and of a re- ural Convection Problem minder, suggests a folding of multivariate polynomials over a finite set of points. From this, the expectation of some Numerical algorithms are studied for a Boussinesq model of polynomial combinations of random variables normally dis- natural heat convection in two domains, motivated by the tributed is computed. This is related to quadrature formu- dynamic core of climate models. One (monolithic) algo- las and has strong links with designs of experiments. This rithm is coupled across the fluid-fluid interface. Another is is joint work with G. Pistone. decoupled for parallel implementation using a partitioned time stepping approach which retains unconditional sta- Eva Riccomagno bility, a property not enjoyed by climate codes. Reliability Politecnico di Torino of computations is critical in climate applications. Here, [email protected] stochastic noise is introduced into two nonlinear coupling AN10 Abstracts 53

terms that play an important role in stability, by modeling x-ray beam entering the object, resulting in reconstruction them with random variables. Uncertainty quantification inaccuracies. In this talk, we discuss a novel mathemat- is performed for each numerical model via the stochastic ical model based on a polyenergetic x-ray spectrum and collocation method. Comparison is drawn in predicting develop statistically based iterative optimization methods average surface temperature with a “one-way” coupled al- for image reconstruction. gorithm, based on a common climate modeling assumption. Uncertainty in average surface temperature is smallest us- Julianne Chung ing the monolithic algorithm and largest using the one-way University of Maryland coupled algorithm. [email protected] Jeff Conners Department of Mathematics MS28 University of Pittsburgh Modeling Combustion Reactions with Step- [email protected] function Kinetics Here we develop reaction-diffusion models for self- MS27 propagating reactions where the reaction rates are reduced Unconditional Convergence of Extrap- to have a step-function dependence on temperature. This olated Crank-Nicolson, Finite Element Method for approach is first studied in the case of a single reaction in the Navier-Stokes Equations both adiabatic and non-adiabatic environments. Of particular interest, however, are systems of two reactions which Error estimates for the Crank-Nicolson in time, finite ele- are thermodynamically coupled. This includes parallel, ment in space (CN-FE) discretization of the Navier-Stokes competing and sequential reactions with both analytical equations require a discrete version of the Gronwall in- and numerical studies. equality, which leads to a time-step restriction. Previous convergence analyses of CN-FE with linear extrapolation Erin Lennon rely on a similar time-step restriction as the full CN-FE. Northwestern University We show that CN-FE with linear extrapolation is uncon- [email protected] ditionally convergent in the energy norm. We also show optimal convergence of CN-FE with extrapolation in a discrete L∞(H1)-norm and convergence of the corresponding MS28 discrete time derivative in a discrete L2(L2)-norm. Non-linear Wave Interactions in Rotating Strati- fied Fluid Flow Ross Ingram Univeristy of Pittsburgh By utilizing the asymptotic renormalization theory of Department of Mathematics Wirosoetisno et. al. (2002), we propose a dynamical ex- [email protected] planation of the origin, nature, and energetics of the spontaneously generated inertia gravity waves which appear in the trough of the baroclinic mode in the rotating annular MS27 experiment of Williams et. al. (1995). We compute the Continuum-microscopic Interaction Computation O() Wirosoetisno et. al. correction term to the under- of Viscoelastic Turbulent Flow lying quasi-geostrophic dynamics and compare our results with the location, amplitude, and morphology of the IGWs A continuum-microscopic approach is presented for com- observed in the lab. We also present energy results which puting dilute polymer flow at high Reynolds number. o?er a strong indication that in a real ?uid, spontaneously The finitely extensible nonlinear elastic (FENE) model is emitted IGWs are an extremely efficient way to transfer adopted to describe the polymer. The continuum conser- geostrophic energy to ageostrophic energy, ultimately to vation equations require a closure based upon the micro- be dissipated by viscosity scopic configuration state of the polymer. A fast computational method to obtain the closure is presented based Dawn Ring upon a multiphysics PARAREAL approach that simulta- Wentworth Institute of Technology neously solves stochastic differential equations for the poly- [email protected] mer state and a Fokker-Planck equation for the probability distribution function of the states. The PARAREAL algorithm is implemented on graphical processing units. The MS28 microscopic configuration of the polymer is investigated at The Mechanical Stability of Growing Arteries maximum drag reduction conditions. In many cylindrical structures in biology, residual stress Sorin Mitran fields are created through differential growth. The possible University of North Carolina Chapel Hill role of axial residual stress in regulating stress in arteries [email protected] and preventing buckling instabilities is investigated. It is shown that axial residual stress lowers the critical internal pressure leading to buckling and that a reduction of ax- MS28 ial loading may lead to a buckling instability which may Numerical Methods for a Problem arising in 3D eventually lead to arterial tortuosity. Breast Image Reconstruction Rebecca Vandiver Digital tomosynthesis imaging, the process of reconstruct- Bryn Mawr College ing a 3D object from a few 2D projection images, is a vi- [email protected] able alternative to standard mammography in breast cancer imaging. However, current algorithms for image reconstruction do not incorporate the polyenergetic nature of the 54 AN10 Abstracts

MS29 bility. Our numerical results suggest the use of high-order An Implicit Asymptotic Preserving Maxwell Solver schemes in both time and space is advantageous when considering the Vlasov-Maxwell system. We present an extension of the Boundary Integral Treecode (BIT), a grid free electrostatic O(N log N) field solver, to Guang Lin an implicit electromagnetic field solver. The new method Pacific Northwest National Laboratory computes a magnetic field that is by construction diver- [email protected] gence free in the computational domain. The implicit Maxwell solver is Asymptotic Preserving, recovering the Jingmei Qiu Darwin limit of Maxwell’s equations in the long time limit. Colorado School of Mines The method is used to simulate the wave equation for a Department of Mathematical and Computer Sciences range of geometries. [email protected]

Andrew J. Christlieb Fengyan Li Michigan State Univerity Rensselaer Polytechnic Institute Department of Mathematics [email protected] [email protected] Yingda Cheng Benjamin Ong Dept. of Math and ICES Department of Mathematics University of Texas at Austin Michigan State University [email protected] [email protected]

MS29 MS29 A Hybrid Method for Particle Transport Based on Quadrature-based Moment Methods for Gas- a Collided/ Uncollided Split particle Flows We present methods for solving particle transport prob- Gas-particle flows can be modeled by a kinetic equation lems by splitting the phase space density into particles that (KE) for the particle velocity distribution function. The have collided during a time step and particles that have not KE contains terms for acceleration due to fluid drag and collided in the step. Using this paradigm we can exploit gravity, transport due to the particle velocity, and inelastic benefits of particular methods: moment based methods be- particle-particle collisions. The KE is coupled to the conti- have well for particles that have undergone many collisions nuity and momentum equations for the gas phase through whereas other methods such as Monte Carlo and integral the particle volume fraction and fluid drag, respectively. methods are inefficient in the absence of collisions. We an- In most practical gas-particle flows, the particle Knudsen alyze our splitting technique and apply it to several prob- and Mach numbers are far from the equilibrium limit so lems of interest in linear transport and radiative transfer. that hydrodynamic descriptions of the KE are invalid. In this talk we describe how quadrature-based moment meth- Ryan G. McClarren ods can be used to capture non-equilibrium solutions to the Texas A & M KE. Examples for gas-particle riser flows ranging from very [email protected] dilute to moderately dense particle hold up will be used to illustrate the quadrature-based numerical methods. Cory Hauck Alberto Passalacqua, Cansheng Yuan Oak Ridge National Laboratory Iowa State University [email protected] [email protected], [email protected] MS30 Rodney O. Fox A Least Squares Interpolation Method for Param- Iowa State University eterized Systems of Equations Department of Chemical and Biological Engr. [email protected] Exhaustive parameter studies for engineering models are typically infeasible, particularly for high dimensional parameter spaces; cheap and accurate surrogate models are MS29 necessary. We propose a reduced basis method for approx- A High-order WENO Method for the Vlasov- imating the model output given a set of snapshots. The Maxwell System method requires only the residual of the model and poses a least squares problem to compute the coefficients of the In this talk, we propose a high-order Vlasov-Maxwell solver approximation. We derive the method in the linear case based on high-order Runge-Kutta scheme in time and high- and extend its application to nonlinear problems order WENO (weighted essentially nonoscillatory) reconstruction in space. The spatial WENO reconstruction de- Paul Constantine veloped for this method is conservative and Lax- Friedrichs Sandia National Labs flux is employed. While the third, fifth, seventh and ninth [email protected] order reconstructions are presented in this talk, the scheme can be extended to arbitrarily high order. WENO recon- Qiqi Wang struction is able to achieve high-order accuracy in smooth Massachusetts Institute of Technology parts of the solution while being able to capture sharp in- [email protected] terfaces without introducing oscillations. The quality of the proposed method is demonstrated by applying the approach to classical plasma problems, such as Weibel’s insta- AN10 Abstracts 55

MS30 MS31 A Geometric Interpretation of Stochastic Processes Self-correcting Estimates from the Differential Equations Method The time-dependent stochastic harmonic oscillator can geometrically be described as the Lie-derivative of a 1-form In this talk we discuss applications of the differential equa- on a cylinder, [a, b] × S1 tions method for random graph processes in which the (1) bounds on variation around the expected trajectory de- LX α =0, crease as the process evolves. These methods are illus- (1) trated in the context of the random greedy algorithm for where α is the 1-form which describes the probability constructing a large partial Steiner-Triple-System. This distribution and X is the vector field on the cylinder. This (1) stochastic graph process is defined as follows: We begin equations means that α does not change along the flow with a complete graph on n vertices and proceed to remove generated by X. In this talk a discrete polynomial repre- the edges of triangles one at a time, where each triangle re- sentation of differential forms will be given which possesses moved is chosen uniformly at random from the collection the invariance under general transformations. As a conse- of all remaining triangles. The process terminates when it quence, integrals are preserved. arrives at a triangle-free graph. We show that with high probability the number of edges in the final graph is at Mark Gerritsma 7/4 5/4 Delft University of Technology most O(n log n). [email protected] Tom Bohman Carnegie Mellon University MS30 Department of Mathematics [email protected] Proper Generalized Decomposition and Separated Representations for Uncertainty Propagation Alan Frieze A family of model reduction methods, called Proper Gen- Carnegie Mellon University eralized Decompositions methods, has been recently pro- [email protected] posed for the propagation of parametric uncertainties in very high dimensional stochastic models. It is based on the Eyal Lubetzky a priori construction of separated representations of the so- Microsoft Research lution of stochastic partial differential equations. They can [email protected] be seen as generalizations of Karhunen-Loève decompositions. Here, we review basic definitions of decompositions and propose new definitions in order to improve conver- MS31 gence properties of separated representations. A Probabilistic Technique for Finding Almost Pe- riods in Additive Combinatorics Anthony Nouy GeM, Ecole Centrale Nantes We (E. Croot and Olof Sisask) introduce a new probabilis- University of Nantes, CNRS tic technique for finding ‘almost periods’ of convolutions [email protected] of subsets of finite groups. This allows us to give: a new probabilistic proof of Roth’s theorem; a new way to ap- Mathilde Chevreuil proach the 2D corners problem; a new result on the exis- GeM - CNRS tence of long arithmetic progressions in sumsets A+B; a Ecole Centrale Nantes, University of Nantes translation-invariance result for “discontinuous sets’ (sets [email protected] A whose convolution function A*A is somewhat discontinuous); and several non-abelian analogues of classical theorems. In many cases, the proofs we give are the shortest MS30 known, and in some cases, like the case of long APs in Practical Rare Event Simulation in High Dimen- A+B, we obtain the strongest bounds to date. sions Ernie Croot I will discuss an importance sampling method for certain Georgia Institute of Technology rare event problems involving small noise diffusions. Stan- [email protected] dard Monte Carlo schemes for these problems behave exponentially poorly in the small noise limit. Previous work in rare event simulation has focused on developing, in specific MS31 situations, estimators with optimal exponential variance Maximal Independent Sets in Graphs with No decay rates. I will introduce an estimator related to a de- Quadrilaterals terministic control problem that not only has an optimal variance decay rate under certain conditions, but that can There has recently been substantial attention on studying even have vanishingly small statistical relative error in the the problem of studying the size of a maximal independent small noise limit. The method can be seen as the limit of set in a d-regular graph of girth g. The most precise results a well known zero variance importance sampling scheme for large girth and fixed d are recent, due to Gamarnik and for diffusions which requires the solution of a second order Goldberg, following from an analysis of a natural random- partial differential equation. I will also report on progress ized greedy algorithm, and generalizing earlier results of toward applying the algorithm within the design of mag- Lauer and Wormald. In this talk I will present a new re- netic memory devices. sult stating that every d-regular n-vertex graph containing no cycles of length four contains a maximal independent Jonathan Weare set I such that NYU |I| log d + O(1) = [email protected] n d 56 AN10 Abstracts

and this is best possible in light of random regular graphs nonlinear biharmonic equation describing the stream func- containing no cycles of length four, and in view of unions of tion. For the Stokes problem (Re = 0), the accuracy dete- complete bipartite graphs with d vertices in each part. In riorates in the neighborhood of the singularities in the two particular, this shows that it is the lack of cycles of length upper corners. Enlarging the space spanned by the RBF four in a random d-regular graph which gives maximal in- basis functions with additional functions that capture the dependent sets of this size. The degree ratio of a graph singular behavior of the solution restores the spectral con- G is defined to be the maximum degree divided by the vergence of the RBF method. minimum degree. We show that there are n-vertex graphs with degree ratio c>1 and maximum degree d such that Manuel Kindelan every maximal independent set has size at least roughly Universidad Carlos III de Madrid n/2d2/(c−1) , which shows that the condition of regularity [email protected] is necessary in the above-mentioned result. We conjecture that such graphs should have maximal independent sets Francisco Bernal of size at most n/2d1/c up to logarithmic factors in d for UT Dresden each c>1. Some possible applications of the result will be [email protected] mentioned. Jacques Verstraete MS32 University of California-San Diego Approximation of Linear PDEs by Gaussian Pro- [email protected] cesses via Matérn Functions N M Given discrete data X1 = {xi}i=1 ⊂ Ω, X2 = {xN+j }j=1 ⊂ Paul Horn N,M,n,m Emory University ∂ΩandY = {fk(xi),gl(xN+j )}i,j,k,l=1 generated from a [email protected] linear partial differential equations model ··· ∈ MS31 L1u(x)=f1(x), ,Lnu(x)=fn(x),xΩ, B1u(x)=g1(x), ···,Bmu(x)=gm(x),x∈ ∂Ω, Optimal Inverse Littlewood-Offord Theorems

Let ηi,i=1,...,n be iid Bernoulli random variables, tak- where Lk are linear differential operators, Bl are linear ± 1 ing values 1 with probability 2 .GivenamultisetV of n boundary operators and Ω is a bounded domain in R . integers v1,...,vn, we define the concentration probability A Gaussian process (Gaussian field) is firstly constructed as on a reproducing-kernel Hilbert space corresponding to ρ(V ):=supPr(v1η1 + ...vnηn = x). aMatérn function. Combining this with a Bayesian ap- x proach, we are able to obtain confidence interval for u(x) A classical result of Littlewood-Offord and Erd˝os from (instead of an explicit approximating solution) through a the 1940s asserts that if the vi are non-zero, then ρ(V ) covariance matrix for the above differential operators and is O(n−1/2). Since then, many researchers obtained im- boundary operators on the data. proved bounds by assuming various extra restrictions on V . About 5 years ago, motivated by problems concern- Qi Ye, Greg Fasshauer ing random matrices, Tao and Vu introduced the Inverse Illinois Institute of Technology Littlewood-Offord problem. In the inverse problem, one [email protected], [email protected] would like to give a characterization of the set V ,given that ρ(V ) is relatively large. In this talk, I describe a new method to attack the inverse problem. As an application, MS32 we strengthen a previous resultof Tao and Vu, obtaining an RBF Interpolation using Gaussians with Domain optimal characterization for V . This characterization im- Decomposition on GPUs mediately implies several classical theorems, such as those of Sárközy-Szemerédi and Halász. As another application, We have developed a parallel algorithm for radial basis we obtain an asymptotic, stable version of a famous theo- function (RBF) interpolation with Gaussians that uses a rem of Stanley that shows that under the assumption that GMRES iterative solver with a restricted additive Schwarz method (RASM) as a preconditioner and a fast matrix- the vi are different, ρ(V ) attains its maximum value when V is a symmetric arithmetic progression. All results ex- vector algorithm. The fast decay of the Gaussian basis tend to the general case when V is a subset of an abelian function allows rapid convergence of the iterative solver, while retaining the interpolation accuracy. The precon- torsion-free group and ηi are independent variables satisfying some weak conditions. The method also works well ditioning and matrix-vector product have been ported to in the continuous setting, and gives a simple proof for the CUDA to accelerate the most computationally intensive β-net theorem of Tao and Vu, parts of the algorithm.

Van Vu Rio Yokota Rutgers University University of Bristol [email protected] [email protected] Lorena Barba MS32 Department of Mechanical Engineering RBF Solution of Lid-Driven Cavity Problem using Boston University the Stream Function Formulation. [email protected] An RBF meshless formulation of the lid-driven cavity problem is presented. It uses the streamfunction-vorticity for- MS33 mulation so that the problem reduces to the solution of a Nonlinear Model Reduction Using Petrov-Galerkin AN10 Abstracts 57

Projection and Data Reconstruction MS33 Nonlinear Model Reduction for Porous Media Flow A computational method for constructing a stable nonlinear reduced-order model and analyzing it as fast as A Discrete Empirical Interpolation Method (DEIM) is ap- possible is presented. This method operates on a semi- plied in conjunction with Proper Orthogonal Decomposi- discretized partial differential equation, relies on a time- tion (POD) to construct a nonlinear reduced-order model variant Petrov-Galerkin projection for performing model of finite difference discretized system used in the simula- reduction, and on a reconstruction of gappy data for ap- tion of nonlinear miscible viscous fingering in a 2-D porous proximating the reduced system in order to accelerate its medium. POD is first applied to extract a low-dimensional analysis. Its performance is highlighted for sample prob- basis that optimally captures the dominant characteris- lems in nonlinear structural dynamics and computational tics of the system trajectory. This basis is then used in fluid dynamics a Galerkin projection scheme to construct a reduced-order system. DEIM is then applied to greatly improve the effi- Kevin T. Carlberg, Charbel Farhat ciency in computing the projected nonlinear terms in the Stanford University POD reduced system. DEIM achieves a complexity reduc- [email protected], [email protected] tion of the nonlinearities which is proportional to the number of reduced variables while POD retains a complexity MS33 proportional to the original number of variables. Numer- ical results demonstrate that the dynamics of the viscous Interpolation for Adaptation of Parameterized fingering in the full-order system of dimension 15000 can Reduced-Order Models be captured accurately by the POD-DEIM reduced system Differential geometry-based interpolation methods are pre- of dimension 40 with the computational time reduced by sented for adapting parameterized reduced-order models factor of 1000. to new configurations. Two different approaches are dis- Danny C. Sorensen, Saifon Chaturantabut cussed. The first one is based on the interpolation of the Rice University underlying reduced-order bases, and the second one on the [email protected], [email protected] interpolation of the reduced-order models themselves. It is shown that the first approach privileges robustness and stability at the expense of CPU time, whereas the second MS34 approach delivers real-time performance at the expense of Correctors and Field Fluctations for the p(x)- generality and robustness. Laplacian With Rough Exponents

Charbel Farhat, David Amsallem We provide a corrector theory for the strong approximation Stanford University of fields inside composites made from two materials with [email protected], amsallem @stanford.edu different power law behavior. The correctors are used to develop bounds on the local singularity strength for gradi- MS33 ent fields inside micro-structured media. The bounds are multi-scale in nature and can be used to measure the am- A Projection-based Moment-matching Interpola- plification of applied macroscopic fields by the microstruc- tion for Large-scale Frequency Response Problems ture. Frequency response problems appear in many computa- Silvia Jiménez Bolaños tional engineering applications. Our attention is focused − 2 −1 Louisiana State University on evaluating functions H(σ)=(K + iσD σ M) f on [email protected] an interval [σl,σr]. The matrices K, D,andM are very large and they may have complex entries. We will present a method that exploits values of H and its derivatives at mul- Robert P. Lipton tiple frequencies to construct a reduced-order model for H, Department of Mathematics with a rational Krylov algorithm. The computations of val- Louisiana State University ues and derivatives of H at multiple frequencies will use a [email protected] domain-decomposition based iterative solver for large-scale indefinite systems. Numerical experiments from structural MS34 dynamics and fluid-structure interaction problems will illustrate the method. Simultaneous Seismic Imaging and Inversion Using an Inverse Scattering Algorithm for One Dimen- Charbel Farhat sional Media Stanford University [email protected] We present the theoretical development and numerical tests for an acoustic inverse scattering algorithm for simultaneous geophysical imaging and amplitude correction Ulrich Hetmaniuk directly from measured data. No knowledge about the University of Washington medium under investigation is assumed. We model several Department of Applied Mathematics one-dimensional earth configurations and show how the al- [email protected] gorithm can find the precise location and a good estimate of the layers’ parameters. Our tests will include different Radek Tezaur number of layers, high/low contrasts, velocity inversions Stanford University and noisy data. [email protected] Ashley Ciesla, Bogdan G. Nita Montclair State University [email protected], [email protected] 58 AN10 Abstracts

MS34 MS34 A Split Sparse/Dense Matrix-vector Multiplication A Novel Pseudospectral Method for Solving a Non- Routine linear Volterra Partial Integro-differential Equa- tion on a Polar Geometry A new approach for performing sparse matvecs consists of two stages: (i) reordering the original general sparse In this talk we study a nonlinear Volterra partial integrod- matrix A, and (ii) tearing it into two parts – a dense banded ifferential equation used to model swelling porous mate- matrix B and a sparse matrix E of much lower rank. The rials where the problem domain is a unit disk. We show multiplication of B by a block of vectors is accomplished well-posedness is established under a given set of assump- via dense BLAS level-3. Comparisons are made against tions and introduce a novel approach to constructing pseu- Intel’s MKL matvec routine, mkl csrmm, and an extension dospectral differentiation matrices in a polar geometry for using multi-level splitting will be discussed. computing the spatial derivatives. An exponential time- differencing scheme proposed by Cox and Matthews and Eric Cox, Murat Manguoglu, Faisal Saied stabilized by Kassam and Trefethen is employed for the Purdue University time-stepping. [email protected], [email protected], [email protected] Keith Wojciechowski Department of Mathematical Sciences Ahmed Sameh University of Colorado Denver Department of Computer Science [email protected] Purdue University [email protected] Lynn S. Bennethum University of Colorado at Denver [email protected] MS34 Understanding the Impact of Low Permeability Jinhai Chen Media on Groundwater Remediation University of Colorado Denver [email protected] In groundwater remediation, contaminants trapped in low permeability soil after clean-up can cause re-contamination in the same area after a long period of time. This study fo- Kristian Sandberg cuses on analyzing and improving existing transport mod- GeoEnergy, Corp. els to understand the contaminant behavior in terms of [email protected] the rate and extent of release from its storage at the HPM/LPM interface. Current approaches include a sensi- MS35 tivity analysis of MT3D model, constructing a numerical simulator using dual-resistance model, and lab cell experi- Tensor Decomposition and Application in Signal ments. and Image Processing Xiaojing (Ruby) Fu We describe a module of n-by-n matrices upon which every linear transformation can be represented by tensor-matrix Clarkson University multiplication by a third-order tensor. An inner product is [email protected] defined upon this space, which leads to natural extensions of many familiar linear algebra concepts including length Kathleen Fowler and orthogonality of matrices and symmetry of tensors. Clarkson University Using these tools, we investigate applications in the areas Department of Mathematics of image reconstruction and pose estimation. [email protected] Karen S. Braman, Randy Hoover Michelle Crimi, Guannan Jiang South Dakota School of Mines Clarkson University [email protected], [email protected] [email protected], [email protected] Misha E. Kilmer Tufts University MS34 [email protected] Option Pricing Using Monte Carlo Methods

One main problem in mathematical finance is calculating MS35 the fair price of derivatives. The fair price of these deriva- Tensor-SVD with Applications in Image Processing tives can be complicated to obtain analytically. Monte Carlo simulation offers a way to compute the fair price, We define a new type of multiplication between two ten- relying on the approximation of an expected value by the sors that allows for the representation of tensors as prod- average of the simulated values. We created a random num- ucts of tensors that is reminiscent of matrix factorizations. ber generator and used it in the Monte Carlo simulations In particular, a tensor-SVD is introduced which gives a to compute the fair price of a European Call Option. representation of tensors as the sum of outer-products of matrices. This alternate representation of tensors shows Steven Melanson, Yered Pita-Juarez promise with respect to the tensor approximation problem California State University in the context of image processing. We test our approach [email protected], [email protected] on an image deblurring application. Ning Hao Tufts University AN10 Abstracts 59

Department of Mathematics Carmeliza Navasca [email protected] Clarkson University [email protected] Misha E. Kilmer Tufts University [email protected] MS36 On Multirate SSP Methods for Hyperbolic PDEs

Carla Martin We discuss a set of explicit multirate time discretization James Madison University methods for hyperbolic conservation laws based on multi- Department of Mathematics step and Runge-Kutta methods. Multirate methods allow [email protected] different time steps to be used in different parts of the spatial domain while preserving the consistency and conser- MS35 vation properties of the ”classical” methods. Linear and nonlinear stability are guaranteed only under local CFL Iterative Methods for Multilinear Systems conditions. The necessity to take small global time steps We have shown a tensor group endowed with the Einstein restricted by the largest CFL number is thus avoided. The (contracted) product is isomorphic to the general linear theoretical results are illustrated on advection and Burgers group of degree n. In consequence, higher order tensor equations. inversion is possible for even order. Although odd order Emil M. Constantinescu tensors are not invertible under the Einstein product, their Argonne National Laboratory inversions are still possible through pseudo-inversion tech- Mathematics and Computer Science Division niques. With the notion of tensor inversion, multilinear [email protected] systems are solvable. Numerically we solve multilinear systems arising from partial differential equations and quantum mechanics. Iterative methods for tensors are the main Adrian Sandu computational techniques. We demonstrate the efficacy of Virginia Tech these iterative methods through some motivating exam- [email protected] ples. Carmeliza Navasca MS36 Clarkson University The History of SSP Methods [email protected] Abstract not available at time of publication. Michael Brazell Sigal Gottlieb Clarkson University Department of Mathematics Dept. of Mechanical Engineering University of Massachusetts, Dartmouth [email protected] [email protected]

Na Li Clarkson University MS36 Dept. of Mathematics On the Sharp SSP Timestep for Runge-Kutta Dis- [email protected] cretizations of IVPs

Christino Tamon The product of the absolute monotonicity radius of the Clarkson University Runge-Kutta (RK) method and the strong stability pre- Department of Computer Science serving (SSP) timestep of the explicit Euler method is of- [email protected] ten used as a timestep limit that guarantees strong stability preservation of the RK method. In this talk we relax this limit in two ways. First, for certain subsets of the initial MS35 vector we prove that in the above limit a much larger factor Tensors as Module Homomorphisms over Group than absolute monotonicity rules the SSP property. Sec- Rings ond, for some classical RK methods we prove SSP property also in the case when the explicit Euler method is not SSP Abstract not available at time of publication. for any positive timestep. Finally, we demonstrate our results by computational experiments. Michael Opperman Clarkson University Zoltan Horvath Department of Mathematics Sz´echenyi Istv´an University [email protected] [email protected]

Timothy Penderghest MS36 Clarkson University [email protected] Multi-step Multi-stage SSP Runge–Kutta Methods High-order strong stability preserving (SSP) time integra- Christino Tamon tors of are often desirable in the numerical solution of hy- Clarkson University perbolic PDEs. Multistep Runge–Kutta methods general- Department of Computer Science ize both linear multistep methods and multistage Runge– [email protected] Kutta methods. We present some recent results on SSP multistep Runge–Kutta methods, including numerically 60 AN10 Abstracts

optimal methods, both implicit and explicit. The meth- location. The spatial domain is decomposed into a series of ods are tested with numerical experiments. small subdomains (coarse grid) of either Stokes or Darcy type. The flow solution is resolved locally (on each coarse David I. Ketcheson element) on a fine grid, allowing for non-matching grids Mathematical and Computer Sciences & Engineering across subdomain interfaces. Coarse scale mortar finite King Abdullah University of Science & Technology elements are introduced on the interfaces to approximate [email protected] the normal stress and impose weakly continuity of flux. The transport equation is discretized via a local discon- Sigal Gottlieb tinuous Galerkin method. Computational experiments are Department of Mathematics presented. University of Massachusetts at Dartmouth [email protected] Benjamin Ganis University of Pittsburgh Colin Macdonald Department of Mathematics Oxford University [email protected] [email protected] Danail Vassilev University of Pittsburgh MS37 [email protected] Hydrodynamics Coupled with Bed Morphology for Modeling Sediment Scour and Deposition Ivan Yotov Univeristy of Pittsburgh Abstract unavailable at time of publication. Department of Mathematics [email protected] Clint Dawson Institute for Computational Engineering and Sciences University of Texas at Austin Ming Zhong [email protected] University of Pittsburgh [email protected]

MS37 MS37 Adaptive Strategies in the Multilevel Multiscale Mimetic (M3) Method for Two-phase Flows in Stochastic Collocation Data Assimilation Porous Media In this work, a stochastic data assimilation approach is pre- The Multilevel Multiscale Mimetic (M3) method was de- sented for estimating model parameters such as permeabil- veloped to simulate accurately two-phase flows in highly ity and porosity from direct and indirect measurements. heterogeneous media with long correlation lengths. A mul- This approach combines the advantages of the ensemble tilevel approximation strategy is used to build a hierarchy Kalman filter (EnKF) for dynamic data assimilation and of models that are locally conservative at each level. The the polynomial chaos expansion (PCE) for efficient uncer- mimetic finite difference method is used to handle arbi- tainty quantification. In the latter, the model parameters trary meshes and tensor permeability fields. We describe are represented by the Karhunen-Loeve expansions and the adaptive strategies that reduce further the cost of the M3 model responses such as pressure and saturation are ex- method and illustrate them with numerical simulations of pressed by the PCE. The coefficients of PCE are solved well-driven flows. with a collocation technique. The approach is non-intrusive in that such realizations are solved forward in time via ex- Daniil Svyatskiy, Konstantin Lipnikov isting deterministic solver independently. The needed en- Los Alamos National Laboratory tries of the state covariance matrix are approximated with [email protected], [email protected] the PCE coefficients. It is shown that the approach is computationally efficient and provides satisfactory estimations David Moulton of the model parameters with dynamic measurements. Los Alamos National Laboratory Dongxiao Zhang Applied Mathematics and Plasma Physics USC [email protected] [email protected]

MS37 MS38 Stochastic Multiscale Modeling of Coupled Adaptive Rational Krylov Subspaces for Time- Surface-subsurface Flow and Contaminant Trans- invariant Dynamical Systems port The rational Krylov space is recognized as a powerful tool We discuss a multiscale stochastic framework for uncer- within Model Order Reduction techniques for linear dy- tainty quantification in modeling flow and transport in namical systems. However, its success has been hindered surface-subsurface hydrological systems. The governing by the lack of procedures, which would generate the se- flow equations are the Stokes-Darcy system with Beavers- quence of shifts used to build the space with good approx- Joseph-Saffman interface conditions. The permeability in imation properties. We start with a-priori and adaptive the Darcy region is stochastic and it is represented with a approaches generating such shifts for the first order prob- Karhunen-Loève (KL) expansion. The porous media can lems. Then a-priori approach is generalized to structure be statistically non-stationary, which is modeled by differ- preserving algorithms for high order systems. ent KL expansions in different regions. Statistical moments of the solution are computed via sparse grid stochastic col- Vladimir Druskin,L.Knizhnerman,C.Lieberman,V. AN10 Abstracts 61

Simoncini, M. Zaslavsky TU Braunschweig Schlumberger Doll Research [email protected] [email protected], [email protected], [email protected], [email protected], [email protected] Alexander Vendl TU Braunschweig, Germany Institut Computational Mathematics, AG Numerik MS38 [email protected] Robust Low-order Models for Flow Control The main issue discussed will be how to build a low-order Stefan Görtz, Ralf Zimmermann model that is robust to parameter variation. To do that an DLR Braunschweig, Germany optimal sampling strategy of the parameter space based on [email protected], [email protected] the full model residuals is proposed. In addition to that, the reduced model is calibrated using Tikhonov regulariza- MS39 tion. This system identification approach can accurately describe unsteady phenomena encountered in flow control. A Geometric Approach to Partition Functions Computing partition functions to get normalizing con- Angelo Iollo stants or marginals is an ubiquitous, yet generally in- Institut de Mathématiques de Bordeaux tractable, task in statistical modelling. Many tricks and [email protected] workarounds have been developed to make such computations feasible. I discuss how some of these strategies can be understood, and new ones manufactured, using tensor M Bergmann geometry. Universite Bordeaux [email protected] Jason Morton Pennsylvania State University E. Lombard [email protected] Université Bordeaux 1 [email protected] MS39 Combinatorial Commutative Algebra in Action: MS38 Markov Moves from Classical Algebraic Construc- Model Reduction Algorithm for Robust Control of tions Linear PDE Systems Markov bases, as a fundamental object of study in algebraic We consider the computation of a robust control law for statistics, can often be difficult to construct and compute. large-scale finite dimensional linear systems and a class of It is often the case that a sub-basis may be sufficient for linear distributed parameter systems. The controller is ro- the problem at hand; however, theoretically, one would like bust with respect to left coprime factor perturbations of the to really understand the variety of the model, its algebraic nominal system. We present a convergent algorithm based and geometric properties. In this talk I will describe chal- on balanced proper orthogonal decomposition to compute lenges in Markov bases constructions, posed by the poorly the nonstandard features of this robust control law. Nu- understood geometry of the models, illustrated on an ex- merical results are presented for a convection diffusion par- ample. tial differential equation. Sonja Petrovic John Singler University of Illinois, Chicago Missouri S & T [email protected] Mathematics and Statistics [email protected] MS39 Belinda Batten Algebraic Statistics Framework for Causal Infer- Mechanical, Industrial, and Manufacturing Engineering ence and Data Privacy with Discrete Data Oregon State University [email protected] We present an algebraic computational framework that handles special cases of latent class analyses. Specifically, we consider discrete data problems with unobserved vari- MS38 ables such that arbitrary linear constraints are imposed on Model Order Reduction for Steady Aerodynamic the possible realizations of the complete data, and thus on Applications the possible states of the joint distribution of all the variables (observed and unobserved) in the analysis. The con- An approach combining proper orthogonal decomposition straints are imposed either by the modeling assumptions, (POD) with linear regression, which is called gappy POD, the structure of the latent variables or for consistency rea- is used to obtain complete flow solutions in steady aero- sons. We illustrate our methods by applying them to two dynamic applications from knowledge of a (suitable) POD important related problems. The first problem pertains basis and the solution at very few points. In practice the to the assessment of disclosure risk of releasing potentially partial or gappy data can easily be obtained by experimen- sensitive information from a latent class analysis in the tally measuring the flow variables. Therefore this method form of class membership probabilities and probability dis- is effective in combining experimental with computational tribution of covariates conditional on the classes. The sec- data. ond problem pertains to estimation of average causal effect in presence of unobserved confounders , under the Neyman- Heike Fassbender Rubin framework of potential outcomes. The code is im- 62 AN10 Abstracts

plemented in R, but interfaces with 4ti2. the approach to the Boussinesq system is also discussed. The resulting schemes are well suited for the simulation Aleksandra Slavkovic of moderate to high Reynolds and Rayleigh number flows. Penn State University Accuracy checks, simulations of the lid-driven cavity flow, [email protected] of a differentially heated cavity flow, and of a Rayleigh- Bernard convection problem for Rayleigh number up to 1010 are presented to demonstrate that the schemes are MS39 capable of producing accurate results at a reasonable com- Betti Numbers of Experimental Designs putational cost. For polynomial regression models in the context of factorial Hans Johnston experimental design there have been both formal and infor- Department of Mathematics & Statistics mal way of representing estimable effects and interactions. University of Massachusetts Amherst We generalize this to a larger study of the combinatorial [email protected] structure of models derived by the algebraic method, that is using ideals-of-points theory. It turns out, by exploit- Cheng Wang ing known results on monomial ideals, that the complexity University of Massachusetts of models can be measured by the size of the Betti num- Dartmouth, MA bers of the Stanley-Reisner complex. It transpires that the [email protected] most complex models are available for designs which are generic in the sense of ’corner cut’ theory. An complete enumeration for Plackett-Burman designs gives 19 equiva- Jian-guo Liu lence classes of complex. Dept. of Mathematics and Physics Duke University Henry Wynn [email protected] London School of Economics [email protected] MS40 Numerical Approxima- MS40 tion for Generalized-Newtonian Flows with Flow Dual-mixed Finite Element Methods for the Rate Boundary Conditions Navier-Stokes Equations We consider a generalized-Newtonian fluid with defective In many applications within mechanical, materials, and boundary conditions where only flow rate are prescribed on biomedical engineering, it is important to accurately pre- a part of boundary. The defect boundary condition prob- dict fluid stresses. However, most existing numerical lem is formulated as an minimization problem in which schemes for fluids are formulated with velocity as the pri- a Neumann or Dirichlet boundary control is used for the mary unknown of interest. In this talk, a dual-mixed finite flow rate matching. We will discuss the derivation of an element method for the Navier-Stokes equations, in which optimality system based on the first necessary condition the stress is a primary unknown of interest, is derived and and examine the corresponding adjoint problem. Com- analyzed. The method employs symmetric tensor finite putational algorithms and numerical results will be also elements for stress and is well-suited for non-Newtonian presented. fluids. Hyesuk Lee Jason Howell Clemson University Carnegie Mellon University Dep. of Mathematical Sciences Department of Mathematical Sciences [email protected] [email protected] MS40 Noel Walkington Carnegie Mellon University Optimal Control of Flow Past a Rectangle [email protected] We address optimal control of the frequency and amplitude of two-dimensional vortex-shedding behind a rectangular MS40 obstacle. Control is effected by small periodic oscillation of the rigid obstacle. Numerical results are presented. Local Boundary Condition based Spectral Colloca- tion Methods for 2D and 3D Naiver-Stokes Equa- Mike Sussman tions Department of Mathematics, University of Pittsburgh [email protected] We present a simple approach to accurately computing local boundary conditions in spectral collocation schemes for the Navier-Stokes equations in 2D and 3D. Access to these MS41 local boundary values makes possible the decoupling of Using Sequence Coverage Statistics to Determine the computation of the primary flow variables, resulting in Protein Binding Sites in a Genome highly efficient schemes. In 2D the local vorticity boundary values are employed in the vorticity-stream function for- Inspired by the notion of persistence in topological data mulation, while in 3D local values of a Neumann boundary analysis, we introduce a tree depicting sequence coverage condition for the pressure in the velocity-pressure formu- via fragment placement on a genome. We then describe lation are used. In both cases these boundary conditions statistically the trees that correspond to random fragment are approximated by differentiating a local Lagrange inter- placement and use this theory to determine the binding polant at the boundary. The straightforward extension of sites for a given protein in a genome. Our method for AN10 Abstracts 63

calling statistically signi?cant protein binding sites reduces introduction to some of these methods and applications, in- to the study of certain tree-based statistics derived from cluding some open problems. This talk (in fact, the entire the data. minisymposium) is intended to support the plenary lecture of Charles Wampler. Valerie Hower University of California, Berkeley Daniel J. Bates [email protected] Colorado State University Department of Mathematics [email protected] MS41 Lower and Upper Bounds on the Probability Dis- tributions of the Wasted Spaces of a Processor- MS42 Sharing Storage Allocation Model Regeneration and Numerical Algebraic Geometry We consider a storage allocation model with m primary Large-scale polynomial systems that often arise in kine- holding spaces, infinitely many secondary ones, and one matics and other engineering applications typically have processor servicing customers. We define the traffic inten- fewer solutions than their total degree root count. Regen- sity ρ to be λ/μ where λ is the customer arrival rate and eration can solve such large-scale polynomial systems by μ is the service rate of the processor. We study the lower algorithmically revealing the underlying structure of the and upper bounds on the probability distributions of the polynomial system during the equation-by-equation solv- wasted spaces and the largest index of the occupied spaces ing process. After describing regeneration, we will apply for fixed rho,0<ρ<1, and ρ =1− (heavy traffic case). it to polynomial systems arising in kinematics and other engineering applications. Eunju Sohn Jonathan Hauenstein University of Georgia Texas A&M University [email protected] [email protected]

Andrew Sommese MS41 Department of Mathematics, University of Notre Dame Mechanisms of Simple Perceptual Decision-making Notre Dame, IN 46556-4618, USA Processes [email protected] Perceptual decision-making, an omnipresent component of everyday life, plays a pivotal role in cognitive tasks. In Charles Wampler this presentation, I will talk about mechanisms underlying General Motors Research Laboratories, Enterprise simple two-option perceptual decision-making processes by Systems Lab studying a biological-realistic reduced two-variable model 30500 Mound Road, Warren, MI 48090-9055, USA and phenomenological drift-diffusion models. [email protected] Xueying Wang Statistical and Applied Mathematical Science Institute MS42 [email protected] Basic Algebraic Geometry of Acoustic Arrays This talk is on the basic algebraic geometry of acoustic MS41 arrays. Given an array of microphones and a point P there Oscillations in NFkB Signaling Pathway is a set of time delays that, when applied to the signals collected by the microphones, lead to a focusing of the Upon stimulation, oscillations of NF-kB localization are microphones towards P. The locus of such coherent time observed at both single cell and population levels. A re- delays determine an algebraic variety. We will discuss this cent work reported that different frequencies of the oscil- variety, an associated moduli space and will discuss themes lations leads to different gene expression. Many authors in common with kinematic varieties. point out that NF-kB may interact with other pathways. However, the existence and mechanism of those potential Chris Peterson interactions are not clear. In this talk, we study this is- Colorado State University sue by considering the pathway subjected to two types of [email protected] putative signals: sinusoid and pulsatile signals. Michael Kirby Yunjiao Wang Colorado State University Ohio State University Department of Mathematics [email protected] [email protected]

Josh Thompson MS42 Colorado State University Numerical Methods for Solving Polynomial Sys- [email protected] tems

The term numerical algebraic geometry describes a variety MS42 of numerical methods for ﬁnding and manipulating the so- Numerical Matrix Computation in Algebraic Ge- lution sets of polynomial systems. There are numerous ap- ometry plications throughout the sciences and engineering as well as many within mathematics. This talk will serve as a brief Numerical polynomial algebra and numerical algebraic ge- 64 AN10 Abstracts

ometry become fast growing fields of studies where tremen- MS43 dous progress has been achieved and new challenges emerge Numerical Simulations of Radiative Shock Tube (e.g. handling ill-posedness). On the other hand, numeri- Experiments: Challenges and Approaches cal polynomial algebra is a natural extension and an application area of numerical linear algebra, as matrix compu- The Center for Radiative Shock Hydrodynamics (CRASH) tation plays an indispensible role. This talk introduces the investigates ways to improve the predictive capability of matrix computation strategies in numerical polynomial al- models for shock waves produced when a laser is used gebra and numerical algebraic geometry using several case to shock, ionize, and accelerate a beryllium plate into a studies along with computing results. xenon-filled shock tube. These shocks, when driven above a threshold velocity of about 100 km/s, become strongly Zhonggang Zeng radiative and convert most of the incoming energy flux to Northeastern Illinois University radiation. What results is a complex, evolving, radiation- Department of Mathematics hydrodynamic, multiphysics environment. I will discuss [email protected] the challenges and approaches we use to model this system as a tractable problem in large-scale parallel computing. MS43 Eric S. Myra Hybrid Monte Carlo Methods for Kinetic Equa- University of Michigan tions [email protected]

Probabilistic techniques such as DSMC (Direct Simulation Monte Carlo) are extensively used in real simulations of MS43 the Boltzmann equation for their great flexibility, ability High-order Discontinuous Galerkin Schemes for in treating different collision terms and low computational 2+2 Vlasov Models on Unstructured Grids cost compared to any type of deterministic scheme. On the other hand, solutions are affected by large fluctuations The purpose of this work is to explore mesh-based alterna- and, in non stationary situations, the impossibility of aver- tives to the Particle-In-Cell (PIC) methods that are cur- aging quantities leads to, or low accurate solutions, or high rently favored in many plasma physics applications. In costly simulations. Moreover, close to thermodynamical particular, we present here a technique for solving the equilibrium, the cost of Monte Carlo methods increases. In Vlasov-Poisson system that is based on operator splitting this talk, emphasis will be addressed to a recent developed in time and high-order discontinuous Galerkin discretiza- new family of Hybrid Monte Carlo methods which permits tions in space. The efficiency of the method is increased by to treat both accurately and fast transitional regimes and considering semi-Lagrangian approaches for the advection multiscale problems. The key aspects, on which methods in phase space. The flexibility of the approach is enhanced rely, are the choice of a suitable hybrid representation of by allowing the mesh in physical space to be unstructured. the solution and a merging of Monte Carlo methods in non- equilibrium regimes with deterministic methods in equilibrium ones. James A. Rossmanith,DavidSeal University of Wisconsin Giacomo Dimarco Department of Mathematics Institut de Mathématiques de Toulouse [email protected], [email protected] [email protected]

Lorenzo Pareschi MS44 Department of Mathematics Asynchronous Time Integration for Periodic Dy- University of Ferrara namical Systems with Uncertain Parameters [email protected] Application of PC expansions to stochastic dynamical systems exhibiting cyclic oscillations frequently leads to a MS43 broadening solution spectrum, and consequently to exces- An Asymptotic Preserving Scheme for Non- sive computational requirements. This talk outlines an classical Particle Transport asynchronous integration framework that offers to substantially mitigate this problem. The approach is based on a We present a numerical scheme to solve the nonclassical stochastic time rescaling which is implemented so that the particle transport model suggested by Larsen [Larsen, A spectrum of the rescaled solution remains narrow-banded. generalized Boltzmann equation for non-classical particle Different variants of this approach are illustrated for simple transport, ANS M&C 2007]. This model has applications systems having almost surely a stable limit cycle, including in radiative transfer through clouds and novel nuclear reac- a stochastic linear oscillator, and a stiff nonlinear chemical tor types. While basically any scheme for linear transport system with uncertain rate parameters. has a diffusion limit (albeit with the wrong diffusion coefficient), we show here that the discretization of the transport Omar M. Knio part has to be chosen carefully so that the scheme has a Dept. of Mech. Eng. (correct) diffusion limit. Johns Hopkins University [email protected] Martin Frank RWTH Aachen University Olivier LeMaitre Center for Computational Engineering Science LIMSI-CNRS [email protected] [email protected]

Lionel Mathelin LIMSI - CNRS AN10 Abstracts 65

[email protected] Sandia National Laboratories, Livermore CA [email protected] M. Yousuﬀ Hussaini Florida State University Sonday/Najm Sonday/Najm [email protected] Princeton [email protected]

MS44 Phase Conditions for Autonomous Oscillators with MS44 Random Parameters Uncertainty Quantification via Codimension One Domain Decomposition and a New Concentration We consider autonomous systems of ordinary differen- Inequality tial equations (ODEs) or differential algebraic equations (DAEs), which exhibit periodic solutions. Since a contin- We propose a localized variant of McDiarmid’s inequality uum of periodic solutions exists, we require a phase condi- in order to obtain upper bounds on the probability that a tion to isolate a particular solution. We assume uncertain- system of interest assumes certain values (“fails’). By par- ties in some parameters of the autonomous systems. Hence titioning the input parameter space appropriately, much the relevant parameters are replaced by random variables. sharper bounds than the usual McDiarmid bound are ob- We apply the technique of the generalized polynomial chaos tained. We prove an error estimate for the method, define to resolve the stochastic model. A Galerkin approach yields a codimension one recursive partitioning scheme and prove a larger coupled system of ODEs or DAEs. The phase con- its convergence properties, and use a new concentration in- ditions of the original systems imply additional boundary equality to give confidence levels when empirical means are conditions in the periodic problems of the larger coupled used in place of exact ones. systems. However, the expected value and the variance of the solution depend on the choice of the phase condition. Timothy J. Sullivan We construct an alternative constraint, which minimizes California Institute of Technology the variance of the solution. Numerical simulations of a [email protected] test example are presented. Houman Owhadi Roland Pulch Applied Mathematics University of Wuppertal Caltech [email protected] [email protected]

MS44 MS45 Eigenvalue Analysis of Uncertain ODE Systems Operator Splitting Methods for Maxwell’s Equa- tions in Dispersive Media The polynomial chaos expansion provides a means of rep- 2 resenting any L random variable as a sum of polynomi- We consider Maxwell’s equations in dispersive media of De- als that are orthogonal with respect to a chosen measure. bye type. In such relaxing dielectric media, the presence Examples include the Hermite polynomials with Gaussian of different wave speeds leads to stiffness in the temporal measure on the real line and the Legendre polynomials with domain. We present an operator splitting scheme that de- uniform measure on an interval. Polynomial chaos can couples fast and slow moving processes in the problem to be used to reformulate an uncertain ODE system, using develop separate sub-problems. This alleviates the strin- Galerkin projection, as a new, higher-dimensional, deter- gent requirements on the time-step which along with sta- ministic ODE system which describes the evolution of each bility conditions requires small spatial steps and hence ex- mode of the polynomial chaos expansion. It is of interest to cessive computations for long-time integration of Maxwell’s explore the eigenstructure of the original and reformulated equations. ODE systems, by studying the eigenvalues and eigenvectors of their Jacobians. In this talk, we study the distribution Vrushali A. Bokil of the eigenvalues of the two Jacobians. We outline in gen- Oregon State University eral the location of the eigenvalues of the new system with [email protected] respect to those of the original system, and examine the effect of expansion order on this distributio MS45 Benjamin Sonday Overlapping Domain Decomposition Method for Princeton University the Helmholtz Equation [email protected] The model problem addressed in this talk concerns the Robert Berry analysis and computation of a radiated or scattered time- Sandia National Laboratories harmonic acoustic solution, where the obstacle is composed [email protected] of dielectric and metal. A new adaptive radiation condition method, that localizes the artificial interface only around Habib N. Najm the dielectric object, is described. An appropriate algo- Sandia National Laboratories rithm coupling finite and boundary element methods is Livermore, CA, USA solved iteratively using an overlapping domain decompo- [email protected] sition method. Numerical results are presented validating the theoretical results. Bert J. Debusschere Yassine Boubendir Energy Transportation Center Department of Mathematical Sciences 66 AN10 Abstracts

[email protected] very ill-conditioned. Based on our analysis, we propose a regularization of the local model problem that leads to much more effective steps. We demonstrate our approach MS45 on nonlinear least-squares problems arising in shape-based A Numerical Method for Simulating EM Wave regularization for diffuse optical tomography. Propagation in Dielectrics that Exhibit Fractional Relaxation Eric De Sturler Virginia Tech The frequency-dependent Havriliak-Negami dielectric per- [email protected] s−∞ mittivity model, (ω)=∞+ (1+(iωτ)α)β ,where0<α,β< 1, generates the entire class of dielectric models used in nu- Misha E. Kilmer merical simulations of time-domain propagation and scat- Tufts University tering of electromagnetic waves. We present a numerical [email protected] method to incorporate this model in a solver for Maxwell’s equations which now contain fractional differential operators. We give a complete stability and error analysis of the MS46 method and a validation against the exact solution avail- A Numerical Scheme for Monge-Kantorovich Mass able in some simple cases. Transfer Problem, in the Context of Image Regis- tration Matthew F. Causley New Jersey Institute of Technology (NJIT) The Monge-Kantorovich mass transfer problem addresses [email protected] the question of how to move a pile of soil from one location to another with minimal cost. In this work we Peter Petropoulos introduce computationally efficient numerical method for Department of Mathematical Sciences non-rigid image registration based on the optimal mass New Jersey Institute of Technology transport theory. We will consider the formulation of [email protected] Banemou and Brenier (2000), which requires the solution of a time-dependent PDE constrained optimization, with mass-preserving PDE. MS45 Raya Horesh Polynomial Chaos Approach for Approximating Emory University Cole-Cole Dispersive Media Atlanta, GA Time-domain simulations involving the Cole-Cole model [email protected] are not straight-forward as the model corresponds to a fractional order ODE. We introduce an alternative approach Eldad Haber based on using the first order linear ODE Debye model, Department of Mathematics but with distributions of relaxation times. We apply gen- The University of British Columbia eralized Polynomial Chaos, and then discretize the system [email protected] coupled with Maxwell’s equations. We present a stability and dispersion analysis of the overall method and discuss the impact of the variance of relaxation times. MS46 Iteratively Regularized BFGS-type Algorithm for Nathan L. Gibson an Inverse Problem in Groundwater Hydrology Oregon State University Department of Mathematics A novel iteratively regularized BFGS-type algorithm with [email protected] simultaneous updates of the operator

∗ −1 MS46 (F (xn)F (xn)+βnG (xn − ξ)) Scalable Algorithms for Large-Scale Inverse Wave Propagation is suggested for solving nonlinear ill-posed operator equa- Abstract not available at time of publication. tions of the first kind F (x)=fδ,H1 → H2, on a pair of Hilbert spaces H1 and H2. A convergence theorem is Carsten Burstedde proved. The stability of the process towards noise in the University of Texas at Austin data is analyzed, and a stopping time is chosen so that [email protected] the method converges as the noise level tends to zero. The proposed scheme is illustrated by a numerical example in MS46 which a nonlinear inverse problem of groundwater hydrology is considered. A Regularized Trust Region Model for Ill- conditioned Nonlinear Problems Alexandra Smirnova Georgia State University For ill-conditioned nonlinear problems, we must carefully Department of Mathematics and Statistics balance the convergence rate with step-size control for ro- [email protected] bustness. In particular, the optimization steps must reflect the local nature of the model problem solved in each step. We will show that standard methods such as damped Necibe Tuncer Gauss-Newton, Levenberg-Marquardt, and others tend to Mathematics Department make relatively poor steps if the Jacobian (or Hessian) is University of Florida tuncer@ufl.edu AN10 Abstracts 67

MS48 mesh cells. The spatial error is local and superconvergent Non-oscillatory Behavior of IMEX Schemes Ap- at the roots of the Radau polynomials. Application of these plied to Hyperbolic Problems findings to error estimation, error control and adaptivity in space and time will be discussed. The application of a Method-of-Lines approach to a hyperbolic PDE with stiff source terms gives rise to a sys- Lilia Krivodonova tem of ODEs containing terms with very different stiffness University of Waterloo properties. In such situations, it is convenient to use addi- [email protected] tive Runge Kutta schemes. Implicit-Explicit Runge-Kutta (IMEX-RK) schemes are particularly useful, because they allow an explicit handling of the convective terms, which MS48 can be discretized using the highly developed shock cap- SSP Properties of General Linear Methods turing technology, and an implicit treatment of the source terms, necessary for stability reasons. In this talk we are Abstract not available at time of publication. concerned with certain numerical difficulties associated to Adrian Sandu the use of high order IMEX-RK schemes in a direct dis- Dept. of Computer Science cretization of balance laws with stiff source terms. We Virginia Tech consider a simple model problem, introduced by LeVeque [email protected] and Yee in [J. Comput. Phys 86 (1990)], as the basic test case to explore the ability of IMEX-RK schemes to produce and maintain non-oscillatory reaction fronts. In the first MS49 part of the talk, we consider first order time discretizations, Swimming of Waving Cylindrical Rings in a Stokes which are the basic building blocks of higher order IMEX Fluid schemes, and we establish a convenient framework to study the non-oscillatory properties of numerically computed re- The classical 1952 paper of G.I. Taylor examined the action action fronts. In the second part, we extend the results to of a waving cylindrical tail in a Stokes fluid. Motivated higher order IMEX schemes. This is a joint work with R. by the intriguing function of the dinoflagellate transverse Donat (Departament de Matemàtica Aplicada, Universi- flagellum, we ask the question, what if the cylindrical tail tat de València, 46100 Burjassot, Spain, [email protected]) and was wrapped into a closed circle? We present numerical A. Mart´ınez-Gavara (Departamento de Ecuaciones Difer- studies that address the fundamental fluid dynamics of a enciales y Análisis Numérico, Universidad de Sevilla, 41012 waving helical ring in a viscous fluid. Sevilla, Spain, [email protected]) Lisa Fauci Inmaculada Higueras Tulane University Departamento de Ingenieria Matematica e Informatica [email protected] Universidad Publica de Navarra [email protected] MS49 Simulation of Permeable Membranes using Regu- MS48 larized Source-doublets Optimal Time Integration for Runge-Kutta Discon- tinuous Galerkin Discretizations To compute small-scale fluid flows, it is convenient to use regularized versions of known singular solutions. We com- Runge-Kutta discontinuous Galerkin methods typically bine the method of regularized Stokestlet with regular- employ optimal strong stability preserving (SSP) time inte- ized source-doublets to solve the Stokes equations in the grators. Although these integrators are optimized in terms presence of membranes permeable to fluids or to diffusive of the SSP coefficient, the practical timestep is governed fluxes. Numerical examples are used to investigate the rela- by linear stability constraints. In order to achieve a larger tionship between the permeability/diffusivity of the mem- stable timestep, we develop methods that optimize the brane and the strength of the source-doublets, and to val- minimum of the linear and nonlinear (SSP) timestep con- idate the method. straints. We demonstrate that these methods yield better performance than those obtained by optimizing either one Marian Hernandez-Viera of the SSP coefficient or the linear stability without regard Tulane University to the other. [email protected]

David I. Ketcheson Mathematical and Computer Sciences & Engineering MS49 King Abdullah University of Science & Technology Simulations of Flagellar Motion near a Rigid Sur- [email protected] face

We present a computational model for the simulation of MS48 Stokes flows generated by forces and torques close to a rigid An Analysis of the Spatial and Temporal Errors plane and apply it to study the swimming motion of flag- of the Local Runge-Kutta Discontinuous Galerkin ellated organisms near a rigid surface. The model is based Method on an extension of the method of regularized Stokeslets in which a regularization parameter provides support for We analyze the total error of discontinuous Galerkin so- forces and torques exerted on the fluid by the organism, lutions of one-dimensional scalar hyperbolic problems. We and eliminates the singularity of the velocity expressions. show that the error can be split into two components which can be thought of as temporal and spatial errors. The tem- Ricardo Ortiz poral error is of global character and propagates between Tulane University 68 AN10 Abstracts

[email protected] rectangular solids to the deformed grid made up of hexahedra results in a method that is convergent only in case Ricardo Cortez the hexahedra of the deformed grid are parallelepipeds. Tulane University Several possibilities have been proposed for grids that are Mathematics Department made up of true hexahedra with planar faces. However the [email protected] deformations may lead to grids in which at least one side of some of the elements is non planar: for example the unit cube [0, 1]3 may be deformed by moving the two vertices MS49 (0, 0, 1) and (1, 1, 1) to (0, 0, 2) and (1, 1, 2) respectively. The Hydrodynamic Origin of Whale Flukeprints We propose a mixed finite element method that converges for grids made up of such ”generalized hexahedra”. Whale flukeprints are characteristic smooth oval shaped patches on the surface of the ocean which form behind a Jean E. Roberts,Jérôme Jaffré whale during cruising or diving. Conjecture for the forma- INRIA Paris-Rocquencourt tion of these flukeprints fall into two categories: surfactant France or hydrodynamic based. We present a coherent theory of [email protected], jerome.jaff[email protected] flukeprint formation which is entirely hydrodynamic in nature. We draw upon our own laboratory experiments as well as many aspects of the literature including mathemat- MS50 ical biology, mathematical models, and numerical simula- Superconvergence for Control-volume Mixed Fi- tions. nite Element Methods on Rectangular and Quadri- lateral Grids David T. Uminsky Dept. of Mathematics Control-volume mixed finite element methods associate a UCLA control volume (covolume) with the vector variable as well [email protected] as the scalar variable. In the context of flow in porous media, this yields a local Darcy law on the covolume as- Rachel Levy sociated with each discrete vector equation, in addition to Harvey Mudd College the usual local mass conservation arising from the scalar [email protected] equation on each grid cell. We formulate these methods on rectangular and distorted quadrilateral grids, and briefly discuss their relationships to some other locally conserva- John Calambokidis tive schemes that model flow on distorted grids. Exploiting Cascadia Research a relationship to the lowest-order Raviart-Thomas mixed [email protected] FEM, we demonstrate second-order superconvergence for the vector variable in a discrete H(div)-norm and for the 2 MS50 scalar variable in a discrete L -norm. In the quadrilateral case, this requires that the elements be second-order A Priori and A Posteriori Analysis of Mixed Finite approximations of parallelograms as the mesh is refined. Element Methods for Nonlinear Elliptic Equations Thomas F. Russell We study the mixed finite element approximation of nonlin- National Science Foundation ear second-order elliptic problems. Existence and unique- Ofc. of Integrative Activities ness of the approximate solution are proved and optimal [email protected] order apriorierror estimates in Lm(Ω) are obtained. Also, reliable and efficient a posteriori error estimators measured in the Lm(Ω)-norm are derived. Numerical examples are Mary F. Wheeler provided to illustrate the performance of the proposed es- Center for Subsurface Modeling timator. University of Texas at Austin [email protected] Eun-Jae Park Dept of Computational Science and Engineering-WCU Ivan Yotov Yonsei University Univeristy of Pittsburgh [email protected] Department of Mathematics [email protected] Dongho Kim University College Yonsei University MS50 [email protected] A Posteriori Error Estimation based on Potential and Flux Reconstruction for the Heat Equation: A Unified Framework MS50 Mixed Finite Elements for Deformed Cubes We derive a posteriori error estimates for the discretization of the heat equation in a unified setting comprising Mixed finite element methods and the associated cell cen- the discontinuous Galerkin, finite volume, and mixed finite element methods in space and the backward Euler scheme tered finite volume methods are known to have many ad- 1 vantages for the numerical modeling of flow in porous me- in time. Our estimates are based on a H -conforming po- dia. For many problems involving flow in porous media, tential reconstruction, continuous and piecewise affine in however engineers prefer to use grids that are deforma- time, and a locally conservative H(div)-conforming flux tions of regular grids made up of 3D rectangular solids. reconstruction, piecewise constant in time. They yield a Unfortunately the adaptation via the Piola transformation guaranteed upper bound. Local-in-time lower bounds are of classical mixed finite elements for a grid made up of AN10 Abstracts 69

also derived. MS51 On the Connection Between Model Reduction and Martin Vohralik N-Widths Approximation Université Pierre et Marie Curie Paris, France The connection between two important model reduction [email protected] techniques, namely balanced proper orthogonal decomposition (POD) and balanced truncation is investigated for Alexandre Ern infinite dimensional systems. In particular, balanced POD Universite Paris-Est is shown to be optimal in the sense of distance minimization CERMICS, Ecole des Ponts in a space of integral operators under the Hilbert-Schmidt [email protected] norm. Whereas balanced truncation is shown to be a particular case of balanced POD for infinite dimensional systems for which the impulse response satisfies certain finite MS50 energy constraints. POD and balanced truncation are re- Iterative Coupling of Two-Phase Flow on General lated to certain notions of metric complexity theory. In Hexahedral Grids particular both are shown to minimize different n-widths of partial differential equation solutions including the Kol- We present an iterative coupling method for the two-phase mogorov and Gelfand n-widths. The n-widths quantify in- flow in porous media on the corner point geometry. The herent and representation errors due to lack of data and pressure equation is solved by the multipoint flux mixed loss of information. finite element (MFMFE) method. Discontinuous Galerkin method is employed for the saturation equation. Numerical Seddik Djouadi examples show the efficiency of this approach. Department of Electrical Engineering and Computer Science Guangri Xue, Mary F. Wheeler University of Tenneessee, Knoxville Center for Subsurface Modeling [email protected] University of Texas at Austin [email protected], [email protected] MS51 Ivan Yotov A Thick-Restart Krylov Subspace Method for Or- Univeristy of Pittsburgh der Reduction of Large-Scale Linear Descriptor Department of Mathematics Systems [email protected] In recent years, Krylov subspace techniques have proven to be powerful tools for order reduction of large-scale lin- MS51 ear dynamical systems. The most widely-used algorithms A Model Predictive Controller Design for employ explicit projection of the data matrices of the dy- Parabolic PDE Systems namical systems, using orthogonal bases of the Krylov subspaces. For truly large-scale systems, the generation and Abstract unavailable at time of publication. storage of such bases becomes prohibitive. In this talk, we explore the use of thick-restart Krylov subspace techniques Antonios Armaou to reduce the computational costs of explicit projection. Department of Chemical Engineering The Pennsylvania State University Roland W. Freund,EfremRensi [email protected] University of California, Davis Department of Mathematics [email protected], [email protected] MS51 Model Reduction with Stability Guarantee for Lin- ear and Nonlinear Systems Arising in Analog Cir- MS51 cuit Applications Including Broadband Interactions and Boundary Forcing in Low and Least Order Galerkin Models In this talk I present recently developed techniques for gen- of Fluid Flows erating stable reduced models from linear and nonlinear systems arising in analog applications. These techniques Abstract unavailable at time of publication. combine the standard model reduction notions of projection and fitting along with convex optimization, and are Gilead Tadmor capable of generating guaranteed stable reduced models Northeastern University from systems for which traditional algorithms are unreli- [email protected] able, such as when the original systems are highly nonlinear, described by unstructured and indefinite matrices, or Bernd Noack even mildly unstable. CNRS UniversitédePoitiers [email protected] Brad Bond MIT Michael Schlegal [email protected] Berlin Institute of Technology [email protected] Luca Daniel M.I.T. Research Lab in Electronics MS52 [email protected] A Variant of Nonlinear Conjugate Gradient using 70 AN10 Abstracts

a Little Second-derivative Information Department of Mathematics Simon Fraser University We propose an algorithm for minimization of uncon- [email protected] strained strongly convex functions that uses a small amount of second derivative information. It is based on Ne- mirovsky and Yudin’s generalized conjugate gradient but MS52 appears to perform better in practice than their method First-order Methods in Sparse Optimization and other variants of conjugate gradient. The method also extends to unconstrained nonconvex optimization. We discuss gradient-based methods in regularized logistic regression, compressed sensing, and support vector ma- Sahar Karimi chines with kernel approximation. These sparse optimiza- University of Waterloo tion problems are convex, involve simple nonsmooth func- [email protected] tions, and have very high dimension in primal and/or dual space, with only a small fraction of the variables being nonzero at the solution. Such approaches as gradient sam- MS52 pling, nonstandard step lengths, and limited use of curva- Accelerated Stochastic Approximation Methods ture information will be presented. for Composite Convex Minimization and Statistical Learning Stephen J. Wright University of Wisconsin In this talk, we present accelerated stochastic algorithms Dept. of Computer Sciences as well as novel accurate certificates for a few stochastic [email protected] composite optimization problems including those involving strong convexity. We show that these algorithms are optimal in terms of expected rate of convergence, and also MS53 demonstrate that these convergence rates exhibit or can Solving PDEs with RBFs: Applications in Geo- be improved so as to have a logarithmic dependence on a science Modeling given reliability level. We demonstrate the significant advantages of these algorithms applied to statistical learning, Radial basis functions have the advantage of being spec- such as the classic regression and support vector machine trally accurate for arbitrary node layouts in multiple di- models. mensions with extreme algorithmic simplicity, and naturally permit local node refinement. We will show test ex- George Lan amples ranging from vortex roll-ups, modeling idealized Dept of ISE cyclogenesis, to unsteady nonlinear flows posed by the shal- University of Florida low water equations on a sphere to 3-D mantle convection [email protected]fl.edu in the earth’s interior. Their performance will be evaluated based on numerical accuracy, stability and computational performance. MS52 Primal-Dual First-Order Methods for a Class of Natasha Flyer Cone Programming National Center for Atmospheric Research Division of Scientific Computing In this talk, we study first-order methods for a class of cone fl[email protected] programming problems which, for example, include the MAXCUT semidefinite programming relaxation, Lovász capacity and those arising in compressed sensing. In par- MS53 ticular, we first present four natural primal-dual smooth Radial Basis Functions for Solving Partial Differ- convex minimization reformulations for them, and then ential Equations discuss first-order methods, especially a variant of Nes- terov’s smooth (VNS) method for solving these reformula- Compared to pseudospectral methods, radial basis functions. The associated worst-case major arithmetic operations (RBFs) have relinquished orthogonality properties in tion costs of the VNS method are estimated and compared. exchange for much improved simplicity and geometric flex- We conclude that the VNS method based on the last refor- ibility, offering spectral accuracy together with local node mulation generally outperforms the others. Finally, as one refinement. A counterintuitive parameter range (making example, we discuss the application of the VNS method all the RBFs flat) is of special interest. Computational to the Dantzig selector (DS) problem recently proposed cost and numerical stability were initially seen as potential by Candès and Tao, which has numerous applications in difficulties, but major progress have recently been made sparse signal recovery, variable selection and model fitting also in these areas. in linear regression. Though the DS problem can be reformulated and solved as a linear program, it is extremely Bengt Fornberg challenging to the well-known methods such as simplex and University of Colorado interior point (IP) methods due to high dimensionality and Boulder full density of the data often encountered in practice. The [email protected] performance of the VNS method is finally compared with the IP method that is tailored for the DS problem on a set of randomly generated instances. Our computational MS53 results demonstrate that while low-accuracy solutions are 2D Radial Basis Function Interpolation on Irregu- sought, the VNS method when applied to the most suitable lar Geometry through Conformal Transplantation reformulation mentioned above substantially outperforms the IP method that is superior to simplex methods. Radial Basis Function (RBF) method for interpolating two dimensional functions with localized features defined on ir- Zhaosong Lu regular domain is presented. RBF points are chosen such AN10 Abstracts 71

that they are the image of conformally mapped points on MS54 concentric circles on a unit disk. On the disk, fast RBF Soap and Slope: Exploration of Gradients through solver to compute RBF coeﬃcients developed by Kara- Hands-on Experiments with Surfactants (Outreach georghis et al. is used. Approximation values at desired Module for Grades 7-12) points in the domain can be computed through the process of conformal transplantation. The purpose of this session is to share outreach activities used successfully with middle and high school students. I Alfa Heryudono will demonstrate (and you can try!) activities to introduce University of Massachusetts Dartmouth the concept of slope (gradient) through activities with sim- Department of Mathematics ple and inexpensive materials. We will also discuss how to [email protected] tie outreach activities to discussions with students about research in applied mathematics. MS53 Rachel Levy C-inﬁnity Compactly Supported Radial Basis Harvey Mudd College Function Methods for PDEs [email protected]

Approximations based on analytic radial basis functions (RBFs), such as Gaussians and multiquadrics, are in many MS54 cases unstable when scattered nodes are used. On the other Applied Mathematics for High School Outreach hand, methods based on RBFs of finite smoothness converge at algebraic rates even when the target function is Contests can be a valuable motivator for introducing mid- smooth. Numerical experiments suggest that collocation dle and high school students to applied mathematics. This methods based on C∞ compactly supported radial basis talk will introduce some of the competitions that are avail- functions are stable and yield exponential convergence. In able. Opportunities for both professional development and this talk we explore the use of C∞ RBFs for the solution for student-based activities in applied mathematics will be of PDEs. presented. The talk will also provide a brief introduction to the remainder of the minisymposium. Platte Rodrigo Oxford Peter R. Turner [email protected] Clarkson University School of Arts & Sciences [email protected] MS54 K-12 Outreach with Integrated Math and Physics for Roller Coaster Design MS54 Computational Math, Science and Technology (C- We present an overview of learning experiences focused MST) at K-12 on roller coaster design that integrate mathematics and physics for grades 7-12. This workshop will include some An integrated (computational) approach to STEM educa- hands-on design aspects and ideas that can easily be im- tion offers many benefits to improve teaching and learning plemented in the classroom or as part of an after-school en- at both college and secondary school classrooms. Compu- richment program. These projects are motivated in part by tational thinking (CT) is now recognized as a fundamen- a NYSED funded school year program targeted at middle tal skill to be taught along reading and writing. Our CT and high school students that culminates at a week long, experience at K-12 shows a significant impact on student roller coaster camp each summer and the use of a pro- achievement in an urban school district. To sustain these grammable Maxight 2002 Virtual Reality Roller Coaster experiences in K-12 classrooms, we need to improve techno- that resides on our campus and a visit to Six Flags to col- logical pedagogical content knowledge (TPCK) of current lect data on real roller coasters. and future teachers. Kathleen Fowler Osman Yasar Clarkson University State University of New York Department of Mathematics Department of Computational Sci. [email protected] [email protected]

David Wick Peter Veronesi Department of Physics State University of New York Clarkson University [email protected] [email protected] Leigh J. Little Michael Ramsdell Department of Computational Science Clarkson University State University of New York, Brockport [email protected] [email protected]

Peter R. Turner Jose Maliekal Clarkson University State University of New York, Brockport School of Arts & Sciences [email protected] [email protected] MS55 On Non-singular Assembly Mode Change of Paral- 72 AN10 Abstracts

lel Manipulators Plasmas

Non singular assembly mode change of parallel manipu- We consider a fully implicit solution algorithm for the lators has been discussed for a while within the robotics Vlasov-Poisson equation. By design, we employ the community. This term means that a parallel robot can pass particle-in-cell (PIC) approach to describe kinetic pop- from one solution of direct or inverse kinematics into an- ulations. Algorithmically, we employ preconditioned other without crossing a singularity. We will show that all Jacobian-free Newton-Krylov techniques to solve the re- generic planar 3-RPR parallel manipulators have this abil- sulting nonlinear systems. Our implicit PIC approach is ity. Using geometric and algebraic properties of the singu- unique in that it guarantees exact conservation of mass, larity surface we will give a proof and extend the question momentum, and energy. Additionally, it is free from delete- to other manipulators. rious ﬁnite-grid (aliases) instabilities, which have imposed fundamental eﬃciency limitations in other PIC implemen- Manfred Husty tations. University of Innsbruck [email protected] Luis Chacon Oak Ridge National Laboratory [email protected] MS55 Title Not Available at Time of Publication Daniel Barnes Coronado Consulting Abstract not available at time of publication. [email protected] Michael McCarthy University of California, Irvine Diego Del-Castillo-Negrete, Raul Sanchez [email protected] Oak Ridge National Laboratory [email protected], [email protected]

MS55 Managing Uncertainties in Kinematics MS56 An Asymptotic Preserving Scheme for Kinetic Uncertainty is an inherent feature of kinematics problems. Equations and Related Problems with Stiff Sources Indeed geometrical modeling, that leads to the kinematic equations, involves physical parameters (e.g. link lengths) Granular gases appear in various situations, such as dissi- that are only known up to some bounded error. We will pative diluted flows or pollen dispersion. Their mesoscopic show how interval analysis allows one to determine the description is given by the inelastic Boltzmann equation. influence of these uncertainties on the kinematic perfor- We design numerical schemes to perform simulations on mances. If this influence leads to unsatisfactory perfor- the evolution of the macroscopics quantities associated to mances a variant of the analysis algorithm allows to deter- this equation in different regimes. A numerical scheme for mine almost all possible values for the physical parameters. this equation might be able to deal both with the kinetic regime and its (stiff) hydrodynamic regime, obtained re- Jean-Pierre Merlet spectively when the mean free path goes to zero. Such INRIA a scheme is called Asymptotic Preserving (A.P.). In this [email protected] talk we present a quasi-elastic model and the associated A.P. scheme, and compare the macroscopic quantities associated to this scheme with the ones obtained by Euler MS55 equations for dissipative gases. The technique used to de- Compliant Mechanism Analysis and Synthesis via rive the scheme is rather smooth and might be applied for Polynomial Solvers a large class of problems, such as hyperbolic ones with relaxation or semiconductor equations. This talk presents the use of polynomial solvers in the analysis and synthesis of compliant mechanisms. The motion Francis Filbet, Thomas Rey of compliant mechanisms is governed by a set of kine- University of Lyon tostatic (kinematics and statics) equations which can be fi[email protected], [email protected] transformed into a polynomial system. Solving these polynomial systems is one important step towards the innovative design of these compliant mechanisms. It has been MS56 found that a large portion of the solutions obtained by High Order Semilagrangian Methods for BGK and polynomial solvers have no physical meaning. Sifting out Vlasov Equations these mathematical solutions can be tedious even challenging in many cases. We also present a new technique called In this talk we review some recent results on high order “constrained homotopy’ technique for excluding unwanted numerical schemes for some class of kinetic equations. We solutions from a polynomial system. first describe high semilagrangian schemes for the BGK model of the Boltzmann equation. The schemes are based Haijun Su on writing the equation in characteristic form, and inte- University of Maryland Baltimore County grating it by high order diagonally implicit Runge-Kutta [email protected] methods. The implicit treatment of the collision term allows the numerical solution of the equation even near the fluid dynamic regime. Peculiar property of the BGK equa- MS56 tion are exploited to explicitly compute the implicit term. Fully Implicit Methods for Kinetic Simulation of The semilagrangian nature of the scheme allows the use of large time steps, overcoming the usual CFL limitation. High order in space is obtained by suitable high order AN10 Abstracts 73

WENO reconstruction. A recently developed conservative [email protected] version of the scheme is proposed. A similar scheme is applied to the solution of the BGK equation in a domain with moving boundary. The equation is solved on a fixed MS57 grid. The solution is computed on the grid points inside Wave Scattering by Randomly Shaped Objects the domain, which change in time. Boundary conditions are satisfied by suitably defined ghost values on grid points Abstract not available at time of publication. near the boundary, in the exterior of the domain. As a last application, new high order semilagrangian methods for the Adi Ditkowski Vlasov equation will be presented. The method is based on Department of Applied Mathematics writing the equation in characteristic form. At each grid Tel-Aviv University, Israel node in space and velocity, the characteristics are traced [email protected] back in time, and the value at the foot of the characteristics are computed by high order WENO reconstruction. MS57 Preliminary results show the effectivenes of the approach. Non-intrusive Polynomial Chaos Application to Giovanni Russo Acoustic Rough Surface Scattering University of Catania Department of Mathematics A computational inverse Riemann map allows acoustic [email protected] modeling of rough sea surface scattering by sound speed variations in the Helmholtz equation with flat surface. Use of a standard underwater acoustic propagation model Pietro Santagati with the resulting sound speeds provides the basis for non- Department of Mathematics and Computer Science intrusive polynomial chaos calculations. Applications in- University of Catania clude typical acoustic field variability measures. This re- [email protected] search is sponsored by the Office of Naval Research.

Francis Filbet Roger Oba Universite Claude Bernard, Lyon, France Naval Research Laboratory Institute Camille Jordan [email protected] ﬃ[email protected]

Jing Mei Qiu MS57 Mathematics and Computer Science Uncertainty Quantification Methodologies for Cli- Colorado School of Mines mate Model Data with Discontinuities mailto:[email protected] Uncertainty quantification in climate models is challenged by the sparsity and bifurcative character of the available MS57 climate data. To circumvent these challenges we propose Characterization of Discontinuities in High- a methodology that employs Bayesian inference to locate dimensional Stochastic Problems on Adaptive discontinuities in the model output, followed by an efficient Sparse Grids propagation of uncertain quantities using spectral expansions of random parameters/fields. Stochastic emulators The behavior of financial, chemical, mechanical, environ- are used to assess the performance of the proposed ap- mental and many other processes are often characterized proach. by a large number of variables. The relationship between the variables that drive the system (inputs) and the sys- Cosmin Safta, Khachik Sargsyan tem response (outputs) can be highly non-linear, discon- Sandia National Laboratories tinuous and correlated. Knowledge of the relationships [email protected], [email protected] between the model inputs and outputs can be extremely useful when attempting to quantify uncertainty, construct Habib N. Najm surrogate models or evaluate high-dimensional integrals. Sandia National Laboratories This talk presents a numerical procedure for determin- Livermore, CA, USA ing jump discontinuities in high dimensional functions on [email protected] sparse adaptive grids. This method combines the strength of dimension adaptive sparse grid approximation and poly- Bert J. Debusschere nomial annihilation edge detections to construct a high or- Energy Transportation Center der method, which provides easy and effcient detection of Sandia National Laboratories, Livermore CA jump discontinuities in highly variable functions. [email protected]

Rick Archibald Computational Mathematics Group MS58 Oak Ridge National Labratory Decreasing of the Perimeter under Generalized [email protected] Steiner Symmetrization and Characterization of Cases of Equality John Jakeman ANU Abstract not available at time of publication. [email protected] Filippo Cagnetti Department of Mathematics Dongbin Xiu Instituto Superior Tecnico, Lisbon, Portugal Purdue University [email protected] 74 AN10 Abstracts

MS58 Stress Variational Approaches to Bar Code Reconstruc- tion Abstract not available at time of publication. In this talk we will discuss TV-based energy minimiza- Marta Lewicka tion for deblurring and denoising of 1D and 2D bar codes. University of Minnesota For 1D bar codes, we consider functionals consisting of the [email protected] TV-seminorm together with various fidelity terms involving deconvolution and a convoluted signal of a barcode. MS59 Key length scales and parameters are the X-dimension of the bar code, the sizes of the supports of the convolution Using Homotopy Continuation to Quickly and Ac- and deconvolution kernels, and the fidelity parameter. For curately Solve Polynomial Systems these functionals we establish parameter regimes (sufficient Homotopy continuation solves any size polynomial system conditions) wherein the underlying barcode is the unique of equations, but as the number of variables rise, so do com- minimizer. We present some numerical experiments exper- plications and computation time. Since the systems may iments which suggest that these sufficient conditions are be unsolvable by hand, it is hard to obtain an accurate not optimal, and the energy methods are quite robust for count of how many solutions there are. Poor approxima- significant blurring. For 2D barcodes, we discuss minimiza- tions cause lengthy calculation due to evaluating diverg- tion of a functional comprised of an anisotropic TV norm 1 ing homotopy paths. By eliminating these early, we can and an L fidelity term. We present necessary and suffi- cut computation time and devote resources to accurately cient conditions for a minimizer and apply our results to tracking the roots. denoising and deblurring of 2D bar codes. We also present numerical experiments. Aaron Allen, Mark Holmes Rensselaer Polytechnic Institute Rustum Choksi TBA, [email protected] Department of Mathematics McGill University [email protected] MS59 Numerical Simulation of a Brownian Elastic Fila- Yves van Gennip ment in Random Stokes Flow Department of Mathematics Simon FRaser University The dynamics of elastic filaments in Stokes flow has sig- [email protected] nificant effects on their ability to be transported. We numerically investigate the dynamics of an elastic filament in a random Stokes flow using Tonberg and Shelley algo- MS58 rithm. This includes the filament susceptibility to buck- Stability in the Wulff Inequality and Applications ling instability, and its effective diffusivity. Furthermore, thermal fluctuations are incorporated, and their effects on The equilibrium shape of a crystal is determined by the filament transport in Stokes flows are quantified. Finally, minimization under a volume constraint of its free energy, preliminary work on the hydrodynamic interaction effects consisting of an anisotropic interfacial surface energy plus on filament transport will be presented. a bulk potential energy. In the absence of the potential term, the equilibrium shape can be directly characterized Steven Elliott in terms of the surface tension and turns out to be a con- New Jersey Institute of Technology vex set, the Wulff shape of the crystal. Our first result is a TBA sharp quantitative inequality implying that any shape with almost-optimal surface energy is close in the proper sense to the Wulff shape. This is a joint work with Francesco MS59 Maggi (Florence) and Aldo Pratelli (Pavia). Under the ac- Adaptive Hybrid Trigonometric Polynomial Re- tion of a weak potential or, equivalently, if the total mass of constructions the crystal is small enough, the surface energy of the equilibrium shape is actually close to that of the correspond- Fourier series approximations have difficulties with discon- ing Wulff shape, and the previous result applies. However, tinuous functions. Our approach to remedy this problem stronger geometric properties are now expected, due to the is to use a hybrid method. In this method, polynomial fact that the considered shapes are minimizers. Indeed we approximation is used near the discontinuity and Fourier can prove their convexity, as well as their proximity to the approximations are used on the other regions. We present Wulff shape with respect to a stronger notion of distance. numerical differences between our methods and other pre- This is a joint work with Francesco Maggi (Florence). vious methods applied to similar popular problems. More- over, we attempt to reduce the error caused by aliasing. Alessio Figalli Department of Mathematics The University of Texas at Austin Zachary Grant fi[email protected] University of Massachusetts at Dartmouth TBA

MS58 A Hierarchy of Elastic Plate Models with Residual MS59 Distributed Compressive Imaging Compressive imaging oﬀers the possibility of completely new imaging sensor design which can dramatically reduce AN10 Abstracts 75

the sampling rates currently required for perfect image re- MS60 construction. Distributed Compressive Imaging (DCI) of- Mathematical Models for Predicting Survival and fers a type of joint image compression/reconstruction of Internal pH for Food Pathogens imaging sensors which have overlapping fields-of-view. We formulate the mathematical model of the sensing network The risk of disease outbreaks from acidified vegetable prod- in terms of distributed compressive sensing and simulate ucts due to microbial pathogens such as Escherichia coli (E. the image reconstruction results over a variety of sensor coli) O157:H7 is of recent concern. For conditions similar configurations and a priori knowledge. to these products, we developed a mechanistic model describing the internal pH of E. coli. In addition, a Weibull Christopher Huff model was used to relate survival to internal pH and ex- University of Central Florida perimental methods were implemented to validate model TBA predictions. Our efforts may result in improved methods for inactivating these pathogens. MS59 Althea Hosein Jump Discontinuity Detection with Noisy Fourier North Carolina State University Data [email protected]

The detection of jump discontinuities in physical space using frequency (Fourier) data is an essential aspect of Medi- MS60 cal Resonance Image processing. The diﬃculty of the task Mathematical Models of Interneurons in Hip- lies in extracting local information from the global Fourier pocampus data, and is further complicated by noise. In this talk, we discuss a recently developed algorithm that uses frequency The hippocampus is an intensely studied brain structure data to recover the jump discontinuities. The expected ac- that is involved in learning and memory. It expresses sev- curacy of the detector has been modeled using statistical eral population activities that are controlled by a diverse hypothesis testing. collection of inhibitory cells, or interneurons. These interneurons have distinct characteristics that can contribute Alex Petersen to network output in diﬀerent ways. I will describe our Arizona State University work involving the development and analysis of detailed TBA models of hippocampal interneurons so as to help understand the contribution of their distinct natures. MS59 Frances Skinner High-Order Adaptive Methods for Drawing Para- Division of Cellular and Molecular Biology metric Curves Division of Cellular and Molecular Biology

A naive way to draw a parametric curve is to plot a finite number of equally spaced parameter values and interpolate MS60 them with lines. Linear interpolation has low accuracy, es- Boolean Models Can Explain Bistability in the Lac pecially near points of high curvature and uniformly spaced Operon points over-resolve some parts of a curve while under- resolving others. We develop a method that places the The lac operon is a well-studied gene system known to ex- points adaptively and interpolates them with higher-order hibit bistability. While most models are based on complex interpolants called Catmull Rom Spline–piecewise Bezier functions, it has been suggested that specifiying network Curves. We validate this with numerical experiments. topology is sufficient to capture dynamics. We present a Boolean model and show that it accurately reproduces the Priyanka Shah, Casayndra Basarab operon’s dynamics. Further we identify a core subnetwork New Jersey Institute of Technology that maintains bistability. These results support the hy- tba, [email protected] pothesis that topology is the key to model qualitative dynamics in gene systems. MS60 Brandilyn Stigler Stochastic Modeling of Parasites in Host Popula- Southern Methodist University tions [email protected] The complexity of the host-parasite relationship, and its depression of host populations has been investigated and MS61 successfully modeled for large populations using determin- Better Methods Through Optimization, Or How to istic methods. These models fail to accurately predict in- Avoid Doing the Hard Work Yourself teractions within smaller populations, and require a statistical component to reclaim some degree of accuracy. This We use optimization and control ideas to formulate better research employs stochastic differential equations to better numerical methods for PDEs. Two applications are pre- forecast changes in small populations, and, in a practical sented: an additive decomposition approach for coupled setting, seeks to write software that will automate this pro- multi-physics problems, and bounds preserving remap al- cedure. gorithm. In the first case, we synthesize scalable solvers for advection-dominated PDEs that work for all Peclet num- Armando Arciniega bers from standard AMG solvers that fail in the advection University of Texas at San Antonio dominated regime. In the second case, we derive a com- University of Texas at San Antonio patible transport algorithm that ensures monotonicity of a 76 AN10 Abstracts

tracer. ticity with DG Jumps and Mortars

Pavel Bochev, Denis Ridzal, Kara Peterson A nonoverlapping mortar domain decomposition algorithm Sandia National Laboratories is formulated for a poroelastic payzone region coupled with [email protected], [email protected], an elastic non-payzone region. A continuous Galerkin [email protected] method is used for the displacement variables and the interface operator is constructed using discontinuous Galerkin jump conditions. Optimal order error estimates are pre- MS61 sented, as well as a multiscale algorithm which increases Coarse-scale Models for Flows in High-contrast the computational efficiency. Numerical results are pre- Multiscale Media and their Applications sented for a 2D example with an analytic solution and a more complicated 3D example. In this talk, I will discuss special coarse spaces for multiscale finite element and domain decomposition methods. Tim M. Wildey These spaces allow a coarse-scale representation of the so- The University of Texas at Austin lution of multiscale flow problem. The focus will be on Austin, USA problems that have high variations in the media proper- [email protected] ties. It is known that the number of iterations in domain decomposition and many iterative methods is adversely af- Mary F. Wheeler fected by the contrast in the media properties. One way Center for Subsurface Modeling to decrease the number of iterations is to choose coarse University of Texas at Austin spaces appropriately. In the proposed methods, the coarse [email protected] spaces are constructed based on a local eigenvalue problem. We show that if domain decomposition methods use Gergina Pencheva these coarse spaces then the condition number of precon- CSM, ICES ditioned system is independent of the contrast in media The University of Texas at Austin properties. The coarse space can have large dimension. In [email protected] this talk, we discuss dimension reduction for the proposed coarse spaces and hierarchical computations of multiscale basis functions. The latter results to domain decomposi- Vivette Girault tion preconditioners that have the condition number which University of Paris VI is independent of contrast. We will discuss the accuracy of [email protected] coarse-scale solutions using these proposed coarse spaces. Numerical results will be presented. MS62 Yalchin Efendiev Scenario Discovery Using Nonnegative Tensor Fac- Dept of Mathematics torization and Visual Analytics Texas A&M University [email protected] Automated approaches for the identification and clustering of semantic features or topics are highly desired for text mining applications. Moving beyond two-way factor- Juan Galvis izations, we demonstrate how non-negative tensor factor- Texas A&M University izations (NNTFs) can be used to capture temporal and [email protected] semantic proximity for tracking targeted and latent discussions. Visualization of NNTF outputs for topic detec- MS61 tion and tracking using email corpora from Enron and the Climate Research Unit (CRU) at the University of East Iterative Algorithms based on the Algebraic Mul- Anglia is demonstrated. tiscale Finite Volume Method Michael W. Berry In the Multiscale Finite-Volume (MsFV) method a con- University of Tennessee servative velocity field is constructed from an approximate [email protected] pressure field, which is obtained by juxtapposition of local solutions coupled through a global problem. Due to localization assumption, the MsFV solution differs from Andrey Puretskiy the exact solution of the problem. The accuracy of the University of Tennessee method can be improved by constructing an iterative al- Department of Electrical Engineering and Computer gorithm that arbitrarily reduces the localization error. We Science present these iterative algorithms and several applications. [email protected]

Ivan Lunati MS62 University of Lausanne Sparse Optimization with Least-squares Con- [email protected] straints The use of convex optimization for the recovery of sparse Seong H. Lee signals from incomplete or compressed data is now com- Chevron ETC mon practice. Motivated by the success of basis pursuit [email protected] in recovering sparse vectors, new formulations have been proposed that take advantage of diﬀerent types of sparsity. MS61 We propose an eﬃcient algorithm for solving a general class of sparsifying formulations. For several common types of Domain Decomposition for Poroelasticity and Elas- sparsity we provide applications, along with details on how AN10 Abstracts 77

to apply the algorithm. ary integral equation.

Michael P. Friedlander Yassine Boubendir Dept of Computer Science Department of Mathematical Sciences University of British Columbia [email protected] [email protected] MS63 MS62 Regularization Methods for Biological Fluid Flow Generalizations of Subspace Identification for Problems Learning from High-Dimensional Time Series Data Biological flows surrounding swimming microorganisms or Kalman filters and HMMs are staples for analyzing time beating cilia are modeled using the Stokes equations with series data. Factor analysis methods (such as PCA) external forcing. The organism surfaces are flexible inter- are staples for analyzing high-dimensional data. In the faces imparting force or torque on the fluid. I will present linear-Gaussian case, subspace identification methods have recent advances of the Method of Regularized Stokeslets, brought together these two model classes to analyze high- which is based on integral expressions for the exact fluid dimensional time-series data. Recently, researchers have velocity field resulting from localized regularized forces. I begun to generalize subspace ID beyond linear-Gaussian will present the idea of the method, some of the known models, to handle representations such as HMMs. I will results and several examples from biological applications. discuss our work in this direction, using examples and results from robot sensor data. Ricardo Cortez Tulane University Geoffrey Gordon Mathematics Department Machine Learning Department [email protected] Carnegie Mellon University [email protected] MS63 A Non-stiff Boundary Integral Method for 3D MS62 Porous Media Flow with Surface Tension Nonnegative Matrix Factorization using Bicliques An efficient, non-stiff boundary integral method for 3D Nonnegative matrix factorization is an important data porous media flow with surface tension is presented. Sur- mining technique, with applications in genomics, the nat- face tension introduces high order (i.e., high derivative) ural sciences, and information retrieval. These are usually terms into the evolution equations, and this leads to severe recovered using optimization techniques requiring dense stability constraints for explicit time-integration methods. representation of the factors, which sharply limits the num- Furthermore, the high order terms appear in nonlocal oper- ber of rank-one components we can identify; a problem be- ators, making the application of implicit methods difficult. cause of the fat-tail (power-law) distribution of those com- Our algorithm employs a special representation of the in- ponents. We demonstrate how to use biclique enumeration terface which enables efficient application of implicit time- algorithms to obtain much more complete factorizations, integration methods via a small-scale decomposition. The and show results on some real datasets. algorithm is found to be effective at eliminating the severe time-step constraint that plagues explicit time-integration Michael J. O’Hara methods. Lawrence Livermore National Laboratory [email protected] Michael Siegel Department of Mathematical Sciences Manda Winlaw New Jersey Institute of Technology University of Waterloo [email protected] [email protected] David Ambrose Van Henson Drexel University Lawrence Livermore National Laboratory [email protected] [email protected] Svetlana Tlupova Department of Mathematics MS63 University of Michigan Domain Decomposition Methods for Stokes-Darcy [email protected] Systems with Boundary Integrals We consider a coupled problem of Stokes and Darcy equa- MS63 tions. This involves solving PDEs of different orders si- Solution of Coupled Free/porous Media Flow using multaneously. To overcome this difficulty, we apply a non- Boundary Integral Equations overlapping domain decomposition method based on Robin boundary condition obtained by combining the velocity Fluids partly flowing freely and partly filtrating through and pressure interface conditions. The coupled system is a porous medium are modeled by a coupled Stokes-Darcy then reduced to solving each problem separately by an it- system with carefully chosen interface conditions. In this erative procedure using a Krylov subspace method. The talk, we describe a boundary integral formulation for this numerical solution in each subdomain is based on bound- problem, where the Green’s function is regularized and correction terms are added for higher accuracy. A preconditioner based on the regularization-correction method is de- 78 AN10 Abstracts

veloped to improve the convergence of a Krylov subspace well known examples of orbitopes and show how an old con- method to solve the integral formulation. jecture by Harvey and Lawson appears in new light, when discussed in this context. If time permits we will discuss Svetlana Tlupova first steps towards the resolution of this conjecture in par- Department of Mathematics ticular cases as well as convincing evidence using numerical University of Michigan algebraic geometry. [email protected] Philipp Rostalski, Raman Sanyal Department of Mathematics MS64 UC Berkeley Geometry of Sums of Squares Relaxations [email protected], [email protected] Lasserre relaxations are a very common optimization tool to approximate semi-algebraic sets by projections of spec- MS64 trahedra. In this talk we will revisit a result of Netzer, Convex Algebraic Geometry Plaumann and Schweighofer on the geometry of these sets and present a more elementary proof for it. We will then Convex algebraic geometry, which is the study of convex procceed to do a few extensions of this result and solve semi-algebraic sets, is a discipline that arose from optimiza- some related open questions. tion, specifically semidefinite programming and polynomial optimization. It seeks to develop algorithms and software Joao Gouveia to treat convex sets defined by algebraic equations and in- University of Washington equalities, as well as to better understand such sets, and ex- [email protected] ploit this understanding in applications, from optimization to algebraic statistics to control. This minisymposium will Tim Netzer present current work in this new field from foundational University of Leipzig material to applications and algorithms. [email protected] Frank Sottile Texas A&M University MS64 [email protected] Geometry of Restricted Boltzmann Machines The restricted Boltzmann machine is a graphical model for MS65 binary random variables. Based on a complete bipartite Promoting Professional Development for Under- graph separating hidden and observed variables, it is the graduates Through Calculus Projects binary analog to the factor analysis model. We study this graphical model from the perspectives of algebraic statis- WepresentprojectsusedinFreshmenCalculusIandII tics and tropical geometry, starting with the observation courses that promote professional development at a very that its Zariski closure is a Hadamard power of the first early phase of undergraduate education. We focus on secant variety of the Segre variety of projective lines. We some that are based on designing a safe and thrilling roller derive a dimension formula for the tropicalized model, and coaster. Students integrate Mathematics and Physics in we use it to show that the restricted Boltzmann machine their analysis with a strong emphasis on technical com- is identifiable in many cases. Our methods include coding munication throughout. We discuss extensions to other theory and geometry of linear threshold functions. courses and our experiences in managing projects in large lecture sections with more than 100 students. MariaAngelicaCueto University of California, Berkeley Kathleen Fowler [email protected] Clarkson University Department of Mathematics Jason Morton [email protected] Pennsylvania State University [email protected] Joseph Skufca Clarkson University Bernd Sturmfels [email protected] University of California , Berkeley [email protected] MS65 Career Preparation of Undergraduate and Gradu- MS64 ate Students through an Interdisciplinary Consult- Semidefinite Representations for Orbitopes ing Approach

Orbitopes are highly symmetric convex bodies obtained by It is vital for Mathematicians and Statisticians to inter- taking the convex hull of an orbit of a compact group acting act eﬀectively with colleagues from other ﬁelds. We have linearly on a real vector space. For linear algebraic groups implemented a training approach through consulting with and rational representations, the orbit is a real variety and clients from application areas to provide our students with thus the orbitope can be approximated by projections of demonstrated experience of their skills in this area. On spectrahedra via Lasserre’s moment relaxation. We show the graduate level, we use a consulting center, and on the that the level at which the relaxation is exact can often undergraduate level, we have created an REU Site using be analysed based on simpler objects and in some case be the same philosophy. This talk will show both the ideas determined exactly by studying the geometry of certain as- and their implementation in more detail. sociated polytopes. We will discuss this method on several Matthias K. Gobbert AN10 Abstracts 79

University of Maryland, Baltimore County mixture theory. Department of Mathematics and Statistics [email protected] Mansoor A. Haider North Carolina State University Nagaraj Neerchal Department of Mathematics Department of Mathematics and Statistics m [email protected] University of Maryland, Baltimore County [email protected] MS66 A Multi-scale Model for Polymer-laden Flows Cou- MS65 pling Stochastic Particle Dynamics with Contin- Career Training Opportunities at the University of uum Fluid Mechanics Tennessee Polymer-laden flows exhibit complex rheology, especially Opportunities at the University of Tennessee and the Na- on length scales comparable to individual extended macro- tional Institute for Mathematical and Biological Synthesis molecules. Such flows occur in biological systems and in will be presented. Unique training programs through new microfluidic devices. To simulate these problems we have graduate fellowship grants will be discussed. Our REU and developed an efficient and stable kinetic method, which REV (research experiences for veterinary students) sum- couples constrained stochastic particle dynamics with an mer program and the institute postdoc program will be incompressible second-order accurate Navier-Stokes solver. highlighted. The algorithm is based Kramers’ bead-rod approximation of a polymer, with a reverse coupling approximated via Suzanne M. Lenhart a discrete (cloud-in-cell) delta function. The constrained University of Tennessee particle dynamics are expressed as a system of stochastic Department of Mathematics ODEs with explicit Lagrange multipliers, and discretized [email protected] with a second-order Ito-Taylor expansion. By itself, this particle method is second-order accurate in both strong and weak senses. To make the particle method stable with MS65 fluid CFL-limited time steps, we use a Duhamel formula- The Applied Mathematics & Statistics, and Scien- tion of the dynamics. The Navier-Stokes continuum solver tific Computation Program (AMSC) at the Uni- is based on a second-order projection method with the em- versity of Maryland: Interdisciplinary Research in bedded boundary technique to represent complex fluid do- a Flexible and Structured Environment mains.

Abstract unavailable at time of publication. Bakytzhan Kallemov Departments of Applied Science Konstantina Trivisa University of California, Davis University of Maryland [email protected] Department of Mathematics [email protected] David Trebotich Lawrence Berkeley National Laboratory [email protected] MS66 Interaction of Elastic Biological Structures with Greg Miller Complex Fluids University of California Often, biological fluids are non-Newtonian and exhibit vis- Department of Applied Science coelastic responses. We will present recent progress on [email protected] the development of computational models of pumping and swimming in a viscoelastic fluid. An immersed boundary MS66 framework is used, with the complex fluid represented by a continuum Oldroyd-B model. Multiphase Mixture Modeling of Microbial Biofilms Lisa Fauci Tulane University Much of the earth’s microbial biomass resides in sessile, [email protected] spatially structured biofilms consisting of large numbers of single celled organisms living within self-secreted biologically and chemically active viscoelastic matrices made MS66 of polymers and other molecules, with important conse- Mechano-Chemical Models of Ionic Effects in the quences to both form and function. Here we present a mul- Cellular Microenvironment of Articular Cartilage tiphase mixture model including physical (e.g. mechanics), chemical (e.g. mineral precipitation), and biological (e.g. Articular cartilage extracellular matrix (ECM) is com- growth) components, and discuss implications. prised of collagen fibers and proteoglycan macromolecules. Proteoglycans have a net negative charge, giving rise to Isaac Klapper a fixed charge density that couples with ions dissolved in Montana State Univ. the interstitial fluid to alter tissue mechanical properties Department of Mathematical Sciences with fluid osmolarity. In this talk, I will present mod- [email protected] els for quantifying the contribution of fixed charge density to ECM stiffness in the microenviroment of cartilage cells Tianyu Zhang based on the use of triphasic (fluid-solid-ion) continuum Mathematics Montana State University 80 AN10 Abstracts

[email protected] MS67 Efficient, Energy-stable and Convergent Finite Dif- ference Schemes for the Phase-field Crystal and MS67 Modified Phase-field Crystal Equations Exploiting Group Theory in Spectral Methods for PDEs We present unconditionally energy stable finite difference schemes for the phase-field crystal (PFC) and modified By exploiting symmetry, the cost of two-dimensional inter- phase-field crystal (MPFC) equations. The methods are polation and/or summation by Legendre polynomials can based on a convex splitting of a discrete energy and are be reduced by a factor of 3/2 (for large N) compared to semi-implicit. The equation at the implicit level is nonlin- transforms that exploit only the double parity symmetry ear but represents the gradient of a strictly convex function of the square. In three dimensions, the savings is a factor and is uniquely solveable regardless of the time step size. of 18/5. These group-theory based tricks are valuable in By controlling the energy, the stability of the scheme is high order spectral elements. We also explain how group guaranteed and local-in-time error estimates can be used symmetry can be exploited in collocation discretizations of to prove convergence of the schemes. We solve the nonlin- PDEs when only the domain has symmetry. ear equations at the implicit time level using an efficient nonlinear multigrid. Numerical simulations are presented John P. Boyd that confirm the stability, efficiency and accuracy of the University of Michigan schemes. Ann Arbor, MI 48109-2143 USAUSA [email protected] John Lowengrub Department of Mathematics University of California at Irvine MS67 [email protected] Automatic Fréchet Differentiation for the Spectral Solution of Boundary-value Problems MS68 To solve a nonlinear BVP, a Newton iteration solves for cor- Convex Relaxation for the Planted Cluster Prob- rections obtained through a Fréchet derivative, analogous lem to a Jacobian matrix. Automatic differentiation techniques are applied to compute the Fréchet derivative from a coded It is well-known that the problem of finding the maximum expression in the chebfun software system, a Matlab pack- set of vertices comprised of k disjoint cliques of a graph, age that represents functions and operators using Cheby- called a k-clique subgraph, is NP-hard. This problem can shev expansions and collocation. Thus, one can solve BVPs be formulated as a semidefinite program subject to a rank with automatic spectral methods, requiring only natural constraint. In the special case that the input contains a expressions of the equation and boundary conditions. single large k-clique subgraph obscured by diversionary edges and nodes, this hidden structure can be recovered Tobin Driscoll efficiently by solving the convex optimization problem ob- University of Delaware tained by relaxing rank with the nuclear norm. We provide Mathematical Sciences two analyses when our algorithm succeeds. In the first, the [email protected] diversionary edges are placed by an adversary. In the second, they are placed at random. MS67 Brendan Ames Polynomial Chaos Methods for Differential Equa- University of Waterloo tions with Singular Sources [email protected] Singular sources represented by the Dirac δ-function in differential equations play a crucial role in determining the MS68 global solution. Physical parameters associated with the δ- Guranteed Rank Minimization with Singular Value function are highly sensitive to measurement errors. Poly- Projection nomial chaos methods are used for the uncertainty analysis with uncertainties in location and strength of the δ- Minimizing the rank of a matrix subject to affine con- function for steady and time-dependent PDEs. The direct straints is a fundamental problem with many important collocation projection method is also used to deal with the applications in machine learning and statistics. In this Gibbs phenomenon. talk we present a simple and fast algorithm SVP (Singular Value Projection) for rank minimization with affine con- Jae-Hun Jung straints (ARMP) and show that SVP recovers the mini- Department of Mathematics mum rank solution for affine constraints that satisfy the SUNY at Buffalo restricted isometry property (RIP). We show robustness of jaehun@buffalo.edu our method to noise and prove a geometric convergence rate even for noisy measurements. Our method is simple Yunfei Song to analyze and easier to implement in comparison to the SUNY Buffalo recent trace norm based methods of Recht, Fazel and Par- [email protected] illo and Lee and Bresler. We also improve the existing RIP recovery results and achieve exact recovery under strictly Dongin Xiu weaker assumptions on the RIP constants than previously Purdue known. [email protected] Raghu Meka University of Texas at Austin AN10 Abstracts 81

[email protected] Methods for Vlasov Equations

Prateek Jain We present arbitrary order time integration methods and Microsoft Research their application to the Vlasov equations within a semi- [email protected] Lagrangian framework. These integral deferred correction (IDC) methods solve an error equation to improve Strang splitting error beyond second order. We discuss benefits Inderjit S. Dhillon and limitations of higher order split time integrators ob- University of Texas at Austin tained with the IDC framework in a semi-Lagrangian set- [email protected] ting. Principles in this work can be extended to other operators suitable for splitting methods, such as Maxwell’s MS68 equations. On Reweighted Trace Minimization for Low-rank Maureen M. Morton, Andrew Christlieb Matrix Recovery Dept. of Mathematics Michigan State University The problem of recovering a low-rank matrix consistent [email protected], [email protected] with noisy linear measurements is a fundamental problem with applications in machine learning, statistics, and control. Reweighted trace minimization, which extends Jing-Mei Qiu and improves upon the popular nuclear norm heuristic, Mathematical and Computer Sciences has been used as an iterative heuristic for this problem. Colorado School of Mines We present theoretical guarantees for the reweighted trace [email protected] heuristic. We quantify its improvement over nuclear norm minimization by proving tighter bounds on the recovery MS69 error for low-rank matrices with noisy measurements. Our analysis is based on the Restricted Isometry Property Finite Element Methods for Regularized 13- (RIP). Along the way we also improve the existing RIP Moment-Equations recovery conditions for the nuclear norm heuristic, show- This talk discusses numerical methods for the linearized ing that recovery happens under a weaker assumption on regularized 13-moment equations (R13) based on finite el- the RIP constants. ements. The R13 equations have been derived from ki- Maryam Fazel netic gas theory to model non-equilibrium gas flows. In University of Washington linearized steady form these equations can be viewed as an Electrical Engineering extended version of the Stokes equation. We will present [email protected] analytical solutions for the flow past a sphere and investigate variational formulations to be used in a finite element discretization. The software package FEniCS allows us to MS68 experiment easily with different formulations. Title Not Available at Time of Publication Manuel Torrilhon, Kaspar Muller Abstract not available at time of publication. ETH Zurich [email protected], [email protected] Kim-Chuan Toh National University of Singapore Department of Mathematics MS70 [email protected] Wave Propagation in Random Polycrystals Abstract not available at time of publication. MS69 Roger Ghanem The Turbulent Cascade of Entropy in Kinetic Sim- University of Southern California ulations of Plasma Turbulence Aerospace and Mechanical Engineering and Civil Abstract not available at time of publication. Engineering [email protected] William Dorland University of Maryland Arash Noshadravan [email protected] University of Southern California [email protected]

MS69 Peta-scale Full Facility Linear Radiation Transport MS70 Calculations for Shielding Analysis. UQ for Fluid Mixing

Abstract not available at time of publication. New results are presented for several stochastic fluid mixing problems: turbulent Rayleigh-Taylor and Richtmyer Tom Evans Meshkov flows, primary breakup of a high speed jet and Oak Ridge National Laboratory fluid mixing for chemical processing. We present the fluctu- [email protected] ations associated with variation across an ensemble of spatially averaged quantities.In some cases, the experiments do not fully characterize the flow. In addition to obtaining MS69 experimental agreement (validation) with the simulations, High Order Split Integral Deferred Correction 82 AN10 Abstracts

we study the uncertainties associated with the actual ex- be non-compliant towards treatment. Specifically, we com- perimental data (UQ). pare a treatment program that targets the most problematic drinkers to a program that targets the most compliant Hyunkyung Lim individuals. SUNY at Stony Brook Dept of Applied Mathematics Tony Furtado [email protected] Rensselaer Polytechnic Institute [email protected] James G. Glimm Stony Brook University Elliott Rakestraw, Joe Santamarina Brookhaven National Laboratory Rensselaer Polytechnic Institute [email protected] or [email protected] Department of Mathematical Sciences [email protected], [email protected] MS70 Accelerated Optimal Bayesian Experimental De- MS71 sign for Nonlinear Problems Approximation of Detailed Hodgkin-Huxley-Type Neuronal Models by Exponential Integrate-and- The optimal selection of experimental conditions is essen- Fire Models tial to maximizing the value of data for both inference and prediction. We propose a general Bayesian framework Using current-voltage curves and spike metrics, optimal for optimal experimental design with nonlinear simulation- strategies are developed for finding the parameters in the based models. The formulation fully accounts for uncer- exponential integrate-and-fire point neuron model with tainty in model parameters, experimental conditions, and adaptation current that give the best approximation to observables. Straightforward evaluation of the objective the membrane potential and firing rate dynamics of a cor- function—which reflects expected information gain due to responding Hodgkin-Huxley-type model. The adaptation an experiment—is computationally intractable. Instead, current is modeled explicitly, but has a prescribed jump at the present construction relies on (i) polynomial chaos ex- each spike time. The results of computations using both pansions, which capture the dependence of observables on systems give excellent agreement. Bifurcations in both uncertain model parameters and design conditions; and (ii) models are compared. efficient stochastic optimization methods to maximize expected utility. We demonstrate these methods on stiff non- Dan Johnson linear chemical kinetic systems. Brown University tba Youssef M. Marzouk,XunHuan Massachusetts Institute of Technology [email protected], [email protected] MS71 A Comparative Examination of CUDA and OpenCL for a Gravitational Wave Source Mod- MS70 elling Application Uncertainty Quantification for Sparse Random PDEs As CPU clock speeds stall out around 3 GHz, multicore systems are used to increase performance. But they have limi- An approach for quantifying parametric uncertainty in a tations (power consumption, heat dissipation). By making stochastic model output is presented. It relies on point- use of GPU programming languages (OpenCL, CUDA), wise evaluations of the output response surface. If the one can harness the power of hardware already contained stochastic model output has a reasonably sparse represen- in a desktop system, and obtain over an order of magni- tation in the retained approximation basis, the method re- tude gains in performance. In my work I will apply these trieves the dominant modes of the solution approximation aforementioned programming techniques to illustrate their from a minimal number of evaluations. The methodology power in a Gravitational Wave Source Modelling Applica- is applied to the solution of a 8-D stochastic Shallow Water tion. problem and is shown to perform well. Justin McKennon Lionel Mathelin University of Massachusetts Dartmouth LIMSI - CNRS tba [email protected]

Kyle Gallivan MS71 Florida State University Nonlinear Waves and Delay in Modeling Spiking [email protected] Neurons Synaptic delay plays a key role in understanding neurolog- MS71 ical disorders including Alzheimer’s and Parkinson’s dis- Comparison of Treatment Approaches in Alcohol eases. In our work we model synaptic plasticity with delay Epidemiology equations. Specifically, we incorporate delay in a nonlinear wave equation to study conduction velocities and their de- This talk considers the spread of alcohol abuse through pendence on timing between neural spikes, and determine a social network model accounting for peer influence and phase and group velocities. We compare the computed innate characteristics. The efficacy of several treatment results with available experimental data. In addition, we approaches in reducing the prevalence of alcohol abuse is study interaction of two waves moving along an axon with considered in scenarios where the individuals may generally AN10 Abstracts 83

time overlap. Pacific Northwest National Laboratory [email protected], [email protected], Ann Motl, DeJurnett Prioleau, Natasha Wright [email protected], [email protected], University of St. Thomas [email protected] [email protected], [email protected], [email protected] MS72 Comparison of Several Computational Methods for MS72 Variable Subset Selection Adjoint Models in Sensitivity Analysis and Pre- dictability In this talk we report on an investigation of several computational methods for variable subset selection which is an Adjoint models are an important tool for sensitivity analy- important element for quantifying uncertainties in com- sis and targeting strategies in variational data assimilation. plex systems. The methods considered are: (1) correlation We will discuss the use of first- and second-order adjoint analysis using the method of Spearman, (2) the Morris models for sensitivity analysis and targeting strategies. A screening method, (3) a modified Delta test, (4) the ap- novel observation-targeting approach based on the second- proximate model method based on the multivariate adap- order adjoint (SOA) model, to account for quadratic er- tive regression splines, and (5) sum-of-trees methods. Our ror growth, will be presented. The performance and re- contributions in this study are modifications made to some liability of the SOA targeting strategy is compared with of these methods for enhanced robustness in variable se- more traditional strategies through experiments with a lection as well as a numerical study of the effectiveness of two-dimensional shallow-water model. these methods.

Humberto Godinez Charles Tong Los Alamos National Laboratory Lawrence Livermore National Laboratory [email protected] [email protected]

Dacian N. Daescu Portland State University MS73 Department of Mathematics and Statistics Reflected Waves in Nonlocally Coupled Neural [email protected] Networks Recent experimental results show that propagation of MS72 waves between two different regions in the visual part of Parameter Estimation in Stochastic Equations the brain lead to compression and sometimes reflection of That are Second-Order in Time the waves. The experimentalists suggest that this may be due to a change in the degree of inhibition. We show that Consider the following problems: 1. Given an undamped this is unlikely and that a better explanation is a change in harmonic oscillator driven by additive Gaussian white excitability. Analytic and numerical calculations back up noise, estimate oscillator’s frequency from the observations our assertion. of the oscillations; 2. Given an undamped wave equation driven by additive space-time white noise, estimate the Bard Ermentrout propagation speed from the observations of the solution. University of Pittsburgh It turns out that the the first (one-dimensional) problem Department of Mathematics is not necessarily easier to study than the second (infinite- [email protected] dimensional) problem. The objective of the talk is to describe the asymptotic properties of the maximum likeli- Julie Goulet hood estimator in both problems and to discuss various University of Pittsburgh generalizations. [email protected] Sergey Lototsky Department of Mathematics MS73 University of Southern California Generalized Sensitivity Functions for Delay Differ- [email protected] ential Equations Delay differential equations are useful to model various bi- MS72 ological processes in which there are hysteretic effects. A Uncertainty Quantification (uq) for Component- popular example is Hutchinson’s equation, also known as Level Power System Models the delay-logistic equation. We use this example to determine the effect of a delay on generalized sensitivity func- The goal of the paper is for uncertainty quantification (UQ) tions (which provide insight on sensitivity of estimated pa- of component level power system models, which can pro- rameters to data). We compare the numerical approxima- vide an error bar on component level modeling of power tions of the generalized sensitivity functions for the delay- systems. Procedures include: Identify the most sensitive logistic equation to the equation without delay. uncertain parameters; Represent these parameters with the given distributions; Generate probabilistic collocation Danielle Robbins points in the random parameter space; Perform simulations North Carolina State University for each realization (sampling point set); Post-process the [email protected] outputs and obtain the statistical results of the outputs. Shuai Lu, Guang Lin, Marcelo Elizondo, Ning Zhou, Larry Chilton 84 AN10 Abstracts

MS73 work alignment solvers, a sparse variant of the problem, Mathematical Approach to Modeling the Effects and a new algorithm based on a message passing or be- ofOceanAcidificationOnthePteropodandPink lief propagation heuristic. This algorithm is fast – run- Salmon Population ning in minutes on graphs with over 1000000 edges. Our codes are available online: http://www.stanford.edu/ dgle- Ocean acidification is an extension of increased atmo- ich/publications/2009/netalign/index.html. spheric CO2 content. One species greatly affected by ocean acidification are euthecosomatous pteropods, which may David F. Gleich suffer shell and skeleton deterioration and growth delay. Sandia National Labs Furthermore, the pink salmon population in the North Pa- [email protected] cific, targeted by commercial fisheries, have been known to prey heavily on pteropods. A discrete stage-structured model is developed to model the dynamics of this interac- MS74 tion in the wake of ocean acidification. Predictive Modeling for Relational and Network Domains Kehinde Salau Arizona State University Recently there has been a surge of interest in methods [email protected] for analyzing complex social networks (e.g., communication and friendship networks). For predictive modeling, the dependencies among linked entities in the networks MS73 present an opportunity to improve inference about proper- Data Assimilation Study using a Simple ties of individuals. This presentation will outline the char- Atmosphere-Ocean Model acteristics of network data that differentiate it from the traditional settings for inference and learning, and discuss The coupled ocean-atmosphere system has instabilities specific techniques for incorporating relational information that span time scales from a few minutes to years. It is into statistical models and algorithms. not clear whether data assimilation focused on long-term variability should include the smaller time scales, since the Jennifer Neville faster scales distort the slower longer time-scale solution. Computer Science Department To study this problem, we employ two data assimilation Purdue University schemes onto a simple nonlinear chaotic model of fast and [email protected] slow versions of the Lorenz (1963) model with different strengths of coupling. MS74 Tamara Singleton-Goyea Clustered Embedding of Massive Online Social University of Maryland, College Park Networks [email protected] In this talk we will describe a novel technique called clustered spectral graph embedding, to capture fundamental MS74 structure in social network graphs. The proposed proce- Application of Datamining in Analyzing Large- dure is an effective and highly scalable tool for various Scale Network Evolution tasks in computational analysis of social networks. We will demonstrate our approach to (1) approximate prox- Analysis of large-scale networks, such as social and biolog- imity measures and (2) predict new friendship links using ical systems, is extensively used to understand their char- three very large real-world social network data sets: Flickr, acteristics and temporal evolution. However, most analy- Live-Journal and MySpace. sis algorithms do not take into account the properties of the underlying applications. In this talk we will discuss Berkant Savas how data mining can be used to classify networks based on University of Texas at Austin their properties and use this information to predict whether [email protected] there will be significant modifications to the community structure, under addition or deletion of certain edges. Han Hee Song, Tae Won Cho, Vacha Dave, Zhengdong Lu The University of Texas at Austin Sanjukta Bhomick [email protected], [email protected], Department of Computer Science [email protected], [email protected] University of Nebraska at Omaha [email protected] Inderjit S. Dhillon University of Texas at Austin Prashant Paymal [email protected] University of Nebraska at Omaha [email protected] Yin Zhang, Lili Qiu The University of Texas at Austin MS74 [email protected], [email protected] Large, Sparse Network Alignment Problems and a New Algorithm MS75 Network alignment is a standard problem in data mining A Cartesian Grid Method For Two-phase Gel Dy- and bioinformatics. We begin by comparing a network namics on an Irregular Domain from Wikipedia with one from the Library of Congress. We develop a numerical method for simulating models of We describe a unified mathematical framework for net- two-phase gel dynamics in an irregular domain using a reg- AN10 Abstracts 85

ular Cartesian grid. Multigrid with Vanka-type box relax- MS75 ation scheme is used as preconditioner for the Krylov sub- A Forcing Method for Simulations of Chemical space solver to solve the momentum and incompressibility Transport in Blood Flow equations. Ghost points are used to enforce the boundary conditions. The behavior of the new method is explored The activated platelets in blood ﬂow play a very important through numerical experiments for a problem with strong roles in blood clotting since they are at the central stage of phase separations. the processes of aggregation and coagulation. To study the eﬀect of chemical reactions on the surface of platelets for Jian Du clotting, we use direct forcing formulation to treat the ir- Department of Mathematics regular and moving surfaces with Cartesian grid discretiza- University of Utah tion of the computational domain. Both implicit and ex- [email protected] plicit form of the method will be showed for our problem.

Aaron L. Fogelson University of Utah Lingxing Yao [email protected] Utah University [email protected]

MS75 Aaron L. Fogelson Computation of Porous Media Flows using Octree University of Utah Adaptive Mesh Refinement [email protected] In this talk I will describe a novel approach for the simulation of two-phase flows in porous medium. This approach MS76 makes use a a newly devised framework for solving partial Nonnegative Polynomials and Sums of Squares differential equations on Octree adaptive grids. A hallmark of this approach is that non graded adaptive grids Sums of Squares (SOS) relaxations are often used as a sub- can be used and boundary conditions are imposed implic- stitute for testing whether a polynomial is non-negative. itly, which avoids the difficulties associated with remeshing. Testing whether a polynomial is SOS is a Semi-definite Examples of such simulations will be presented. Programming problem and thus computationally tractable. We use techniques from convex geometry to study the re- Frederic G. Gibou lationship between sums of squares and non-negative poly- UC Santa Barbara nomials. We will present results about the boundary struc- [email protected] ture and quantitative relationship between SOS and nonnegative polynomials, which allow us to understand the Emmanuel Brun quality of SOS relaxations. UCSB [email protected] Greg Blekherman Virginia Tech [email protected] MS75 Simulating Biochemical Signaling Networks in Complex Moving Geometries MS76 Discriminants and Nonnegative Polynomials

Signaling networks regulate cellular responses to environ- n mental stimuli through cascades of protein interactions. For a semialgebraic set K in R ,letPd(K)={f ∈ R[x]≤d : f(u) ≥ 0 ∀ u ∈ K} be the cone of polynomials in External signals can trigger cells to polarize and move in n a specific direction and maintain spatially localized activ- x ∈ R of degrees at most d that are nonnegative on K. This paper studies the geometry of its boundary Pd(K). ity of proteins. To investigate the effects of morphological n changes on intracellular signaling, we present a numerical When K = R and d is even, we show that its boundary Pd(K) lies on the irreducible hypersurface defined by the scheme consisting of a cut cell finite volume discretization n coupled with level set methods. This method is then used discriminant Δ(f)off.WhenK = {x ∈ R : g1(x)= to simulate models of signaling networks in time-dependent ··· = gm(x)=0} is a real algebraic variety, we show that geometries. Pd(K) lies on the hypersurface defined by the discriminant Δ(f,g1,...,gm)off,g1,...,gm.WhenK is a gen- Wanda Strychalski eral semialgebraic set, we show that Pd(K) lies on a union Department of Mathematics of hypersurfaces defined by the discriminantal equations. University of California, Davis Explicit formulae for the degrees of these hypersurfaces [email protected] and discriminants are given. We also prove that typically Pd(K) does not have a barrier of type − log ϕ(f)when David Adalsteinsson ϕ(f) is required to be a polynomial, but such a barrier ex- Department of Mathematics its if ϕ(f) is allowed to be semialgebraic. Some illustrating University of North Carolina, Chapel Hill examples are shown. [email protected] Jiawang Nie University of California, San Diego Timothy Elston [email protected] University of North Carolina, Chapel Hill [email protected] MS76 Conic Representations for Positive Polynomials on 86 AN10 Abstracts

Equality-constraint Domains This talk will review what we have done.

We establish a simple connection between the set of polyno- Mark Holmes mials that are non-negative on a given domain and the set Rensselaer Polytechnic Institute of polynomials that are non-negative on the intersection [email protected] of the same domain and the zero of a given polynomial. This connection has interesting algorithmic implications. Gregor Kovacic For instance, it readily yields a succinct derivation of a Rensselaer Polytechnic Inst copositive programming formulation for quadratically con- Dept of Mathematical Sciences strained quadratic programs. [email protected] Javier Pena Carnegie Mellon University Peter R. Kramer [email protected] Rensselaer Polytechnic Institute Department of Mathematical Sciences [email protected] Juan Vera University of Waterloo [email protected] Fengyan Li Rensselaer Polytechnic Institute [email protected] Luis Zuluaga University of New Brunswick [email protected] MS77 Undergraduate Research Experiences in Computa- MS76 tional Mathematics The Convex Hull of a Parametrized Curve I will describe several initiatives being undertaken at Ari- zona State University. (1) Undergraduate research experi- Understanding and computing the facial structure of the ences under the auspices of the NSF Computational Science convex hull of a curve is generally a diﬃcult problem. It Training Program for Undergraduates in the Mathemati- becomes more tractable when the curve is parametrized by cal Sciences; (2) the Computational Mathematical Sciences polynomials. We describe a general method for comput- degree program; (3) curriculum development ideas at the ing the boundaries of convex hulls of parametrized curves advanced undergraduate level. or segments of such curves. We’ll give qualitative results in special cases, and we present many examples and pic- Eric J. Kostelich tures. Applications to spectrahedra, discrete geometry, Arizona State University and statistics will also be discussed. Department of Mathematics [email protected] Cynthia Vinzant University of California, Berkeley [email protected] MS77 Undergraduate CSE Programs in the U.S.

MS77 This talk will discuss the current state of Computaitonal Open Discussion Moderated by: Science programs in the US (and abroad) with reference to the updated SIAM Undergraduate CSE report. The new Abstract unavailable at time of publication. SIAM Undergraduate Research Online publication will also Matthias K. Gobbert be presented as a suitable outlet for publishing quality un- University of Maryland, Baltimore County dergraduate research in applied and computational math- Department of Mathematics and Statistics ematics. [email protected] Peter R. Turner Clarkson University Peter R. Turner School of Arts & Sciences Clarkson University [email protected] School of Arts & Sciences [email protected] MS78 Channel Flow Simulations of a Microstructural MS77 Model for Wormlike Micellar Solutions (‘Living Undergraduate and Graduate Training at the Polymers’) Rensselaer Polytechnic Institute The two-species VCM model is designed to capture the flow One of the challenges facing any applied mathematics pro- behavior of concentrated wormlike micellar solutions. The gram is to have students develop a strong mathematical constitutive equations, which include scission and reform- foundation as well as an understanding of the relevant ap- ing (and viscoelastic relaxation) along with conservation of plication areas. Our current approach includes close in- mass and momentum, form a coupled nonlinear system of tegration with researchers from multiple application dis- partial differential equations. Simulations of the model in ciplines, which includes lab work, involvement of our stu- a pressure-driven channel flow, using an adaptive spectral dents in significant mentoring and leadership roles, and collocation method, show that the velocity profile exhibits post-graduation involvement with our current students. a plug-like (shearbanding) flow. Stability of the steady- AN10 Abstracts 87

state solutions is examined. the principal components of a data matrix even though a positive fraction of its entries are arbitrarily corrupted. Pamela Cook We present applications in the area of video surveillance, Dept of Mathematical Sciences where our methodology allows for the detection of objects UofDelaware in a cluttered background. [email protected] Emmanuel Candes Michael Cromer Stanford University University of Delaware Departments of Mathematics and of Statistics [email protected] [email protected]

Gareth McKinley MS79 Dept of Mechanical Engineering Massachusetts Institute of Technology Mathematical Sensing , Dennis Healy’s Vision [email protected] Throughout Healy’s work before and during his Darpa years, we see sensing with coded waveforms as a tool for MS78 conversion of physical analog inputs into information. We will describe his visionary approaches to signal processing Title Not Available at Time of Publication on the hardware , designed to achieve both efficiency in re- Abstract unavailable at time of publication. sources and higher information ratios , these include coded methodologies both passive and active for signal acquisi- M. G. Forest tion and processing. UNC [email protected] Ronald Coifman Yale University Department of Computer Science MS78 [email protected] Kinetic-molecular Interaction Computation of Long-chain Polymer MS79 Abstract unavailable at time of publication. Deconvolution using Geometrically-based Repre- sentations Sorin M. Mitran Dept. of Mathematics, Applied Math Prog. We propose deconvolution techniques based on transform- University of North Carolina ing the data into geometrically-based representations such [email protected] as the curvelet and shearlet representations. The representation implementations are designed to handle any assumed boundary conditions for the associated matrix in- MS78 version problem. Unique to these approaches is the ability A New Phase-Field Model for Incompressible Two- to adaptively solve matrix inversion problems to estimate Phase Flows with Large Density Ratios the coefficients of the representations by taking advantage of the different conditioning of the problems. We present a new phase-field model for the incompressible two-phase flows with variable density which admits Glenn Easley an energy law. We also construct weakly coupled time dis- Systems Planning Corporation cretization schemes that are energy stable. Efficient numer- [email protected] ical implementations of these schemes are also presented. The model and the corresponding numerical schemes are particularly suited for incompressible flows with large den- MS79 sity ratios. Ample numerical experiments are carried out Recent Advances in Computational Electromag- to validate the correctness of these schemes and their ac- netics for Metamaterials curacy. Metamaterial design will require rapid forward modeling Jie Shen of Maxwell’s equations in complex microstructured mate- Department of Mathematics rials. We will describe a new fast solver for this purpose Purdue University that combines multiple scattering theory, high-order ac- [email protected] curate integral equation discretizations and fast multipole acceleration.

MS79 Leslie Greengard, Zydrunas Gimbutas Robust Principal Component Analysis? Courant Institute New York University This is about a curious phenomenon. Suppose we have [email protected], a data matrix, which is the superposition of a low-rank [email protected] component and a sparse component. Can we recover each component individually? We show that under mild conditions, it is possible to recover both the low-rank and the MS80 sparse components exactly by solving a very convenient A Machine Learning Approach to Intrusion Detec- convex program. This suggests the possibility of a princi- pled approach to robust principal component analysis since our methodology and results assert that one can recover 88 AN10 Abstracts

tion for High Performance Computing N-fold 4-block Decomposable Integer Programs

Abstract not available at time of publication. In this talk we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4- Juan C. Meza, David H. Bailey block decomposable integer programs. We show that for Lawrence Berkeley National Laboratory fixed blocks but variable N, these integer programs are [email protected], [email protected] polynomial-time solvable for any linear objective. More- over, we present a polynomial-time computable optimality certificate for the case of fixed blocks, variable N and any MS80 convex separable objective function. We conclude with two Compressively Sensed Complex Networks sample applications. We present a method, based on compressive sensing, to Raymond Hemmecke construct lossy compressions of complex networks. The Dept. of Mathematics method is based on the assumption that the adjacency ma- Technische Univ. Munchen Germany trix of the undirected complex graph can be represented [email protected] compactly in some wavelet basis. We sample the adjacency matrix and reconstruct the original graph using a Matthias Köppe Staggered Orthogonal Matching Pursuit algorithm. We Dept. of Mathematics explore whether the compressed form of the graph can be University of California, Davis, USA used for comparison purposes. [email protected] Ray Jaideep Sandia National Laboratories Robert Weismantel [email protected] University of Magdeburg, Germany [email protected] Ali Pinar Sandia National Labs MS81 [email protected] On Algorithms Based on Cutting Plane Trees for General Mixed-integer Linear Programs MS80 Recently, we gave a finite disjunctive programming proce- Cyber-Physical Trade-offs for Distributed Detec- dure to obtain the solution of general mixed-integer linear tion Networks programs with bounded integer variables, which we refer We consider a mathematical formulation of a generic de- to as the cutting plane tree (CPT) algorithm (Chen et al, tection problem using a network of sensors that measure 2009). In this talk, we propose decomposition schemes to intensity levels due to a source, whose intensity decays solve the cut generation problem arising in CPT effectively. away from the source possibly in discrete jumps, and sensor We summarize our computational experience with the pro- measurements are random due to the nature of source and posed algorithms. background. Under very general smooth and non-smooth Simge Kucukyavuz conditions on source intensity functions and measurement Dept of Integrated Systems Engineering distributions, we mathematically prove that better detec- Ohio State Univ. tion probability, compared to a single or co-located sensors, [email protected] at any given false alarm probability can be achieved by: (i) spreading out sensors across the network, and (ii) utilizing measurements at the fusion center. Binyuan Chen Systems and Industrial Eng Nageswara Rao University of Arizona Oak Ridge National Laboratory [email protected] [email protected] Suvrajeet Sen David Yau, Jren-Chit Chin, Chris Ma Integrated Systems Eng Purdue University Ohio State Univ [email protected], [email protected], [email protected] [email protected] MS81 MS80 Local Search vs. LP for Matroid Matching Scalable, Parallel Stochastic Decomposition Algo- rithms for Risk Mitigation in Critical Infrastruc- We consider the classical matroid matching problem. Un- ture Applications weighted matroid matching for linear matroids was solved by Lovász, and the problem is known to be intractable Abstract not available at time of publication. for general matroids. We present a PTAS for unweighted matroid matching for general matroids. In contrast, we Jean Paul Watson show that natural LP relaxations that have been studied Sandia National Laboratories have an Ω(n) integrality gap and moreover, Ω(n) rounds [email protected] of the Sherali-Adams hierarchy are necessary to bring the gap down to a constant. More generally, for any fixed k ≥ 2and>0, we obtain a (k/2+)-approximation for MS81 matroid matching in k-uniform hypergraphs, also known A Polynomial Time Algorithm for Optimizing over as the matroid k-parity problem. As a consequence, we AN10 Abstracts 89

obtain a (k/2+)-approximation for the problem of find- MS82 ing the maximum-cardinality set in the intersection of k C0 Penalty Methods for the Fully Nonlinear matroids. We also design a 3/2-approximation for the Monge-Ampere Equation weighted version of a known special case of matroid matching, the matchoid problem. In this talk, we develop and analyze C0 penalty methods for the fully nonlinear Monge-Ampere equation Jon Lee, Maxim Sviridenko det(D2u)=f in two dimensions. The key idea in design- IBM T.J. Watson Research Center ing our methods is to build discretizations such that the [email protected], [email protected] resulting discrete linearizations are symmetric, stable, and consistent with the continuous linearization. We are then Jan Vondrak able to show the well-posedness of the penalty method as IBM Almaden Research Center well as quasi-optimal error estimates. Finally, we present [email protected] some numerical experiments which support the theoretical results and discuss extensions to the three dimensional case as well as more general Monge-Ampere type equations. MS81 Solving Symmetric Integer Programs Michael J. Neilan Louisiana State University We will discuss mechanisms for dealing with integer pro- Mathematics and Center for Computation and grams that contain a great deal of symmetry. The meth- Technology ods use information encoded in the symmetry group of [email protected] the integer program to guide the branching decision and prune nodes of the search tree. Computational results will demonstrate the great improvements in solution time ob- MS82 tainable when symmetry is exploited. Convergent and Efficient Numerical Schemes for the Elliptic Monge Ampere Equation even in the Jeff Linderoth Singular Case Dept. of Industrial and Sys. Eng. University of Wisconsin, Madison The Monge-Ampere equation is challenging to solve nu- [email protected] merically for the following reasons: 1. Singularites: If the source function f is not strictly positive, then solutions need Francois Margot twice differentiable. Weak (geometric) solutions allow even Carnegie Mellon University for f to be Dirac measure, which leads to solutions with Tepper School of Business corners. 2. The convexity constraint: the solution must [email protected] be convex in order for the equation to be elliptic. With- out the convexity constraint, this equation does not have Jim Ostrowski a unique solution. In the singular case, many things break Dept. of Mgmt. Sciences down: regularity, uniqueness, ellipticity of the equation. University of Waterloo Correspondingly, from a numerical point of view, most so- [email protected] lutions methods which rely on ellipticity become slow near singular solutions. In this talk we present and study the performance of three methods. The baseline method is Fabrizio Rossi, Stefano Smriglio provably convergent to the viscosity solution of the equa- Dipartimento di Informatica tion. For better performance, we study two other methods. Universita di L’Aquila The first method, which is simply the natural finite differ- [email protected], [email protected] ence discretization of the equation, is more accurate, and the time to solve is independent of the regularity of the MS82 equation. The second method is faster in the non-singular case, but becomes very slow in the singular case. It also Phase Field Methods for Strongly Anisotropic Sys- provided a model for generic methods which involve the tems solution of linear elliptic systems.

We study the influence of surface and strain energies on Adam Oberman heteroepitaxial thin-film growth. We propose an alternate Simon Fraser University way of simulating anisotropy for the surface energy by us- Dept. of Mathematics ing the higher order terms in the free energy. To the second [email protected] order, the system only have isotropic properties. We can produce different anisotropy by adding higher order terms to the energy. By choosing the right parameters, we can MS82 study the behavior SiGe/Si thin film. This type of ex- Unconditional Stable Numerical Schemes for Phase tended Cahn-Hilliard model has been previously studied Field Crystal (PFC) Equations to the 4th order, but to our knowledge no one has ever implemented all the terms in this system. One advantage Highly efficient, unconditionally energy stable and uniquely of this energy is that it has the intrinsic regularization. solvable finite difference schemes for the Phase Field Crys- We present numerical results using an adaptive, nonlinear tal (PFC) equation, a nonlinear sixth order parabolic equa- multigrid finite-difference method. tion, are presented in the talk. A convex splitting of the corresponding physical energy is utilized. As a result, a John Lowengrub combination of an implicit treatment for the convex part Department of Mathematics and an explicit treatment for the concave part leads to a University of California at Irvine numerical scheme with a non-increasing energy. Both the [email protected] first and second order splittings in time, both the centered 90 AN10 Abstracts

difference and the fourth order long stencil difference spa- answer to this question can be tackled by analyzing the tial approximations, are analyzed and proven to be uncon- uncertainty in the problem. Both Bayesian and Frequentist ditionally stable. In turn, a local in time numerical conver- approaches can be used. We show that while the statistical gence can be derived. These ideas can be applied to other interpretation of each approach is different they lead to a models of gradient systems, such as Cahn-Hilliard equa- rather similar mathematical treatment. We then discuss tions, a modified PFC model, epitaxial thin film growth the solution of the design problem and show that better models, etc. Some numerical simulation results are also solutions can be obtained by using appropriate design presented in the talk. Eldad Haber Cheng Wang Department of Mathematics University of Massachusetts The University of British Columbia Dartmouth, MA [email protected] [email protected] Luis Tenorio Colorado School of Mines MS83 [email protected] Data-free Inference of the Joint Distribution of Un- certain Model Parameters MS83 While the correlation structure in the joint distribution The Effects of Data Assimilation on Uncertainty of model parameters is critical to uncertainty analysis of Propagation the model, very often studies in the literature only report nominal values (and usually confidence intervals) for pa- The performance of popular uncertainty propagation rameters inferred from data, but no details on the corre- schemes, including Monte Carlo methods, polynomial lation or full joint distribution of these parameters. We chaos, stochastic collocation, and sensitivity based meth- demonstrate, using a Bayesian inference procedure, how to ods are analyzed and assessed in a setting that is down- construct a posterior density for the parameters exhibiting stream of data assimilation. We devise a test problem self-consistent correlations, in the absence of data. where the source of uncertainty is generated by a process that is blinded from the uncertainty quantification process. Robert Berry Standard statistical method is performed to quantify the Sandia National Laboratories source of uncertainty, which is then propagated using vari- [email protected] ous methods to the output quantity of interest. The methods for propagating uncertainty is assessed by comparing Habib N. Najm againt the true distribution of the quantity of interest, com- Sandia National Laboratories puted with knowledge of the process generating the source Livermore, CA, USA of uncertainty. [email protected] Qiqi Wang Massachusetts Institute of Technology MS83 [email protected] Uncertainty Quantification in Inverse Problems for Subsurface Flows Paul Constantine Sandia National Labs In this talk, I will discuss uncertainty quantification in in- [email protected] verse problems with applications to subsurface flows. The inverse problem is set in Bayesian framework. The posterior probability distribution is complicated and involves MS84 solving systems of very large nonlinear PDEs. In this talk, Numerical Approximations of Stochastic Elliptic I will focus on identifying permeability features such as Models facies and distribution within facies given integrated response, such as cumulative oil production. I will discuss The stochastic elliptic Model (I): −∇·(a(x,ω)∇u(x,ω)) = sparse representations for the prior and efficient sampling f(x) is widely used in engineering applications, where techniques using multiscale models and hybrid techniques. a(x,ω) is a positive random process, such as log-normal This is a joint work with Anirban Mondal, Jia Wei, Bani process. Another stochastic elliptic Model (II): −∇ · Mallick and A. Datta-Gupta. (a(x,ω) ∇u(x,ω)) = f(x) has also been widely studied, but mainly from the mathematical point of view, where Yalchin Efendiev indicates the Wick product. We will show that Models (I) Dept of Mathematics and (II) are in general not comparable. We then present Texas A&M University a new stochastic elliptic model, which is also based on the [email protected] Wick product, to establish the comparability with Model (I). Numerical results will be shown and related numerical MS83 issues will be discussed. Reducing Uncertainty in Inverse Problems by De- Xiaoliang Wan sign Louisiana State University [email protected] Inverse problems are inertially ill posed and therefore no unique solution exists to the data fitting problem. One can use the wealth of regularization methods in order to MS84 obtain a unique solution. The question arise, how can we Scattering of Shock Waves by Random Roughness: get better solutions to the problem? We shoe that the AN10 Abstracts 91

Effects of Correlation Length MS86 Ion Concentration Dynamics: a Novel Mechanism The oblique shock problem is a fundamental problem in for Bursting and Seizing high-speed aerodynamics and has been studied extensively. Instead of assuming smoothness, we take into account ran- We develop a conductance-based model neuron that in- dom roughness on the wedge surface to investigate the pres- cludes intra- and extra-cellular ion concentration dynam- sure distribution on the wedge. The roughness (of length ics. We further formulate a reduction of this model to d) starting at the wedge apex is modeled as stochastic identify the bifurcation structure. Using these models, we process with zero mean and correlation length A.Both describe a novel mechanism for bursting and seizing that multi-element probabilistic collocation method (ME-PCM) results in behavior that is strikingly similar to that seen in on sparse grid and analysis of variance method (ANOVA) experiments. are employed to solve the stochastic Euler equations while a WENO scheme is used to discretize the equations in E. Barreto two spatial dimensions. The results by different meth- George Mason University ods are compared with the analytical solution obtained by [email protected] the second-order stochastic perturbation analysis for small roughness height. We present the effects of different roughness length as well as different correlation length on the lift MS86 and drag forces on the wedge beyond the rough region. We Estimating the Directed Information to Infer also compare the accuracy and computational complexity Causal Relationships in Ensemble Neural Spike of ME-PCM and ANOVA for different number of random Train Recordings dimensions in the representation of the random roughness. Neuroscientists now often record many brain signals simultaneously. This provides potential to understand dy- Xiu Yang namic, complex, causal relationships in the brain. Here, Brown University we present a probably-good technique to estimate the di- xiu [email protected] rected information – an information-theoretic measure of causality philosophically wed to Granger causality. This Guang Lin is tested synthetically and correctly identifies all pairwise Pacific Northwest National Laboratory relationships. In ensemble M1 spike train recordings of an [email protected] awake monkey, it identifies relationships consistent with wave propagation of simultaneously recorded local field po- Minseok Choi, George Karniadakis tentials. Brown University Todd Coleman minseok [email protected], [email protected] University of Illinois [email protected] MS85 Title Not Available at Time of Publication MS86 Abstract not available at time of publication. Serotonin Chemistry and Neural Firing Patterns Ansu Bagchi Serotonin is a neurotransmitter that is thought to play an Merck & Co., Inc. important role in mood, in eating behavior, in aggression Ansuman [email protected] and risk-taking, and in obsessive-compulsive disorder. A mathematical model for serotonin synthesis, release, and reuptake, is being used to understand the connections be- MS85 tween serotonin metabolism and neural firing patterns. Modeling the Effect of an Enzymatic Inhibitor on One goal of the project is to understand the mechanisms Amyloid Beta Dynamics: The Role of Amyloid of action of selective serotonin uptake inhibitors. These Clearance mechanisms remain elusive despite years of experimental research. Abstract not available at time of publication. Janet Best Raibatak Das The Ohio State University University of British Columbia Department of Mathematics Department of Mathematics [email protected] [email protected] Michael Reed Duke University MS85 [email protected] An Analytic, Time-Dependent Model of a Product Development Pipeline H. F. Nijhout TBA Abstract not available at time of publication. [email protected] Jeffrey Saltzman Merck Research Laboratories MS87 jeffrey [email protected] Multidimensional HLLE Riemann Solver; Applica- 92 AN10 Abstracts

tion to Euler and Magnetohydrodynamic Flows ﬂows.

In this work we present a general strategy for constructing Gretar Tryggvason multidimensional HLLE Riemann solvers. This is accom- Mechanical Engineering Department plished by introducing a constant resolved state between Worcester Polytechnic Institute the states being considered, which introduces sufficient dis- [email protected] sipation for systems of conservation laws. Closed form expressions for the resolved fluxes are also provided to facilitate numerical implementation. The Riemann solver MS88 is proved to be positively conservative for the density A Prototyping Effort variable; the positivity of the pressure variable has been in Developing an Engineering-Scale Nuclear Fuel demonstrated for Euler flows when the divergence in the Performance Code fluid velocities is suitably restricted so as to prevent the formation of cavitation in the flow. We also focus on the Nuclear fuel undergoes substantial changes throughout construction of multidimensionally upwinded electric fields nominal and transient operation as uranium fissions into for divergence-free magnetohydrodynamical (MHD) flows. new isotopes and the materials change due to macro- and micro-structural and chemical changes. This complex problem has historically leveraged one-dimensional approx- Dinshaw Balsara imations with empirical data for well- characterized fuels. NotreDameUniversity This talk will explore the numerical and computational Physics Department challenges associated with the development of a prototype [email protected] code, AMP, which will be used to evaluate the physics- based requirements of a future predictive code. MS87 Kevin Clarno Fast and Accurate Simulations of Proto-Planet Mi- Oak Ridge National Laboratory grationinDisks [email protected] In this talk, we present a fast and accurate numerical method for simulations of interaction between the proto- MS88 planetary disk and embedded proto-planets. Our hydro Overview of the Nuclear Energy Advanced Mod- algorithm is at least an order of magnitude faster than eling and Simulation Waste Forms Integrated Per- other standard solvers. Our self-gravity solver costs less formance and Safety Codes Program than 10% of the total computation cost. An embedded Lagrangian adaptive mesh refinement speeds up our com- The Nuclear Energy Advanced Modeling and Simulation putation by another order of magnitude. (NEAMS) Waste Forms (WF) Integrated Performance and Safety Codes (IPSC) is a new, long-term program respon- Shengtai Li sible for providing an integrated suite of Thermal, Hy- Los Alamos National Lab. drological, Chemical, and Mechanical (THCM) computa- [email protected] tional modeling and simulation capabilities for predicting the performance of nuclear waste forms within storage or disposal repository environments. These capabilities will MS87 be used for predictive simulation-based, risk-informed de- Hierarchical Reconstruction With Only Quadratic cision making about managing future US nuclear waste. Remainder For Computing Non-smooth Solutions Carter Edwards In this talk I will briefly introduce the hierachical recon- Sandia National Laboratory struction (HR) useful for discontinuous Galerkin method [email protected] (DG), central DG, central and finite volume schemes on regularorirregularmeshes.Inparticular, A recently de- G. Freeze, J. Arguello, R. Bartlett, P. Schultz, Y. Wang veloped technique allows the use of only quadratic remain- Sandia National Laboratories der in HR without hurting formal order of accuracy, which [email protected], [email protected], further improves the quality of numerical solutions for the [email protected], [email protected], 4th and 5th order cases. [email protected] Yingjie Liu School of Mathematics, Georgia Inst of Tech MS88 [email protected] On Computational Frameworks for Multi-Physics Nuclear Reactor Simulation

MS87 Assembling a multi-physics reactor core simulation code Simulations of Complex Flows using a Front Track- requires a computational framework which can handle ing Method both legacy and more recent physics modeling components. These simulations must support execution at both ends of Numerical methods for multiphase flows have now made it the performance spectrum, to allow both high-fidelity sim- possible to study in considerable detail the flow of hundreds ulations (for the purpose of validation), and faster-running of bubbles, drops, and solid particles. For more complex simulations informed by those higher-fidelity models, for flows, such as those including phase change, mass transfer use in design studies. In this talk we will describe the and chemical reactions, it is necessary to solve for addi- SHARP framework, which is being designed to meet these tional physics that introduces new length and time-scales. requirements. Here, we discuss the extension of a front-tracking method for flows with sharp interfaces to deal with various complex Tim Tautges AN10 Abstracts 93

Argonne National Laboratory MS89 [email protected] A Two-grid Discontinuous Galerkin Method for Quasi Linear Elliptic Problems J. Kraftcheck University of Wisconsin We propose a two-grid discretization technique for the [email protected] SIPG method for a class of quasi-linear elliptic problems. With the proposed technique, solving a quasi-linear elliptic A. Caceres problem on the fine space is reduced into solving a linear Argonne National Laboratory problem on the fine space and solving the quasi-linear el- [email protected] liptic problem on a much coarser space. A convergence estimate is derived to justify the efficiency of the proposed algorithm. MS88 Victor E. Ginting Phase Field Simulations of Irradiation-Induced Mi- Department of Mathematics crostructure Evolution University of Wyoming The evolution of irradiation-induced defects such as voids [email protected] and fission gas bubbles in nuclear fuel and structural alloys is critically important to the performance of fission reac- MS89 tors. Here, defect evolution in irradiated microstructure is modeled using a phase-field technique solved with a par- A New Mixed Method for the Reissner-Mindlin allel finite element method. Multiple point defect species Plate Model are randomly generated in space and time to represent col- The Reissner-Mindlin plate problem is written as a system lision cascade events and the effect of grain boundaries as of first order equations and all the resulting variables are well as stress gradients are also considered. approximated. A hybrid form of the method is presented Michael Tonks, P. Millett which allows one to eliminate all the variables locally and Idaho National Laboratory have a final system only involving the Lagrange multipliers [email protected], [email protected] which approximate the transverse displacement and rotation at the edges of the triangulation. Optimal estimates independent of the plate thickness are proved for the trans- A. El-Azab verse displacement, rotation and bending moment. A post- Florida State University processing technique is provided for the displacement vari- [email protected] able and we show numerically that it converges faster than the original approximation. This work is in collaboration D. Gaston, C. Permann with Edwin M. Behrens. Idaho National Laboratory [email protected], [email protected] Johnny Guzman Brown University S. Rokkam johnny [email protected] Florida State University [email protected] Edwin Behrens Universidad Catolica de la Santisima Concepcion D. Wolf [email protected] Idaho National Laboratory [email protected] MS89 Higher Order Nonconforming Finite Elements for MS89 H(curl) ∩ H(div) A Hybridizable Discontinuous Galerkin Method for Many problems in electromagnetics can be posed on sub- Steady-state Convection-diffusion-reaction Prob- ∩ lems spaces of H(curl) H(div). However finite element subspaces of (curl) ∩ H(div) are necessarily subspaces of H1 We introduce and therefore not appropriate for electromagnetic prob- a hybridizable discontinuous Galerkin method for steady- lems on nonconvex domains. On the other hand there is a state convection-diffusion-reaction problems. The method natural interpolation operator from H(curl) ∩ H(div)into is hybridizable, which renders it efficiently implementable. the well-known weakly continuous (vector) P1 element, When the method uses polynomial approximations of the which makes this nonconforming element useful for prob- same degree for both the total flux and the scalar vari- lems posed on H(curl) ∩ H(div) and general domains. In able, optimal convergence properties are obtained for both this talk we will discuss higher order nonconforming (vec- variables; Moreover, the method exhibits superconvergence tor) elements that have similar properties. properties of the approximation to the scalar variable; this allows us to postprocess the approximation in an element- Li-yeng Sung by-element fashion to obtain another approximation to the Department of Mathematics scalar variable which converges faster than the original one. Louisiana State University [email protected]

Bo Dong Drexel University MS90 [email protected] Multi-Scale Methods for Simulating Turbulent At- 94 AN10 Abstracts

omization Fluid Interface Reconstruction Algorithm

Atomization involves processes on scales spanning several I will describe a volume-of-fluid interface reconstruction orders of magnitude. We will discuss numerical methods algorithm that is second-order accurate pointwise, pro- to address this multi-scale nature. These include the use vided the curve z(x(s),y(s)) is two-times continuously dif- of multiple concurrent meshes to resolve processes occur- ferentiable and the (non-dimensional)√ grid size h satisfies −1 −1 ring on different scales, like turbulent flow structures, ther- κmax ≤ min{Chh , ( h) } locally, where κmax is the mal boundary layers near the phase interface, and topology (non-dimensional) local maximum of the curvature z.I change events. In addition we will discuss a hybrid multi- will present examples of computations and an outline of a scale Eulerian/Lagrangian technique to deal with the vast proof that this method is second-order accurate in the max number of spray droplets generated in atomization. norm. Peter Brady Elbridge G. Puckett School of Mechanical, Aerospace, Chemical and Materials University of California, Davis Engi Department of Mathematics Arizona State University [email protected] [email protected]

Juan Lopez MS90 Arizona State University Field-induced Motion of a Ferroﬂuid Droplet in a [email protected] Viscous Medium

Marcus Herrmann The effect of applied magnetic fields on the deformation of School of Mechanical, Aerospace, Chemical and Materials a biocompatible hydrophobic ferrofluid drop suspended in a Engi viscous medium is investigated numerically and compared Arizona State University with experimental data. At high magnetic fields, experi- [email protected] mental drop shapes deviate from numerical results when a constant surface tension value is used. One hypothesis for the difference is the dependence of interfacial tension on MS90 the magnetic field in the experimental data. This idea is Multiphase Flows in Complex Geometries: A Dif- investigated computationally. fuse Domain Approach Yuriko Renardy We present a new method for simulating two-phase flows in Virginia Tech complex geometries, taking into account contact lines sepa- Department of Mathematics rating immiscible incompressible components. We combine [email protected] the diffuse domain method for solving PDEs in complex geometries with the diffuse-interface (phase-field) method Shahriar Afkhami for simulating multiphase flows. In this approach, the com- Department of Mathematical Sciences plex geometry is described implicitly by introducing a new New Jersey Institute of Technology phase-field variable, which is a smooth approximation of [email protected] the characteristic function of the complex domain. The fluid and component concentration equations are reformu- Annette Tyler lated and solved in larger regular domain with the bound- School of Physics ary conditions being implicitly modeled using source terms. The University of Western Australia The method is straightforward to implement using stan- [email protected] dard software packages; we use adaptive finite elements here. We present numerical examples demonstrating the ef- Michael Renardy fectiveness of the algorithm. We simulate multiphase flow Department of Mathematics inadrivencavityonanextendeddomainandfindvery Virginia Tech good agreement with results obtained by solving the equa- [email protected] tions and boundary conditions in the original domain. We then consider successively more complex geometries and Judy Riffle simulate a droplet sliding down a rippled ramp in 2D and Department of Chemistry 3D, a droplet flowing through a Y -junction in a microflu- Virginia Tech idic network and finally chaotic mixing in a droplet flowing judyriffl[email protected] through a winding, serpentine channel. The latter example actually incorporates two different diffuse domains: one describes the evolving droplet where mixing occurs while Tim St. Pierre, Robert Woodward the other describes the channel. This is joint work with School of Physics Sebastian Aland and Axel Voigt. The University of Western Australia [email protected], John Lowengrub [email protected] Department of Mathematics University of California at Irvine [email protected] MS91 Dynamic Moduli of Nematic Liquid Crystal Poly- mers with Parallel Anchoring Conditions MS90 A Pointwise Second-Order AccurateVolume-of- We apply anchoring conditions to a nematic liquid crystal polymer system so that the major director lies parallel to AN10 Abstracts 95

the plates of a shear cell and then apply a small ampli- MS91 tude shear flow at an arbitrary angle to the direction of Title Not Available at Time of Publication the anchoring. We use a Doi-Marrucci-Greco tensor model with one dimensional heterogeneity to predict the dynamic Abstract unavailable at time of publication. moduli. For anchoring that lies in the flow-flow gradient plane, the system effectively recovers Leslie-Ericksen the- Ruhai Zhou ory. If logrolling anchoring, the solution is also analytically Department of Mathematics and Statistics solvable. For the oblique angles in between in-plane and Old Dominion University logrolling, we solve the system numerically. The viscos- [email protected] ity is smaller for logrolling anchoring than in-plane, and logrolling thins above a critical frequency, unlike in-plane anchoring. The in-plane storage modulus is slightly larger MS92 than logrolling for low frequencies. However, for higher Efficient Methods for Random Field Approxima- frequencies, logrolling can be two-to-three orders of mag- tion with Application to Nonlinear Schr?odinger nitude larger than in-plane. Equation Eric P. Choate Either due to the randomness in nature or the insufficiency Dept of Mathematics of knowledge, most physical or engineering systems in- University of North Carolina at Chapel Hill volve uncertainty to a certain degree. To gain a better [email protected] understanding of the intrinsic dynamics, such uncertainty should be modeled and analyzed. Bose-Einstein conden- sate (BEC) with disorder is such an example. In physical MS91 experiments, the disorder (or random potential) has been Stability of Active Suspensions generated through optical speckle patterns, and stable soliton waves were observed when the disorder has appropriate We investigate the linearized structure of a recently de- strength. But the complete dynamics of the solution is still rived kinetic model describing suspensions of active parti- largely unknown. This prototype problem can be modeled cles near a state of uniformity and isotropy. We show that by the nonlinear Schrödinger equation (NLSE) with a ran- system instability can arise only from the dynamics of the dom potential (also called the Gross-Pitaevskii equation), first azimuthal mode in swimmer orientation, and that at which governs the evolution of the mean-field wave func- small-scales the system is controlled independently of the tion in BECs. We study the formation and evolution of nature of the suspension. A prediction about the onset of the soliton waves in the 1D and 2D NLSEs with a random the instability is made. potential. Christel Hohenegger Qian-Yong Chen New York University Department of Mathematics & Statistics [email protected] U. of Massachusetts at Amherst [email protected]

MS91 An Integrative Model of Spermatozoa Motility MS92

2+ A Local Vorticity Boundary Condition Spectral Calcium (Ca ) dynamics in mammalian sperm are di- Collocation Method for 2D Incompressible Fluids rectly linked to motility. These dynamics depend on diffusion, nonlinear fluxes, Ca2+ channels specific to the sperm A simple spectral collocation method for viscous incom- flagellum, and other signaling molecules. The goal of this pressible flow in a bounded 2D domain is presented for the work is to couple Ca2+ dynamics to a mechanical model of vorticity-stream function formulation of the incompressible a motile sperm within a viscous, incompressible fluid. We Navier-Stokes equations, along with its extension to the will present recent progress on elements of this integrative Boussinesq system. The no-slip boundary condition for model. velocity is converted into a local boundary formula for the vorticity, which when used in conjunction with an explicit Sarah Olson time stepping scheme allows decoupling the computation Mathematics Department of the vorticity and stream function time updates. Numer- Tulane University ical results are presented for the singular lid-driven caivity [email protected] problem, a benchmark differentially heated cavity problem, and a Rayleigh-Bernard convection problem for Rayleigh Susan Suarez number up to 1010, demonstrating the efficiency of the Department of Biomedical Sciences method, and in particular that it is well suited for high College of Veterinary Medicine, Cornell University Reynolds or high Rayleigh number regime simulations. [email protected] Hans Johnston Lisa J. Fauci Department of Mathematics & Statistics Tulane University University of Massachusetts Amherst Department of Mathematics [email protected] [email protected] MS92 Numerical Simulation of Cahn-Hilliard-Hele-Shaw Equations Unconditionally energy stable and solvable schemes for the Cahn-Hilliard-Hele-Shaw (CHHS) equation are presented 96 AN10 Abstracts

in the talk. This equation arises in models for spinodal traditional DC in that the integral of the residual appears decomposition of a binary fluid in a Hele-Shaw cell, tu- in the error equation rather than the derivative of the resid- mor growth and cell sorting, and two phase flows in porous ual. In this work, we investigate several formulations of media. A convex splitting technique for this specialized IDC in order to generate high order split methods for a conserved gradient flow is utilized, which gives a non- range of PDEs. The eventual goal is to develop efficient increasing energy. Some numerical simulation results are methods for high order phase field models on GPUs. also presented in the talk. Andrew J. Christlieb Cheng Wang Michigan State Univerity University of Massachusetts Department of Mathematics Dartmouth, MA [email protected] [email protected] Jing-Mei Qiu Mathematical and Computer Sciences MS92 Colorado School of Mines An Unconditionally Stable Second-Order Scheme [email protected] for the Slope Selection Equation and Related Epi- taxial Thin Film Models Maureen M. Morton In this talk I describe a second-order convex splitting Dept. of Mathematics scheme for the Slope Selection equation, which is a model Michigan State University thin film roughening and subsequent coarsening. Like the [email protected] first-order convex splitting scheme that we introduced in an earlier work, the scheme is unconditional energy-stable MS93 (and norm stable) and unconditionally uniquely solvable. I prove that the (fully discrete) scheme results as the gra- Combining a Multi-grid Approach with Deferred dient of a strictly convex functional, and hence gradient- Correction Methods based solvers, e.g., Newton’s method, are globally con- In a deferred correction method, a standard numerical vergent. In the talk I discuss issues concerning practical method is used to first compute a provisional solution at and efficient solution of the scheme using nonlinear multi- a number of intermediate points in a integration interval. grid and nonlinear conjugate gradient methods. This work Then an equation for the error in the approximation is con- is joint with Cheng Wang (UMass) and Xiaoming Wang structed and solved iteratively using a low-order method to (FSU). generate increasingly accurate approximations. By com- Steven M. Wise bining a multi-grid approach with the deferred correction Mathematics Department methods, we obtained a class of methods that are highly University of Tennessee efficient in computing high-order approximations for multi- [email protected] scale partial differential equations. Anita T. Layton MS93 Duke University Department of Mathematics A Multi-explicit Spectral Deferred Correction [email protected] Method Applied to Regularized Stokeslets

In this discussion, regularized Stokeslets are used to model MS93 immersed elastic objects with stiff spring forces. In certain scenarios, the fluid velocity can be decomposed to isolate RIDC: Parallel High-order Time-stepping stiff terms. The multi-explicit spectral deferred correction RIDC (revisionist integral deferred correction) methods are method utilizes such a decomposition and integrates stiff a class of time integrators well-suited to parallel multicore velocity components with a small time step while treating computing. RIDC methods can achieve high-order accu- non-stiff components with a larger time step. This elimi- racy in wall-clock time comparable to forward Euler. The nates unnecessary expensive calculations while still treat- methods use a predictor and multiple corrector steps. Each ing the system explicitly in a stable, efficient manner. corrector is lagged by one time step; the predictor and each Elizabeth L. Bouzarth of the correctors can then be computed in parallel. This Duke University presentation introduces RIDC methods and demonstrates Department of Mathematics their effectiveness on some test problems. [email protected] Andrew Christlieb Michigan State University Michael Minion [email protected] University of North Carolina-Chapel Hill Mathematics Department Colin Macdonald [email protected] Oxford University [email protected] MS93 Integral Deferred Correction and High Order Split- Ben Ong ting Method for PDEs michigan state university [email protected] Integral Deferred Correction (IDC) belongs to the general family Defect Correction (DC)algorithms. IDC differs from AN10 Abstracts 97

MS94 and his work in fast MRI. Mathematical Tools for Management of System Complexity Daniel Rockmore Dartmouth College My conversations with Dennis always included issues in [email protected] complexity, be it on tools for characterizing complexity of system design, its architecture or management of complexity in engineered systems. In this talk I will reflect on MS95 these topics within the context of dynamical systems the- Cutting Planes and Maximal Lattice-free Convex ory and discuss various tools for taming complexity, many Sets coming from the realm of harmonic analysis, but also utilizing graph theory and ergodic theory. I will also highlight This talk is based on joint work with Borozan, Basu, Con- discussions we had on architecture of microfluidic systems forti and Zambelli. We consider a model that arises in and our ideas on architecture of microengines. integer programming, and show that all irredundant inequalities are obtained from maximal lattice-free convex Igor Mezic sets in an affine subspace. We also show that these sets are polyhedra. The latter result extends a theorem of Lovász University of California, Santa Barbara n [email protected] characterizing maximal lattice-free convex sets in R . Gerard Cornuejols MS94 Tepper School of Business Moving Innovation Forward: The Biosensors Pro- Carnegie Mellon University gram at NIH [email protected]

In 2000, the National Institute on Alcohol Abuse and Alco- holism (NIAAA), part of the National Institutes of Health MS95 (NIH), embarked on a small but innovative venture, mod- Some Relationships between Disjunctive Cuts and eled in part on DARPA. The first goal of the program was Cuts based on S-free Convex Sets the development, in five years, of biosensors for alcohol consumption in humans. Dennis Healy was asked to head Pursuing a line of research proposed by Balas (2009), we this effort, working with NIH staff in development of the establish exact correspondence between 2-branch disjunc- program. Dennis didn’t want merely to develop sensors, tion and a strict subclass of S-free cuts for the two row however. His idea was to push development and innova- constrained group relaxation (2RCGR). We propose a new tion a step further, by requiring each sensor to have a fully class of nonsymmetric 2-branch disjunctive operation that integrated data analysis system. In 2002, 5 unique biosen- canbeusedtoobtainallthe2dS-freecutsfor2RCGP. sor system projects were funded. Two of these systems We also study relationship of symmetric and nonsymmet- will be described, highlighting the integration of science, ric disjunctions applied to general mixed integer sets with engineering, and mathematics in their design, as well as cuts from its 2RCGRs. how these systems fit into Dennis’ vision for biomedical Sanjeeb Dash applications of sensor technologies. IBM T.J. Watson Research Center Karen Peterson [email protected] National Institute of Biomedical Imaging and Bioengineering Santanu Dey [email protected] School of Industrial and Systems Engineering Georgia Institute of Technology [email protected] MS94 Manifold Matching Classification: Joint Optimiza- Oktay Gunluk tion of Fidelity and Commensurability IBM T.J. Watson Research Center [email protected] We consider the statistical pattern recognition task in which data is available in multiple disparate spaces, but no data belonging to the classes of interest is available in the MS95 space of interest. We consider fusion and inference from On Families of Split Cuts that can be Generated multiple disparate data sources via joint optimization of Efficiently fidelity and commensurability. We study several heuristics to generate new families of Carey Priebe split cuts, by considering integer linear combinations of the Johns Hopkins University rows of the simplex tableau, and deriving the correspond- [email protected] ing mixed-integer Gomory cuts. In particular, we propose several cut generation algorithms that share the following aims: reducing the number of nonzeroes, obtaining small MS94 coefficients, generating orthogonal cuts. We present a com- Dennis Healy’s work at Dartmouth in Computa- putational evaluation that shows the usefulness of these tional Harmonic Analysis new cuts in a Branch-and-Cut framework.

In this talk we survey Dennis Healy’s tenure at Dartmouth Giacomo Nannicini, Gerard Cornuejols and his signiﬁcant contributions to applied and computa- Tepper School of Business tional noncommutative Fourier analysis and wavelet anal- Carnegie Mellon University ysis. In particular, his work on an FFT for the 2-sphere [email protected], [email protected] 98 AN10 Abstracts

MS95 MS96 On the Rank of Cutting-plane Proof Systems Incorporating Intervariable Geminals into Sums of Products We introduce a natural abstraction of propositional proof systems that are based on cutting planes. This new Representing a multivariate function as a sum of products class of proof systems includes well-known operators such of one-variable functions bypasses the curse of dimension- as Gomory-Chvátal cuts, lift-and-project cuts, Sherali- ality. However, the wavefunction of a quantum-mechanical Adams cuts, and Lovász-Schrijver matrix cuts. We show system has dependencies on the differences of pairs of vari- that whenever a specific cutting-plane based proof sys- ables, which makes such sums converge slowly. A represen- tem has (maximal) rank n on a particular family of in- tation with intervariable geminals times sums of products stances, then any cutting-plane proof system in our class should allow faster convergence. This representation re- has rank Ω(n/ log n) for that family. We also construct a quires interesting algorithms, which can be represented as new cutting-plane proof system that has worst-case rank sequences of graphs. O(n/ log n) for any polytope without integral points, showing that the universal lower bound is essentially tight. Martin J. Mohlenkamp Furthermore, we prove that whenever some cutting-plane Ohio University proof system in our class has rank n, then the rank of any [email protected] one of the known proof systems mentioned above is at least n − 1. Finally, we provide a complete characterization of all polytopes without integral points in the n-dimensional MS96 0/1-cube of maximal Gomory-Chvátal rank n. Matters of the Heart: Mathematical Modeling with Tensors Sebastian Pokutta Technische Universität Darmstadt This talk focuses on the possible development, analysis and Germany computer implementation of mathematical models of the [email protected] cardiovascular system. Our goal is to automatically gauge the anatomic structure and the physiological response of Andreas S. Schulz the human cardiovascular system as healthy or diseased Massachusetts Institute of Technology states. The mathematical analysis of these problems is [email protected] complicated and the related numerical analysis difficult. Our goal encompasses the idea of representing data that have been extracted non-invasively as 3-dimensional ten- MS96 sors. This include fore mostly, echocardiograms, electro- Nontraditional Tensor Decompositions and Appli- cardiograms and perhaps MRI’s as these methods have cations minimal invasion to the patient and the resulting data can be viewed as a sequence of related images (matrices). Tra- This presentation will discuss two tensor decompositions ditional numerical linear algebra is not enough in these that are not as well known as PARAFAC (parallel factors) data mining applications; a comprehensive set of numerical and Tucker, but have proven useful in informatics appli- multilinear algebra tools will be required to spot patterns cations. Three-way DEDICOM (decomposition into direc- in n-way data. Tensor decompositions have proven to be tional components) is an algebraic model for the analysis successful in extracting the underlying structure in such of 3-way arrays with nonsymmetric slices. PARAFAC2 is datasets. a related model that is less constrained than PARAFAC and allows for different objects in one mode. Applications Mechie Nkengla of both models to informatics problems will be shown. University of Illinois at Chicago [email protected] Brett W. Bader Sandia National Laboratories Computer Science and Informatics Department MS97 [email protected] Distributional Sensitivity Analysis for Factor Pri- oritization

MS96 Factor prioritization is the identiﬁcation of factors causing Small Tensor Rank is in RP the greatest reduction in output variance when subject to factor uncertainty reduction, and is an important aspect Hastad has shown that determining the rank of a 3-tensor of the application of complex models for decision-making. is an NP-hard problem in general. Nevertheless Hastad’s We present a distributional sensitivity analysis for factor construction involves a l × m × n tensor of rank strictly prioritization that assumes the portion of a particular fac- larger than max(l, m, n). We show that if we restrict our- tor’s variance that can be reduced is a random variable. selves to tensors of rank not more than max(l, m, n), then Our method is applied directly to the results of a global the rank of such tensors may be computed in randomized sensitivity analysis using acceptance/rejection sampling. polynomial (RP) time. A consequence is that computing rank for this smaller class of tensors is unlikely to be in Doug Allaire, Karen Willcox NP (unless of course P = NP). We will discuss a readily Massachusetts Institute of Technology implementable algorithm. [email protected], [email protected] Lek-Heng Lim University of California at Berkeley MS97 [email protected] Numerical Solutions of Optimal Control Problems Governed by Stochastic Partial Diﬀerential Equa- AN10 Abstracts 99

tions MS98 Optimal Choice of Sample Times Abstract not available at time of publication. Based on an abstract notion of sampling procedures in- Yanzhao Cao volving probability measures on the sampling interval we Department of Mathematics & Statistics present an algorithm for determining optimal sampling Auburn University times in the given sampling interval. Fundamental for the [email protected] approach is the fact that the set of probability measures on an interval is a metric space under the so called Prohorov MS97 metric. As optimality criterion one can take any continuous function of the Fisher information matrix corresponding to Distributional Sensitivity for Uncertainty Quantifi- the chosen sampling times. cation Franz Kappel In this talk we present a novel technique that quantifies sen- Department of Mathematics sitivity in a model when epistemic uncertainty is present University of Graz in the density function of random variables. This nonin- [email protected] trusive method is easily applicable to existing codes and can easily be implemented as a post-processing operation. Using generalized Polynomial Chaos, we show examples il- H. T. Banks lustrating the effectiveness and efficiency of our approach. CRSC, NC State University [email protected] Akil Narayan, Dongbin Xiu Purdue University [email protected], [email protected] MS98 Optimal Design for Imaging

MS97 Experimental design is an important topic for imaging sci- Stochastic Optimal Design of Complex Systems us- ence. It has broad applications in the areas of physics, biol- ing Approximate Models ogy and engineering. In this talk, we examine the Bayesian AandAπ optimal designs. Our methods have the capa- We advocate a simulation strategy that recasts the opti- bility to improve the image quality while maintaining low mization problem as a sampling problem in the expanded experimental cost. Several imaging experiments, such as space which apart from the random variables includes the super resolution will be presented. Moreover, we explore design parameters. To that end we employ adaptive Se- eﬃcient methods for large scale design problems. quential Monte Carlo (SMC) methods that scale well in high dimensions, are directly parallelizable and can iden- Zhuojun Magnant tify multimodal densities. We propose a hierarchical strat- Department of Mathematics and Computer Science egy where approximate forward models can be rigorously Emory University incorporated in order to give accurate estimates at a re- [email protected] duced computational cost. Eldad Haber Raphael Sternfels Department of Mathematics School of Civil & Environmental Eng, Cornell University The University of British Columbia [email protected] [email protected]

Phaedon-Stelios Koutsourelakis School of Civil and Environmental Engineering & MS98 Center for Applied Mathematics, Cornell University Optimal Experimental Design in Geophysical Ap- [email protected] plications In this talk we discuss the design of experiments for ill- MS98 posed problems that arise in biological applications. We Optimal Experimental Design in Biological Appli- show that the problem is cast is a nonlinear stochastic pro- cations gramming problem and suggest efficient methods for its solution. We then discuss biological applications and show Dynamical systems are the right tool to simulate and model the effectiveness of our approach. biological systems. In biological disciplines the choice of the design of an experiment is most important to recover Luis Tenorio model parameters. The strong interplay between accuracy Colorado School of Mines of the results and efficiency of experiment need to be con- [email protected] sidered carefully. We present the computational framework for ordinary differential equations, optimization, parame- Eldad Haber ter estimation, and optimal experimental design and apply Department of Mathematics these methods to target the questions arising from the bi- The University of British Columbia ology. [email protected]

Matthias Chung Department of Mathematics and Computer Science MS99 Emory University Compressed Sensing: How Sharp is the RIP? [email protected] The Restricted Isometry Property (RIP) has become a 100 AN10 Abstracts

widely used tool for the analysis of signal recovery algo- of these properties in compressive sensing. We will first rithms used in compressed sensing. Through an asymmet- give the definitions of weak,sectional and strong “balanced- ric interpretation of the RIP and by developing the best ness” properties for linear subspaces and their applicaitons known bounds on the RIP constants for matrices from the in sharply characterizing or bounding the performances of Gaussian ensemble, we are able to make quantitative state- compressive sensing. Using tools from high dimensional in- ments regarding the theoretical guarantees for these algo- tegral geometry and geometric probability, we give a uni- rithms. Moreover, we translate these results into the phase fied Grassmann Angle framework for analyzing these “bal- transition framework advocated by Donoho et al. which ancedness” properties, and give sharp performance bounds permits direct comparison across algorithms and to alter- for the “balancedness” that a linear subspace can achieve native methods of analysis. in various cases. We will further discuss the applications of this analytical framework in analyzing and designing pow- Jeff Blanchard erful signal recovery algorithms such as weighted or iter- Grinnell College ative reweighted 1 minimization algorithms. This work jeff@math.grinnell.edu concerns random projections of high dimensional polytopes and fundamental properties of linear subspaces, so it may Coralia Cartis, Jared Tanner, Andrew Thompson be of independent mathematical interest. Recent progress University of Edinburgh on investigating the p,0

MS100 to show excellent performance. Differential Contribution of Potassium Currents to Neuronal Excitability Xinfeng Liu University of South Carolina The excitability of a neuron depends on the different in- xfl[email protected] ward and outward currents that flow across its membrane. Drosophila is used as a model system to examine the theoretical plausibility of existing hypotheses about the differ- MS101 ential involvement of A-type currents in delaying spiking Eulerian Flow Solvers for Three Temperature activity. The model is constructed using known macro- Plasma Physics scopic biophysical properties of voltage-dependent, slowly inactivating and fast inactivating A-type channels and con- We study a plasma physics model that includes electron strained using electrophysiological data. heat conduction and energy exchange between electrons and ions. For simple shock flows, the model reduces to Marco Herrera-Valdez an autonomous system of ordinary differential equations Arizona State University that allows for a phase space analysis and semi-analytical [email protected] solutions. We have adapted an Eulerian Godunov-based scheme to compute such shocks. We provide details of the numerical scheme and compare the computed and semi- MS100 analytic solutions. A Minimal Biophysical Model of Phase Precession Tom Masser Some pyramidal cells in the rodent hippocampus called Los Alamos National Lab. place cells, fire at specific locations called place fields dur- [email protected] ing spatial tasks. The spiking in place cells is also modulated by oscillations in the local field potential. As the rat moves through a place field, place cell firing occurs at pro- MS101 gressively earlier phases of the oscillation within the theta A Conservation Constrained Dis- band (7-12 Hz). A minimal biophysical model is used to continuous Galerkin Method with Improved CFL study phase precession. Number for Conservation Laws Adrian Smith We present a new formulation of the RKDG method for University of Arizona conservation Laws, which requires the computed RKDG [email protected] solution in a cell to satisfy additional conservation constraint in adjacent cells. This new formulation improves Marco Herrera-Valdez the CFL number over the original RKDG formulation with- Arizona State University out increasing the complexity comparing with the regular [email protected] RKDG formulation. It also effectively improves the robustness of the DG scheme and improves the resolution of the numerical solutions in multi-dimensions. MS101 Zhiliang Xu Central Discontinuous Galerkin Methods for MHD Department of Mathematics Equations University of Notre Dame In this talk, central discontinuous Galerkin (DG) methods [email protected] will be presented for ideal MHD equations. Originally introduced for hyperbolic conservation laws and recently de- MS102 veloped for Hamilton-Jacobi equations, central DG methods combine ideas in central schemes and DG methods. Simulations of Xe Redistribution in Uranium Dioxi They avoid the use of Riemann solvers which are compli- Abstract unavailable at time of publication. cated and costly for MHD equations, while evolving two copies of approximating solutions on overlapping meshes. David Andersson Los Alamos National Laboratory Fangyan Li [email protected] Department of Mathematical Sciences Rensselaer Polytechnic Institute [email protected] MS102 Numerical and Software Engineering Challenges in MS101 the NEAMS Waste Forms Sub-Program Compact Integration Factor Methods for Complex Abstract unavailable at time of publication. Domains and Adaptive Mesh Refinement Roscoe A. Bartlett To reduce the cost of solving stiff reaction diffusion equa- Sandia National Laboratories tions, we introduce a compact implicit integration factor [email protected] (cIIF) method for efficient storage and calculation of exponential matrices associated with the diffusion operators. In addition, we present a method for integrating cIIF with MS102 adaptive mesh refinement (AMR) with large time steps by Scalable Methods for the Neutron Transport Equa- taking advantage of excellent stability condition for cIIF. tion under Development at Argonne National Lab- An example of simulating a cell signaling system is given 102 AN10 Abstracts

oratory MS103 A Posterior Error Estimate for Finite Element Abstract unavailable at time of publication. Methods for the Stokes Equations Micheal Smith We establish a posterior error analysis for finite element Argonne National Laboratory methods of the Stokes equations. This residual estima- [email protected] tor can be applied to almost all the existing finite element methods including conforming, nonconforming and discon- MS102 tinuous finite elements. Controlling Defect Segregation in Uranium Dioxide Xiu Ye University of Arkansas, Little Rock Abstract unavailable at time of publication. [email protected] Cetin Unal Los Alamos National Laboratory MS104 [email protected] Adaptive Mesh Refinement Techniques for Free Boundary Problems MS103 In this talk, I will describe a new paradigm for solving On FEM Approximations to the Navier-Stokes partial differential equations on Quadtree/Octree grids. In Equations with Scott-Vogelius Elements particular, I will describe the level-set technology and how Abstract unavailable at time of publication. to enforce implicitly boundary condition at a moving front. Examples will include single and two-phase flows as well as Michael Case the solution of the Poisson-Bolztmann equations. Dept. of Mathematical Sciences Clemson University Frederic G. Gibou [email protected] UC Santa Barbara [email protected]

MS103 Maxime Theillard A Strongly Conservative, Monolithic Finite Ele- UCSB ment Method for Stokes-Darcy Coupling maxime [email protected] maxime Divergence conforming finite elements have been applied successfully to the Stokes and Navier-Stokes problem, us- Asdis Helgardottir ing discontinuous Galerkin techniques. On the other hand, UCSB these elements are natural for porous media flow modeled Mechanical Engineering by Darcy’s equations. In this presentation, we will show [email protected] the opportunities offered by a uniform discretization with Raviart-Thomas elements for the free and the porous media flow. The stability of the method will be discussed and MS104 numerical examples will confirm the applicability of the Numerical Analysis of Non-extensible Interfaces in new scheme. Incompressible Flow Guido Kanschat Non-extensible but deformable interface in an incompress- Texas A&M University ible flow, for example, shear flow, can be used to study [email protected] the deformation of red blood cells in mathematical biology. The governing equations are incompressible Stokes or Navier-Stokes equations with an unknown surface tension MS103 that should be determined in a such way that the inter- Penalty-factor-free Discontinuous Galerkin Meth- face is incompressible along the tangential direction. Thus ods for 2-dim Stokes Problems the problem is essential an inverse problem that is sensitive to perturbations. In the literature, often boundary We present two new finite element methods for two- integral methods are used for Stokes flows. Geometrically, dimensional Stokes problems. These numerical schemes the problem implies that both the area and the length of are developed by relaxing the constraints of the classi- thecellshouldbepreservedastheinterfaceevolves.In cal Crouzeix-Raviart nonconforming P1 finite elements. this talk, we present the immersed interface method with Penalty terms are introduced to compensate lack of con- some regularization technique for simulating such problems tinuity or divergence-free property. However, there is no with both Stokes and Navier-Stokes equations. For Navier- need for choosing penalty parameters and the formulations Stokes equations, we propose a modified projection method are symmetric. These new methods are easy to implement so that the pressure jump condition corresponding to the and avoid solving saddle-point linear systems. Numerical unknown surface tension can be strictly enforced. In our experiments are presented to illustrate the proved optimal numerical methods, the bending force can be also included. error estimates. Numerical analysis are carried out with different Reynolds Jiangguo Liu numbers, circularity, and the initial orientation of the cells. Colorado State University [email protected] Zhilin Li North Carolina State Univ Department of Mathematics AN10 Abstracts 103

[email protected] MS105 Numerical Policy Function on Auto-tuned Sparse Iterative Solver Xabclib MS104 Stability Analysis of a Coflowing, Bended, Conventional auto-tuning software focuses on optimization Gas/liquid Jet Flow with execution speed. However, the requirement of auto- tuning depends on situation of software usage for end-users. A Numerical technique based on the pseudo-spectral In this presentation, we develop a new function of auto- method is presented for performing a linear spatial sta- tuning, named “Numerical Policy Function”. The policy bility analysis for a bended co-flowing gas/liquid jet. The function optimizes execution speed, memory amount, and numerical method that will be presented is an extension computational accuracy. A result of performance evalua- of the method developed by Gordillo and Perez-Saborid tion will be shown with one node of the T2K Open super (2005) for a non-bended co-flowing gas/liquid jet. The lin- computer (16 cores) for the Xabclib, which is an OpenMP ear stability analysis of a bended liquid jet is applied to the parallelized numerical library with the policy function for problem of the break-up of a liquid jet in a cross-flow. Re- sparse iterative solvers. The Xabclib is also implemented sults of the linear stability analysis are compared against with OpenATLib, which is a library of APIs to establish the results derived from directly computing solutions of the common interface for auto-tuning functions. original two-phase Navier-Stokes equations. Takahiro Katagiri Yaohong Wang Univ. of Tokyo Department of mathematics [email protected] Florida State University [email protected] Takao Sakurai Central Research Laboratory Mark Sussman Hitachi Ltd. Florida State University [email protected] [email protected] Satoshi Ohshima MS104 Univ. of Tokyo [email protected] Multiscale Issues in DNS of Multiphase Flows

In DNS of multiphase flows it is frequently found that fea- Mituyoshi Igai tures much smaller than the “dominant’ flow scales emerge. HITACHI Ltd. Those features consist of thin films, filaments, and drops, [email protected] and usually the geometry is simple and inertia effects are relatively small for the local evolution. In isolation these Hisayasu Kuroda features are therefore often well described by analytical Univ. of Tokyo / Ehime U. models. Here we describe the use of thin film models as [email protected] subgrid models in DNS of multiphase flows. Kengo Nakajima Gretar Tryggvason,JiacaiLu The University of Tokyo Mechanical Engineering Department Information Technology Center Worcester Polytechnic Institute [email protected] [email protected], [email protected] Ken Naono MS105 HITACHI Ltd. Mapping Communication-Avoiding QR Decompo- [email protected] sition to Various Architectures Shoji Itoh The large and increasing costs of communication motivate Univ. of Tokyo redesigning algorithms to avoid communication whenever [email protected] possible. Recent development of the “Communication- Avoiding QR” algorithm has been shown to minimize (in an asymptotic sense) the communication costs of comput- MS105 ing the QR decomposition on either a sequential or parallel Redesign of Higher Level Matrix Algorithms for computer, yielding speedups over conventional algorithms Multicore and Hybrid Architectures: A Case in both theory and practice. In order to minimize commu- Study for Green’s Function Calculation in Quan- nication, the algorithm must be mapped to the underlying tum Monte Carlo Simulation architecture. In this talk we will discuss how this mapping is done for a sequential machine and a distributed-memory The emerging multicore computing systems require signifi- parallel machine, and we will discuss extensions of the al- cant modification to today’s computational tools and tech- gorithm to other interesting architectures. nologies. A great deal of efforts have been focused on the redesign of essential matrix computations, such as matrix Grey Ballard multiplication or the QR decomposition for optimal per- Univ. of California at Berkeley formance on multicore systems. However, by nature, not [email protected] every matrix operation can be efficiently parallelized, for example, the QR decomposition with column pivoting, and explicit matrix inversion. The performance of these matrix operations is still lack behind and substantial slower on par- 104 AN10 Abstracts

allel environments. In this paper, we take an approach to MS106 re-design numerical algorithms for higher-level algorithm Multiple Scales in Numerical Models of Ocean Cir- so that they only uses easily parallelizable linear algebra culation building blocks: matrix multiplication and QR decomposition’, but not column pivoting and the explicit matrix The circulation of the ocean plays a major role in the global inversion. Specifically, we will redesign the higher-level al- climate system. A fundamental property of this circulation gorithms for communication avoidance in the application of is its very wide ranges of space and time scales. In keep- quantum Monte Carlo simulation. A new algorithm, called ing with the purposes of this minisymposium, this talk will structure orthogonal factorization (SOF), is proposed for include a general survey of how these ranges of scales can parallelizing the Green’s function calculations, it only uses influence modelers’ choices of time discretization, vertical easily parallelizable linear algebra building blocks and sig- coordinate, and physical parameterizations. I will also out- nificantly reduces the communication cost. The new algo- line some of my own work on time splitting and time step- rithm is as stable as the previous algorithm. The previous ping and make some comments about spatial discretiza- algorithm requires less flops but uses the QR decomposition tions. with column pivoting, which is a communication intensive. Although the new algorithm uses a factor of 3 more flops Robert Higdon than the previous algorithm, it is 16% faster on a quad- Oregon State University core system, and 2.5 times faster on a 1024-CPU hybrid [email protected] systems. Che-Rung Lee MS106 National Tsinghua University, Taiwan Mathematical Issues in Data Assimilation of Data [email protected] and Models in Climate Research

Zhaojun Bai Climate data is remarkably sparse and poorly constrained, University of California, Davis and models for climate are far from complete. How does [email protected] one make meaningful forecasts? What are the challenges in this peculiar forecasting framework? What are the tools? I will frame these questions, provide a survey of key ideas, MS105 and show some of the work done by my group in nonlinear Automatic Tuning for Parallel 3-D FFTs non-Gaussian data assimilation. In this talk, an implementation of parallel 3-D fast Juan Restrepo Fourier transform (FFT) with automatic performance tun- University of Arizona ing method is presented. An blocking algorithm for parallel [email protected] FFTs utilizes cache memory effectively. Since the optimal block size may depend on the problem size, we propose a MS106 method to determine the optimal block size that minimizes the number of cache misses. Performance results of parallel Bifurcations, and their Implications, in a Simple 3-D FFTs on clusters of multi-core processors are reported. Model of Arctic Sea Ice Eisenman and Wettlaufer (PNAS 2009) proposed a sim- Daisuke Takahashi ple ODE model for Arctic sea ice subjected to seasonally- Graduate School of Systems and Information Engineering varying solar forcing. We extend their box model to de- University of Tsukuba scribe both polar and subpolar sea ice, and analyze the [email protected] dynamics of the coupled system. Subpolar winter sea ice loss is abrupt and causes complete sea ice loss in the polar region as well. Summer sea ice loss does not show thresh- MS106 old behavior and progresses smoothly from south to north. Investigating a Convective Cloud Feedback Mech- anism for Warm Climates using Simple and Com- Mary C. Silber plex Climate Models Northwestern University Complex climate models have difficulty simulating the Arc- Dept. of Engineering Sciences and Applied Mathematics tic climate of ancient warm periods and diverge impres- [email protected] sively in their forecast of future sea ice at high CO2. A convective cloud feedback has been proposed that might Dorian Abbot, Raymond Pierrehumbert help resolve these issues. The strength of this feedback and University of Chicago CO2 at which it activates vary widely among the models. [email protected], [email protected] Here we use a hierarchy of climate models to investigate the factors that control the activation and strength of this feedback. MS107 Near Field Imaging of the Surface Displacement on Dorian Abbot An Infinite Ground Plane University of Chicago [email protected] This work is concerned the numerical study of the inverse diffraction problem for an unbounded obstacle. The obsta- Eli Tziperman cle is a ground plane with a local disturbance. A recon- Harvard University struction scheme based on the integral equation method is [email protected] proposed to image the surface displacement at near field. The method utilizes the evanescent waves effectively, which AN10 Abstracts 105

signiﬁcantly improves the spatial resolution of the image. Heterogeneous Media The on-going research project on this topic will also be highlighted. Abstract unavailable at time of publication.

Junshan Lin Igor Terentyev Department of Mathematics Dept. of Computational and Applied Mathematics Michigan State University Rice University [email protected] [email protected]

Gang Bao MS108 Michigan State University [email protected] Finite Element Algebraic Multigrid Methods for Biomechanics of the Cellular Microenvironment in Articular Cartilage MS107 We present a set of algebraic multigrid methods tailored A New Approximations of Effective Hamiltonians to simulating inhomogeneous deformation in the biome- A new formulation to compute effective Hamiltonians for chanical microenvironment of the cells in articular carti- homogenization of a class of Hamilton-Jacobi equations is lage using the finite element method. 3D finite elements proposed. Our formulation utilizes an observation made by on unstructured meshes that conform to the shape of in- Barron-Jensen about viscosity supersolutions of Hamilton- ternal interfaces are employed. Applications that simulate Jacobi equations. The key idea is how to link the effective the elastic deformation of soft cellular inclusions within an Hamiltonian to a suitable effective equation. The main ad- isotropic or transversely isotropic extracellular matrix will vantage of our formulation is that only one auxiliary equa- be discussed. tion needs to be solved in order to compute the effective ¯ Zhengzheng Hu Hamiltonian H(p) for all p. Error estimates and stability Department of Mathematics are proved and numerical examples are presented to show North carolina State University very encouraging results. [email protected] Songting Luo Department of Mathematics Mansoor Haider Michigan State University North Carolina State University [email protected] [email protected]

Hongkai Zhao MS108 University of California, Irvine Department of Mathematics Title Not Available at Time of Publication [email protected] Abstract unavailable at time of publication. Yifeng Yu Chun Liu University of California Penn. State University Irvine University Park, PA [email protected] [email protected]

MS107 MS108 A Discontinuous Galerkin Method for Wave Prop- Phase-field Model of Biofilm-flow Interaction agation in Coupled Acoustic-Elastic Media We derive a set of phase field models for biofilms using the Our goal is to develop scalable methods for global full- one-fluid two-component formulation in which the combi- waveform seismic inversion. The first step we have taken nation of extracellular polymeric substances (EPS) and the towards this goal is the creation of an high-order accu- bacteria are effectively modeled as one fluid component rate discontinuous Galerkin method for simulation of wave while the collective ensemble of nutrient and the solvent propagation in coupled elastic-acoustic media. We use are modeled as the other. The biofilm is assumed an in- adaptive mesh refinement to resolve local variations in wave compressible continuum. The dynamics of the biofilm is speeds with appropriate element sizes. The numerical ac- governed by a modified Cahn-Hilliard equation. Numerical curacy and convergence of the method is studied for clas- simulations are carried out and biofilm growth, expansion, sical wave propagation interface problems. streaming, rippling, and detachment in shear cells are captured. Viscoelastic properties of the biofilm is investigated Georg Stadler,LucasWilcox,CarstenBurstedde,Omar as well. Ghattas University of Texas at Austin Tianyu Zhang [email protected], [email protected], Mathematics [email protected], [email protected] Montana State University [email protected] MS107 Accurate Numerical Methods for Waves in Very MS108 Particle Alignment and Voronoi Tessellation of a 106 AN10 Abstracts

Sphere for time-dependent problems will be examined. Software for implementing RBF methods with extended precision We are interested in the orientation of non-spherical par- will be presented. ticles such as liquid crystal molecules, nanoparticles and colloidal particles due to interactions with each other and Scott A. Sarra external fields. Since the orientation of a rod-like par- Marshall University ticle corresponds to a point on a unit sphere, the time [email protected] evolution of the orientational distribution function typically corresponds to nonlinear diffusion on a sphere. Since the nonlinearity results in mode coupling, obtaining solu- MS109 tions in terms of spherical harmonics is not straightforward. Two Improved Algorithms for Stable Computa- We therefore turn to a direct discretization based scheme. tions with “Flat” Radial Basis Functions (RBFs) Since in general it is not possible to construct a regular uniform lattice on a sphere, we construct a random lat- Smooth RBFs, which feature a free shape parameter, tice for our discretization. Two interesting problems arise are receiving considerable attention for numerically solv- in this approach. One is the identification of neighboring ing PDEs since they combine high-order/spectral accu- points on the sphere, required for the evaluation of deriva- racy with meshless flexibility. Using shape parameters tives; the other is the effective approximation of differential that produce “flat” RBFs typically lead to smaller dis- operators on a random lattice. To identify nearest neigh- cretization errors in applications. However, the direct nu- bors, we construct the Voronoi diagram, using the Fortune merical approach of computing with flat RBFs is severely sweep line algorithm which we have modified and adapted ill-conditioned. We present two improved algorithms for to be used on a sphere. To approximate differential opera- bypassing this ill-conditioning, compare them to others tors, we have developed expressions for approximating the presently available, and give some applications. derivatives together with error estimates. In this talk, we give motivation for undertaking this work, discuss the first Grady Wright of the above two topics in some detail, and give examples Department of Mathematics implementing our strategy. Boise State University, Boise ID [email protected] Xiaoyu Zheng Dept of Mathematics Kent State University MS109 [email protected] A Phase-field Model for Two-phase Flows with Large Density Ratio and its Numerical Approxi- Peter Palffy-Muhoray mation Liquid Crystal Institute Modeling and numerical approximation of two-phase in- Kent State University compressible flows with different densities and viscosities mpalff[email protected] are considered. A physically consistent phase-field model that admits an energy law is proposed, and several energy MS109 stable, efficient and accurate time discretization schemes for the coupled nonlinear phase-field model are constructed High Order Finite Volume Wave Propagation with and analyzed. Ample numerical experiments are carried Application to Stegotons out to validate the correctness of these schemes and their We present a high order method for solving general hyper- accuracy for problems with large density and viscosity ra- bolicproblems, based on wave-propagation form Riemann tios. solvers, WENO reconstruction, and Runge-Kutta time in- Xiaofeng Yang tegration. The method is very general in that it can be ap- UNC plied to systems with spatially varying flux or systems that [email protected] are not in conservation form. The robustness and accuracy of the method are demonstrated through application to the study of solitary waves in a periodic non-dispersive MS110 medium. IMEX Runge-Kutta Schemes for Hyperbolic Sys- David I. Ketcheson tems with Stiff Diffusive Relaxation Mathematical and Computer Sciences & Engineering Hyperbolic systems of conservation laws often have relax- King Abdullah University of Science & Technology ation terms that, under a suitable scaling, lead to a reduced [email protected] system of parabolic or hyperbolic type. The development of numerical schemes to solve systems of this form has an MS109 active area of research. Implicit-explicit (IMEX) schemes have been used for the time integration of such systems. Radial Basis Function Methods Implemented us- Typically an implicit scheme is used for the relaxation term ing Extended Floating Point Precision - Examples, and an explicit scheme is used for the convection term. In Insights, and Software this talk we will focus our attention to hyperbolic system Radial Basis Function (RBF) methods often fail to realize of conservation laws with stiff diffusive relaxation. Usu- their theoretical accuracy due to poor conditioning. We ally these systems in addition to the stiff relaxation term discuss how extended precision floating point arithmetic have the convection term stiff too. We will mainly con- can be used to improve the accuracy of RBF methods in an centrate on the study of the stiff regime. In fact in the efficient manner and use scattered data interpolation and stiff regime most of the popular methods for the solution steady PDE problems as examples. The effect of floating of these systems fail to capture the correct behavior of the point precision on the eigenvalues stability of RBF methods relaxation limit unless the small relaxation rate is numeri- caly resolved. Other schemes present in the literature are AN10 Abstracts 107

able to overcome such a restriction, and relax to an explicit subspace approximations to the matrix exponential oper- method for the underlying parabolic equations, thus suffer- ator. Then we apply this novel time discretization tech- ing from the usual CFL stability restriction. Here we will nique to Discontinuous Galerkin methods on unstructured show how to construct new IMEX schemes that overcome meshes. such difficulties by introducing additional algebraic order condition and maintain both the correct asymptotic limit Shanqin Chen (i.e., the correct zero-relaxation limit should be preserved Department of Mathematical Sciences at a discrete level) and the correct order of the scheme. Our Indiana University South Bend findings are demonstrated on several numerical examples. [email protected]

Sebastiano Boscarino Yong-Tao Zhang University of Catania Department of Mathematics [email protected] University of Notre Dame [email protected] MS110 Adaptive Mesh Refinement for Discontinuous MS111 Galerkin Schemes via Local Time-stepping Exploiting Vector Space Properties to Strengthen the Relaxation of Bilinear Programs. Application: We present a strategy for adaptive mesh refinement for Global Optimization of Process Networks discontinuous Galerkin schemes that is based on unstructured conforming meshes. The main difference between our In this paper we present a methodology to find tight convex approach and the standard strategies commonly found in relaxations for a special set of quadratic constraints given the literature is that we allow for a different time-step on by bilinear and linear terms that frequently arise in the each element. In this sense, the proposed method makes optimization of process networks. The basic idea lies on use of ideas from both the structured and unstructured exploiting the interaction between the vector spaces where approaches. The main advantage is that we are able to the different set of variables are defined to tighten the re- save computational effort by not taking small time-steps laxation of traditional approaches. on coarse elements. The disadvantage is that interpolation in time must be applied in order to facilitate communica- Juan Pablo Ruiz tion between elements. We present a variety of numerical Dept. Chemical Engineering examples to test the proposed numerical scheme. Carnegoie Mellon University [email protected] James A. Rossmanith University of Wisconsin Ignacio Grossmann Department of Mathematics Dept. of Chemical Engineering [email protected] Carnegie Mellon University [email protected] MS110 High-Order Simulation of Electrical Activity in MS111 Cardiac Tissue Fast Summation for Non-linear Mixed-integer Op- Mathematical models of electric activity in cardiac tissue timization are often based on ordinary differential equations that de- By viewing the maximum of a function as the limit of cer- scribe the ionic currents at the cell level coupled with par- tain sums or integrals, efficient summation / integration tial differential equations that describe how the electricity procedures yield approximation algorithms for optimiza- flows at the tissue level. The physiological accuracy of tion problems. We report on recent advances in exact inte- tissue-scale models is often limited by the efficiency of the gration, summation and mixed summation procedures for numerical method. In this talk, I relate our experiences polynomial functions. The methods are related to Brion’s with high-order numerical methods for the efficient solu- formulas, exponential sums, Barvinok’s intermediate valu- tion of cardiac electrophysiological models. ations, and to the polynomial Waring problem (polynomi- Raymond J. Spiteri alsassumsoffewlinearforms). University of Saskatchewan, Canada Matthias Koeppe Department of Computer Science Dept. of Mathematics [email protected] Univ. of California, Davis [email protected] MS110 Implicit Integration Factor Methods for Spatial MS111 Discretization on High Dimensional Unstructured MINOTAUR: A New Solver for Mixed-Integer Meshes Nonlinear Optimization Implicit integration factor (IIF) methods are a class of effi- We present a new package for solving mixed-integer non- cient ”exactly linear part” methods for systems with both linear optimization problems, called MINOTAUR. MINO- stiff linear and nonlinear terms. The challenge in applying TAUR implements a range of branch-and-cut algorithms IIF methods for high spatial dimensional problems is how within a flexible object-oriented framework. We will com- to evaluate the matrix exponential operator. For spatial ment on some software design issues and describe some discretization of PDEs on unstructured meshes, how to ef- recent work on tighter integrating nonlinear solvers into a ficiently apply the IIF temporal discretization was open. In this paper, we solved this problem by applying the Krylov 108 AN10 Abstracts

branch-and-cut framework. gaming) accelerating our reconstruction times from hours to seconds. Sven Leyffer Argonne National Laboratory Miki Lustig leyff[email protected] TBA [email protected] Ashutosh Mahajan Argonne National Laboratory [email protected] MS112 Message Passing Algorithms for Compressed Sens- ing MS111 Valid Inequalities and Convex Hulls for Bounded Compressed sensing aims to undersample certain high- Multilinear Functions dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction We study the convex hull of the nonconvex set defined by is possible when the object to be recovered is sufficiently a product of N variables, with bounds on each variable and sparse in a known basis. Currently, the best known on the product itself. (For n=2 and unbounded product, sparsity-undersampling tradeoff is achieved when recon- the classical McCormick inequalities define the convex hull, structing by convex optimization – which is expensive in but less is known for more general cases.) We will discuss important large-scale applications. Fast iterative thresh- strong valid linear inequalities, motivated by the fact that olding algorithms have been intensively studied as alter- many exact solvers for nonconvex optimization problems natives to convex optimization for large-scale problems. use polyhedral relaxations to compute bounds via linear Unfortunately known fast algorithms offer substantially programming. Time permitting, we will also discuss strong worse sparsity-undersampling tradeoffs than convex opti- nonlinear inequalities for such sets. mization. We introduce a simple costless modification to iterative thresholding making the sparsity-undersampling Andrew Miller tradeoff of the new algorithms equivalent to that of the Institut de Mathématiques de Bordeaux corresponding convex optimization procedures. The new France iterative-thresholding algorithms are inspired by belief [email protected] propagation in graphical models. Our empirical measurements of the sparsity-undersampling tradeoff for the new algorithms agree with theoretical calculations. We MS112 show that a state evolution formalism correctly derives the Compressive Sensing: a Paradigm Shift in Signal true sparsity-undersampling tradeoff. There is a surprising Processing agreement between earlier calculations based on random convex polytopes and this new, apparently very different We survey a new paradigm in signal processing known theoretical formalism. as ”compressive sensing”. Contrary to old practices of data acquisition and reconstruction based on the Shannon- Arian Maleki Nyquist sampling principle, the new theory shows that it is TBA possible to reconstruct images or signals of scientific inter- [email protected] est accurately and even exactly from a number of samples which is far smaller than the desired resolution of the image/signal, e.g., the number of pixels in the image. This MS112 new technique draws from results in several fields of math- Efficient Algorithms for Non-orthogonal Atomic ematics, including algebra, optimization, probability the- Decompositions ory, and harmonic analysis. We will discuss some of the key mathematical ideas behind compressive sensing, as well as Building on the success of generalizing compressed sensing its implications to other fields: numerical analysis, infor- to matrix completion, this talk discusses progress on fur- mation theory, theoretical computer science, and engineer- ther extending the catalog of objects and structures that ing. can be recovered from few measurements. I will focus on a suite of data analysis algorithms designed to decompose Olga Holtz signals into sums of simple atomic signals. I will show University of California, Berkeley how to generically construct such decompositions and dis- Technische Universitat Berlin cuss which sets of atoms admit efficient decomposition al- [email protected] gorithms with performance guarantees.

Ben Recht MS112 TBA Compressed Sending in Medical Imaging: Progress [email protected] in Applications and Implementation

Compressed sensing has already stimulated lots of new re- MS113 search in MR imaging. Applications are already being de- A Stochastic Relationship between Fine and Coarse livered: for example in pediatric MRI we can speed up Scale Constitutive Parameters image aquisition from 8 minutes to 1 minute while maintaining diagnostic quality and confidence. This speedup is One objective of current multiscale research efforts is to significant because children can actualy still still for one incorporate fine-scale information into coarse-scale consti- minute and the same equipment can be used many more tutive laws in some “approximate’ sense. This approxi- times per hour. I will also discuss recent implementation mation necessarily introduces modeling error in the fine- advances on GPUs (ie processors originally developed for to-coarse scale property relationship. The present work treats this relationship as a stochastic mapping and em- AN10 Abstracts 109

ploys the maximum entropy principle to characterize this gate stochastic dimension reduction techniques for certain stochastic relationship by using fine-scale responses, that classes of network coupled systems that exploit their inher- are also meaningful at the coarse level, as constraints for ent structure to reduce the cost of the expansion. Applica- the coarse-scale responses. tions of these techniques to nuclear engineering problems will be presented. Sonjoy Das,YoussefM.Marzouk Massachusetts Institute of Technology Eric Phipps [email protected], [email protected] Sandia National Laboratories Optimization and Uncertainty Quantification Department [email protected] MS113 Efficient Algorithms for Computing Failure Proba- Mike Eldred bility Sandia National Laboratories Optimization and Uncertainty Estimation Department Computing failure probability is a critical step in many ap- [email protected] plications such as reliability based optimization. The most straightforward method is to sample the response space. This can be prohibitively expensive because each sample Roger Ghanem point requires a full scale simulation of the underlying phys- University of Southern California ical system. The other approach is to adopt an accurate Aerospace and Mechanical Engineering and Civil surrogate model for the system and sample the surrogate. Engineering This can be extremely efficient as long as one can con- [email protected] struct such a surrogate. In this talk we demonstrate that a naive surrogate approach is fundamentally flawed, no mat- Roger Pawlowski ter how accurate the surrogate is. Furthermore, we present Sandia National Labs a hybrid algorithm that combines the surrogate and sam- [email protected] pling approaches. The resulting method is accurate and much more efficient than direct sampling. Rigorous error John Red-Horse estimate will be presented, along with numerical examples. Validation and Uncertainty Quantification Processes Sandia National Laboratories [email protected] Jing Li, Dongbin Xiu Purdue University Rod Schmidt [email protected], [email protected] Sandia National Laboratories Electrical and Microsystems Modeling Department MS113 [email protected] Surrogate Driven Hazard Analysis Hayes Stripling Creating hazard maps for large jurisdictions threatened by Texas A&M University floods, landslides, debris flows involves physics models that Nuclear Engineering Department are highly non-linear and have dimensions of the inputs and [email protected] outputs that are both high subjecting us to a particularly acute form of the “curse of dimensionality”. We describe here a solution methodology based on creating a fast sur- MS114 rogate computational solver using the output of the sim- Models of Influenza Dynamics with Mixing in a ulator as data for a Bayesian statistical model, which we Cross-classified Population refer to as an emulator. The simulator is run for a few hun- dred to few thousand inputs, an emulator is created, and In this talk I will present some preliminary results on in- re-sampling uses the emulator to generate desired statis- fluenza dynamics obtained by incorporating heterogeneous tics. For example, an emulator might be constructed from mixing among strata in a cross-classified population model. 1024 simulations, and a Monte Carlo sampling can then be With the refinements in mixing, risks associated with par- performed using the emulator. We will describe here devel- ticular outcomes of interest to policy-makers can be more opment of a hierarchical version of this methodology that reliably assessed from multiple stochastic realizations of the enables parallel computation of the simulator runs and its model. use in generating a hazard map. Zhilan Feng Abani K. Patra Department of Mathematics SUNY at Buffalo Purdue University Dept of Mechanical Engineering [email protected] [email protected]ffalo.edu MS114 MS113 Mathematics of the 2009 Pandemic H1N1 Stochastic Dimension Reduction for Network Cou- I will present a model for the transmission dynamics of pled Systems the novel influenza H1N1 pandemic in a population. The Stochastic expansion techniques such as polynomial chaos model, which stratifies the infected population in terms of provide a powerful means for propagating uncertainty in risk of developing severe illness, will be rigorously analysed many types of nonlinear applications. However the cost to gain insight into its dynamical features. The impact of of these methods becomes prohibitive when large numbers mass vaccination on the disease spread will also be assessed. of stochastic variables are present. In this talk we investi- 110 AN10 Abstracts

EOS, and how mixtures of materials can be treated.

Abba Gumel John W. Grove University of Manitoba Computational Physics & Methods, CCS-2 Department of Mathematics Los Alamos National Laboratory [email protected] [email protected]

MS114 MS115 Mathematical Modeling of the Effectiveness of Front Tracking and its Coupling with Convection Facemasks in Reducing the Spread of Influenza Dominated Problems With limited supplies of antivirals and lack of effective vac- The renovated FronTier library, equipped with high or- cines, countries and individuals are looking at other ways der surface algorithms, is coupled with a set of new PDE to reduce the spread of novel H1N1. We construct and solvers. This includes the AMR-enabling compressible analyze a mathematical model in which a portion of the solver, the incompressible Navier-Stokes solver and the pre- population wears a facemask during the pandemic. We cipitation solver. We apply these new solvers to simulations conclude from our model that, if worn properly, facemasks of fluid mixing, bubbling, jet, fluid-structure interaction are an effective intervention strategy in reducing the spread and convection driven precipitation of subsurface flow. We of novel H1N1. will present some interesting verification and validation on these problems. James (Mac) Hyman Tulane University Xiaolin Li [email protected] SUNY at Stony Brook [email protected]

MS114 Responding to Pandemics in Real Time MS115 The Piecewise-Parabolic Boltzmann Advection I will discuss the challenges of allocating limited interven- Scheme (PPB) for Multifluid Gas Dynamics tions for pandemic influenza given the limited and biased data available at the time decisions must be made, focusing A new and powerful approach to multifluid hydrodynam- on the types of data that are and are not available, and on ics has been developed and applied to the turbulent mix- methods to use those data as effectively as possible. Case ing of fluids. The multifluid fractional volume variable is studies will include two or more of: assessing severity, as- advected using the Piecewise-Parabolic Boltzmann (PPB) sessing transmissibility, and targeting interventions. scheme, an extension to 3-D constrained advection of van Leer’s Scheme VI for 1-D. Ten moments in each grid cell Marc Lipsitch are updated by PPB in a strictly conserving formulation. Harvard School of Public Health Advantages of this approach and the results it delivers on [email protected] multiple applications are discussed. Paul R. Woodward MS115 Laboratory for Computational Science and Engineering Compressible Fluid Simulations Using OpenCL on University of Minnesota Modern Architectures [email protected] OpenCL is a new framework for portable code development across accelerated and multicore computing architectures. MS116 This talk will cover some of the challenges encountered Shallow Water Flow through Channels in developing a multiphysics solver for compressible fluid simulations using OpenCL. In particular, we will discuss The talk will discuss shallow water flows through channels several mid-level abstractions that we have developed to of variable cross section. The equations model nearly hor- improve the accessibility of OpenCL for scientific applica- izontal flows, and may derived from the Euler equations tions developers. by cross sectional averaging. They form a set of nonlinear hyperbolic conservation laws with geometric source terms. Ben Bergen The presence of geometric source terms gives rise to a range Los Alamos National Laboratory of interesting flows including a variety of non-trivial equi- [email protected] librium solutions. Recent years have seen a rapidly growing interest in development of numerical methods for shallow water systems. The talk will discuss a Roe-type upwind MS115 scheme for flows through rectangular channels, channels So You Want to Use a ”Real” Equation of State with trapezoidal cross sections, and channels with general cross section. General channel walls are approximated by We discuss the algorithmic, numerical, and practical con- piecewise linear segments, leading to piecewise trapezoidal siderations needed to use general equations of state (EOS) cross sections. Conservation, near steady-state accuracy, in a hydrodynamic code. Such models raise a host of is- velocity regularization and positivity near dry states will sues that must be addressed in a useful code. These include be discussed and results will be shown. the implementation of the EOS’s (e.g. analytic verses tab- ular), how material stiffness will affect the hydro solver, Gerardo Hernandez-Duenas, Smadar Karni what happens when a material leaves the domain of its University of Michigan Department of Mathematics [email protected], [email protected] AN10 Abstracts 111

MS116 putational challenges associated with these problems. For A Pseudo-spectral Method with the Window Tech- illustration purposes we consider the problem of estimat- nique for Kadomtsev-Petviashvili Equation ing the temperature in a flow field through thermostats with the specific application to designing efficient control In this talk, we will present a numerical method to study systems for high performance buildings. the initial value problem of the KP equation with certain initial waves. The numerical approach is based on the Lizette Zietsman peuso-spectral method with a window technique to take Virginia Tech care of the non-periodic condition at the computational Blacksburg, VA 24061-0123 boundary. We show that, for those initial waves, the so- [email protected] lutions asymptotically converge to some of the exact solutions in a locally defined L2-sense. MS117 Chiu-Yen Kao hp-Discontinuous Galerkin Method for Two-phase The Ohio State University Flow in Porous Media [email protected] There is a need for efficient and accurate numerical meth- Yuji Kodama ods for solving multiphase flow problems. In this talk, Ohio State University we show that high order discontinuous Galerkin meth- Department of Mathematics ods are promising candidates. In particular, we consider [email protected] two different formulations of the incompressible two-phase flow problems arising in porous media: ”phase-pressure, phase-saturation” formulation and ”global pressure, phase- MS116 saturation” formulation. We introduce implicit, fully cou- Streamline Visualization of Discontinuous Galerkin pled hp-schemes based on discontinuous Galerkin meth- Solutions Using Smoothness-Increasing Accuracy- ods to solve numerically the two-phase flow problem. Nu- Conserving Filters merical analysis (existence of the discrete solution, convergence) of the introduced schemes and simulations of the Visualizing streamlines obtained from discontinuous two-phase flow in homogeneous and heterogeneous media Galerkin (DG) approximations can be a challenging task are presented. due to the inter-element discontinuities. Recently, a smoothness-increasing accuracy-conserving filter has been Yekaterina Epshteyn applied as a tool to enhance the smoothness of the field Carnegie Mellon University and eliminate discontinuities between elements, thus re- [email protected] sulting in more accurate streamlines. Additionally, it also increases the order of accuracy of the approximation MS117 from O(+∞)toO(∈+∞) for linear hyperbolic equations Analyzing HDG Methods like Mixed Methods solved over a uniform mesh. We present an analysis of HDG methods closely paralleling The two alternative strategies for filtering the discontinu- the analysis of mixed methods. Specifically, we construct a ous Galerkin method take into account filtering over the en- projection operator with certain weak commutativity prop- tire field as well as filtering along a one-dimensional stream- erties, tailored to the structure of the HDG method. With line. The first implementation aids in the ability to use a this natural projection, the HDG method can be analyzed less restrictive time integrator. This filtering is done in a elegantly and transparently. tensor-product way. However, filtering near a boundary can become a problem. Additionally, this type of filtering Jay Gopalakrishnan can become expensive for computing solutions over multi- University of Florida dimensional geometries. The second alternative involves [email protected]fl.edu filtering as the streamline integration is performed using Forward Euler. This filtering along a streamline allows for reduction in computational cost. However, in previous im- MS117 plementations an improved one-sided post-processor was An Efficient S-DDM Scheme for Compressible needed as well as higher-order derivative information. In Flows in Porous Media this presentation, we discuss how to improve both types of streamline filtering through the use of more accurate Porous media flows are important in many areas of science one-sided filtering as well as using higher order derivative and engineering such as groundwater contamination mod- information. eling, environmental protection, and reservoir simulation, etc. The problems involve the physical features of the cou- Jennifer K. Ryan pling, nonlinearity, convection dominance, large scale field Delft University of Technology and long term prediction. In this talk, for solving large [email protected] scale compressible flows in porous media, we propose an efficient S-DDM scheme by combining the non-overlapping domain decomposition and the splitting technique. Nu- MS116 merical experiments are given to show the efficiency and MeasuresforSensorPlacementforEstimationof accuracy of the S-DDM approach. The method takes the PDE Systems attractive advantages of both the non-overlapping domain decomposition method and the splitting technique, which The location of sensors is critical in the design of controlled reduces computational complexities, large memory require- systems. In this talk we describe different measures to aid ments and long computational durations. The theoretical in the placement of sensors (and actuators). In particular, analysis of stability and convergence are also discussed in functional gains and system radii, and discuss the com- 112 AN10 Abstracts

this talk. This is joint work with C. Du. MS118 An Embarrassingly Parallel Benchmark to Study Dong Liang Architecture Heterogeneity York [email protected] Abstract unavailable at time of publication.

Brian Van Straalen MS117 Lawrence Berkeley National Laboratory Adaptive Discontinuous Galerkin Method for Con- Department N E R S C taminant Transport in Fractured Porous Media [email protected] Fractures play an important role in flow and transport processes through saturated and unsaturated geologic me- MS118 dia. Because the permeability in fractures is generally Algebraic Multigrid for Multicore Architectures greater than it in matrix by many orders of magnitude, fracture networks have the potential for being highly ef- Algebraic multigrid (AMG) solvers have proven to be fective pathways for conducting fluid containing contam- extremely efficient on distributed-memory architectures. inant species. One challenge in numerical simulation of However, when executed on modern multicore cluster ar- contaminant transport in this system arises from the dra- chitectures, we face new challenges that can significantly matic difference of convection rates between the matrix harm AMG’s performance. We discuss our experiences on and the fractures. In addition, the concentration in the various multicore architectures and present a set of tech- matrix is also tightly coupled with it within the fractures niques that help users to overcome the associated problems, by the molecular diffusion and mechanical dispersion in including thread and process pinning and correct memory the transverse direction. To treat this problem effectively, associations. We present results using both an MPI-only adaptive spatial and/or adaptive temporal discretizations and a hybrid MPI/OpenMP model. are necessary. In this talk, we will present adaptive discontinuous Galerkin method as applied to the simulation Allison H. Baker of the convection-diffusion-adsorption processes in cracked Center For Applied Scientific Computing porous media. Lawrence Livermore National Laboratory [email protected] Shuyu Sun Clemson University and KAUST Todd Gamblin, Martin Schulz, Ulrike M. Yang [email protected] Lawrence Livermore National Laboratory [email protected], [email protected], [email protected] MS117 Discontinouos Finite Volume Element Methods for MS119 Darcy’s Law Algebraic Multigrid for Incompressible Resistive Magnetohydrodynamics Motivated by the Crouzeix-Raviart finite elements, we develop nonconforming and discontinuous finite volume Magnetohydrodynamics (MHD) is a fluid theory that de- methods for the Darcy’s equation. Numerical experiments scribes plasma physics by treating the plasma as a fluid will be presented. We shall discuss also comparison with of charged particles. Hence, the equations that describe the mixed finite element method and coupling with trans- the plasma form a nonlinear system that couples Navier- port solvers. This is a joint work with Jiangguo Liu Stokes’ with Maxwell’s equations. This talk develops a (ColoState) and Xiu Ye (UALR). nested-iteration-Newton-FOSLS-AMG approach to solve this type of system. Most of the work is done on the Haiying Wang coarse grid, including most of the linearizations. We show Michigan Tech University that at most one Newton step and a few V-cycles are all [email protected] that is needed on the finest grid. Here, we describe how the FOSLS method can be applied to incompressible re- MS118 sistive MHD and how it can be used to solve these MHD problems efficiently in a full multigrid approach. An al- OPAL, A Parallel Accelerator Simulation Frame- gorithm is developed which uses the a posterior error esti- work for Present and Future Modeling Challenges mates of the FOSLS formulation to determine how well the Abstract unavailable at time of publication. system is being solved and what needs to be done to get the most accuracy per computational cost. A reduced 2D Andreas Adelmann time-dependent test problem is studied. The latter equa- Paul Scherrer Institut, Switzerland tions can simulate a large aspect-ratio tokamak. The goal tba is to resolve as much physics from the test problems with the least amount of computational work. This talk shows that this is achieved in a few dozen work units. (A work MS118 unit equals one fine grid residual evaluation.) In addition, Efficient, High-Quality Image Contour Detection a discussion of how the above methods relate to the energetics of the system will be given. Abstract unavailable at time of publication. James Adler Bryan Catanzaro Department of Mathematics EECS Department Penn State University University of California; Berkeley [email protected] [email protected] AN10 Abstracts 113

MS119 Michael Nicholas Algebraic Multigrid on the GPU Tulane University [email protected] Abstract unavailable at time of publication.

Nathan Bell MS120 NVIDIA Research Creep Ringing in Non-linear Viscoelastic Models [email protected] In rheometry, when a step stress is applied to certain materials, the initial response is an oscillating strain. These free MS119 oscillations arise form a coupling between the elasticity of Angular Multigrid Methods for Boltzmann Trans- the sample and the inertia of the apparatus. Studies using port Equations linear viscoelastic models have shown that analysis of this ringing can provide meaningful information of the coupling Beams of microscopic particles penetrating scattering between micro-structure and bulk viscoelastic properties. background matter play an important role in several appli- In this work we extend those studies to non-linear models. cations. Grid-based discretization of the governing Boltz- We compare signature responses from several models and mann transport equation leads to a very large system of their relation to the sample’s micro-structure. algebraic equations, as the continuum solution itself is a function of many variables. We discuss an angular multi- Paula Vasquez grid algorithm for a two-dimensional model problem, based Dept of Mathematics on a careful choice of relaxation and coarse-grid correc- University of North Carolina, Chapel Hill tion processes. Numerical experiments show rapid, grid- [email protected] independent convergence for typical electron-beam scattering. MS120 Scott Maclachlan, Christoph Börgers Flow Behavior in Sheared Biaxial Liquid Crystal Department of Mathematics Polymers Tufts University [email protected], [email protected] I will present a kinetic theory for flows of biaxial liquid crys- tals. This theory applies to both ellipsoidal and bent-core type nematogens. Phase behavior and phase transition in MS119 sheared biaxial liquid crystal flows will be discussed. In Algebraic Multigrid for Problems in Electromag- addition, rheological consequence and their dependence on netics the conformation of the nematogens will be presented as well. Problems in electromagnetics are a challenge for algebraic multigrid solvers. The discrete operator is often complex- Qi Wang valued, indefinite, and non-self-adjoint, resulting in low- University of South Carolina energy oscillatory error components. These oscillatory [email protected] modes are not effectively handled by standard relaxation and coarsening procedures. We propose elements in the multigrid process that recognize the wave-like near null- MS120 space in the problem. Along with improved coupling infor- Are Viscoleastic Fluids Observable? mation and more accurate interpolation, this results in a more robust method for scattering problems. Observability is the ability to determine uniquely the state of the system from observable quantities. We apply the Luke Olson, Jacob Schroder observability rank condition to study the observability of Department of Computer Science various viscoleastic fluids under imposed shear of exten- University of Illinois at Urbana-Champaign sional flows. [email protected], [email protected] Hong Zhou Department of Applied Mathematics MS120 Naval Postgraduate School, Monterey, CA Regularized Slender Body Theory [email protected] Various slender body theories allow for the representation of filaments in Stokes’ flow by a distribution of fundamen- MS121 tal solutions along the filament center line. We revisit the Sensitivity Analsysis for Glucose Insulin Model theory in the context of regularized forces in a small neighborhood along the center line. The regularization produces This talk we will presents a sensitivity identifiably analysis a smooth final expression that helps eliminate the compu- of a mathematical model of glucose insulin system. This tational instabilities of the unregularized formulas. The model incorporates sufficient structure and complexity to derivations of theories corresponding to those of Lighthill allow for examining the metabolic action and regulation of and of Keller and Rubinow are outlined. Consistency with glucose and insulin systems. The complexity of the model these theories is verified and numerical examples are pre- allows for the representation of a variety of modes and sites sented. for action but at the same time the number of parameters renders the validation with accessible data problematic. Ricardo Cortez Sensitivity identifiability techniques are employed to ex- Tulane University amine which parameters are mostly likely identifiable for Mathematics Department a variety of potential sources of data on the state of the [email protected] system. The information provided by this analysis allows 114 AN10 Abstracts

for a reasonable reduction in parameters to be estimated coelasticity of Ovine Arteries and can be used to consider which experimental tests might best allow for study of the control response patterns. A better understanding of the biomechanical properties of the arterial wall can aid in the improvement of graft de- Mostafa Bachar sign and implementation. In this study we focus on the Department of Mathematics constitutive relationship of the arterial wall to describe the King Saud University dynamic response of changes in cross-sectional vessel area [email protected] induced by time-varying arterial blood pressure. We used inverse mathematical modeling on a 4-parameter Kelvin Karl Thomseth (linear) viscoelastic model and a 5&6 -parameter nonlinear Istituto di Ingegneria Biomedica del CNR viscoelastic models and tested them on in-vitro data from Area di Ricerca di Padova Corso Stati Uniti, 4 I-35127 male Merino sheep. Parameter estimation, sensitivity and Pado statistical analysis approaches were used to investigate and [email protected] describe the viscoelastic vascular wall properties by allowing us to compare models and choose the most adequate Jerry Batzel one that enabled parameter estimation within physiological Institute for Mathematics and Scientiﬁc Computing ranges. University of Graz Daniela Valdez-Jasso [email protected] Department of Mathematics North Carolina State University MS121 [email protected] Generalized Sensitivity Functions for Multiple Output Systems Daniel Bia, Yanina Zocalo, Ricardo Armentano Universidad de La Republica, Montevideo Generalized sensitivity functions as introduced by K. Uruguay Thomaseth and C. Cobelli can also be deﬁned for multi- [email protected], [email protected], ple output systems and allow deciding if measurements for [email protected] an additional output of a system may improve the quality of parameter estimates. It is also shown that generalized Mansoor Haider, Mette Olufsen sensitivity functions provide a reasonable approximation Department of Mathematics of the partial derivatives of the estimated parameter vec- North Carolina State University tor with respect to the coordinates of the nominal or true [email protected], [email protected] parameter vector.

Franz Kappel MS122 Department of Mathematics Towards Implicit Immersed Boundary/finite Ele- University of Graz ment Methods [email protected] As part of a long-term research effort to develop realistic three-dimensional models of cardiovascular fluid-structure MS121 interaction (FSI), we have recently developed a new version Nonlinear Filtering and Parameter Estimation for of the immersed boundary (IB) method which allows for Complex Biological Systems finite element (FE) representations of the elasticity of the immersed elastic structures. In this talk, I will provide an Mathematical modeling plays an important role in study- overview of this new IB/FE method and its application ing complex biological systems and parameter estimation is to cardiovascular FSI, and describe progress towards the an essential component of developing mathematical mod- development of an efficient implicit IB/FE method. els. However, accurate estimation of parameters is computational challenging as high fidelity models can contain Boyce E. Griffith a large number of parameters. Nonlinear filtering is one Leon H. Charney Division of Cardiology method that can be used to sequentially estimate both the New York University School of Medicine state and parameters. We shall examine the application of boyce.griffi[email protected] these filtering techniques on nonlinear models with varying sets of parameters. MS122 Brett Matzuka A Multigrid Method for the Coupled Implicit Im- Biomathematics Graduate Program mersed Boundary Equations North Carolina State University [email protected] In this talk a multigrid method for solving the linearized immersed boundary equations that arise in implicit time Hien T. Tran discretizations is presented. The method simultaneously Department of Mathematics solves the equations on the Eulerian and Lagrangian grids. North Carolina State University Numerical tests which compare the efficiency of the method [email protected] with an explicit-time method are presented for a variety of test problems. Analytical results are presented for sim- plifed model problems to provide insight into the success MS121 and limitations of the method. Modeling and Model Analysis of Nonlinear Vis- Robert D. Guy Mathematics Department AN10 Abstracts 115

University of California Davis algorithm is investigated using applications in the areas of [email protected] signal processing and image reconstruction.

Bobby Philip William Hager Oak Ridge National Laboratory University of Florida [email protected] [email protected]ﬂ.edu

MS122 MS123 An Implicit Immersed Interface Method with the An Augmented Lagrangian Approach for Sparse Velocity Decomposition Approach Principal Component Analysis

The implicit time-stepping method that we present is based Principal component analysis (PCA) is a widely used tech- on the velocity decomposition approach, in which fluid ve- nique for data analysis and dimension reduction with nu- locity is split into a Stokes part, determined by the Stokes merous applications in science and engineering. However, equations and the singular interfacial force, and a regular the standard PCA suffers from the fact that the principal part, given by the Navier-Stokes equations with a body components (PCs) are usually linear combination of all the force resulting from the Stokes part. The immersed in- original variables, and it is thus often difficult to interpret terface is advanced implicitly, using an approach that is the PCs. To alleviate this drawback, various sparse PCA cost-effective and does not require the iterative solution of approaches were proposed in the literature. Despite success a system of coupled nonlinear equations. in achieving sparsity, some important properties enjoyed by the standard PCA are lost in these methods such as uncor- Anita T. Layton relation of PCs and orthogonality of loading vectors. Also, Duke University the total explained variance that they attempt to maximize Department of Mathematics can be too optimistic. In this talk we propose a new formu- [email protected] lation for sparse PCA, aiming at finding sparse and nearly uncorrelated PCs with orthogonal loading vectors while ex- plaining as much of the total variance as possible. We also MS122 develop a novel augmented Lagrangian method for solving The Use of Projection in the Immersed Boundary a class of nonsmooth constrained optimization problems, Method which is well suited for our formulation of sparse PCA. We show that it converges to a feasible point, and moreover This study focuses on the role of projection in the im- under some regularity assumptions, it converges to a sta- mersed boundary method. Analogous to how projection tionary point. Additionally, we propose two nonmonotone is used to enforce incompressibility, projection can also be gradient methods for solving the augmented Lagrangian used to meet the no-slip constraint. The present implicit subproblems, and establish their global and local conver- approach requires no ad-hoc relations for determining the gence. Finally, we compare our sparse PCA approach with boundary force and can be extended to fluid-structure in- several existing methods on synthetic, Pitprops, and gene teraction problems. Techniques for accelerating the com- expression data, respectively. The computational results putation (nullspace method) and satisfying other physical demonstrate that the sparse PCs produced by our approach constraints will be presented. substantially outperform those by other methods in terms of total explained variance, correlation of PCs, and orthog- Kunihiko Taira onality of loading vectors. Moreover, the experiments on Honda R&D Co., Ltd. random data show that our method is capable of solving Fundamental Technology Research Center large-scale problems within a reasonable amount of time. [email protected] Zhaosong Lu Clarence Rowley Department of Mathematics Princeton University Simon Fraser University Department of Mechanical and Aerospace Engineering [email protected] [email protected] Yong Zhang Tim Colonius Simon Fraser University Division of Engineering and Applied Science [email protected] California Institute of Technology [email protected] MS123 Regularization Methods for Sum of Squares Relax- MS123 ations in Large Scale Polynomial Optimization Gradient-based Methods for Sparse Recovery We study how to solve sum of squares (SOS) and Lasserre’s The convergence rate is analyzed for the SpaSRA algorithm relaxations for large scale polynomial optimization. When (Sparse Reconstruction by Separable Approximation) for interior-point type methods are used, typically only small minimizing a sum f(x)+ψ(x), where f is smooth and or moderately large problems could be solved. This pa- ψ is convex, but possibly nonsmooth. It is shown that per proposes the regularization type methods which would if f is convex, then the error in the objective function at solve significantly larger problems. We first describe these iteration k is bounded by a/(b + k) for suitable choices methods for general conic semidefinite optimization, and of a and b. Moreover, if f is strongly convergence, then then apply them to solve large scale polynomial optimiza- the convergence is R-linear. An improved version of the tion. Their efficiency is demonstrated by extensive numer- algorithm based on a cycle version of the BB iteration and ical computations. In particular, a general dense quar- an adaptive line search is given. The performance of the tic polynomial optimization with 100 variables would be 116 AN10 Abstracts

solved on a regular computer, which is almost impossible University of Pittsburgh by applying prior existing SOS solvers. [email protected]

Jiawang Nie University of California, San Diego MS124 [email protected] Energy Minimizers of a Thin Film Equation with Born Repulsion Force

MS123 We consider a singular elliptic equation modeling steady A Derivative-free Regularized Trust Region Ap- states of thin film equation with both Van der Waal force proach for Least-squares Minimization and Born repulsion force. We studied the corresponding energy minimizing solutions and their behavior as Born We develop a framework for a class of derivative-free algo- repulsion force tends to zero. rithms for the least-squares minimization problem. These algorithms are based on polynomial interpolation models Huiqiang Jiang and are designed to take advantages of the problem struc- Department of Mathematics, University of Pittsburgh ture. Under suitable conditions, we establish the global [email protected] convergence and local quadratic convergence properties of these algorithms. Promising numerical results indicate the algorithm is efficient and robust when finding both low ac- MS124 curacy and high accuracy solutions. Comparisons are made Transonic Flow and Isometric Embedding with standard derivative-free software packages that do not exploit the special structure of the least-squares problem Transonic flows in gas dynamics and isometric embedding or that use finite differences to approximate the gradients. problem in geometry will be discussed. Their connection will be presented.

Hongchao Zhang Dehua Wang Department of Mathematics and CCT University of Pittsburgh Louisiana State University Department of Mathematics [email protected] [email protected]

MS124 MS125 Regularity of The Free Boundary in the Inverse Fast Sampling by Polynomial Acceleration First Passage Problem We give a new analysis that shows the equivalence of Gibbs We study the inverse ﬁrst passage problem: Given a dif- samplers for normal distributions and the classical station- fusion process {Xt}t≥0 on a probability space (Ω,P)and ary iterative processes used to solve linear systems, that a probability p on [0, ∞), ﬁnd a boundary, x = b (t), such are now considered very slow. We establish a general form that p is the survival probability that X does not fall below of this result, and then show how these samplers can be b, i.e., for each t ≥ 0, sped up appreciably by preconditioning and polynomial acceleration which are common acceleration techniques from p (t)=P ({ω ∈ Ω|Xs (ω) ≥ b (s)for∀s ∈ (0,t)}) . numerical linear algebra.

We show that when p is smooth and has negative slope, Colin Fox this viscosity solution, and therefore also the unique usc University of Otago, New Zealand solution of the inverse problem, is smooth. Consequently, [email protected] this viscosity solution furnishes a unique classical solution to the free boundary problem associated with the inverse first passage problem. Albert Parker Montana State University Xinfu Chen Department of Mathematics University of Pittsburgh [email protected] [email protected] MS125 MS124 Couplings and Variance Reduction for MCMC Global Existence in Critical Spaces for Compress- ible Barotropic Viscoelastic Flows In this talk, I will explain how Markov couplings can be used to improve the accuracy of Markov chain Monte We investigate the global existence of strong solutions to Carlo calculations in some situations where the steady- the compressible barotropic viscoelastic flow. The initial state probability distribution is not explicitly known. The data are supposed to be close to a stable equilibrium with technique generalizes the notion of control variates from constant density. Using uniform estimates for an auxiliary classical Monte Carlo integration. The method will be il- hyperbolic-parabolic system with a convection term, we get lustrated using simple models of nonequilibrium transport. the global well-posedness in a functional setting invariant Time permitting, I will discuss extensions of these ideas to with respect to the scaling of the associated equations. We stochastic differential equations. also show a smoothing effect on the velocity, a L1 decay on the difference between the density and the constant refer- Kevin K. Lin ence state, and a L1 decay on the difference between the Department of Mathematics deformation gradient and the constant reference state. University of Arizona [email protected] Xianpeng Hu AN10 Abstracts 117

Paul J. Atzberger response to epidemiological events. University of California-Santa Barbara [email protected] Alhaji Cherif Arizona State University Jonathan Goodman [email protected] Courant Institute USA MS126 [email protected] A Sensitivity Matrix Based Methodology for In- verse Problem Formulation Jonathan C. Mattingly Duke University We propose an algorithm to select parameter combina- [email protected] tions that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations MS125 that correspond to full-rank sensitivity matrices. Second, Large-scale Stochastic Newton Methods for Statis- the algorithm involves uncertainty quantification by using tical Inverse Problems Governed by PDEs the inverse of the Fisher Information Matrix. Nominal values of parameters are used to explore the effects of remov- Abstract not available at time of publication. ing certain parameters from those to be estimated using James R. Martin OLS procedures. University of Texas at Austin Ariel Cintron-Arias Institute for Computational Engineering and Sciences East Tennessee State University [email protected] Johnson City, TN [email protected] Omar Ghattas University of Texas at Austin [email protected] MS126 Forecasting the Impact of Pandemic (H1N1) 2009 in the United MS125 Multiscale Inversion Techniques for Flow in Porous In this talk, I will discuss the results from a study that fore- Media casted the impact of pandemic (H1N1) 2009 in the United States. The results indicated that the overall impacts of We present a statistical inversion technique for flow and pandemic (H1N1) 2009 were mild and similar to seasonal transport problems in which measurements occur at dif- influenza. However, unlike seasonal influenza, which usu- ferent spatial scales. A Bayesian framework, employing ally targets the elderly, pandemic (H1N1) 2009 targeted a Karhunen-Loève representation of the material proper- school-age children. ties of interest, enables inference from sparse direct and indirect data. In particular, we explore multi-level Markov Sara Del Valle chain Monte Carlo algorithms aimed at improving the com- Los Alamos National Laboratory putational efficiency and accuracy of estimating multiscale Los Alamos National Laboratory permeability fields. [email protected]

Bart G. Van Bloemen Waanders, Jaideep Ray Sandia National Laboratories MS126 [email protected], [email protected] Epidemic Spread of Influenza Viruses: The Impact of Transient Populations on Disease Dynamics Youssef M. Marzouk Massachusetts Institute of Technology The recent “swine flu” pandemic and “avian flu” outbreaks [email protected] have brought increased attention to the study on the role of animal populations as reservoirs for pathogens that could Sean A McKenna invade human populations. Here, we study the interac- Sandia National Laboratories tions between transient and resident bird populations and [email protected] their role on dispersal and persistence in the control of avian diseases. Our results show that mixing residents and migratory bird populations play an important role on the MS126 patterns of disease spread. Homo Psychologicus: Behavioral Aspects of Ratio- Karen Rios-Soto nal and Bounded Rational Epidemics Universidad de Puerto Rico Recently, we have seen an increase in the use of theoretical karen [email protected] models to reveal the subtleties of contact processes underlying the transmission mechanisms and the biological con- PP1 straints of host-pathogen interactions. However, individual objective and subjective vulnerabilities to disease and Statistical Analysis of La1−xSrxCoO3−d Perovskite their behavioral outcomes have been ignored. In this talk, Oxygen Vacancy Data we formulate a model of homo psychologicus’s pathogen- La1−xSrxCoO3−d perovskite is an essential material for avoidance mechanism and investigate aversive behavioral solid oxide fuel cells. How the oxygen vacancy concentration (d) changes with temperature, partial pressure, and 118 AN10 Abstracts

strontium content (x) determines the performance of the in this area. material. We have performed statistical analysis and inference on the extensive and scattered experimental values Nicholas D. Brubaker, John A. Pelesko of d by developing code to visualize the data and apply- University of Delaware ing weighted regression methods. Our model to predict d [email protected], [email protected] and our regression methods will be presented. Advisers: James Saal, Penn State; Jingyan Zhang, Penn State; Gre- gory Somers, State College Area High School; Qiang Du, PP1 Penn State; and Zi-Kui Liu, Penn State. A Boom Model: Trader Herding and Autocorrela- tion Through Communication Akos Albert, Daniel Clothiaux, David Liu, Christoph Schlom In this paper we study noise traders that communicate and State College Area High School trade with each other in a market. We begin by comput- [email protected], [email protected], ing a statistic which identifies a boom, and use it on the [email protected], [email protected] NASDAQ-100 dot-com “bubble.’ We next generalize the classical geometric Brownian motion stock model accord- ingly. We represent individual traders that observe each PP1 others’ past n daily returns using a nonlinear vector au- Allosteric Regulation of Ribonucleotide Reductase: toregressive NLVAR(n) process. We model traders endoge- A Qualitative Model nously creating a market price. We measure autocorrelation and herding as functions of traders’ communication We developed a qualitative mathematical model of the al- level (α) and number of past daily returns (n)thatthe losteric regulation of Ribonucleotide Reductase (RNR). Us- traders rely on. We find that autocorrelation and herding ing a system of ordinary differential equations, we modeled increase with communication level α, and they decrease the kinetic behavior of substrate production and regulation with n. Under this model, we can specify α and n lead- of RNR which utilizes two regulatory sites to modulate the ing to traders forming spontaneous herds without specific outflow of the four types of dNDPs. The model reproduces leaders and thus to price booms. Finally we see that our and predicts behavior consistent with the enzyme’s func- model replicates the statistical property we examined of tion in several special cases. Experiments designed to test the NASDAQ-100 boom. the validity of the model are proposed. Advisers: Hongyu He and Naohiro Kato, Louisiana State University. Suneal K. Chaudhary Monmouth University Philip Benge, Nicholas Cobar, James Stowe [email protected] Louisiana State University [email protected], [email protected], [email protected] PP1 Parallel Lagrange-Newton-Krylov-Schwarz Algo- rithms for Shape Optimization of Steady Incom- PP1 pressible Flows A Modified Wilson-Cowan Model to Describe Mi- tral and Granule Cell Behavior in the Mouse Ol- We study parallel Lagrange-Newton-Krylov-Schwarz algo- factory Bulb rithms for two dimensional shape optimization problems governed by steady incompressible Navier-Stokes equa- We explore the behavior of mitral and granule cells in tions discretized by finite element methods on unstructured the mouse olfactory bulb using a modified Wilson-Cowan meshes. .A one-shot approach is introduced and the large model. This model describes the average activity of ex- KKT system is solved with a domain decomposition pre- citatory and inhibitory neural populations. We have per- conditioned Newton-Krylov method. The main focus is on formed stability analysis and calculated bifurcation dia- the robustness of the method and the parallel scalability of grams, power spectral densities, and leading Lyapunov ex- the algorithms on supercomputers with a large number of ponents to study the effects of external excitation to the processors. system. We furthermore define parameter regimes that quantitatively match experimental data relating to local Rongliang Chen field potentials in the bulb. Adviser: Matthew Valley and Department of Computer Science, University of Colorado Stuart Firestein, Columbia University. [email protected]

Chanan Braiman, Chagit Braiman Xiao-Chuan Cai Columbia University University of Colorado, Boulder [email protected], [email protected] Dept. of Computer Science [email protected] PP1 Electrostatic Deﬂections of An Elastic Membrane PP1 Modeling Sensory Input to the Lamprey Spinal Surface tension and electrostatic forces have been observed Cord in many physical systems. Now, with interest piqued by applications to many micro- and nanoelectromechanical sys- We develop and evaluate a neural model of the lamprey’s tems (MEMS and NEMS), their study is more relevant central pattern generator of locomotion, implemented as than ever. Such systems that include the interplay of both a chain of coupled oscillators. We simulate sensory in- forces become more complicated and compelling to ana- put from edge cells, which measure the body’s curvature, lyze. In this talk, we explore recent theoretical work work by forcing the chain at various positions, one at a time. Simulations that vary chain length, forcing position, and AN10 Abstracts 119

forcing connection strength have shown a monotonic in- PP1 crease in entrainment range as a function of forcing position A Simple Tonotopic Model of the Mammalian Au- along the chain. Advisers: Kathleen Hoffman, University ditory Pathway of Maryland Baltimore County; Tim Kiemel, University of Maryland, College Park; and Eric Tytell, University of This poster will show some interesting features of a sim- Maryland, College Park. ple tonotopic model of the auditory system in mammals. This is demonstrated with the frequency domain as well as Geoffrey D. Clapp through spectral content. University of Maryland - Baltimore County [email protected] Rebekah D. Downes University of North Florida [email protected] PP1 Role of Transportation, Social Distance, and De- layed Vaccination on the Spread of A/H1N1 in PP1 Mèxico During 2009 (SIAM-WCD) Neuronal Bursting: Interactions of the Persistent Sodium and CAN Currents A metapopulation model was developed to investigate possible mecha-nisms underlying the different epidemic waves Previous modeling efforts for individual neurons in the pre- observed in Mexico during the novel swine origin influenza Bötzinger complex have focused on either the persistent SOI-A/H1N1 pandemic of 2009. The model captures dy- sodium current (INaP) or the calcium-activated nonspe- namics present in official data about the AH1N1 epidemic cific cationic current (ICAN). Here, we analyze the effects in Mexico. The model considers six different epidemio- of including both INaP and ICAN within one model. In- logical classes: susceptible, incubating, infected but un- terestingly, we find that the presence of INaP enhances the confirmed, infected and confirmed, recovered and vacci- ability of the cell to emit bursts featuring a period of de- nated. The model allows the study of transient, and possi- polarization block; previously, such bursts were only seen bly random perturbations of the parameters in the model, in the model with ICAN. thus enabling the study of possible scenarios and their different outcomes, but without restricting the dynamics to Justin Dunmyre fixed rules. Populations were assumed to be arranged as University of Pittsburgh a starred graph with center at Mexico City. The differ- [email protected] ent populations were assumed to interact by means of land transportation. The effects of social distancing and school Jonathan E. Rubin closures to the time course of the epidemic were investi- University of Pittsburgh gated in conjunction with local transportation. Our simu- Department of Mathematics lations indicate that transportation alone does not explain [email protected] the observed delays in the epidemic outbreaks for the different Mexican states. Nevertheless, a combination of local transport, and decrease in contact at specific dates during PP1 the year is sufficient to explain the different waves and Anisotropic Phase Field Equations and Macro- general characteristics of the epidemic outbreak observed scopic Conditions within Mexico. The numerical paradigm implemented to obtain the simulations for this model is suitable for other Recently [to appear in DCDS]we derived, from an integral phenomena in which changes in the dynamics of the system form, an extended version of phase field equations of arbi- change, whether or not randomly. trary order (for smooth interfaces with anisotropy) under the assumption that kernel (interaction potential) of the MayteéCruz-Aponte integral form consisted of finite sum of Fourier modes. We Arizona State University show that, even when the interaction kernel is only contin- [email protected] uous, the same macroscopic quantities,in the asymptotic limit, are well defined and satisfy thermodynamic relations at the interface. PP1 Numerical Simulations Surfactant Spreading on Emre Esenturk Thin Liquid Films University of Pittsburgh [email protected] Surfactant deposited on a liquid surface spreads due to im- balance of forces at its leading edge, acting on the liquid to create an expanding surface wave. Numerical simula- PP1 tions of this surfactant-liquid system are performed to ex- Hybrid Asymptotic-Numerical Method for ODEs plore how different initial conditions affect resulting wave dynamics. Both one- and two-dimensional regimes are con- Our research was motivated by the desire to develop an sidered. Data from numerical simulations is compared to ODE solver that encapsulates the properties of the differ- experimental results. Adviser: Rachel Levy, Harvey Mudd ential equation into a numerical method. We formulate College. a hybrid asymptotic-numerical method by incorporating the initial conditions into the differential equation so that Georgi Dinolov we arrive at a better understanding of the local proper- Harvey Mudd College ties and their influence on the solution. Using dimensional [email protected] analysis to scale the solution, we were able to formulate a novel approach to the solution that is extremely competitive with existing methods. Advisers: Raymond Chin and Giovanna Guidoboni, Indiana University-Purdue Univer- 120 AN10 Abstracts

sity Indianapolis. Department of Mathematics [email protected] Tyler Foxworthy Indiana University Purdue University Indianapolis Ivan Yotov [email protected] Univeristy of Pittsburgh Department of Mathematics Eric Angleton [email protected] Indiana University-Purdue University [email protected] Ming Zhong University of Pittsburgh PP1 [email protected] Vaccinating Against Hpv in Dynamical Social Net- work PP1 We develop a dynamical network model to examine the rel- Time-Optimal Control of Emergency Response Lo- ative merits of strategies for vaccinating women against the gistics: A Case Study sexually transmitted Human Papillomavirus, which can in- This paper begins the analysis of optimal control of emer- duce cervical cancer. The model community is represented gency response logistics under a bioterror attack in the as a sexual network of individuals with links dynamically case of anthrax, which is a hybrid system consisting of a created and destroyed through statistical rules based on continuous-time dynamics and a resetting dynamics. The the node characteristics. Various strategies for distribut- necessary conditions for time-optimal hybrid control are ing an allotted number of doses of vaccine are tested for given, based on the calculus of variations and dynamic pro- effectiveness in reducing the incidence of cervical cancer. gramming. To solve the hybrid Hamilton-Jacobi-Bellman Pamela B. Fuller equation, a wavelet-based approach is proposed. A gradi- Rensselaer Polytechnic Institute ent algorithm is implemented and used to test the queue- [email protected] ing network model as well as the algorithm’s own reliability. Experimental simulation results are presented and discussed. PP1 Qing Hui Analyzing a Gasdynamic System Via Characteris- Department of Mechanical Engineering tics Texas Tech University A wealth of analysis has been completed in applied math- [email protected] ematics involving physical models that incorporate combustion theory. In particular, much attention has been PP1 directed towards the modeling of reactive gasdynamic systems, which typically utilizes asymptotics. In this work Sensitivity and Anisotropy in the Quasilinear El- we analyze such a system without the usage of asymp- liptic Non-Darcy Model totics by considering a numerical estimate for a tempera- We consider several variants of the quasilinear elliptic non- ture function along a characteristic curve. We supplement Darcy model for flow in porous media. We are interested this analysis with the development and implementation of in the effects of anisotropy and in sensitivity to the model a numerical procedure. parameters such as powers of velocity and coefficients. In Daniel J. Galiffa general, sensitivities to model parameters may not be well Penn State defined but in some cases we can express them in terms Penn State Erie, The Behrend College of known quantities. We also explore a coupled transport [email protected] problem and discuss sensitivities in that problem. Ken Kennedy,M.Peszynska PP1 Oregon State University [email protected], A Stochastic Mortar Mixed Finite Element Method [email protected] for Flow in Porous Media with Multiple Rock Types PP1 We present an efficient multiscale stochastic framework for uncertainty quantification of flow through porous media. Applications of a Residual a-Posteriori Estimator The governing equations are based on Darcy’s law with for Coupled Elliptic and Parabolic Systems of Pdes nonstationary stochastic permeability represented as a sum We consider systems modeling coupled flow and transport of Karhunen-Loeve expansions, meant to represent multi- in subsurface and robust a-posteriori estimates for their ple rock types. The approximation uses stochastic colloca- finite element discretizations. The examples include classi- tion on either a tensor product or a sparse grid, and cou- cal Barenblatt model of double-diffusion as well as various ples it with a domain decomposition algorithm known as models in which kinetic relationships replace equilibrium the Multiscale Mortar Mixed Finite Element Method. We isotherms, or phase transition constraints. In particular employ a Multiscale Flux Basis, which reduces subdomain we present modeling methane and carbon dioxide in coal solves on each interface iterations to linear combinations beds and of methane hydrates. The estimator helps to of the basis functions, leading to a very efficient algorithm. construct an adaptive multilevel grid for each component Error analysis and numerical experiments are presented. of the system. Benjamin Ganis Viviane Klein University of Pittsburgh AN10 Abstracts 121

Oregon State University numbers are also investigated in the work [email protected] Hsueh-Chen Lee Malgorzata Peszynska General Education Center Department of Mathematics Wenzao Ursuline College of Languages, Kaohsiung, Oregon State University Taiwan [email protected] [email protected]

Tsu-Fen Chen PP1 Department of Mathematics Extensions of Sub-Linear Spectral Methods to Two National Chung Cheng University Dimensions [email protected]

We investigate spectral methods on sub-Nyquist grids us- Chun-Lin Lee ing randomized and deterministic sub-linear time Fourier Department of Institute of Life Science algorithms. These algorithms identify k of the most sig- National Taitung University,Taitung, Taiwan niﬁcant frequencies in the Fourier expansion of a given [email protected] frequency-sparse signal of length N k and estimate their coeﬃcients in poly(k, log(N)) time, using only a sub-linear number of samples. We extend previous results to two- PP1 dimensional Poisson and Helmholtz equations. Practical Sound Source Separation via Tensor Decomposi- implementation issues are also discussed. tion with Sparse Factors

David J. Lawlor We present a new tensor-based numerical method for sound Michigan State University source separation. From a tensor data structure, each [email protected] waveform of the musical instruments is obtained from a multi-channel signal mixtures. Our technique relies on 1 Andrew Christlieb minimization for higher-order tensors. We demonstrate our Dept. of Mathematics algorithm on several music samples. Michigan State University [email protected] Na Li Clarkson University Anna Gilbert Dept. of Mathematics Department of Mathematics [email protected] University of Michigan [email protected] Carmeliza Navasca Clarkson University [email protected] PP1 An Investigation of An Inequality Involving Roots PP1 In their aritcle, titled ”Simple Trigonometric substitutions AWM Workshop: Direct Sparse Deblurring with broad results” on ”Mathematical Reflections” journal, Campos Daniel and Verdiyan Verdan proposed an inter- We propose a deblurring algorithm that explicitly takes esting inequality which had appeared in several occasions into account the sparse characteristics of natural images in MathLinks forum. In this paper, we will present two and does not entail solving a numerically ill-conditioned new solutions to this inequality problem. We also consider backward-diffusion. The key observation is that the sparse many generalizations to this inequality from different per- coefficients that encode a given image with respect to an spectives. Finally, we will apply the results to solve some over-complete basis are the same that encode a blurred ver- other difficult inequality problems. sion of the image with respect to a modified basis. Follow- ing an “analysis-by-synthesis’ approach, an explicit gener- Tuan N. Le ative model is used to compute a sparse representation of Fairmont High School the blurred image, and the coefficients of which are used to [email protected] combine elements of the original basis to yield a restored image. We compare our algorithm against some state-of- the-art deblurring methods. PP1 Least-Squares Finite Element Methods for Incom- Yifei Lou pressible Non-Newtonian Flow Problems University of California Los Angeles yfl[email protected] The goal of this work is to implement least squares finite element approaches for the equations governing non- Newtonian flows such those occurring in polymer processes PP1 and blood flow in arteries. By properly adjusting the im- AWM Workshop: Application of Population Dy- portance of the mass conservation equation and a carefully namics to Study Heterotypic Cell Aggregations in chosen nonlinear weighting function, the least-squares so- the Near-Wall Region of a Shear Flow lutions exhibit optimal L2-norm error convergence in all unknowns or better in each dependent variable. Numeri- This work focused on the modeling of polymorphonuclear cal solutions for flows through a 4-to-1 contraction channel neutrophils tethering to the vascular endothelial cells, and will be considered. The effects of the viscosity, Weissenberg subsequential tumor cell emboli formation in a shear flow, an important process of tumor cell extravasation from the 122 AN10 Abstracts

circulation during metastasis. A population balance model searchers and as such, decomposing/factoring the data re- is utilized, which for the first time, to our best knowledge, veal some of these useful features. We shall consider the a multiscale near-wall collision model reconciles the effect decompositions and approximation of a high definition im- of deformation on cell coagulation procedure, and works age for compression. We shall offer other algorithms such for general ratios of heterotypic cell. as the FLRMA (Fast Low Rank Matrix Approximation) that approximates such decompositions with smaller com- Yanping Ma putational cost. In addition, we shall analyze the numerical Pennsylvania State University results and compare them to some other well know approx- [email protected] imation schemes such as the Singular Value decomposition and a least square solver. PP1 Mechie Nkengla AWM Workshop: A Mathematical Model for the University of Illinois at Chicago Spread of Animal Diseases in the United States [email protected] with a Case Study on Rinderpest

Animal diseases are important in world economics, national PP1 security, and biodiversity. We create a spatially explicit, Break-up of an Underwater Bubble: Singularity, stochastic model for the spread of multi-host animal dis- Memory and Interference eases in the United States with a case study of the highly virulent rinderpest. We explore geographical spread on a Recent works revealed that dynamics near break-up of an county level and different mitigation strategies. A forward underwater bubble does not evolve into a singular, univer- sensitivity analysis indicates important disease parameters sal form, independent of initial conditions. Instead, asym- and containment approaches. Generalizations of control metries in initial conditions excite vibrations in the neck strategies for rinderpest may be effective for other conta- shape that dominate the final break-up. We show that a gious animal diseases. model approximating the interaction between vibrational modes as linear interference gives outcomes in agreement Carrie A. Manore with simulation results. Exceptions occur for initial states Oregon State University near threshold values for which the model predicts a qual- [email protected] itative change in final outcome. Adviser: Wendy Zhang, University of Chicago. PP1 Samuel Oberdick,LipengLai Optimal Strategies Under Limited Vaccination University of Chicago (SIAM-WCD) [email protected], [email protected]

The importance of preparing for influenza pandemics is critical. We devise optimal vaccination strategies in the PP1 face of limited vaccine doses by using a mathematical The Role of Anti-inflammatories in Pattern Forma- model of influenza transmission. The sensitivity of our tion for Chemotaxis Models results to varying certain epidemiological parameters including the basic reproduction number is studied. In par- The role of anti-inflammatories in pattern formation for ticular, we study scenarios of unlimited and realistically chemotaxis models We study the spread and regulation of limited vaccine scenarios. We introduce a constrained opti- inflammation in the absence of specific pathogenic stim- mal control problem to construct different vaccination poli- uli. We seek to understand the forms of rashes that oc- cies under different vaccine abundance. Finally our results cur due to the innate immune response. We incorpo- suggest important public health recommendations, includ- rate anti-inflammatory cytokines into a reaction-diffsuion- ing a vaccine purchase quota so developed and developing chemotaxis model. Surprisingly, the incorporation of countries can have the same access to vaccines. anti-inflammatories into the model encourages instability. Numerical simulations indicate show that if anti- Romarie Morales infammatories are slow, our model can get moving and Arizona State University dynamic pattern formation whereas the current literature [email protected] largely focuses on stationary patterns. Advisers: Bard Er- mentrout and David Swigon, University of Pittsburgh.

PP1 Kevin Penner AWM Workshop: Fast Low Rank Approximations University of Pittsburgh of Matrices and Tensors [email protected] A tensor is an object which extends the notion of scalars, vectors and matrices to multi-dimension. Modeling of real- PP1 world applications, result in automatic generation of very Mathematical Modeling, Analysis and Simulation large data sets. Such data are often modeled as matri- of a Resonant Optothermoacoustic Sensor ces: An m x n real-valued matrix A, provides a natural structure for encoding information about m objects, each Optothermoacoustic detection using a tuning fork receiver of which is described by n features. However, other data is a new technique for trace gas sensing with potential needing more than two dimensions such as an m x n matrix applications in environmental monitoring and medicine. changing with time requires a higher dimensional structure The thermal source causes the receiver to deform which for encoding. Tensors which are the extension of matrices we model by coupling the heat and linear thermoelasticity in higher dimension in such cases provide a good struc- equations. We study the eﬀect of the source position on the ture for encoding. Such data Tensors often have structural generated signal and validate experimental results showing properties that present challenges and opportunities for re- that the output is largest when the source is focused near AN10 Abstracts 123

the base of the receiver. Ferdowsi Univ. of Mashhad P.O. Box No. 91775-1111, Mashhad, Iran Noemi Petra [email protected] Department of Mathematics and Statistics University of Maryland, Baltimore County [email protected] PP1 An Analytical Solution of Flow Between Two Ro- John W. Zweck tating Spheres with Time-Dependent Angular Ve- University of Maryland Baltimore County locities Mathematics and Statistics [email protected] This research involves the study of an incompressible, New- tonian fluid flow between two concentric, rotating spheres Susan E. Minkoff with time-dependent angular velocities. The main purpose University of Maryland, Baltimore County of the research is to study the use of an approximate analyt- Dept of Mathematics and Statistics ical method for analyzing the transient motion of the fluid sminkoff@umbc.edu in the annulus. The governing equations are linearized by employing perturbation techniques. Then the meridional dependence in these equations is removed by expanding Anatoliy Kosterev the dependent variables in a series of Gegenbauer func- Department of Electrical and Computer Engineering tions with variable coefficients and using the orthogonality Rice University property of these functions. The equations for the vari- [email protected] ables coefficients are solved by separation of variables and Laplace transform methods. Results of the flow dynam- PP1 ics are presented for various Reynolds numbers up to 100. The results are presented for constant and time-dependent Control of Milk Synthesis by Prolactin angular velocities.

Prolactin is a vital regulatory hormone secreted by the pi- Asghar B. Rahimi tuitary. This study focuses on the role of prolactin in the Ferdowsi Univ. of Mashhad regulation of milk synthesis. A previous study described [email protected] the creation of novel mathematical model of the regulation of the prolactin receptor during suckling. The current study focuses on expanding the knowledge surrounding the PP1 role of prolactin and its receptor using various modeling AWM Workshop: Local Existence and Uniqueness techniques. of Solutions to a Pde Model for Criminal Behavior Vikram Raghu The analysis of criminal behavior with mathematical tools University of Pittsburgh is a fairly new idea, but one which can be used to obtain [email protected] insight on the dynamics of crime. In a recent work Short et al developed an agent-based stochastic model for the dy- Jonathan E. Rubin namics of residential burglaries. This model produces the University of Pittsburgh right qualitative behavior, that is, the existence of spatio- Department of Mathematics temporal collections of criminal activities or “hotspots,’ [email protected] which have been observed in residential burglary data. In this paper we prove local existence and uniqueness of solutions to the continuum version of this model, a coupled PP1 system of partial differential equations, as well a continua- Mixed Convection in Cylindrical Annulus with Ro- tion argument. Furthermore, we compare this PDE model tating Outer Cylinder and Radially Constant Mag- with a generalized version of the Keller-Segel model for netic Field chemotaxis as a first step to understanding possible conditions for global existence vs. blow-up of the solutions in In the present study, mixed convection of a fluid in the finite time. fully developed region in horizontal concentric cylindrical annulus with different uniform wall temperatures is numer- Nancy Rodriguez ically investigated. The effects of radial MHD force as well UCLA as heat generation due to viscous dissipation are also taken [email protected] into account. Buoyancy effect is also considered along with Boussinesq approximation. The forced flow is induced by the cold rotating outer cylinder in slowly constant angular PP1 velocity with its axis at the center of annulus. Investiga- How Large should a Forecast Ensemble be for a tions are made for various combinations of non-dimensional Complex Atmospheric Flow? group numbers, Reynolds number (Re), Rayleigh number (Ra), Hartmann number (Ha) and Eckert number (Eck). Complex geophysical flows typically are chaotic. That is, Governing equations are continuity, two-dimensional mo- small uncertainties in initial conditions and localized insta- mentum and energy. bilities grow exponentially in time. Currently, meteorolo- gists use ensembles of initial conditions, at greater com- Asghar B. Rahimi putational expense, to assess forecast uncertainties in a Ferdowsi Univ. of Mashhad complex model. We seek to determine the minimum num- [email protected] ber of ensemble members needed to adequately resolve the multi scale dynamics in an idealized representation of an First NAME:H.R. Last Name:Mozayyeni atmospheric jet using the Weather Research and Forecast- 124 AN10 Abstracts

ing (WRF) model. Adviser: Eric Kostelich, Arizona State the error in our numerical approximations by reducing the University. variance of our estimator. Using the negative correlation properties of antithetic variates in conjunction with various Salvador Salazar, Ryan Haines, Dustin Franklin numerical methods, we were able to reduce the variance of Arizona State University the estimators for the mean and variance of our approxima- [email protected], [email protected], tions. This project was partly funded by the NSF CSUMS [email protected] program.

Sandeep Singh PP1 New Jersey Institute of Technology, AWM Workshop: Computational Aspects of Lie Department of Mathematical Science Algebras and Mubarakhzyanov Algebras [email protected]

We investigate six-dimensional solvable Lie Algebras Megha Billimoria that have a five-dimensional nilradical. Such algebras New Jersey Institute of Technology were classified by the Russian mathematician G. M. Department of Mathematical Sciences Mubarakhzyanov in a paper published in 1963. The pa- [email protected] per contains errors because calculations were done by hand and the list of algebras is incomplete. We make extensive use of MAPLE and some new routines to help finesse David J. Horntrop Mubarakhzyanov’s list. Dept of Mathematical Sciences, Center for Applied Math New Jersey Institute of Technology Anastasia Shabanskaya [email protected] University of Toledo [email protected] PP1 Gas Flow in Naturally Fractured Reservoirs: Nu- PP1 merical Solution of Restricted and Unrestricted Density-Dependence Effects in a Model of Persis- Flows tent Bacterial Infections Double porosity models are usually applied for naturally Persisters are phenotypic bacterial variants which exhibit fractured reservoirs flow. It considers two regions: a low ”antibiotic tolerance”: persisters survive when exposed to conductivity matrix, and high conductivity fractures. Be- bactericidal antibiotics, but the bacterial colonies regrown yond this, two types of flow from matrix to fractures are from persister cells remain susceptible to killing by further analyzed, restricted and unrestricted. In this work, these antibiotic treatments. Exactly how bacteria switch into a two flow kinds are numerically solved using finite difference persister state is unknown, but persister formation is linked and an implicit formulation including non-Darcy effects. to quorum sensing (the ability of bacteria to detect the The discretization scheme plays an important role in well local population density). Persisters are also implicated flowing pressure features, especially in early times. in the formation and maintenance of biofilms, and they are believed to play an important role in chronic bacte- Grazione Souza, Adolfo Puime Pires, Antonio Luiz Zacchi rial infections that resist antibiotic treatment. We present Junior a reaction-diffusion PDE model of bacterial growth which North Fluminense State University incorporates nutrient- and population-density dependent [email protected], [email protected], mechanisms of persister formation. The functional form [email protected] of this dependence is chosen to match experimentally observed relationships between nutrient availability, popula- PP1 tion growth rates, and incidence of persister phenotypes. These relationships involve a separation of temporal and AWM Workshop: A Mathematical Model of Glu- spatial scales in the formation of persister vs. regular bac- tathione Metabolism teria. We explore the effects of various experimentally ac- Glutathione is produced by the liver and is highly impor- cessible parameters related to quorum sensing on the rate tant in neutralizing oxidative stress. Deficiencies have been and distribution of persister formation. correlated with a variety of diseases, including Down syn- William E. Sherwood drome and autism. We have built a mathematical model of Center for Biodynamics glutathione synthesis, transport, and break-down. We ex- Boston University plore the half-life of glutathione and its sensitivity to fluc- [email protected] tuations in amino acid input. Using the model, we simulate the metabolic profiles observed in Down syndrome and autism and compare the model results to clinical data. John Burke Boston University Rachel L. Thomas [email protected] Duke University [email protected] PP1 Variance Reduction for Numerical Simulation of PP1 Stochastic Differential Equations How to Find Relevant Patterns in Climate Data: An Efficient and Effective Framework to Mine Cli- Stochastic differential equations arise in many applications mate Time Series and Remote Sensing Images including finance and materials. Since it is difficult to analytically determine their solution, we desire to minimize This work presents a new unsupervised algorithm aimed at AN10 Abstracts 125

discovering relevant patterns in climate and remote sens- PP1 ing time series. The patterns relate normal and abnormal AWM Workshop: Classification of Libs Protein behavior in data. This new algorithm works on multiple Spectra Using Automatic Machine Learning Tech- time series of continuous data, identifying relevant asso- niques ciations among the time series events. The associations can be visualized in a graphical manner, allowing a better We performed multi-class classification of LIBS spec- identification and comprehension of the discovery patterns. troscopy data which consists of samples from four proteins. Experiments over real climate data were performed. The We performed linear feature extraction by way of Princi- results revealed patterns that the specialists described as pal Component Analysis (PCA). These features are used not been known before and also interesting. as inputs into the classification algorithms. We performed classification on LIBS data using the following classifica- Agma J. Traina tion algorithms: K-Nearest Neighbor, Classification and University of Sao Paulo Regression Trees, Multi-layer perceptrons, Support Vector [email protected] Machines, and Adaptive Local Hyperplane. We compared the classification accuracies of these algorithms using four- Marcela Ribeiro fold cross validation. Federal University of Sao Carlos [email protected] Tia L. Vance Delaware State University Robson Cordeiro Tia L [email protected] University of São Paulo [email protected] PP1 Numerical Simulations of a Locally Forced Thin Luciana Romani Film Embrapa Agriculture Informatics [email protected] We consider a model of a thin film of liquid on an incline driven by Marangoni forces induced by a temperature gra- Elaine Sousa dient. Localized forcing is included in the model. The University of Sao Paulo effect of the forcing, which acts as a valve to constrain [email protected] fluid flow is demonstrated. We describe the transient behavior of the system and the evolution of wave structures, Ana Maria Avila, Jurandir Zullo including N-waves, as a result of the forcing profile and State University of Campinas show agreement with the predictions of hyperbolic theory. [email protected], [email protected] Adviser: Rachel Levy, Harvey Mudd College. Jeffrey Wong Caetano Traina, Jose Fernando Rodrigues Junior Harvey Mudd College University of Sao Paulo [email protected] [email protected], [email protected]

PP1 PP1 Coupling the Newton Dynamics and Aerodynamics Krylov Deferred Correction Embedded With of Insect Flight by the Immersed Interface Method Higher Order Methods To study the stability and maneuverability of insect flight, Spectral deferred correction was created to produce a de- we need to couple the Newton dynamics and aerodynam- ferred correction method of arbitrary order that was more ics. In this talk, I will present: (1) the formulas of the stable than traditional deferred correction methods. This aerodynamic force and torque, (2) a matrix formulation of method was easy to implement as it used only first or- the Newton dynamics of a flying insect, and (3) coupling of der schemes for prediction and correction. Krylov deferred the Newton dynamics and aerodynamics by the immersed correction was then created to accelerate spectral deferred interface method. correction. We are investigating using Krylov deferred correction embedded with higher order schemes and compar- Sheng Xu ing the accuracy and efficiency against traditional Krylov Department of Mathematics deferred correction methods. Southern Methodist University [email protected] Lee Van Groningen Michigan State University [email protected] PP1 AWM Workshop: Periodically Forced Hopf Bifur- Andrew Christlieb cation Dept. of Mathematics Michigan State University We investigate the influence of frequency of a small periodic [email protected] forcing on an ODE system near a point of Hopf bifurcation. The frequency of the forcing is close to the Hopf frequency. Benjamin Ong We use Liapunov-Schmidt reduction and singularity theory Department of Mathematics to find that the number of the forced periodic solutions can Michigan State University be sensitive to tiny changes of the forcing frequency. The [email protected] full picture of bifurcation diagrams is obtained. Yanyan Zhang 126 AN10 Abstracts

Ohio State University can be useful in computational anatomy for the processing [email protected] of cortical surfaces. We derive an integro-differential equation for the flow, and describe numerical experiments on Martin Golubitsky synthetic and cortical surfaces from neuroimaging studies Ohio State University in schizophrenia and auditory disorders. Mathematical Biosciences Institute [email protected] John W. Zweck University of Maryland Baltimore County Mathematics and Statistics PP1 [email protected] Modelling Soil Erosion: Sediment Transportation Sirong Zhang Modify the only multi size soil erosion model Hairsine-Rose Department of Biomedical Engineering model by considering the effects of sediment bedload and The Johns Hopkins University bed elevation. Composite Liska-Wendroff scheme (LwLf4) [email protected] is used for solving the modified HR model. The numerical simulations are compared with MOL and experiment Laurent Younes data under net erosion and deposition condition. Modified Applied Mathematics and Statistics HR model is employed for solving 1-D buffer strip prob- JHU lem. The comparison of numerical approximations with [email protected] experiment data shows good matches. Yiming Zhong Tilak Ratnanather OCIAM, Mathematical Institute, Oxford University Department of Biomedical Engineering [email protected] The Johns Hopkins University [email protected]

PP1 AWM Workshop: Optimal Control of a Cholera Model

This work is to ﬁnd an optimal vaccination rate that minimizes the economic and social losses in an ODE model of cholera. This model contains nine equations tracking movement of susceptible individuals with and without partial immunities. A vaccinated class and age structure are added into this model and the vaccination rate is a control function. Both analytical and numerical results are discussed. Peng Zhong University of Tennessee [email protected]

PP1 Dislocation Dynamics and PSB Formation PSB (Persistent Slip Band) is believed to be the key inner conﬁguration before crack initiation. Though many observations have been conducted to visulize it, few models could explane its formation. The law of motion for any single curve dislocation is proposed by considering the mobili- ties of edge and screw segment both. The stability analysis to rectilinear dislocation gives the critical orientation of a dislocation to cross slip. Then both numerics and asym- potic analysis are applied to a planar dislocation curve, in order to ﬁnd a critical stress for cross slip to happen.

Yichao Zhu OCIAM, Maths Institute, University of Oxford [email protected]

PP1 A Diffeomorphic Mean Curvature Flow for the Pro- cessing of Anatomical Surfaces We introduce the diffeomorphic mean curvature flow, induced by restricting a diffeomorphic flow of Euclidean space to a surface. This flow has the potential advantage of being both topology-invariant and singularity free, which