62 MS13 Abstracts

IP1 and leads, perhaps unexpectedly, into optimal transporta- Motility at Microscopic Scales tion theory (C.Cotar, G.F., C.Kl”uppelberg, Comm. Pure Appl. Math. 66, 548-599, 2013). Motility of cells is at the root of many fundamental processes in biology: from sperm cells swimming to fertilize an Gero Friesecke egg cell, to metastatic tumor cells crawling to invade nearby Centre for Mathematical Sciences tissues. We will discuss the mechanical bases of cellular Technische Universität München, Germany motility by swimming and crawling. Special emphasis will [email protected] be placed on the connections between low Reynolds number swimming and Geometric Control Theory, and on the geometric structure of the underlying equations of motion. IP4 As a concrete example, we will report on reverse engineer- Scaling in Kinetic Mean-field Models for Coarsen- ing of the euglenoid movement. The lessons learned in the ing Phenomena context of swimming motility will be then applied to selected case studies of crawling motility. Coarsening, that is the increase of typical length scales in a microstructure, plays a crucial role in the large-time Antonio De Simone behavior of numerous processes in physics and materials SISSA-International School of Advanced Studies science. An important aspect is the dynamical scaling hy- [email protected] pothesis suggesting that after some transient regime the system evolves in a universal statistically self-similar fashion. Kinetic mean-field models are often used to try to cap- IP2 ture this self-similar behavior. However, despite typically Wrinkle Patterns in Thin Sheets simple looking, their analysis turns out to be a challenge. In this talk I will review the progress of recent years in the When confined in space, solid sheets exhibit a variety analysis of such equations and will also discuss major open of patterns, often described as folds, blisters, wrinkles, problems. creases, and crumples. The most elementary deformation type emerges from the classical buckling-wrinkling instabil- Barbara Niethammer ity of thin objects under compressive loads. Nevertheless, Institute of Applied Mathematics experiments on nano-metrically thin sheets have shown University of Bonn that standard post-buckling theory fails to predict basic [email protected] features of wrinkle patterns. I will describe some recent developments in studies of wrinkling phenomena, emphasiz- ing the “far-from-threshold theory, a singular perturbation IP5 approach to address wrinkles in very thin, highly-bendable Numerical Methods in Molecular Dynamics sheets. Focusing on class of “simplest yet nontrivial (radial stretching) models that exhibits the morphological com- Molecular dynamics is now a very widely used tool to study plexity of thin sheets, I will describe the principles of the the matter at the molecular level. It is used in various FFT wrinkling theory, and a few mechanisms by which fields, such as biology, chemistry or materials science. The wrinkles give way to other patterns. aim is in particular to understand the relationships between the macroscopic properties of a molecular system Benny Davidovitch and its atomistic features. For example, one would like University of Massachusetts Amherst to compute the constitutive relations for materials from Physics Department molecular models, or predict the most likely conformations [email protected] of a protein in a solvent from its amino acid sequence. One of the difficulty to reach this aim is related to timescales: the typical timescale of a molecular dynamics simulation is IP3 much smaller than the typical timescale at which the cru- Asymptotics-based Model Reduction in Electronic cial events, from a macroscopic viewpoint, occur. This is Structure: Old and New related to the metastability of a molecular dynamics trajectory: the system stays for a very long time in some re- It has long been recognized that asymptotic analysis of well gions of the configuration space (called metastable state), chosen scaling limits is a useful alternative (or companion) before hopping to another one, and it is difficult to observe to semi-empirical methods in the design of reduced elec- and simulate such rare events. An associated feature is tronic structure models. Due to the curse of dimensionality the multimodality of the statistical ensemble (a probabil- of the full N-electron Schr”odinger equation, reduced mod- ity measure) sampled by the molecular dynamics trajec- els are necessary to facilitate the computation of ab-initio tories. Many methods have been proposed in the molec- energy levels or potential energy surfaces for large systems. ular dynamics community to deal with these difficulties, Early examples which have retained importance to this day and we will focus on two prototypical ones for which a include Dirac’s (1930) and Becke’s (1988) exchange energy mathematical analysis gives useful insights. We will first functionals. In the talk I will focus on 1) asymptotics- present adaptive importance sampling techniques, which based wavefunction methods which capture the anomalous have been proposed to sample efficiently statistical ensem- filling order of transition metal atoms, missed e.g. by den- bles. Then, we will propose a mathematical analysis of sity functional theory (DFT) even with the best known the parallel replica algorithm which has been introduced functionals such as B3LYP. (Theory: G.F., B.Goddard, by A.F. Voter to generate efficiently metastable dynamics. SIAM J. Math. Anal. 41, 2009; application to transition metals: Ch.Mendl, G.F., J.Chem.Phys.133, 184101, 2010). 2) exchange-correlation functionals in DFT emerg- Tony Lelievre ing from the semiclassical limit of the (exact but unwieldy) Ecole des Ponts ParisTech Hohenberg-Kohn functional. The study of this limit was [email protected] initiated by Seidl, Perdew, Levy, Gori-Giorgi and Savin, MS13 Abstracts 63

IP6 theory of 1D, diffusion-driven solidification. For low val- Tracking Multiphase Physics: Geometry, Foams, ues, the collapse of droplets – i.e. coarsening – drives flow and Thin Films and regulates the growth of needles. Within this regime, we identify and analyze two asymptotic limits: needles that Many scientific and engineering problems involve intercon- are small compared to the typical drop size, and those that nected moving interfaces separating different regions, in- are large. cluding dry foams, crystal grain growth and multi-cellular structures in man-made and biological materials. Produc- Anette Hosoi ing consistent and well-posed mathematical models that Massachusetts Institute of Technology capture the motion of these interfaces, especially at degen- 77 Massachusetts Avenue, Room 3-173, Cambridge MA eracies, such as triple points and triple lines where mul- 02139 tiple interfaces meet, is challenging. Joint with Robert [email protected] Saye of UC Berkeley, we introduce an efficient and robust mathematical approach to computing the solution to two and three-dimensional multi-interface problems involving IP9 complex junctions and topological changes in an evolving Metamaterials: High Contrast Composites with general multiphase system. We demonstrate the method Unusual Properties on a collection of problems, including geometric coarsening flows under curvature, incompressible flow coupled to Composite materials can have properties unlike any found multi-fluid interface problems, and (joint with C. Rycroft), in nature, and in this case they are known as metamateri- the interaction of growing biological clusters with elastic als. Materials with negative Poisson’s ratio or negative re- basement membranes. Finally, we compute the dynamics fractive index are now classic examples. The effective mass of unstable foams, such as soap bubbles, evolving under the density, which governs the propogation of elastic waves in combined effects of gas-fluid interactions, thin-film lamella a metamaterial can be anisotropic, negative, or even com- drainage, and topological bursting. plex. Even the eigenvectors of the effective mass density tensor can vary with frequency. One of the exciting appli- James Sethian cations of metamaterials is to cloaking, yet we show here University of California, Berkeley that there are limitations to electromagnetic cloaking: one Department of Mathematics cannot get broadband passive cloaking if the surrounding [email protected] material is air, at least in the quasistatic limit. Non-linear metamaterials are also interesting and a basic question is what non-linear behaviors can one get in periodic materials IP7 constructed from rigid bars and pivots? It turns out that Toward the Principles of Self Assembly and Self the range is enormous. Materials for which the only easy Replication mode of macroscopic deformation is an affine deformation, can be classed as unimode, bimode, trimode,...hexamode, In biological systems, there are striking examples where acccording to the number of easy modes of deformation. complicated structures (i.e., the bacterial ribosome) can We give a complete chacterization of possible behaviors of spontaneously assemble, driven by specific interactions be- nonlinear unimode materials. tween the components. But how can systems be designed to have this property? Recent technological advances have Graeme W. Milton created the opportunity for making technologically relevant University of Utah systems that self assemble, by e.g. coating colloidal par- Department of Mathematics ticles with DNA. We will discuss how self assembly works [email protected] in this system, through theory, numerical simulation and experiment – and start to speculate as to whether resulting principles might be useful for unravelling the rules of IP10 biological self-assembly. We also outline theoretical con- The Dynamics of Liquid Crystals straints on designing this system for self replication. Many of the beautiful results of solid state physics are Michael Brenner predicated on the positional order of the constituents of Division of Engineering and Applied Science solid crystals. Liquid crystals are soft materials, charac- Harvard University terized by orientational order whose implications and con- [email protected] sequences are less well understood. Emerging new materials bring diversity to the symmetry, composition, length- and time-scales and interactions of orientationally ordered IP8 soft matter systems. The salient feature of these systems is Organic Crystal Growth in Thin Films their symmetry-mandated responsivity to stimuli. In this talk, I will describe dynamic phenomena in a variety of We examine solidification in thin liquid films produced liquid crystalline systems in response to different excita- by annealing amorphous films in a solvent vapor. Micro- tions, and discuss approaches and challenges to modeling graphs captured during annealing reveal the nucleation and the dynamic response. growth of single-crystal needles. The needle lengths scale like power laws in time where the growth exponent depends Peter Palffy-Muhoray on the thickness of the deposited film. The evolution of Department of Chemical Physics and Liquid Crystal the thin film is modeled by a lubrication equation, and Institute an advection-diffusion equation captures the transport of Kent State University material and solvent within the film. We define a dimen- mpalff[email protected] sionless transport parameter which describes the relative effects of diffusion and coarsening-driven advection. For large values of this parameter, needle growth matches the 64 MS13 Abstracts

IP11 MS1 Multiscale Mathematics and Renewable Energy Homogenization of Elliptic Pde in Random Envi- ronments with Long--range Correlations It is well understood that access to cheap energy under- pins modern societies and that there is a direct corre- This talk will be concerned with rates of convergence in lation between a nations energy consumption per capita homogenization of divergence form elliptic PDE in ran- and its GDP. Finding enough energy to fuel industrialized dom environments. Rates of convergence are obtained economies and pull developing countries out of poverty for environments which consist of a simple convolution of without overheating the climate is a central challenge of a function with an environment satisfying a Poincaréin- the 21st century. Meeting it will require new technologies equality. These environments can have long range corre- for producing, storing, and using energy with performance lations, as in the first results on the subject by Yurinskii levels far beyond what is currently possible. Such technolo- (1986), but without his restriction that dimension must be gies spring from scientific breakthroughs in new materials at least 3. Rates of convergence for environments satis- and chemical processes that govern the transfer of energy fying a Poincaré inequality were first proved by Naddaf-- between light, electricity and chemical fuels. In applica- Spencer(1998). The method has been much further devel- tions ranging from renewable fuels production to generat- oped in recent work of Gloria and Otto (2011). Correla- ing electricity from wind and solar through energy stor- tions in environments which satisfy a Poincaré inequality age, advanced materials play a crucial role in accelerating are typically short--range. the development of new energy solutions. In this talk we will discuss mathematical approaches to modeling required Joseph Conlon to address the complexities of renewable energy technolo- Department of Mathematics gies, which include coupled physical, chemical and biolog- The University of Michigan ical processes, broad spans of spatial and temporal scales, [email protected] many sources of uncertainty, and, in some instances, only a primitive understanding of the fundamental processes and phenomena. MS1 Quantitative Homogenization of the Heat Equation Steven Hammond with Random Coefficients National Renewable Energy Laboratory [email protected] We consider the heat equation with random coefficients on Zd. The randomness of the coefficients models the inhomogeneous nature of the medium where heat propagates. IP12 We assume that the distribution of these coefficients is in- How Do Crystals Melt? variant under spatial translations, and has a finite range of dependence. If a solution to this equation is rescaled diffu- I will discuss the mechanism by which crystals melt. I sively, then it converges to the solution of a heat equation will address the classical controversy between Born’s and with constant coefficients. In probabilistic terms, this con- Lindemann’s criteria for melting. vergence corresponds to the fact that the associated random walk satisfies a central limit theorem. I will present Weinan E recent progress on the estimation of the speed of this con- Princeton Univesity vergence, based on the random walk representation. Department of Mathematics [email protected] Jean-Christophe Mourrat EPFL - Institut de mathématiques jean-christophe.mourrat@epfl.ch MS1 Limit Theorems for the Random Conductance Model MS1 Normal Approximation for Random Elliptic Equa- An interesting characteristic of random resistor networks tions comes with the notion of effective conductance and resistance. These are the minimum values of a Dirichlet energy I will discuss solutions to an elliptic PDE with conduc- optimized over potentials or currents subject to appropri- tivity coefficient that varies randomly with respect to the ate boundary conditions. Homogenization theory predicts spatial variable. It has been known for some time that ho- the existence of an almost-surely constant leading-order mogenization may occur when the coefficients are scaled asymptotic for these quantities; my goal will be to go be- suitably. Less is known about fluctuations of the solution yond the leading order and discuss fluctuations. Specifi- around its mean behaviour. For example, imagine a con- cally, I will review recent proofs of the central limit theo- ductor with an electric potential imposed at the boundary. rem for the effective conductance in resistor networks on an Some current will flow through the material. What is the integer lattice where edges are assigned independent and net flux? For a finite random sample of the material, this identically distributed random conductances. Time per- quantity is random. I will describe a recent result about mitting, I will put these in the context of a larger class normal approximation: the probability law of the net cur- of limit theorems for the random conductance model that rent is very close to that of a normal random variable hav- have been made available thanks to the recent ground- ing the same mean and variance. Closeness is quantified breaking work of Gloria and Otto. Based on joint work by an error estimate in total variation; the error vanishes with Michele Salvi and Tilman Wolff. as the size of the material sample goes to infinity.

Marek Biskup James Nolen UCLA Duke University Department of Mathematics Mathematics Department [email protected] [email protected] MS13 Abstracts 65

MS2 ances for liquid crystals using statistical mechanics. I will Time-averaging of ODE Systems with Highly Os- start by considering a discrete system of rigid rods, which cillatory Response motivates an appropriate state space. A probability function is then introduced that satisfies the Liouville equation. A progression of ideas leading to a practical computational This equation serves as the starting point for the derivation technique for time-averaging nonlinear, fast oscillatory re- of all of the continuum-level balances. The terms appear- sponse of ODE systems under slow forcing is described. ing in the derived balances, some being nonstandard, are The key idea is to introduce running finite time-averages interpreted as expected values. of phase functions that are provably robust ‘slow’ variables whose evolution can be approximated. The strategy in- Brian Seguin, Eliot Fried duces a separation of time scales in an augmented dynam- McGill University ics, even when the original system does not come equipped [email protected], [email protected] with one. Amit Acharya MS3 Civil and Environmental Engineering Fluctuation-Dissipation Based Integrators for Carnegie Mellon University Brownian Dynamics [email protected] This talk presents explicit methods for simulating Brown- Marshall Slemrod ian Dynamics with Hydrodynamic Interactions that have University of Wisconsin, Madison the following features: ergodicity with respect to the limit- Dept of Mathematics ing distribution of the governing equations; weak accuracy [email protected] at finite noise; and, higher order accuracy in the small noise limit. The first property is our stability concept, and the second/third properties are our convergence concept. To Likun Tan design methods with these properties, ideas from proba- Carnegie Mellon University bility theory and numerical analysis were used. The ba- [email protected] sic framework consists of combining a Metropolis Monte Carlo method to sample the limiting distribution of the MS2 SDE with an optimized Runge-Kutta type discretization. While Metropolis integrators are known to be ergodic and Statistical Mechanical Foundation of the Peridy- weakly accurate, there are important situations where ex- namic Nonlocal Continuum Theory isting schemes may reject all moves in the small noise limit. My presentation derives the energy and momentum conser- This issue is reminiscent of the scaling problem that occurs vation laws of the peridynamic nonlocal continuum theory with Metropolis algorithms in high dimension. An asymp- using the principles of classical statistical mechanics. The totic analysis of the rejection rate in this limit reveals the peridynamic laws allow the consideration of discontinuous necessity of multiple stages per step. Among two and three motion, or deformation, by relying on integral operators. stage methods, it turns out that the Ralston and Kutta These operators sum forces and power expenditures sepa- methods are optimal. The Metropolis integrator is also rated by a finite distance and so represent nonlocal interac- designed to avoid computing the divergence of the mobil- tion. An important conclusion is that nonlocal interaction ity tensor. An ‘infinitesimal fluctuation dissipation lemma’ is intrinsic to continuum conservation laws when derived guided how to do this while maintaining dynamic accuracy. using the principles of statistical mechanics. Numerical examples including application to Brownian dynamics with hydrodynamic interactions will be presented. Rich Lehoucq For this example, it will be shown that the resulting in- Sandia National Laboratories tegrator is able to accurately compute dynamics at time [email protected] steps an order of magnitude (or more) larger than those permitted with explicit predictor-corrector schemes. The compatibility of the technique with fast multipole method MS2 or Ewald type computational methods for the hydrody- Kinetic Equation for Spatial Averages of Particle namic interactions will also be addressed. Dynamics Nawaf Bou-Rabee We propose a kinetic equation for the moment-generating Mathematics function that contains the dynamics of the continuum spa- Rutgers Camden tial averages of particle systems. The exact, but not closed, [email protected] evolution equation for the generating function is obtained directly from the particle equations of motion. This equation is then closed using the recently developed deconvolu- MS3 tion method. The result is an approximate kinetic equation Coupling a Fluctuating Fluid to Immersed Parti- suitable for liquids and to some extent, solids. cles

Alexander Panchenko Bidirectional coupling of immersed structures, such as col- Washington State University loidal particles or polymer chains, to the surrounding fluid [email protected] flow has been studied extensively; however, thermal fluctuations in the fluid equations are not usually considered even though they are responsible for Brownian motion. Achiev- MS2 ing discrete fluctuation-dissipation balance in the coupled Statistical Foundations of Liquid-Crystal Theory fluid-structure system is not trivial and requires special care in both the fluid solver and the fluid-structure cou- I will outline how one can derive the continuum-level bal- pling. I will describe an extension of the Inertial Cou- 66 MS13 Abstracts

pling Method developed for compressible flow by Usabi- we seek to find a signal due to the fluid’s memory in the aga Balboa, Delgado Buscalioni and Pagonabarraga Mora statistics of the particles velocity autocorrelation. to incompressible flow. The method allows for bidirectional coupling of inertial blob particles with a fluctuat- Christel Hohenegger ing fluid. Our algorithm is based on techniques used in University of Utah the Immersed Boundary Method and recently-developed Department of Mathematics finite volume schemes for fluctuating hydrodynamics. We [email protected] develop a temporal discretization that strictly conserves momentum and is limited in stability only by advection, Scott McKinley and reproduces the correct spectrum and dynamics of the University of Florida thermal fluctuations at both short and long times. scott.mckinley@ufl.edu Aleksandar Donev Courant Institute of Mathematical Sciences MS4 New York University Elastic Theory for Shape Selection of Self- [email protected] Assembled Macromolecular Ribbons

Florencio Balboa Usabiaga We suggest a geometric-mechanical model for chemical sys- Universidad Autónoma de Madrid tems that undergo self-assembly into chiral ribbon struc- Madrid, Spain tures. The model predicts a morphological transition from fl[email protected] twisted to helical configurations and to tubes, as seen in many such systems. Our simple model, based on incompat- Boyce Griffith ible elasticity, allows a quantitative description of a wide New York University School of Medicine variety of systems, using only a few parameters. We iden- griffi[email protected] tify the significant dimensionless parameters that determine the equilibrium configurations and accurately predict the above transition and other morphological phenomena. Rafael Delgado-Buscalioni UAM Hillel Aharoni [email protected] The Racah Institute of Physics The Hebrew University of Jerusalem [email protected] MS3 Modeling of Thermal Fluctuations in Multicompo- Eran Sharon nent Reacting Systems Racah Institute of Physics We present a multicomponent version of the fluctuating The Hebrew University Navier-Stokes equations that includes detailed transport [email protected] and chemical reactions. The resulting system includes stochastic flux terms for momentum, energy and species MS4 transport and a Langevin-type model for fluctuations in the chemical reactions. We discuss isses in the numerical How Bilayer Shape Influences Bilayer Bending solution of the resulting systems and illustrate the impact A bilayer is two thin layers of different materials, bonded of fluctuations on numerical solutions Turing patterns. together. When actuated, the two layers have different Alejandro Garcia equilibrium strains, and the total elastic energy of the bi- San Jose State University layer is decreased by bending. Using computations and [email protected] experiments, we consider how the bilayer shape (in the dimensions normal to the thickness) determines its bending direction, through the presence of edge layers. We consider John B. Bell, Kaushik Balakrishnan rectangles with different aspect ratios, and more general CCSE shapes by developing a hexagonal-lattice discretization of Lawrence Berkeley Laboratory bilayers. [email protected], [email protected] Silas Alben Aleksandar Donev University of Michigan, USA Courant Institute of Mathematical Sciences [email protected] New York University [email protected] Bavani Balakrisnan, Elisabeth Smela University of Maryland [email protected], [email protected] MS3 Immersed Particle Dynamics in Flucuating Fluids with Memory MS4 Blister Patterns and Energy Minimization in Com- Multibead passive microrheology aims at characterizing pressed Thin Films on Compliant Substrates fluid properties via statistically measurable quantities. To correctly model the correlations, it is necessary to include Thin films on compliant substrates subject to compressive a thermally fluctuating force in the Stokes equations. We elastic misfit can display a variety of blistering patterns. present a model for an immersed particle passively ad- We study the minimum energy achievable by blistering on vected by a fluctuating Maxwellian fluid. We then high- a fixed area fraction; a variational problem involving three light the stochastic spectral numerical method. Finally, small parameters. In 1D we determine how the minimum MS13 Abstracts 67

energy scales with respect to these parameters. In 2D we general framework: it is exactly the same manifold whether show that in a certain regime, the energy of a blister lattice the atoms are those of steel, water or air. Some version of is lower than a few, large blisters. this manifold is inherited by all accepted models of continuum mechanics, as well as the Boltzmann equation. Some Jacob Bedrossian of the MD solutions correspond to certain far-from equilib- Courant Institute of Mathematical Sciences rium, unsteady flows, while others are naturally associated New York University with the dynamics of particular nanostructures. Both sim- [email protected] ulations and a study of the Boltzmann equation suggest the presence of certain thermodynamic relations that are completely unexpected in these far-from-equilibrium situ- MS4 ations. We describe these relations. Joint work with Amin Shape Transitions in Hyperbolic Non-Euclidean Aghaei, Kaushik Dayal, and Stefan Mueller. Plates Richard James Swelling thin elastic sheets are ubiquitous in nature and Department of Aerospace Engineering and Mechanics industry and are capable of forming complex patterns of University of Minnesota various geometries. The equilibrium shapes of such sheets [email protected] is usually modeled as the minimum of an elastic energy that is the minimum of a (strong) stretching energy and a (weak) bending energy. In this talk I will present a study MS5 of such swelling sheets when stretching free deformations Multi-Time Scale Modeling of Dynamics of Phase correspond to local isometric immersions of the hyperbolic Transition plane. Motivated by recent experiments studying the morphology of swelling hydrogels, we focus on annuli with pe- We aim to construct coarse evolution equation for au- riodic profiles. tonomous fine ODE systems. The coarse variables are defined as finite time averages of phase functions. The ap- John A. Gemmer proach is based on the idea of Young measure theory. The University of Arizona time averaged coarse variables turn out to be ’slow’ in a [email protected] precise sense. This allows their evolution to be phrased in terms of averaging utilizing limit measures (probability Shankar C. Venkataramani distributions) of the fast flow. University of Arizona Department of Mathematics Likun Tan [email protected] Carnegie Mellon University [email protected]

MS5 Amit Acharya, Kaushik Dayal Effective Dynamics of Phase Transitions in Nonlo- Civil and Environmental Engineering cal Fokker-Planck Equations Carnegie Mellon University [email protected], [email protected] This talk concerns the asymptotic analysis of certain nonlocal and nonautonomous Fokker-Planck equations which model the hysteric behaviour of many-particle systems MS5 with dynamical control (e.g. charging and discharging of From Simple Particle Models to Thermodynamic Lithium-ion batteries). The equations involve two small Flows parameters and are hence capable of describing different types of phase transitions. We focus on the fast reaction The diffusion equation is the scaling limit of Brownian mo- regime, in which the dominant effect can be understood by tion, and can be reformulated as gradient flow of the en- adapting Kramers formula for large deviations, and charac- tropy in the Wasserstein metric. How can we directly ob- terize the small-parameter limit by rate-independent evo- tain this entropic formulation from particle models? More lution equations. generally, how can we obtain thermodynamic flows from simple particle models, that is, infer energy and entropy Michael Herrmann as well as their evolution laws from mesoscopic models? Saarland University, Department of Mathematics The talks will sketch some approaches and results based [email protected] on large deviation principles.

Barbara Niethammer, Juan Velazquez Johannes Zimmer Institute of Applied Mathematics Bath University of Bonn [email protected] [email protected], [email protected] MS6 Solidiﬁcation Fronts in Supercooled Liquids: How MS5 Rapid Fronts Can Lead to Disordered Glassy Solids Unexpected Thermodynamic Properties of Some Exact Far-from-equilibrium Solutions in Molecular We determine the speed of a crystallisation (or more gener- Dynamics ally, a solidiﬁcation) front as it advances into the uniform liquid phase after the system has been quenched into the We describe a time-dependent invariant manifold of the crystalline region of the phase diagram. We calculate the equations of molecular dynamics (MD). The manifold is in- front speed by assuming a dynamical density functional dependent of the description of the atomic forces within a theory model for the system and applying a marginal sta- 68 MS13 Abstracts

bility criterion. Our results also apply to phase field crys- MS6 tal (PFC) models of solidification. As the solidification Scale Coupling in Phase-Field-Crystal Modeling of front advances into the unstable liquid phase, the density Materials Growth profile behind the advancing front develops density modulations and the wavelength of these modulations is a dy- Continuum field theories have been of continuous great in- namically chosen quantity. For shallow quenches, the se- terest in modeling and understanding complex properties lected wavelength is precisely that of the crystalline phase during materials growth and processing. Traditionally such and so well-ordered crystalline states are formed. How- approaches are featured by the description of long wave- ever, when the system is deeply quenched, we find that this length or coarse-grained scale of a system, while typical wavelength can be quite different from that of the crystal, material phenomena involve a variety of spatial and tempo- so that the solidification front naturally generates disor- ral scales that interact and couple. The recently developed der in the system. Significant rearrangement and ageing phase-field-crystal (PFC) methods can overcome such limit must subsequently occur for the system to form the regu- of conventional approaches via incorporating microscopic lar well-ordered crystal that corresponds to the free energy crystalline details into mesoscopic continuum theory. In minimum. Additional disorder is introduced whenever a this talk I will discuss recent progress in the development front develops from random initial conditions. We illus- of the PFC methodology that bridges different scales, in trate these findings with results obtained from the PFC. particular the coupling effects between mesoscopic and microscopic spatial scales identified in the amplitude repre- Andrew Archer sentation of PFC. Department of Mathematical Sciences Loughborough University Zhi-Feng Huang [email protected] Dept Physics Wayne State University Uwe Thiele [email protected] Loughborough University [email protected] MS6 Edgar Knobloch Density Functional Theory and Phase-Field- University of California at Berkeley Crystal Modelling for Liquid Crystalline and Ac- [email protected] tive Systems Liquid crystal exhibit many fascinating meso-phases which MS6 are neither completely disordered nor completely crystalline examples of which include the nematic, smectic or Kinetic Density Functional Theory - Time Depen- plastic-crystalline state. In this talk, it is shown how con- dent Hydrodynamic Density Functional Theory for cepts of density functional theory of freezing and associ- Freezing ated phase-field-crystal modelling can be extended to treat Understanding solid liquid phase transition is of great im- anisotropic liquid crystalline phases. We further extent the portance in many applications starting from growth of theory to polar active particles which are self-propelled nano-crystals in solutions for solar cells to making the along an intrinsic orientation and show that a wealth of perfect ice cream. Classical Density Functional Theory possible crystalline state exist in nonequilibrium. (CDFT) has been very successful in predicting the phase Hartmut Lowen transition of pair potential fluids. However the CDFT only Institut fur Theoretische Physik II characterizes the equilibrium of the system and does not Heinrich-Heine-Universitat Dusseldorf shed light on the time evolution of the system. This talk [email protected] will present an approach starting with the Revised Enskog Kinetic Theory (RET) as a definition of time evolution to develop a hydrodynamic model for freezing of a hard sphere MS7 liquid. The relation between Kinetic Theory, CDFT and Vortices for a Two-Component Ginzburg-Landau Phase Field Crystal (PFC) models will be outlined. Some Model numerical results characterizing the time evolution of the model and its applications will also be discussed. We study Ginzburg–Landau equations for a complex vec- 2 tor order parameter Ψ = (ψ+,ψ−) ∈ C .Wecon- Arvind Baskaran sider symmetric vortex solutions in the plane R2, ψ(x)= Department of Mathematics in θ f±(r)e ± , with given degrees n± ∈ Z, and prove exis- University of California, Irvine tence, uniqueness, and asymptotic behavior of solutions [email protected] as r →∞. We also consider the monotonicity properties of solutions, and exhibit parameter ranges in which both Aparna Baskaran vortex profiles f+,f− are monotone, as well as parame- Brandeis University ter regimes where one component is non-monotone. We Department of Physics also treat the stability of symmetric vortices for degrees [email protected] n± = 1, in the sense of whether the solutions are local minimizers of the energy. Our results partially generalize John Lowengrub those of Alama-Bronsard-Mironescu to more general forms Department of Mathematics of Ginzburg-Landau systems. University of California Irvine [email protected] Stan Alama,QiGao McMaster University Department of Mathematics and Statistics [email protected], [email protected] MS13 Abstracts 69

MS7 magnetic vortices. The Super- heating Current for a Reduced Ginzburg-Landau Lydia Peres Hari, Jacob Rubinstein Model Department of Mathematics Technion, IIT Israel We consider the time-dependent Ginzburg-Landau model [email protected], [email protected] in the absence of a magnetic field but in the presence of an electric current. In the large domain limit, for a gen- Peter Sternberg eral 2D setting we show that for sufficiently small current Indiana University densities (that may result in strong currents) there exists a Department of Mathematics linearly stable purely superconducting solution. For wire- [email protected] like domains, for stronger current densities we also prove the existence of such a solution and discuss its stability. MS8 Yaniv Almog Semiclassical Approximations to Electronic Struc- Lousiana State University ture via Density/Potential Functionals Department of Mathematics [email protected] Kohn-Sham DFT (KS-DFT) computations have become the most employed tool to obtain electronic structure properties of molecules and solids. Further application is MS7 thwarted by two main issues: a) KS-DFT requires solution Thin Film Superconductors in Strong Magnetic of a set of effective Schrodinger equations for the genera- Fields tion of the noninteracting kinetic energy, and b) approximations for the exchange-correlation functional are gener- We consider singular limits of the three-dimensional ally severely limited in their scope. Semiclassical methods Ginzburg-Landau functional for a superconductor with aided with asymptotic analysis provide guiding principles thin-film geometry, in a constant external magnetic field. for the construction of density functionals which could im- The superconducting domain has characteristic thickness prove on the two issues raised above. In this talk the semi- on the scale >0, and we consider the simultaneous limit classical limits of electronic structure theory in the context as the thickness → 0 and the Ginzburg-Landau param- of DFT will be discussed and the leading order corrections eter κ →∞. We assume that the applied field is strong −1 to semiclassical local approximations will be provided for (on the order of in magnitude) in its components tan- 1D systems with box and general boundary conditions. In gential to the film domain, and of order log κ in its depen- particular, accurate uniform approximations to the density, dence on κ. We prove that the Ginzburg-Landau energy density matrix and kinetic energy density of a class of 1D Γ-converges to an energy associated with a two-obstacle systems will be provided and discussed. problem, posed on the planar domain which supports the thin film. The same limit is obtained regardless of the re- Kieron Burke, Raphael Ribeiro lationship between and κ in the limit. Two illustrative University of California, Irvine examples are presented, each of which demonstrating how [email protected], [email protected] the curvature of the film can induce the presence of both (positively oriented) vortices and (negatively oriented) an- tivortices coexisting in a global minimizer of the energy. MS8 Numerical Analysis of Augmented Plane Wave Methods for Full-Potential Electronic Structure Stan Alama, Lia Bronsard Calculations McMaster University Department of Mathematics and Statistics This presentation talks about the augmented plane wave [email protected], [email protected] methods which are widely used in full-potential electronic structure calculations. We first construct a nonconforming Bernardo Galvao-Sousa method based on this idea and present an a priori error Department of Mathematics estimate for both linear eigenvalue problems and nonlinear University of Toronto Kohn-Sham equations. Then we analyze the augmented [email protected] methods under the same framework and show some numerical experiments to support the theory. This presentation is based on the joint work with Reinhold Schneider. MS7 Kinematic Vortices in a Thin Film Driven by An Huajie Chen Electric Current TU Munich [email protected] Using a Ginzburg-Landau model, we study the vortex behavior of a rectangular thin film superconductor subjected to an applied current fed into a portion of the sides and MS8 an applied magnetic field directed orthogonal to the film. BerkeleyGW: A Massively Parallel Tool for Com- Through a center manifold reduction we develop a rigorous puting Quasiparticle and Optical-Properties of Ma- bifurcation theory for the appearance of periodic solutions terials in certain parameter regimes near the normal state. The leading order dynamics yield in particular a motion law The GW-BSE approach has, in practice, been prohibitively for kinematic vortices moving up and down the center line expensive on systems with more than 50 atoms. We show of the sample. We also present computations that reveal that through a combination of methodological and algo- the co-existence and periodic evolution of kinematic and rithmic improvements, the standard GW-BSE approach can be applied to systems with hundreds of atoms. We 70 MS13 Abstracts

discuss improving the traditional GW-BSE methodology crucial information about the original structure. A highly through accurate starting points and reductions in empty interesting question is the reverse process: construct peri- state requirements. We show that the GW-BSE method- odic graphs such that the orbits under their automorphisms ology can scale to tens of thousands of CPUs on high per- result in a prescribed quotient graph. formance supercomputers. Bernd Souvignier Jack Deslippe IMAPP Institute for Mathematics, Astrophysics and National Energy Research Scientiﬁc Computing Center Particle P [email protected] Radboud University Nijmegen [email protected] MS8 Strong Correlation in Density Functional Theory MS9 Nanostructures Arising from Crystallographic The exact strong-interaction limit of density functional Tilings theory provides a highly non-local functional of the density able to capture strong correlation in the self-consistent In this talk, we present geometric models for structural Kohn-Sham formalism. I will discuss the formal aspect of analogues of single wall carbon nanotubes and nanotubes this approach and illustrate it with some examples. I will with non-hexagonal morphologies which arise from color- also show that this limit is equivalent to an optimal trans- ings of vertex transitive plane crystallographic tilings. The port (or mass transportation theory) problem, highlighting approach in determining the symmetry groups of these the advantages of this connection. nanotubes will be discussed using concepts in color symmetry theory. The method is extended to study the symmetry Paola Gori-Giorgi properties of the carbon nanotori. Vrije Universiteit [email protected] Ma. Louise N. de las Penas Department of Mathematics Ateneo de Manila University MS9 [email protected] Minimal Interface Structures

Soap bubble clusters and material structures can be mod- MS10 eled mathematically by minimizing interface areas or en- Homogenization and Elastoplasticity ergies subject to volume constraints. The presence of singularities makes the mathematics interesting and difficult, In this joint work with A. Giacomini, we propose to address requiring geometric measure theory to make sense of the the homogenization of the evolution of a periodic multi- problem, prove that minimal structures exist and are rea- phase elasto-plastic composite. The obtained evolution is sonable, and describe and compute them. The presentation described in terms of the two-scale limits of the various will include open questions and work by undergraduates. kinematic fields. The dependence upon the fast variable cannot be integrated out, resulting in a model with an in- Frank Morgan finite number of internal variables, essentially the plastic Department of Mathematics and Statistics strains at each point of the torus of periodicity. Williams College [email protected] Gilles Francfort UniversitédeParisNord Villetaneuse, France MS9 [email protected] Polyhedral Geometries and Symmetry

Over the past 35 years, various classes of highly symmet- MS10 ric skeletal polyhedra have been described. While these The Nonlinear Elastic Response of Suspensions of structures exhibit the essential characteristics of ordinary Rigid Inclusions in Rubber polyhedra, the more general skeletal polygonal complexes can be viewed as hybrids of polyhedra and incidence ge- In the first part of this talk, we present a solution for the ometries. A complete enumeration of regular polygonal fundamental problem of the overall elastic response of ideal complexes is presented. (Neo-Hookean) rubber reinforced by a dilute isotropic distribution of rigid particles under arbitrarily large deforma- Egon Schulte tions. The derivation makes use of a novel iterative ho- Department of Mathematics mogenization technique in finite elasticity that allows to Northeastern University construct exact solutions for the homogenization problem [email protected] of two-phase nonlinear elastic composites with particulate microstructures. In the second part, we make use of the dilute solution as a fundamental building block to derive a MS9 simple explicit variational solution for the overall nonlinear Capturing the Essence of Infinite Graphs in Quo- elastic response of filled elastomers with finite concentra- tient Graphs tion of particles under arbitrarily large deformations. Describing crystal structures by graphs has the advantage that not only the atoms are represented but also the bonds Oscar Lopez-Pamies between them. Space group elements are transformed into University of Illinois at Urbana-Champaign graph automorphisms and the orbits under these automor- Civil and Environmental Engineering phisms give rise to a quotient graph which still displays [email protected] MS13 Abstracts 71

Taha Goudarzi [email protected] University of Illinois at Urbana-Champaign [email protected] MS11 Kostas Danas Data Mined Compound and Crystal Structure Pre- Ecole Polytechnique diction for High-Throughput Materials Discovery [email protected] Abstract not available at time of publication.

MS10 Geoffroy Hautier Massachusetts Institute of Technology An Energy-Based Variational Approach to In- geoff[email protected] cremental Homogenization of Elasto-Visco-Plastic Composites MS11 An original approach is proposed, based on an incremental variational principle according to which the local stress- Algorithms for Discovery of Nanoporous Materials strain relation derives from a single incremental poten- for Energy Applications tial constructed from free energy and dissipation functions. We present a set of approaches for discovery of porous ma- The key feature of the model is the explicit use of the elastic terials for clean energy. They are based on both enumera- trial strain in order to define a Linear Comparison Compos- tion and optimization based approaches. They also involve ite, representative of the actual composite at a given time tools to analyze the structure and topology of the void step. The proposed method competes well with previously space of porous materials. The latter tools map regions proposed schemes in elasto-(visco)-plasticity. accessible to guest molecules, calculate accessible volume Laurence Brassart and surface areas as well as pore size distributions. Université catholique de Louvain Richard Martin, Maciej Haranczyk Institute of Mechanics, Materials and Civil Engineering Lawrence Berkeley National Laboratory [email protected] [email protected], [email protected] Laurent Stainier Ecole Centrale de Nantes, UniversitédeNantes,CNRS MS11 Institut de Recherche en Génie Civil et Mécanique First Principles View on Chemical Compound [email protected] Space

Issam Doghri, Laurent Delannay Abstract not available at time of publication. Universit´e catholique de Louvain Institute of Mechanics, Materials and Civil Engineering O. Anatole von Lilienfeld [email protected], Argonne National Laboratory [email protected] [email protected]

MS10 MS12 Homogenization and Plasticity: Variational Ap- Modeling and Simulation of Shear Banding in proximations Polymer Solutions from a Monotonic Constitutive Curve In this joint work with N. Lahellec, we discuss the eﬀective response of composite materials made from constituents The current theoretical understanding is that shear band- with a partially reversible and partially irreversible behav- ing requires a nonmonotonic constitutive relationship. ior. Attention is restricted to behaviors deriving from two However, recent experimental studies show that shear potentials. A ”Rate Variational Principle” is derived and banding can occur in entangled polymer solutions although used to propose approximate schemes to predict the over- the constitutive equation is accepted to be monotonic. Ad- all response, as well as the ﬁeld statistics in viscoelastic, ditionally, multiple steady-states have been observed de- elasto-viscoplastic or elasto-plastic composites or polycrys- pending upon the wall ramp speed. Here we provide the tals. The model is applied to particle-reinforced composites theoretical framework for predicting these phenomena as and to polycrystalline ice. well as new results revealing the possibility of > 2 bands, which is not possible through nonmonotonicity. Pierre M. Suquet CNRS Michael Cromer,GlennFredrickson Laboratoire de Mecanique et d’Acoustique University of California, Santa Barbara [email protected] [email protected], [email protected] Gary Leal MS11 Department of Chemical Engineering The Harvard Clean Energy Project: Finding Re- University of California, Santa Barbara newable Energy Materials One Screensaver at a [email protected] Time

Abstract not available at time of publication. MS12 Modeling and Simulation of Shear Banding Phe- Alan Aspuru-Guzik nomena in Concentrated Solutions of Wormlike Mi- Harvard University 72 MS13 Abstracts

celles MS12 Diffusive Effects on the Transient and Steady State In this talk, we present a new model for concentrated Shear Response of the Vcm Model solutions of wormlike micelles, a class of viscoelastic fluids [N. Germann, L.P. Cook, A.N. Beris, Nonequilibrium Wormlike micelles are known as living polymers. In this thermodynamic modeling of the structure and rheology talk, transient and steady state responses of the VCM of concentrated wormlike micellar solutions, J. Non-Newt. model under shear are discussed. The important roles that Fluid Mech. (in press)]. This model is completely based diffusion and elasticity play during the formation of shear on nonequilibrium thermodynamic arguments and there- bands, in the transient stress response, and in the shape fore serves as a viable alternative to the VCM model of the steady-state flow curve are examined. A conformal [P.A. Vasquez, G.H. McKinley, L.P. Cook, A network scis- mapping strategy is used to control the spatial discretiza- sion model for wormlike micellar solutions I. Model for- tion so that the shear-band kink remains well resolved for mulation and viscometric flow predictions, J. Non-Newt. small diffusion. Fluid Mech. 144 (2007) 122-139]. An adaptive collocation method was used to perform time-dependent simulations Lin Zhou on the coupled nonlinear PDE system. The formation of Department of Mathematics, New York City College of localized bands with different shear rates, known as shear Technology, Brooklyn, NY 11201, USA bands, will be analyzed. [email protected]

Natalie Germann,L.PamelaCook Pam Cook University of Delaware Department of Mathematical Sciences [email protected], [email protected] University of Delaware [email protected] Antony N. Beris Department of Chemical and Biomolecular Engineering Gareth H. McKinley University of Delaware Dept of Mechanical Engineering [email protected] Massachusetts Institute of Technology [email protected] Norman J. Wagner Department of Chemical and Biomolecular Engineering, University of Delaware MS13 [email protected] Wrinkling of a Stretched Annular Elastic Thin Sheet - Identification of the Optimal Scaling Law for the Energy of a Ground State MS12 Mesoscale Modeling and Simulation of Transient In [Bella & Kohn: Wrinkles as the result of compressive Networks stresses in an annular thin film, to appear in CPAM] we identified the optimal scaling law of the minimum of the Many soft gels with a polydisperse entangled mesoscale elastic energy of a stretched annular thin elastic sheet. In structure exhibit ”slow” relaxation, compared with expo- this talk I will describe the next step towards the under- nential decay. The slow relaxation behavior is due to the standing of this problem – I will identify the optimal pref- entanglements and the distribution of energetic interac- actor in the scaling law. Moreover, this prefactor can be tions among the network components at the mesoscale. In characterized as a minimum of a much simpler (scalar) vari- order to capture the macroscale behavior, to explore the ational problem. mesoscale interactions, and to avoid inaccurate closure relationships when constructing continuum-scale models, we Peter Bella, Felix Otto perform mesoscale simulation and model the fluid dynam- Max Planck Institute for Mathematics in the Sciences ics of the transient network deformation. [email protected], [email protected] Yun Zeng Department of Mathematical Sciences, University of MS13 Delaware Instabilities in Axisymmetrically Constrained Newark, DE 19716, USA Sheets [email protected] We propose to review different situations where axisym- L. Pamela Cook metric constraints applied to thin sheets induce the forma- University of Delaware tion of radial wrinkles. I a first experiment a thin annulus [email protected] floating at the surface of water is compressed by a contrast of surface tension resulting from the addition of surfactant Lin Zhou molecules. In a second experiment a flat disc is squeezed Department of Mathematics, New York City College of in between a sphere and a hollow shell. We shall describe Technology, Brooklyn, NY 11201, USA in both cases the different morphologies of the wrinkling [email protected] patterns. Jose Bico Gareth H. McKinley Laboratoire PMMH Dept of Mechanical Engineering ESPCI Massachusetts Institute of Technology [email protected] [email protected] Benoit Roman PMMH-ESPCI MS13 Abstracts 73

[email protected] [email protected]

Jeremy Hure LCMMI-CEA MS14 [email protected] A Mathematical Analysis of Temperature Acceler- ated Dynamics

Miguel Pineirua Abstract not available at time of publication. UME-ENSTA [email protected] David Aristoff University of Minnesota [email protected] MS13 Wrinkling Behavior of Highly Stretched Rectangu- lar Elastic Films via Parametric Global Bifurcation MS14 A Scalable Method to Compute Transition Rate We consider the wrinkling of highly stretched thin rectan- Prefactors gular films. We first propose a rational model that correctly accounts for the large mid-plane strain. We then When describing kinetics in the solid state, the role of the carefully perform a numerical bifurcation, continuation and energetic component of the activation free energy is usu- stability analysis. Our results are often at odds with those ally emphasized, while vibrational entropic contributions obtained using the classical Foppl-von Karman (FK) the- are often assumed to behave in a standard way. While this ory of plates, which has been a popular choice in the lit- rule of thumb is often adequate, it can sometimes fail dra- erature. E.g., for a given fine thickness, only a certain matically. I will present a method to efficiently compute range of aspect ratios admit stable wrinkling, whereas the vibrational prefactors in the context of Harmonic Transi- FK theory predicts wrinkling outside of that range as well. tion State Theory. This method is based on a Kernel Poly- Also when stable wrinkling emerges as the applied macro- nomial approximation to the vibrational density of states. scopic strain is steadily increased, the amplitude first in- The algorithm is scalable, enabling calculations on systems creases, reaches a maximum, decreases, and then returns of very large size. to zero again. In contrast, the FK model predicts an ever- increasing wrinkling amplitude as the macroscopic strain Danny Perez, Chen Huang, Arthur F. Voter is increased. Theoretical Division, T-1 Los Alamos National Laboratory Tim Healey danny [email protected], [email protected], [email protected] Department of Mathematics Cornell University [email protected] MS14 A Posteriori Estimates for Accelerated Dynamics MS13 An outstanding problem in the practical implementation of Stretch-induced Wrinkling of Thin Sheets: Exper- parallel replica dynamics is to identify good values of the iments and Modeling decorrelation and dephasing time parameters. We propose to use stationarity testing diagnostics for dynamically de- Experiments were conducted to measure stretch-induced termining when these stages of the algorithm have been run wrinkling of rectangular polyethylene thin sheets with two long enough. We examine various diagnostics for different opposite ends clamped and other two edges free. It was problems and show that this may be an effective way of observed that the wrinkle amplitude first increased and automatically determining the values of these parameters. then decreased with increasing nominal strain. Meanwhile the wrinkle profile remained nearly unchanged with the Gideon Simpson same number of wrinkles. Finite element analyses were School of Mathematics performed to investigate the stretch-induced stress pat- University of Minnesota terns, the critical condition for onset of buckling, and [email protected] post-buckling evolution of the wrinkles. As a prerequisite for wrinkling, development of compressive stresses in the transverse direction is found to depend on both the length- MS14 to-width aspect ratio of the sheet and the applied tensile Combining Hyperdynamics with the Quasicontin- strain in the longitudinal direction. In addition, the criti- uum Method cal condition for wrinkling and the post-buckling behavior both depend sensitively on the sheet thickness. Using a I will decribe our recent progress in combining hyperdy- hyperelastic material model, the wrinkle amplitude first namics, an accelerated molecular dynamics method for increases with the applied strain and then decreases, even- reaching long times in infrequent-event systems, with the tually flattened beyond a moderately large strain. In com- finite-temperature version of the quasicontinuum (QC) parison with the experiments, a hyper-viscoelastic material method, a spatial multiscale method for treating large sys- model is proposed to better capture the rate-dependent be- tems, in which atoms are fully resolved only in spatially im- havior of polyethylene and the residual wrinkles observed portant regions. The resulting “hyper-QC” method, which at high strains. It is found that the wrinkle wavelength is combines the strengths of the two methods, looks promis- less sensitive to the material model and is well predicted ing for reaching experimentally relevant time and length by a scaling analysis. scales for intrinsically multiscale systems.

Vishal Nayyar, K. Ravi-Chandar, Rui Huang Arthur F. Voter University of Texas at Austin Theoretical Division, T-1 [email protected], [email protected], Los Alamos National Laboratory 74 MS13 Abstracts

[email protected] Jeremy K. Mason Lawrence Livermore National Laboratory Woo Kyun Kim [email protected] Department of Aerospace Engineering and Mechanics University of Minnesota Robert D. MacPherson woo [email protected] Institute for Advanced Study [email protected] Mitchell Luskin School of Mathematics David J. Srolovitz University of Minnesota University of Pennsylvania [email protected] [email protected]

Danny Perez Theoretical Division, T-1 MS15 Los Alamos National Laboratory Triple Junctions in Microstructure Design danny [email protected] Many materials properties are governed by the grain boundary (GB) network, and empirical studies that ma- Ellad B. Tadmor nipulate the GB network have demonstrated large improve- Department of Aerospace Engineering & Mechanics ments in properties. We propose that a rigorous materials University of Minnesota design paradigm for GB networks can be centered on the [email protected] so-called triple junction distribution function (TJDF). We demonstrate how the TJDF allows texture to be linked to MS15 GB network topology, which in turn permits network sensitive property predictions and identification of optimal GB Evaluating Microstructural Parameters of Three- networks. dimensional Grains Generated by Phase-field Sim- ulation or Other Voxel-based Techniques Oliver Johnson, Christopher A. Schuh MIT The MacPherson-Srolovitz relation describes the volume [email protected], [email protected] change rate of a grain in a three-dimensional polycrystalline system using microstructural parameters — the mean grain width and the triple line length — as well MS15 as isotropic values for the grain boundary mobility and Statistical Analyses of Complex Microstructures energy. We introduce methods to accurately determine and Its Application to Coarsening Phenomena these microstructural measures for grain structures described by a voxel-based microstructure representation Coarsening is a fundamental subject in materials science, (VBMR), such as those generated by phase-field simula- yet we have limited understanding of this phenomenon for tions, Monte Carlo Potts models, or three-dimensional re- complex microstructures. To develop insights, we have ap- constructions of experimentally measured polycrystalline plied phase-field models to generate a self-similar, bicontin- microstructures. We evaluate the mean rate of volume uous structures and quantified its evolution through statis- change of grains during a phase-field simulation of grain tical analyses of the interfacial morphologies. As an initial growth and discuss the results in terms of the MacPherson- step toward developing a theory of coarsening in morpho- Srolovitz relation. logically and topologically complex systems, we describe the evolution of interfacial shape distribution in the form Kunok Chang of a continuity equation. Katholieke Universiteit Leuven Leuven, Belgium Chal Park [email protected] Department of Materials Science and Engineering University of Michigan [email protected] MS15 Grain Topologies in Three Dimensional Polycrys- Peter W. Voorhees talline Microstructures Department of Materials Science and Engineering The prevailing method of characterizing grain topologies Northwestern University in three-dimensional polycrystalline microstructures con- [email protected] siders only their number of faces. This information is interesting but it is clearly incomplete. For example, it cannot Katsuyo Thornton tell us what fraction of all twelve-faced grains are pentag- Department of Materials Science and Engineering onal dodecahedra, or what fraction of all fourteen-faced University of Michigan grains are truncated octahedra. I will describe an effi- [email protected] cient, graph-theoretic technique that allows for the complete characterization of grain topologies, and show how this can be used to obtain meaningful descriptors of poly- MS16 crystalline microstructures. Cryo-Tem Imaging of Thermotropic Bent-Core Liquid Crystals Emanuel A. Lazar Columbia University Layered [N, SmCP (B2), SmAP, modulated smectic (B7) Department of Applied Physics and Applied Mathematics and helical nanofilament (B4)] phases of bent-core ther- [email protected] motropic liquid crystals have been studied by cryo-TEM technique. The technique is able to visualize a sub- MS13 Abstracts 75

nanometer periodic structure with a wave vector normal generating reactions. In this presentation, we present a to the electron beam and provides complimentary infor- director based model for solutions of active liquid crystal mation to freeze fracture TEM measurements. The results systems and study the model prediction in a systematical will be compared with FFTEM observations, and will be way to identify its prediction for the active liquid crystal in discussed in terms of available theoretical models. various materials and flow regimes. Numerical simulations in the cases where analysis is intractable will be given to Antal Jakli illustrate the solution behavior. Liquid Crystal Institute Kent State University Qi Wang [email protected] University of South Carolina [email protected] Cuiyu Zhang Chemical Physics Kent State University MS17 [email protected] Evolution of Clean Foams Clean, low liquid fraction, two-dimensional foams evolve MS16 by van der Waals rupture of lamillae between bubles caus- Topological Defects and the Ground State Manifold ing their coalesence and the coarsening of the foam. A new network approach to model the evolution follows the Do homotopy groups completely characterize topological creation of disordered states requires a knowledge of in- defects? In this presentation, I will describe the pitfalls to stability conditions for thin free films with thinning flows, this notion and describe some progress in working around non-planar shapes, and finite aspect ratio. This instability the ambiguities and puzzles that arise in such descriptions. to rupture will be discussed in detail. Stephen H. Davis Randall Kamien Dept. of Engineering Sciences and Applied Math Physics Dept Northwestern University University of Pennsylvania [email protected] [email protected] MS17 MS16 Singularities in Electrified Liquid Drops and Jets Orientation Waves: The Order Parameter for Some QuasiCrystals We discuss the presence of singularities at the surface of a drop electrically charged or subject to an external electric In their text ”Statistical Mechanics” Landau and Lifschitz field. These singularities appear in the form of the so-called assert that the Landau order parameter for crystals is a dynamic Taylor cones, whose structure we discuss in detail. density wave. We present convincing evidence that hard We will also present regularization due to electrokinetic tetrahedra, like blue phase liquid crystals, have as an order effects that take into account the finite electric conductivity parameter an orientation wave rather than a density wave, of the liquid medium. with density waves as secondary order parameters. The consequences of this for understanding quasicrystals and Marco A. Fontelos phase transitions will be discussed. Institute for Mathematics, CSIC, Spain [email protected] Rolfe Petschek Case Western Reserve University [email protected] MS17 Towards a Regularity Theory for Thin-film Equa- Brian M. Cox tions Department of Physics Thin-film equations are a class of fourth-order degenerate Case Western Reserve University PDEs which model the evolution of droplets over solid sub- [email protected] strates. We will discuss the regularity of their solutions in the regime of complete wetting, where a null slope is pre- Amir Haji -Akbari scribed at the (free) contact line where solid, liquid, and Department of Chemical and Biological Engineering gas meet. Our focus will be on the case of strong slippage, Princeton University including the classical Navier slip condition. [email protected] Lorenzo Giacomelli Sharon Glozer, Michael Engel Dipartimento Me.Mo.Mat. Deparment of Chemical Enginering University of Rome La Sapienza, Italy University of Michigan [email protected] [email protected], [email protected] MS17 MS16 On the Moving Contact Line Singularity in Diffuse- Analysis of An Active Liquid Crystal Suspension Interface Approaches Model We describe analytically the moving contact line singular- Active liquid crystal systems is common in biological sys- ity and its resolution for diffuse-interface approaches, mod- tems and artificial active materials with microscale force els of increasing interest where a liquid-gas problem is rep- 76 MS13 Abstracts

resented by a single fluid with continuous density varying Luis Bonilla rapidly near the interface. We relate the models to the min- Universidad Carlos III de Madrid isymposium thin-film setting and discuss advances in rig- G. Millan Institute of Fluid Dynamics, Nanoscience & orous modelling of the contact line with density functional IndMath theory, from which the phenomenological diffuse-interface [email protected] models are obtained under certain assumptions. Antonio Prados David N. Sibley Universidad de Sevilla Department of Chemical Engineering Imperial College, Departamento de Fisica Teorica London [email protected] [email protected]

Andreas Nold MS18 Department of Chemical Engineering, Imperial College Compatibility Conditions and Damage Spread in London Lattices [email protected] We consider lattice models of breakable and composite ma- Nikos Savva terials and metamaterials. Particularly, we study compati- School of Mathematics, Cardiff University bility conditions in dense lattices and their continuous lim- savvan@cardiff.ac.uk its, damage propagation and and equilibrium of partially damaged lattices, lattice models of composites and opti- Serafim Kalliadasis mal lattice microstructures. Some results were obtained Department of Chemical Engineering in collaboration with Enrico Rogora and Seubpong Leela- Imperial College London vanichkul. [email protected] Andrej V. Cherkaev Department of Mathematics MS18 University of Utah [email protected] Defects and Ripples in Graphene

Ripples in suspended graphene sheets are small randomly MS18 oriented ondulations with wavelengths below 25 nm. The equations of motion of a suspended membrane discretized Grain Boundaries and Dislocations in the Swift- on a hexagonal lattice yield stable defects as pentagon- Hohenberg Equation heptagon and Stone-Wales defects, vacancies, divacancies, We study existence of defects in the Swift-Hohenberg equa- etc that are dislocations or dislocation pairs. When cou- tion using bifurcation methods. We show how to reduce the pled to stochastically flipping spins, these equations pro- existence problem to universal coupled-amplitude equation duce ripples similar to observed ones. A soft spin version using normal form theory. The reduces equations exhibit of this model can be calibrated using available data from kink-type heteroclinic orbits which represent various types graphene resonators. of defects. This is joint work with Mariana Haragus and Luis Bonilla Qiliang Wu. Universidad Carlos III de Madrid Arnd Scheel G. Millan Institute of Fluid Dynamics, Nanoscience & University of Minnesota IndMath School of Mathematics [email protected] [email protected] Ana Carpio Universidad Complutense de Madrid MS19 Departamento de Matematica Aplicada Random Fluctuations Beyond the Homogenization ana [email protected] Limit Abstract not available at time of publication. MS18 Force-extension Curves of Biomolecules Guillaume Bal Columbia University Force extension curves of molecular proteins, DNA, or Department of Applied Physics and Applied Mathematics RNA hairpins have a sawtooth shape when the overall [email protected] length is fixed. Sweeping the same curves under force controlled conditions, sudden transitions at a critical force appear. We propose a model of coupled molecule modules MS19 undergoing overdamped Langevin dynamics in bistable po- Effective Properties of Bacterial Suspensions tentials under the same external force. For fixed lengths, long-range interactions produce sawtooth curves. Fixing We introduced a stochastic PDE model for a dilute suspen- the force, interactions are short-range. Abrupt transitions sion of self-propelled bacteria with tumbling and obtained encompassing force-extension branches appear. an explicit asymptotic formula for the effective viscosity (E.V.) that explains the mechanisms of the drastic reduc- Ana Carpio tion of E.V. We next introduce a deterministic ODE/PDE Universidad Complutense de Madrid model for bacterial suspensions that includes pairwise in- Departamento de Matemática Aplicada teractions and excluded volume constraints. This model is [email protected] analyzed analytically and numerically. Comparison with MS13 Abstracts 77

dilute case leads to a phenomenon of stochasticity arising [email protected] from deterministic system. Lei Zhang Leonid Berlyand Shanghai Jiao Tong University Penn State University [email protected] Eberly College of Science [email protected] Leonid Berlyand Penn State University Igor Aranson Eberly College of Science Northwestern University [email protected] Argonne National Laboratory [email protected] MS20 Brian Haines Fast Algorithms for Mesoscale Evolution of Large Los Alamos National Laboratory Particle Systems Penn State University [email protected] We design fast algorithms for simulating space-time averages of large systems of ODEs. Averaging produces ex- Dmitry Karpeev act mesoscale PDEs but they cannot be simulated without Argonne National Laboratory solving the underlying microscale ODEs. We use recently [email protected] proposed regularized deconvolution closure method to approximate PDEs. The resulting equations depend only on Shawn Ryan mesoscale variables and thus can be simulated on much Department of Mathematics coarser meshes. We investigate eﬀects of various parame- Penn State University ters on accuracy of approximation and eﬃciency to opti- [email protected] mize performance of closure method. Lyudmyla Barannyk Falko Ziebert University of Idaho ESPCI Department of Mathematics University of Freiburg [email protected] [email protected] Alexander Panchenko MS19 Washington State University [email protected] Homogenization of Dislocation Dynamics

In this talk, we are interested in the collective behaviour MS20 of linear defects in crystal, called dislocations, when the number of dislocations goes to infinity. We will study a Optimal Multicomponent Plane Elastic Compos- simple model for such a dynamics and we will present an ites homogenization result in its simplest form. The goal is to The paper establishes tight lower bound for the energy pass from the dynamics of several dislocation lines to the and effective elastic stress energy of two-dimensional three- dynamics of dislocation density. We will also give some material anisotropic composites. The materials are mixed qualitative properties of the effective hamiltonian. Finally, with fixed volume fractions; one of the materials is void. we will explain how the method developed allows us to get The bound expands the Hashin-Shtrikman and transla- homogenization results for particles system. This is joint tion bounds to multiphase structures. In the high-porosity works with Cyril Imbert and Rgis Monneau. regime, the obtained energy bound is exact and it is re- Nicolas Forcadel alized by special high-rank laminates. Optimal structures CEREMADE, Université Paris-Dauphine for low-porosity strongly anisotropic composites are con- [email protected] juncted. Andrej V. Cherkaev MS19 Department of Mathematics University of Utah Polyharmonic Homogenization, Rough Polyhar- [email protected] monic Splines and Sparse Super-localization We introduce a new variational method for the numeri- Grzegorz Dzierzanowski cal homogenization of divergence form elliptic, parabolic Politechnika Warszawska and hyperbolic equations with arbitrary rough (L∞)coef- [email protected] ficients. Our method does not rely on concepts of ergodicity or scale-separation but on compactness properties of the solution space and a generalization of polyharmonic splines MS20 to differential operators with arbitrary rough coefficients. Sea Ice, Climate, and Multiscale Composites This is a joint work with Lei Zhang (Jiaotong University) and Leonid Berlyand (PSU). Sea ice is a leading indicator of climate change, and a key component of Earth’s climate system. As a material, sea Houman Owhadi ice is a porous composite of pure ice with millimeter scale Applied Mathematics brine inclusions whose volume fraction and connectedness Caltech vary significantly with temperature. Fluid flow through the brine microstructure mediates a broad range of geophysi- 78 MS13 Abstracts

cal and biological processes. Sea ice also displays composite interface fluctuations in the case in which only one leaflet structures over much larger scales. For example, the sea supports compositional domains, is also derived. ice pack itself is a fractal composite of ice floes and ocean, while surface ponds on melting Arctic sea ice exhibit com- Mikko Haataja plex dynamics and self-similar geometrical configurations. MAE Department I will discuss how methods of homogenization and statisti- Princeton University cal physics are being used to study the effective properties [email protected] of such systems. This work helps improve our understanding of the role of sea ice in the climate system, and the Tao Han representation of sea ice in climate models. Princeton University [email protected] Kenneth M. Golden University of Utah Department of Mathematics MS21 [email protected] Three Dimensional Vesicles in Fluid Flow and Elec- tric Fields: Jump Conditions and a Numerical Method MS20 Identifying the Strongest Composites The electrohydrodynamic response of vesicles is due to a complex interplay between the fluid, the shape of the vesi- In this talk we develop variational methods for identifying cle membrane, and the surrounding electric field. In order the strongest composite geometries for prescribed bound- to construct accurate numerical models of vesicle in elec- ary loads. Here the “strongest’ composite has a microge- trohydrodynamic flows the physical jumps in the fluid and ometry for which the local stresses and strains are smallest ∞ electric fields must be determined and accounted for. In in the L norm over all composites comprised of two ma- this talk the jump conditions for the pressure, velocity, terials in fixed proportion. The analysis is carried out for and electric field for a three-dimensional vesicle with dis- composites with and without thermal prestress. continuous viscosities, an in-extensible interface, and with a surface voltage potential are presented. The jump con- Robert P. Lipton ditions are used in a sharp interface immersed interface Department of Mathematics solver. Sample analytic solutions have been developed to Louisiana State University verify the methods and will also be presented. [email protected] David Salac, Prerna Gera University at Buffalo - SUNY MS21 davidsal@buffalo.edu, prernage@buffalo.edu Compositional Interface Dynamics Within Sym- metric and Asymmetric Planar Lipid Bilayer Mem- Mohammad Kolahdouz branes University at Buffalo, SUNY Compositional domains within multicomponent lipid bi- mkolahdo@buffalo.edu layer membranes are believed to facilitate many important cellular processes. Experimentally, it has been shown that MS21 synthetic membranes whose overall compositions mimic those of the extracellular leaflet of the cell membrane can Numerical Algorithms for Vesicle Flows phase separate into distinct liquid phases, while the ones Direct numerical simulations of vesicles, bubbles, and other whose compositions mimic those of the cytoplasmic leaflet soft-particle suspensions in arbitrary confined geometries is do not display any compositional heterogeneities or do- extremely challenging owing to the near-singular interac- mains. Interestingly, in asymmetric membranes, where the tion forces, nonlinear interfacial forces and nonlocal hy- two leaflets have compositions mimicking those of the ex- drodynamics. In this talk, we will present some recent tracellular and cytoplasmic leaflets of the cell membrane, advances in computational algorithms for simulating such phase separation can either be induced or suppressed al- systems. Integral equation formulations for confined flows together. Furthermore, when both leaflets contain com- and mixtures of soft and rigid particles will be discussed. positional lipid domains, they are often found in perfect A new fast algorithm for accelerating the singular integral registry. These observations indicate that a significant evaluations on the interfaces will be presented. Integrating thermodynamic coupling exists between the lipids across semi-implicit time stepping schemes with reparameteriza- the two leaflets. While the effects of the thermodynamic tion and anti-aliasing techniques enables us to overcome coupling between the leaflets has been theoretically investi- numerical instabilities. We will review some of these com- gated recently with regard to equilibrium behavior of asym- putational components, which are essential for simulating metric multicomponent lipid bilayer membranes, its effects large number of particles in dense flows. on the compositional domain dynamics have received less attention. In this talk, I will first derive the general equa- Shravan Veerapaneni tions that describe the dynamics of compositional domains Department of Mathematics within planar membranes with asymmetry in leaflet prop- University of Michigan erties and in the presence of a thermodynamic coupling be- [email protected] tween the leaflets. These equations are then employed to develop analytical solutions to the dynamics of the recur- rence of registration for both laminar and circular domains MS21 in the case of weak coupling. It is shown that experimen- Nonlinear Dynamics of An Incompressible Elastic tally measuring these dynamics will enable one to deter- Membrane in An Electric Field mine the strength of the thermodynamic coupling between the leaflets. A closed-form expression for the decay rate of Cells are enveloped by a lipid membrane, which is imper- MS13 Abstracts 79

meable to ions and acts as a capacitor when an electric MS22 field is applied. In this work we present a long-wave model Wrinkles and Folding on Curved Topographies for the nonlinear dynamics of a planar (unsupported) lipid membrane under a DC field. The lipid membrane is mod- An intrinsically flat, elastic film forced to wrap a curved eled as an interface with a constant area. The governing surface spontaneously develops wrinkles. We show how the equations for the non-linear long-wave dynamics are de- relaxed membrane energy of the wrinkled film, and a sep- rived under different conditions. Analysis on the equilib- arate equation for the wrinkled microstructure appear as rium profile shows the existence of multiple equilibrium the zeroth and first order equations in a multiscale per- profiles. Numerical simulations of the nonlinear dynamics turbation expansion of a fully rotationally invariant plate- illustrate various novel behaviors, and elucidate the impor- bending model. Applying these equations to curved sur- tance of charge distribution on the membrane. We will also faces, we show how geometry can both suppress wrinkles examine the possible effects of tangential electric field on and enhance them into singular folds. the membrane dynamics. Evan Hohlfeld Yuan-Nan Young Physics Department Department of Mathematical Sciences University of Massachusetts Amherst NJIT [email protected] [email protected]

Michael Miksis MS22 Department of Engineering Science and Applied First Steps Toward a Multipole Construction of Mathematics Thin Sheets Northwestern University [email protected] An elastic sheet may contain pointlike conical singularities that carry a metrical ‘charge’ of Gaussian curvature. Adding such elementary defects to a sheet allows one to Shravan Veerapaneni make many shapes, in a manner broadly analogous to the Department of Mathematics familiar multipole construction in electrostatics. However, University of Michigan here the underlying field theory is non-linear, and superpo- [email protected] sition of intrinsic defects is non-trivial as it must respect the immersion of the resulting surface in three dimensions. We Petia Vlahovska consider the first terms of this construction: the monopole Brown University which corresponds to a conical singularity, and the “charge- petia [email protected] neutral’ dipole. Such a dipole is composed of two conical singularities of opposite sign. Unlike the relatively simple electrostatic case, here there are two distinct stable min- MS22 ima and an infinity of unstable equilibria. We determine Mechanics of a Folded Elastic Ribbon the shapes of the minima and evaluate their energies in the thin-sheet regime where bending dominates over stretch- When a thin, annular strip cut out in a sheet of paper is ing. Our predictions are in surprisingly good agreement folded along its circular centerline, it buckles out-of-plane with experiments on paper sheets. (Dias et al., PRL, 2012). We derive an equivalent rod model for the folded strip. A nonlinear effective constitu- Jemal Guven tive law capturing the underlying geometrical constraints is Instituto de Ciencias Nucleares obtained. A stability analysis is presented, which explains Universidad Nacional Autonoma de Mexico the buckled shapes reported in the literature, and predicts [email protected] a new type of buckling patterns. Basile Audoly James A. Hanna University Paris VI, France University of Massachusetts Paris, France Department of Physics [email protected] [email protected]

Osman Kahraman MS22 Universit´e de Lorraine, Metz Folding of a Fluid-Supported Sheet [email protected]

A thin elastic sheet lying on a heavy fluid buckles under Martin Michael Müller uniaxial compression via localized folds. This system is Université de Lorraine, Metz, France integrable, allowing us to analytically describe the entire [email protected] progression from a weakly displaced sinusoidal buckling to a single large fold that contacts itself. Underlying the inte- grability is an unexpected symmetry, which leads to large MS23 ground-state degeneracy. We find a connection between Title Not Available at Time of Publication this nontrivial symmetry and the obvious symmetries of the higher-dimensional sine-Gordon equation. Abstract not available at time of publication.

Haim Diamant Sorin Mitran School of Chemistry University of North Carolina Chapel Hill Tel Aviv University [email protected] [email protected] 80 MS13 Abstracts

MS23 bombardment of a binary material. Title Not Available at Time of Publication R. Mark Bradley Abstract not available at time of publication. Dept. of Physics Colorado St. University Petr Plechac [email protected] University of Delaware Department of Mathematical Sciences [email protected] MS24 Composition Patterning in Irradiation-driven Ma- terials MS23 Title Not Available at Time of Publication Following a brief discussion of recent progress in phase field modeling of radiation effects in materials, this pre- Abstract not available at time of publication. sentation will focus on the problem of composition patter- ing in irradiation driven systems. A coupled set of non- Luc Rey-Bellet linear stochastic PDEs of diffusion-reaction type is devel- Department of Mathematics & Statistics oped in which non-local forcing terms represent the irradi- University of Massachusetts ation field. Aspects of the spatial and temporal stiffness of [email protected] these equations will be discussed as part of presenting the numerical solution and model predictions. MS23 Anter A. El-Azab Title Not Available at Time of Publication Florida State University [email protected] Abstract not available at time of publication.

TBD TBD Santosh Dubey TBD Purdue University TBD [email protected]

MS24 MS24 Spatio-Temporal Self-Organization at the Multi-Scale Modeling of Irradiated Alloys: Nanoscale in Alloys Subjected to Sustained Irra- Atomistically-Informed Continuum Models diation We consider the estimation, by means of atomistic simula- Recent atom probe experiments have shown that, in binary tion, of parameters in theories of ion irradiation of binary alloys, ion irradiation can stabilize self-organized structures materials. By extending the ”crater function” formalism comprised of nanoscale solute-rich precipitates that con- to the case of binary materials, we are able to estimate tain smaller solvent-rich precipitates. We investigate and four important parameters in these theories. This seems to elucidate by kinetic Monte-Carlo simulations the mecha- suggest that an important morphological instability mech- nisms leading to the formation of these precipitate-within- anism may not be active; therefore, we generalize the ex- precipitate structures, which we term ’cherry-pit” struc- isting model to admit the alternate mechanism of phase tures. Asymmetries in thermodynamic and kinetic proper- separation, and discuss its predictions. ties between solvent and solute atoms are shown to play a Scott Norris key role. Department of Mathematics Pascal Bellon Southern Methodist University Dept. of Materials Science [email protected] University of Illinois, Urbana-Champaign [email protected] MS25 Mathematical Modeling of Colloids Shipeng Shu, Brad Stumphy, Robert Averback University of Illinois at Urbana-Champaign This talk deals with mathematical modeling of colloids. We [email protected], [email protected], think of colloids as soft matter systems consisting of par- [email protected] ticles suspended in fluid. These particles may be electrically charged or may posses permanent electric or magnetic dipoles. Renewed interest in colloids occurs in several tech- MS24 nological areas, including liquid crystal display, microflu- Self-Assembled Nanoscale Patterns Produced by idic apparatus and also in modeling particle clustering in Ion Bombardment of Two-Component Materials biology. We will focus on ferromagnetic nano-particles in a liquid crystal matrix. These systems show two very dis- We have developed a theory that explains why astonish- tinctive features: formation of defects around the particles ingly regular hexagonal arrays of nanoscale mounds can and the tendency to form clusters, with the subsequent form on the surface of a binary solid when it is bombarded failure of the device. We will construct effective energies of with a normally-incident, broad ion beam. The coupling ferrofluids and explore how to harness defects to prevent between a surface layer of altered composition and the clustering. The presence of a defect causes a buildup of surface morphology is the key to understanding the phe- elastic energy of the liquid crystal between two particles, nomenon. Our theory also predicts that remarkably defect- hence favoring configurations with an optimal inter-particle free surface ripples can be produced by oblique-incidence MS13 Abstracts 81

distance. Department of Mathematics [email protected] Maria-Carme Calderer Deparment of Mathematics University of Minnesota, USA MS26 [email protected] Microstructure As a Result of Diﬀerential Growth of Thin Films

MS25 In this talk I will discuss wrinkling of a thin elastic sheet Electromagnetic Wave Propagation Through a Liq- caused by a prescribed non-Euclidean metric. This is a uid Crystal Layer model problem for the patterns seen, for example, in torn plastic sheets and the leaves of plants. Following the lead of We study the propagation of electromagnetic waves other authors I adopt a variational viewpoint, according to through a liquid crystal layer paying particular attention to which the wrinkling is driven by minimization of an elastic the problem of optimizing the transmitted intensity. For energy subject to appropriate constraints and boundary a homogeneous liquid crystal orientation field, we derive conditions. The main result is the identification of the analytical formulas for the orientation that maximizes the scaling law (in terms of thickness) for the minimum of the transmission. The minimizing orientation is unique for a elastic energy. given wavelength and we define its value implicitly. For a heterogeneous liquid crystal orientation, we carry out nu- Peter Bella merical simulations to study the optimization problem. Max Planck Institute for Mathematics in the Sciences [email protected] Hong Zhou Department of Applied Mathematics Robert V Kohn Naval Postgraduate School, Monterey, CA Courant Institute of Mathematical Sciences [email protected] New York University [email protected] Eric Choate, Michael Winslow Department of Applied Mathematics Naval Postgraduate School MS26 [email protected], [email protected] Ambrosio-Tortorelli Approximation for Cavitation

An approximation of Ambrosio-Tortorelli type is presented MS25 for the variational model for cavitation and fracture intro- Defect Patterns in Liquid Crystal Films duced by Henao & Mora-Corral (2010). A proof is provided for the liminf inequality in the Γ-convergence, and some We analyze stable textures in thin smectic C* ﬁlms using numerical examples of void coalescence using this model the Ginzburg-Landau type model are shown, following the numerical study by Xu & Henao (2011). 2 2 1 −| |2 2 [ks(div u) + kb(curl u) + 2 (1 u ) ] dx Ω 2ε Duvan Henao UPMC Paris 6 and Catolica de Chile for ε>0 and small. We prove that if the c director u has [email protected] degree deg (u, ∂Ω) = d>0 then the pattern has d degree- one defects. Moreover if 0

els arise as special cases of our results. crostructure

Lucia Scardia In rheological fluids, optimally designed composites, bi- School of Mathematics and Statistics ological materials, structure self-organizes in response to University of Glasgow external loads or applied fields. We relate microstructural [email protected] transformation in such materials to evolution of the spectral measure in an integral representation of the effective Mark Peletier, Ron Peerlings, Marc Geers properties of composite. Using nonlinear diffusion and vis- Technische Universiteit Eindhoven coelasticity examples, we show that Pade approximants of [email protected], [email protected], the spectral measure link evolution of the microgeometry [email protected] to the effective behavior of material and allow to uniquely recover some microstructural parameters.

MS26 Elena Cherkaev About a Γ-Convergence Approach to a Quasicon- University of Utah tinuum Method in 1D Department of Mathematics [email protected] We analyze the validity of a quasicontinuum approximation of a one-dimensional atomistic model for fracture mechanics. To this end we derive a development by Γ-convergence MS28 and compare the limiting functional and its minimizers Models and Analysis for Cohesive Dynamic Frac- with those obtained for a fully atomistic system in [L. Scar- ture dia, A. Schlömerkemper, C. Zanini, MMMAS 21 (2011)]. Further we estimate the minimal size of the atomistic re- We derive models for cohesive dynamic fracture using force gion needed in order to capture boundary layer effects and balance, stationary action, and maximal dissipation, for a discuss the effect of the choice of the representative atoms. range of cohesive energy densities. For 1-D, we give some partial existence results, examples where homogenization is required, and some surprising examples of non-existence. Anja Schlömerkemper This is joint with V. Slastikov. University of Wuerzburg (Germany) Christopher Larsen [email protected] Worcester Polytechnic Institute Math Dept Mathias Schäffner [email protected] University of Würzburg (Germany) mathias.schaeff[email protected] MS28 Double Negative Behavior in Metamaterials and MS27 Multi-Scale Analysis Unstable Multilayer Homoepitaxial Growth: From 2D Islands to 3D Mounds Metamaterials are a new form of structured materials used to control electromagnetic waves through localized reso- Abstract not available at time of publication. nances. In this talk we introduce a rigorous mathematical framework for controlling localized resonances and pre- Jim W. Evans dicting exotic behavior inside optical metamaterials. The Ames Laboratory USDOE and Iowa State University theory is multiscale in nature and provides a rational ba- [email protected] sis for designing microstructure using multiphase nonmag- netic materials to create backward wave behavior across MS27 prescribed frequency ranges. Variational Methods for Crystal Surface Instability Robert P. Lipton Department of Mathematics Abstract not available at time of publication. Louisiana State University Giovanni Leoni [email protected] Carnegie Mellon University [email protected] MS28 Large Deviations, Metastability and Monte Carlo MS27 Methods for Multiscale Problems Motion of Elastic Thin Films by Surface Diffusion We discuss large deviations and Monte Carlo methods for with Curvature Regularization multiscale dynamical systems that are stochastically per- Abstract not available at time of publication. turbed by small noise. The large deviations principle can then be used to study metastability for such problems, as Massimiliano Morini well as asymptotic problems for related PDE’s. Further- Universita degli Studi di Parma more, we derive a change of measure that allows to design Parma, Italy asymptotically efficient importance sampling schemes for [email protected] the estimation of associated rare event probabilities and expectations of functionals of interest.

MS28 Konstantinos Spiliopoulos Spectral Representation and Evolution of Mi- Boston University MS13 Abstracts 83

Department of Mathematics and Statistics and mathematical properties of such systems. [email protected] Ross McPhedran Paul Dupuis, Hui Wang CUDOS ARC Centre of Excellence Division of Applied Mathematics and School of Physics, University of Sydney Brown University [email protected] [email protected], hui [email protected] MS29 MS29 Radiationless Electromagnetic Modes in Open Physical Bounds, Potentials and Fundamental Lim- Plasmonic Nanostructures itations of Metamaterial Cloaks In open systems the energy associated with a photonic In this talk we establish fundamental physical bounds on mode may continuously leak away in the form of a radi- bandwidth and cloaking performance for arbitrary passive ated wave, and hence all the lifetimes are finite. This prop- cloaking schemes. We apply the Bode-Fano theory to de- erty is closely related to the problem of instability of the rive general limitations relating the maximum achievable Rutherford atom in classical physics. Here, we will theoret- bandwidth and overall scattering reduction to the size and ically show that in the limit of no loss plasmonic materials electromagnetic properties of the scatterer to be hidden. may offer an opportunity to have light localization in open We derive a few general theorems limiting ideal cloaking bounded systems with infinitely long lifetimes. performance, which represent a pivotal achievement to un- Mario Silveirinha derstand the applicability of cloaking devices to real-world University of Coimbra problems. [email protected] Andrea Alu Department of Electrical and Computer Engineering MS30 University of Texas at Austin [email protected] The Micromechanics of Colloidal Dispersions What do corn starch, swimming spermatozoa, DNA and Francesco Monticone self-assembling nanoparticles have in common? They are The Univrsity of Texas at Austin all (or can be modeled as) particles dispersed in a con- [email protected] tinuum suspending fluid where hydrodynamic interactions compete with thermal (Brownian) and interparticle forces to set structure and determine properties. These systems MS29 are soft as compared to molecular systems largely because Towards Digital Metamaterials their number density is much less and their time scales much longer than atomic or molecular systems (both scal- Inspired by the Boolean algebra and the notion of digital ing with the colloidal to atomic size cubed). In this talk electronics and the binary number theory, we have devel- I will describe the common framework for modeling these oped the concept of digital metamaterials, in which we ex- diverse systems and the essential features that any hydro- plore how an arbitrary value of the permittivity function dynamic modeling must incorporate in order to capture the can be synthesized by judicious combinations of only two correct behavior. Actually computing the hydrodynamics constituent materials with two different permittivity pa- in an accurate and efficient manner is the real challenge, rameters. We have analyzed the conditions upon which and I will illustrate past successes and current efforts with one can achieve such synthesis, including the role of loss, examples drawn from the diffusion and rheology of colloids shape and dimensions of constituent elements. to the swimming of catalytic nanomotors. Cristian Della Giovampaola John F. Brady University of Pennsylvania Chemical Engineering Department of Electrical and Systems Engineering Caltech [email protected] [email protected]

Nader Engheta Department of Electrical and Systems Engineering MS30 University of Pennsylvania Collective Dynamics in Suspensions of Motile [email protected] Micro-particles We describe a computational method for the dynamics of MS29 thousands of micro-swimmers interacting with each-other, Branch-cuts and Sharp Corners in Composite In- the fluid, and surfaces. The method is illustrated with sus- clusions pensions of pusher and puller motile particles. The model satisfactorily captures the macroscopic structures observed The calculation of effective transport properties such as di- in bacterial baths. We discuss dense and confined swim- electric permittivity or magnetic permeability for systems mer suspensions where organization emerges as a result of containing inclusions immersed in a continuous matrix can steric effects. Last we show examples of swimmers inside be challenging. This is particularly the case in the situa- a peristaltic pump where the dynamics and transport are tion encountered in the study of metamaterials- when the affected. inclusions and matrix have permittivities or permeabilities of opposing signs- and the problem is compounded when Enkeleida Lushi the inclusions have sharp corners. We explain the physical Imperial College London and Courant Institute NYU 84 MS13 Abstracts

[email protected] cross-section of twisted bundles to develop a quantitative theory of defect-riddled optimal packings of twisted (chiral) filament bundles. MS30 Statistical Analysis of Passive Particle Tracking in Gregory M. Grason Microrheology Polymer Science and Engineering University of Massachusetts Amherst Passive particle tracking in microrheology has received [email protected] much attention in the recent years, but the statistical methods for data analysis are still quite primitive. To this end, we develop new methods for analyzing stochas- MS31 tic differential equations (SDEs) driven by colored noise. How to Derive Equilibrium Equations for Fully Traditionally, most SDEs are modeled as driven by white Nonlinear Bending Theories in Euclidean and Non- noise, which implies a Markovian assumption. We present Euclidean Elasticity a method of driving SDEs with colored noise, which provides acces to a rich collection of time-dependent models. A key feature of nonlinear bending theories for thin elastic Our model has a natural discretization scheme, the key to films is an isometry constraint on the admissible deforma- a missing data inference framework for white noise SDEs. tions. It means that only ’pure bending’ deformations are Many computational methods from the white noise set up allowed, i.e., no stretching or shearing is permitted. Such can easily be adapted to our framework. We present appli- a constraint is a serious obstacle when one wants to derive cations of our methodology for single particle tracking for the equilibrium equations satisfied by deformations with passive microrheology. minimal bending energy. In the talk I will explain how to overcome it. Natesh Pillai Statistics Peter Hornung Harvard Max Planck Institute for Mathematics in the Sciences [email protected] [email protected]

MS30 MS31 Biofilm Streamers in Porous Environments Riemannian Analysis of Pre-stressed Elastic Mate- rials Biofilms are ubiquitous and are generally associated with surfaces. Despite their importance, basic information Dimension reduction is a classical theme in elasticity, dat- about biofilm dynamics is common ecological environments ing to centuries ago. Significant progress has been achieved is lacking. Using model flows in microfluidic channels, in recent years in the rigorous derivation of dimension- we demonstrate that in the presence of flow biofilms de- ally reduced theories from 3D elasticity. The recent re- velop three-dimensional thread-like structures, or stream- newed interest in pre-stressed (or incompatible) materials ers, which in common pressure-driven flows can lead to has raised a new challenge in deriving reduced models for sudden clogging of the channels. We document several as- materials that may have complex internal geometries. In pects of the development in space and time, and use bio- this lecture I will present a single theorem that gives in logical mutants to further understand the genes important one fell swoop reduced theories for “Euclidean” and “non- to the streamer formation. Our results are interpreted in Euclidean” plates, shells, and rods. The relevance of these terms of a model that characterizes trapping of cells in a reduced models in several pattern forming systems will be sieve-like network that exhibits exponentially fast growth demonstrated. of the typical streamer radius and is independent of the bacterial growth rate. Finally, we demonstrate similar ef- Raz Kupferman fects in flow through soil-like porous materials, industrial Institute of Mathematics, filters, and medical stents to emphasize how these ideas can The Hebrew University impact environmental, industrial and medical systems. [email protected] Howard A. Stone Mechanical and Aerospace Engineering MS31 Princeton University A Riemannian Approach to Dimension Reduction [email protected] in Non-Euclidean Elasticity The renewed interest in non-Euclidean (or incompatible) MS31 elasticity has raised a new challenge in deriving dimen- Nonlinear Structure and Mechanics of Filament sionally reduced models for such elastic bodies. In this Bundles: Intrinsic Geometry of Twist and Defect- talk I will present a Riemannian approach to this prob- Riddled Ground States lem that enables us to treat Euclidean and non-Euclidean materials with arbitrary number of slender dimensions. I Rope-like bundles of filamentous proteins provide a me- will present two theorems based on this approach one that chanical bridge from the molecular scale to the microscopic gives reduced theories of plates, shells and rods, and the scales of in a broad range of cells and tissues. Motivated other a reduced membrane model. by the “almost crystalline” packing of biofilament bundles, we develop continuum approaches to the non-linear Cy Maor geometric coupling between inter-filament strain and back- Hebrew University, Israel bone orientation in dense bundles. We exploit a correspon- [email protected] dence between stresses induced in elastic sheets subjected to (positive) curvature and inter-filament stresses in the Raz Kupferman, Jake Solomon Hebrew University MS13 Abstracts 85

Israel Department of Mathematical Sciences [email protected], [email protected] Carnegie Mellon University [email protected]

MS32 Critical Aspect Ratio in a Single Crystal Shear Ex- MS32 periment Multiscale Modeling of Ge Nano-Crystallization from Amorphous Phase Consideration is given to a non-convex variational model for a shear experiment in the framework of single-crystal Complex nanostructures are observed in laser-driven crys- linearised plasticity with cross-hardening. The rectangular tallization of amorphous Ge films. In this talk, a mul- shear sample is clamped at each end, and is subjected to a tiscale model will be presented to study the kinetics of prescribed horizontal shear, modelled by a hard Dirichlet rapid phase-transformations and the interplay between nu- condition. We ask: how much energy is required to im- cleation and growth processes. The core of the model is pose such a shear, and how does it depend on the aspect based on the phase-field method and the parameters in- ratio? Assuming that just two slip systems are active, we volved are obtained via molecular dynamics. The results show that there is a critical aspect ratio, above which the from the simulations are compared to observations with energy is strictly positive, and below which it is zero. The dynamic transmission electron microscopy (DTEM).” This energy required to impose a shear depends on the pres- work performed under the auspices of the U.S. Department ence of cross hardening and the energetic penalization of of Energy by Lawrence Livermore National Laboratory un- geometrically necessary dislocations. This result therefore der Contract DE-AC52-07NA27344. provides a way to distinguish microscopic models by their macroscopic behavior. Celia Reina Univ. Pennsylvania Patrick Dondl [email protected] Durham University Department of Mathematical Sciences Luis Sandoval, Jaime Marian [email protected] LLNL [email protected], [email protected] MS32 A Theory and Challenges for Coarsening in Mi- MS32 crostructure Mathematical Challenges in Interpretation of Hedm Data Cellular networks are ubiquitous in nature. Coarsening is governed primarily by the attempt of the system to de- High Energy Diffraction Microscopy (HEDM) is a non- crease the energy of its interfaces. The Grain Boundary destructive orientation and strain mapping technique that Character Distribution, GBCD, represents the distribution uses high energy (¿50KeV) monochromatic x-ray beam. of interfacial energy and its evolution provides some un- Recent experimental developments enable the interroga- derstanding of the order in the system. This gives rise to tion of polycrystalline materials under thermal and me- interesting questions and some challenges. chanical loading resulting in abundant information with resolution at the micron level. The technique provides David Kinderlehrer three dimensional microstructure snapshots during the Carnegie Mellon University loading process. This is the first opportunity to examine [email protected] theories regarding microstructure evolution in such materials using in a non-destructive technique. In this talk I Katayun Barmak will discuss mathematical formulations using optimization Department of Applied Physics and Applied Mathematics techniques that address several problems of engineering in- Columbia University terest including: (i) the extraction of material properties [email protected] such as energy and mobility form HEDM, and (ii) the validation of microstructural evolution theories for material Eva Eggeling behavior under thermal and mechanical loading. Tech- Fraunhofer InstitutComputer Graphics Research IGD niques from optimal transport theory will be reviewed and [email protected] explained in the context of these problems.

Maria Emelianenko Shlomo Ta’asan George Mason University Department of Mathematical Sciences [email protected] Carnegie Mellon University [email protected] Yekaterina Epshteyn Department of mathematics MS33 University of Utah Modeling Defect Structures and Associated Slow [email protected] Processes in 3D Materials with Phase Field Crystal Methods Richard Sharp Microsoft Corp. A wide variety of phenomena in crystalline solids are driven Redmond, WA and/or limited by defect evolution processes. Examples [email protected] include plasticity, structural phase transformations, and recrystallization. It is not currently possible to model Shlomo Ta’asan complex, collective defect processes over the vast range of 86 MS13 Abstracts

length and time scales often involved, but the ability to XPFC) will be singled out and its extension to ternary access diffusive time scales with phase field crystal (PFC) and multi-component alloys will be discussed. Some ex- models should open new avenues of research in this area. amples of the types of phase transformations that are pos- In this talk, applications of the PFC approach to defect sible with this approach will be demonstrated, with partic- statics and dynamics in FCC, BCC, and HCP materials ular emphasis on new results relating to interface kinetics will be discussed. The most prevalent dislocations in FCC and solute trapping, solid-state precipitation and magneto- and BCC crystals have been stabilized within the PFC for- crystalline interactions. We end with a new derivation of an mulation and shown to exhibit properties consistent with amplitude model of structural transformations, discussing both continuum elasticity and molecular dynamics. Ad- the advantages and drawbacks of such models, and illus- ditional levels of structural and dynamic complexity nat- trating their use in solidification and secondary phase for- urally emerge when defected PFC crystals are subjected mation. to slow mechanical, chemical, or thermodynamic driving forces. A few examples of such higher-level effects involv- Nikolas Provatas ing jogs, obstacles, and sources will be explored along with McGill University selected results concerning larger-scale collective defect be- [email protected] haviors. Joel Berry MS33 McMaster University Phase Field Crystal Models of Grain Growth [email protected] Traditional Phase Field Crystal (PFC) models contain Nikolas Provatas solid and liquid phases, however many important materi- McGill University als processing phenomena involve a vapor phase as well. In [email protected] this work, we add a vapor phase to an existing PFC model and show realistic interfacial phenomena. For example, the PFC model exhibits density oscillations at liquid-vapor in- Joerg Rottler terfaces that compare favorably to data available for in- University of British Columbia terfaces in metallic systems. Additionally, the strain field [email protected] beneath a stepped interface is characterized and shown to qualitatively reproduce predictions from continuum mod- Chad W. Sinclair els, simulations, and experimental data. Further examples University of British Colombia will be given. [email protected] Peter Voorhees Northwestern University MS33 Dept. of Material Science and Engineering Particles at Fluid-fluid Interfaces: A New Navier- [email protected] Stokes-Cahn-Hilliard Surface Phase-Field Crystal Model Kuo-An Wu Northwestern University Colloid particles that are partially wetted by two immisci- Dept. Materials Science and Engineering ble fluids can become confined to fluid-fluid interfaces. At [email protected] sufficiently high volume fractions, the colloids may jam and the interface may crystallize. The fluids together with the interfacial colloids form an emulsion with interesting ma- Edwin Schwalbach terial properties and offer an important route to new soft National Institute for Standards and Technology materials. We develop an improved Navier-Stokes-Cahn- [email protected] Hilliard-Surface-Phase-Field-Crystal model based on the principles of mass conservation and thermodynamic con- James Warren sistency. To validate our approach, we derive a sharp in- NIST terface model and show agreement with the improved dif- Metallurgy Division fuse interface model. Using simple flow configurations, we [email protected] show that the new model has much better properties and does not lead to spurious velocities. Finally, we demonstrate the solid-like behaviour of the crystallized interface MS34 by simulating the fall of a solid ball through a colloid-laden Analysis of Two-Dimensional Phases in Bent-Core multiphase fluid. Liquid Crystals

John Lowengrub We consider a Landau-de Gennes type model used in the Department of Mathematics physics literature to describe two-dimensional modulated University of California at Irvine structures in bent-core liquid crystals. We will discuss a [email protected] simpliﬁed version of the model, and present some remarks about the full version.

MS33 Tiziana Giorgi Phase Field Crystal Modeling of Microstructure in Department of Mathematics Multi-Component Alloys New Mexico State University [email protected] This talk will begin with a comparison of diﬀerences and similarities of recent PFC approaches in the context of 2D/3D structural stability and of 3D defect stability. MS34 A recent model for structural transformations (so-called Equidistribution Results for the Renormalized En- MS13 Abstracts 87

ergy and 2D Coulomb Gases [email protected]

The renormalized energy is a Coulomb interaction energy for an inﬁnite number of points in the plane. It has been MS35 introduced and derived by Sandier and Serfaty as the limit Fast Numerical Methods for Electronic Structure interaction energy for vortices in the 2D Ginzburg-Landau Calculations model of superconductivity. It can also be derived as a limit interaction for droplets in the Ohta-Kawasaki energy, as The standard diagonalization method for solving the Kohn well as particles of a Coulomb gas at zero temperature. It Sham density functional theory (KSDFT) scales cubically is expected to be minimized when the points are arranged with respect to system size. In the recently developed pole in an ”Abrikosov” triangular lattice. In joint work with expansion plus selected inversion method (PEXSI), KS- Simona Rota Nodari, we show that for minimizers of the DFT is solved by evaluating the selected elements of the renormalized energy in various suitable senses, as well as inverse of a series of sparse symmetric matrices. We show for minimizers of the Coulomb gas Hamiltonian, the energy that the PEXSI method scales at most quadratically with and the points are uniformly distributed at any scale larger respect to system size for all materials, and can scale to tens than the interpoint distance. of thousands of processors on leadership class machines.

Sylvia Serfaty Lin Lin laboratoire Jacques-Louis Lions, France Lawrence Berkeley National Laboratory UPMC Paris 6 [email protected] [email protected]

Simona Rota Nodari MS35 Université de Cergy-Pontoise Many-Body Propagators and the GW Approxima- [email protected] tion of the Self-Energy Operator We discuss the Green’s function formalism of many-body MS34 perturbation theory. In this approach, the excitation of Vortex Dynamics with Pinning and Strong Fields the material is described in terms of quasi-particle energies of a single-particle Hamiltonian that contains a self- We study a mixed heat and Schrödinger Ginzburg-Landau energy term. The self-energy operator should properly evolution equation that is meant to model a superconduc- describe many-body excitation effects. It can be approx- tor containing impurities and subjected to an applied elec- imated properly by the so-called GW method. We will tric current and electromagnetic field. Such a current is point out the advantage and computational challenges of expected to set the vortices in motion, while the pinning this approach. term drives them toward minima of the pinning potential and pins them there. We derive the limiting dynamics of a Fang Liu,LinLin finite number of vortices in the limit of a large Ginzburg- Lawrence Berkeley National Laboratory Landau parameter, or → 0, when the intensity of the fl[email protected], [email protected] electric current and applied magnetic field on the boundary scale like | log |. We show that the limiting velocity of Chao Yang the vortices is the sum of a Lorentz force, due to the cur- Lawrence Berkeley National Lab rent, and a pinning force. Comparing the two then allows [email protected] us to identify the critical depinning current.

Ian Tice MS35 Carnegie Mellon University Exciton Diﬀusion in Organic Solar Cells: First-- [email protected] Principles Investigations

Sylvia Serfaty Exciton diffusion length and time are among the most im- laboratoire Jacques-Louis Lions, France portant factors that govern the performance of organic so- UPMC Paris 6 lar cells and light-emitting diodes. We have developed a [email protected] first-principles approach based on time-dependent density functional linear response theory to describe the energy and many-body wave-functions of excitons. The non-adiabatic MS34 ab initio molecular dynamics is used to calculate phonon- On the Nature of Defects in the Q-Tensor Theory assisted transition rates between localized exciton states of Nematic Liquid Crystals with the spontaneous emission determined by the dipole approximation. With Mont Carlo simulations, we are able Nematic liquid crystals are modelled mathematically us- to calculate the exciton diffusion length, time, and diffu- ing either: unit-length vectors in the Oseen-Frank theory sivity for a prototype polymer system P3HT, and have ob- (2 degrees of freedom), scalars and unit-length vectors in tained excellent results comparing to experiments as well Ericksen theory (3 degrees of freedom) or symmetric and as physical insight into the microscopic nature of exciton traceless 3x3 matrices in Landau-de Gennes theory (5 de- diffusion. The work was partially supported by NSF-Solar grees of freedom). We will look into specific features of grant DMR-1035480. nematics that require a tensorial description, with an emphasis on the interpretation of defects in various theories. Gang Lu California State University Northtridge [email protected] Arghir Zarnescu University of Sussex, Xu Zhang, Zi Li 88 MS13 Abstracts

California State University Northridge course banquet, including a Whale Steak named for him.) [email protected], [email protected] Curiously, from our vantage point 95 years later, the then- recent vindication by x-ray diﬀraction of his periodic model of crystal structure went uncelebrated in the great hall. MS35 Which of his achievements had mineralogists gathered to Fixed-Point Optimization of Atoms and Density in celebrate? And which should we celebrate in 1914, the Dft International Year of Crystallography?

DFT methods require solving a fixed-point problem for the Marjorie Senechal density, and all practical codes use a multisecant variant of Smith College Broyden’s second (bad) method. I will describe an exten- [email protected] sion including the atomic positions within the same fixed- point problem. The method involves an implicit trust- region for the unpredicted step and adapting the concept MS36 from optimization of a Broyden family to the fixed-point Coincidence Site Lattices and Well-rounded Sub- problem with a conventional stability constraint, plus fail- lattices in the Plane safe trust region controls. Given a lattice Γ a lattice of the form Γ ∩ RΓ is called a Laurence Marks CSL if it is a sublattice of full rank. A lattice is called Department of Materials Science and Engineering well-rounded, if its lattice vectors of minimal length span Northwestern University the underlying space. We use the connection between a [email protected] certain class of CSLs and the well-rounded sublattices of a lattice to determine all its well-rounded sublattices, to count them, and to calculate the asymptotic growth rate MS36 via suitable generating functions. Recent Advances in Mathematical Diffraction The- ory Peter Zeiner Department of Mathematics The discovery of quasicrystals called for an extension of University of Bielefeld classical diffraction results to aperiodic systems. For cut [email protected] and project sets, the diffraction is pure point, and the locations and intensities of Bragg peaks can be calculated explicitly. Recent rigorous and constructive approaches to MS37 the case of diffuse scattering provide a better understand- On the Coupling Between Transformation and ing of systems with singular continuous and absolutely con- Plasticity in Polycrystals tinuous diffraction. This talk reviews the development of mathematical diffraction theory following the discovery of Abstract not available at time of publication. quasicrystals. Kaushik Bhattacharya Uwe Grimm Howell N. Tyson Sr. Professor of Mechanics Department of Mathematics & Statistics California Institute of Technology The Open University [email protected] [email protected] MS37 MS36 Nonlinear Asymptotic Homogenization of Thermo- A Stroll Along Structural Paths: Symmetry, electric Composites Pseudo-Symmetry and Their Exploitation to Un- derstand and Design Structures We develop a nonlinear asymptotic homogenization theory to analyze the effective behavior of layered thermoelectric Structural relations between aristotypes (”basic struc- composites. The nonlinearly coupled thermoelectric trans- tures”) and hettotypes (”derivative structures”) are of port equations are homogenized using asymptotic analysis, paramount importance to understand at the atomic level from which the macroscopic field distributions are derived how a displacive phase transition occurs, what features dif- with local fluctuation averaged out, and overall thermoelec- ferent structures share, how a structural continuity is re- tric conversion efficiency is established using an idealized alized at the interface separating crystal associations. The thermoelectric module. The analysis sheds considerable approach and the method will be illustrated with the help insight into the effective behavior of thermoelectric com- of several examples. posites for their design and optimization. Massimo Nespolo Yang Yang, Jiangyu Li Cristallographie, Résonance Magnétique et Modélisations U. Washington Université de Lorraine [email protected], [email protected] [email protected] MS37 MS36 Constitutive Models for Magneto-Active Elas- Periodicity, Aperiodicity and Prehistory tomers at Finite Strains

On February 28, 1918, the American Museum of Natu- This paper deals with the application of a finite-strain ho- ral History in New York hosted a gala birthday party for mogenization framework to develop constitutive models for the great French mineralogist RenéJustHaüy. (The hon- magneto-active elastomers consisting of initially aligned, oree, having died 96 years before, missed out on the seven rigid magnetic particles distributed randomly in an elas- MS13 Abstracts 89

tomeric matrix. For this purpose, a novel strategy is pro- Loss Level posed to partially decouple the mechanical and magneto- static effects. The theory predicts the existence of certain Anomalous localized resonance (ANR) phenomena appears extra stresses that can be directly linked to changes in the at the interface between negative index and and positive effective magnetic permittivity with the deformation. We index materials when approached by a charge distribution. show that particle rotations can be used to generate large This phenomenon manifests itself in a very large ”unnat- magnetostriction. ural” accumulation of dissipated power in a small layer around the respective interface between the two materi- Pedro Ponte Castañeda als. In this talk we will discus about the (two-dimensional) University of Pennsylvania anomalous localized resonance phenomena appearing at [email protected] BOTH interfaces between a slab (infinite in the y-direction) with permittivity having a real part equal to -1 and small dissipation d¡¡1 and two ”natural” materials, one to the left MS37 with a permittivity 1 + i ∗ (d + db) and the other to the Continuum Electromechanical Theory for Nematic right with permittivity 1, when one approaches the slab Continua with Applications to Freedericksz Insta- with a discrete or continuous localized charge distribution. bility We will briefly highlight several results already know in the literature and then present our recent findings which show A general theory for nematic continua that accounts for a high dependence of the ANR phenomenon on b when electromechanical coupling is presented, based on a La- 0

Nicolas Triantafyllidis MS38 Ecole Polytechnique, Palaiseau, FRANCE Optical Topological Insulators and Spin-cloaking [email protected] Based on bi-anisotropic Metamaterials

Gianpiero Pampolini Science thrives on analogies, and a considerable number of Laboratoire de Mecanique des Solides inventions and discoveries have been made through mak- Ecole Polytechnique ing an unexpected connection to a very different field of [email protected] inquiry. Perhaps one of the best known examples is that of photonic crystals (PhCs) that have been referred to as semiconductors of light because of the far-reaching analo- MS38 gies between electron propagation in a crystal lattice (the Lagrangian Treatment of Systems Composed of domain of condensed matter physicists) and light propa- High-Loss and Lossless Components gation in a periodically modulated photonic environment (the domain of engineers and applied physicists). More re- We study here Lagrangian dissipative properties of com- cently, photonic crystals have been followed in their foot- posite systems with two components one of which is highly steps by their close cousins: electromagnetic metamate- lossy and the other is lossless. A principle result of our rials. Metamaterials dramatically expand the space of studies is that any general Lagrangian system, with losses possible electromagnetic responses enabling such exotic accounted by a Rayleigh dissipative function, its dissipa- phenomena as negative index propagation and invisibil- tive properties can be studied within the general framework ity cloaking of macroscopic objects. However, one as- introduced in our previous work Dissipative properties of pect of electron behavior, its spin, so far escaped emu- systems composed of high-loss and lossless components, J. lation by photonic systems. Emulation of the electron Math. Phys. 53, 123508 (2012). The phenomenon of over- spin and spin-orbit coupling which is known to give rise damping in such composite systems is studied and the eec- to one-way states will be reported in this talk. Using suit- tiveness of this framework demonstrated. ably designed electromagnetic media (metamaterials) we theoretically demonstrate a photonic analogue of a topo- Alexander Figotin logical insulator. We show that meta-crystalssuperlattices Department of Mathematics of metamaterials with judiciously designed propertiespro- University of California at Irvine vide a platform for designing topologically non-trivial pho- afi[email protected] tonic states, similar to those that have been identified for condensed-matter topological insulators. The interfaces Aaron Welters of the meta-crystals support helical edge states that ex- Massachusetts Institute of Technology hibit spin-polarized one-way propagation of photons, ro- [email protected] bust against disorder. Our results (Khanikaev et. al., Nature Materials 12, 233 (2013)) demonstrate the possibility of attaining one-way photon transport without ap- MS38 plication of external magnetic fields or breaking of time- On the Sensitivity of the Annomallous Localized reversal symmetry. Such spin-polarized one-way transport Ressonance Phenomenon to Small Variations in the enables exotic spin-cloaked photon sources that do not ob- 90 MS13 Abstracts

scure each other. MS39 A Sequence-dependent Rigid Base Model of DNA, Gennady Shvets and its Continuum Birod Limit The University of Texas at Austin [email protected] A recent rigid base model of DNA (http:lcvmwww.epfl.ch/cgDNA) will be described, and its continuum birod limit (a generalization of the Worm Like MS38 Chain model) will be computed. Then various predictions Causality of the Inverse of Causal Constitutive Pa- of the model pertaining to crystal structure data, persis- rameters for Natural Materials and Metamaterials tence length, and looping probabilities will be discussed. Given a causal function, χ(x) − χ(∞), that satisfies the John H. Maddocks Kramers-Kronig relations, we determine the sufficient con- EPFL ditions for the related inverse function john.maddocks@epfl.ch

1 ξ(x)= − 1 MS39 χ(x) − χ(∞)+1 Torsion of Fluctuating DNA to also be a causal function that satisfies the Kramers- We will present a heterogeneous fluctuating rod model for Kronig relations. For χ(∞) = 0, the function ξ(x) corre- studying the statistical mechanics of DNA. We will inter- sponds to the inverse of the traditional continuum relative pret DNA torsion experiments where base pair level varia- permittivity or permeability minus 1 and, in this case, a tion in mechanical properties is measured. The two key ap- similar result is obtained by N.N. Meiman (see sec. 123 of plications we consider are: (a) determine whether a newly Statistical Physics, 3rd Ed. by Landau and Lifshitz). discovered left-handed DNA conformation called L-DNA is a mixture of two known DNA states, and (b) what is Arthur D. Yaghjian the mechanical behavior of DNA when drugs and small Research Consultant molecules bind to it. Concord, MA 01742 USA [email protected] Prashant K. Purohit Mechanical Engineering and Applied Mechanics University of Pennsylvania MS39 [email protected] The Chemo-mechanics of Cytoskeletal Force Gen- eration MS40 In this talk we will present an extension of our recent work Elastic Concertina and Tearing of Sheets on focal adhesion dynamics [Olberding, JE, Thouless, MD, Arruda, EM and Garikipati, K. The non-equilibrium ther- We consider a thin elastic film, pushed laterally up to a modynamics and kinetics of focal adhesion dynamcs, PLoS distance d,atonepointofarimoflengthW .Weshow ONE, 5(8), e12043, 2010] to address sub-cellular contrac- experimentally and numerically that the ”constitutive relation” of this system is more complex than a power law tile force generation. The problem is a chemo-mechanical n one, which is at mechanical equilibrium. The chemistry, F ∼ (d/W ) , as previously assumed. When the ends of however, is far from equilibrium. The mathematical model, the rim are allowed to propagate via cracks, their evolu- computations and experimental comparisons will be shown. tion is determined by the way in which the film stores and releases elastic energy.

Krishna Garikipati Eugenio Hamm Mechanical Engineering Departamento de Fisica University of Michigan, Ann Arbor. Universidad de Santiago de Chile [email protected] [email protected]

MS39 MS40 Coarse-grained Molecular Dynamics Modeling of Disclination Induced Wrinkles in Free Standing the Disordered Domain of Nuclear Pores Smectic Membranes

The molecular transport between the cytoplasm and nu- The ability to create any curved surface merely by imprint- cleus in eukaryotic cells is solely controlled by the nuclear ing its metric onto a ﬂat sheet has great appeal for use pore complex (NPC). To gain insight into the transport in materials, manufacturing, and diagnostics applications. mechanism, the conformation of the disordered proteins The eﬀects of topological defects and anisotropic elasticity (FG-Nups) that cover the interior of the NPC is inves- in a free standing monolayer of cylinder-forming diblock tigated through super-coarse-grained molecular dynamics copolymers generate curved surfaces. Disclinations prove simulations. The results show that the FG-nups adopt a to be sources of Gaussian curvature, which when coupled unique conformation inside the pore which is encoded in with surface tension and elasticity, produce a long-ranged the sequence of the FG-nups and driven by hydrophobic pattern of wrinkles perpendicular to the underlying smectic and electrostatic interactions. layers. Ali Ghavami, Erik van der Giessen, Patrick Onck Elisabetta Matsumoto University of Groningen Princeton University [email protected], [email protected], [email protected] [email protected] MS13 Abstracts 91

Nicol´as Garc´ıa then reweighting to calculate averages. I will demonstrate Universidad Nacianal del Sur that the method outperforms others for selected problems [email protected] and show its use in simulating a living system.

Daniel A. Vega Aaron Dinner Universidad Nacional del Sur James Franck Institute [email protected] University of Chicago [email protected]

MS40 MS41 Geometry of a Crumpled Sheet A Micro / Macro Parareal Algorithm for a Class I will report on experiments in which we investigate the 3- of Multiscale-in-time Systems dimensional spatial structure of crushed elastic and plastic sheets. One of the objectives of the experiments is to un- We introduce and analyze a micro/macro parareal al- derstand the effect of the protocol and boundaries imposed gorithm for the time-parallel integration of a class of on the crumpling process. We follow the development of multiscale-in-time systems. The systems we consider in- stress-focused structures as well as the emergent organi- cludes some fast and some slow variables, the limiting dy- zation of structural elements, such as the condensation of namics of which (in the limit of infinite time scale separa- planar facets. I will discuss the evidence for an ordering tion) is known. The algorithm first computes a cheap but transition underlying the complex geometry of the object. inaccurate macroscopic solution using a coarse propagator (by only evolving the slow variables according to their limiting dynamics). This solution is iteratively corrected Narayanan Menon by using a fine-scale propagator (simulating the full micro- Physics Department scopic dynamics on both slow and fast variables), in the University of Massachusetts Amherst parareal algorithm spirit. The efficiency of the approach is [email protected] demonstrated on the basis of numerical analysis arguments and representative numerical experiments. Joint work with T. Lelievre and G. Samaey. MS40 Computational Crumpling via Discrete Devel- Frederic Legoll opable Surfaces LAMI, ENPC [email protected] When thin developable shells such as a sheet of paper or an aluminum can are crushed, they deform nearly isomet- rically, with stretching concentrated near ridges and cone MS41 points. We exploit this observation by discretizing the shell Transition Path Sampling as an isometric embedding of a discrete developable surface – an r- and h-adaptive meshing of the development of the We are investigating collections of atoms as their positions surface by discrete ridges and rulings. This reduced rep- evolve under Brownian (over-damped Langevin) dynamics. resentation of the surface does not require the very fine In the cases where the collection changes conformation, an elements needed to resolve the stiff stretching force, and energy barrier often exists. Such transitions are rare events does not suffer from membrane locking. We demonstrate when the thermal energy is small compared to the energy that our method produces the familiar Yoshimura diamond barrier. The understanding of such rare events is the goal patterns seen when axially compressing a thin cylindrical of our studies. I will display some results for transitions in shell. small atomic clusters.

Etienne Vouga Frank Pinski Columbia University Department of Physics [email protected] University of Cincinnati [email protected] Max Wardetzky U. Goettingen MS41 [email protected] Reaction Pathways of Metastable Markov Chains with Application to Lennard-Jones Clusters Reor- Eitan Grinspun ganization Computer Science Dept Columbia University Abstract not available at time of publication. [email protected] Eric Vanden Eijnden Courant Institute MS41 New York University Rare Event Simulations for Systems Far from Equi- [email protected] librium

This talk will introduce steered transition path sampling MS42 (STePS), which allows eﬃcient study of transient relax- Analyzing Upper Tails of Grain Size Distributions ation properties of microscopically irreversible dynamics. Using Extreme Value Theory The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, Polycrystalline materials generally display grain size distri- modifying the dynamics based on that probability, and butions thought to correspond to the log-normal distribu- 92 MS13 Abstracts

tion. While the grains size distribution near the mean is of- the local crystal state and which localizes and characterizes ten lognormal, significant tail departure from log-normality crystal defects. In particular, the local crystal orientation is observed for extreme values. Due to the importance of and elastic distortion are detected, as well as dislocations, large grains in applications such as fatigue, understand- and grain and twin boundaries. To this end an energy func- ing the distribution of extreme values beyond the assump- tional is devised whose minimization yields a tensor field tion of complete log-normality is necessary. We present a G describing the local crystal strain at each point. The method to fit the upper tail of grain size distributions based desired information about the local crystal state can then on extreme value theory. The method fits the grains sizes be read off from this tensor field; in particular, its curl pro- above a chosen threshold value to the generalized Pareto vides information about grain boundaries and dislocations. distribution (GPD). The fitted GPD allows for the proba- As is typical for variational image processing, the energy bility for particular extreme grain sizes to be calculated. functional is composed of a fidelity and a regularization term. It has a simple L2-L1 type structure so that its min- Sean Donegan imization can be performed via a split Bregman iteration. Carnegie Mellon University GPU parallelization results in short computing times. [email protected] Matt Elsey Anthony Rollett Courant Institute Carnegie Mellon University New York University Materials Science and Engineering [email protected] [email protected] Benedikt K. Wirth Courant Institute, New York University MS42 [email protected] Finding Order in Disorder: Shape Matching and Other Tricks MS43 Abstract not available at time of publication. Analysis of Liquid Crystal Phase Transitions in Bi- ological Networks Sharon C. Glotzer Chemical Engineering Cytoskeletal networks consist of rigid, rod-like actin pro- University of Michigan tein units jointed by ?exible crosslinks, presenting coupled [email protected] orientational and deformation effects analogous to liquid crystal elastomers. The alignment properties of the rigid rods influence the mechanical response of the network to MS42 applied stress and deformation, affecting functionality of Modeling Heterogeneous Materials via Lower- the systems. Parameters that characterize these networks order Spatial Correlation Functions Extracted from include the aspect ratio of the rods and the average length Limited Experimental Data of the crosslinks, with a large span of parameter values found across in-vivo networks. For instance, cytoskele- Heterogeneous materials abound in nature and synthetic tal networks of red blood cells have very large linkers and situations. Examples include porous media, composites small rod aspect ratio, whereas those of cells of the outer and alloys. It is well known that the effective properties hair of the ear have large aspect ratio and short linkers of heterogeneous materials depend on their complex mi- favoring well aligned nematic, in order to achieve optimal crostructures, which can be characterized via certain sta- sound propagation. We propose a class of free energy den- tistical descriptors (spatial correlation functions). Here, I sities consisting of the sum of polyconvex functions of the will present an efficient computational procedure that en- anisotropic deformation tensor and the Landau-de Gennes ables one to generate virtual 3D material microstructure energy of lyotropic liquid crystals. The growth conditions from a wide class of correlation functions, obtained either of the latter, with respect to the rod density and the ne- from 2D slices/surface images of the sample or from scat- matic order tensor at the limit of the minimum eigenvalue tering experiments. The accuracy of the reconstruction -1/3 are essential to recover the limiting deformation map is ascertained by quantitatively comparing it to the ac- from the minimizing sequences of the anisotropic deforma- tual microstructure obtained via x-ray tomography. Our tion gradient. We consider a bulk free energy density en- reconstruction procedure is employed to characterize an coding properties of the rod and the network based on the anisotropic multiphase Al-alloy, to model microstructure Lopatina-Selinger construction for the Maier-Saupe theory. evolution in a Pb-Sn alloy during annealing, and to study We then analyze the phase transition behavior under uni- microphase separation in a nano-porous material. These form expansion, biaxial extension and shear deformation, examples show that our procedure enables one to model showing that the nematic-isotropic transition may be ac- a wide class of heterogeneous materials via the associated companied by a change of volume, which manifests itself spatial correlation functions. in the nonconvexity of the stress-strain relation. We also Yang Jiao account for the fact that in-vivo networks are found in the Princeton University gel state. We conclude with some remarks on the roles of [email protected] active elements in the model. Maria-Carme Calderer MS42 Deparment of Mathematics University of Minnesota, USA Fast Automated Detection of Crystal Distortion [email protected] and Crystal Defects in Polycrystal Images

Given an image of an atomic crystal, we propose a vari- MS43 ational method which at each image location determines Liquid Crystals: Revisiting Kinetic Equations and MS13 Abstracts 93

Picking the Best Order Parameters In experiments, the arm length grows with universal power law L = t3/4, which we understand via a model for the I will review the general problem of deriving mean-field and transport of an inviscid fluid into the fracture tip of an kinetic equations from microscopic dynamics in the context incompressible Neo-Hookean material. of nematic liquid crystals. Analytical results will then be compared to numerical studies of the defect core structure. Joshua Bostwick Department of Mathematics, North Carolina State Ibrahim Fatkullin University University of Arizona [email protected] Department of Mathematics [email protected] Mark Shillaci, Karen Daniels North Carolina State University MS43 [email protected], [email protected] Chevron-Like Defects in Smectic Liquid Crystals MS44 We investigate the structure of a smectic C liquid crystal body trapped between two parallel plates. This is modeled Thin Film Models of Liquid Displacement on using the Chen-Lubensky energy that couples a second or- Chemically Patterned Surfaces for Lithographic der energy that accounts for smectic layer formation and Printing Processes the first order nematic Frank energy. In the smectic C We examine in this work a model problem relevant to the phase the smectic layers meet the plates at an acute an- liquid displacement that occurs in lithographic printing gle. In order for this to happen the layers’ profiles should processes. The model problem consists of two stratified form a zig-zag or chevron pattern. We prove that these thin liquid films confined between parallel plates, one of patterns occur in minimizers for this model, for the case which is chemically heterogeneous. The results provide that the layer bending constant is small. This is carried physical insights into and numerical estimates of the small- out by using gamma convergence. est and largest feature sizes that can be printed, as well as Daniel Phillips the minimum spacing between feature sizes that can be Department of Mathematics, Purdue University tolerated. [email protected] Satish Kumar Chemical Engineering and Materials Science Lei Cheng University of Minnesota Indiana University Kokomo [email protected] [email protected]

MS44 MS43 Boundary Conditions for the Moving Contact Line Efficient Energy Stable Numerical Schemes and Problem and the Spreading of Thin Films Simulations of Two Phase Complex Fluids on Phase Field Method In this talk, I will discuss a contact line model derived based on principles of non-equilibrium thermodynamics Our goal here is to expand the hydrodynamic toolkit to and molecular dynamics simulations. Macroscopic ther- two-phase fluids consisting of an immiscible homogeneous modynamic is used to place constraints on the form of the LCP phase (initialized as droplets) immersed in a vis- boundary conditions; the detailed constitutive relations are cous or polymeric phase. To do so, we first put the two- then computed from molecular dynamics. The contact line phase kinetic model through the same preliminary bench- model consists of the Navier-Stokes equation, a boundary marks that were applied to the Doi-Hess theory for LCPs. condition for the slip velocity, and a relation between the We project onto the scalar zeroth moment and tensorial dynamic contact angle and the contact line velocity. A thin second-moment of the rod number density function to film model is formulated based on lubrication approxima- achieve a generalized Landau-deGennes model for equilib- tion, and different spreading regimes are identified. ria and imposed shear of LCP droplets in a viscous fluid. A numerical algorithm in two space dimensions is developed Weiqing Ren to study global droplet defect structure versus interfacial National University of Singapore and IHPC, A-Star anchoring energy. The simulations reveal topological de- [email protected] fects (surface boojums for tangential anchoring and interior degree 1/2 or radial defects for normal anchoring), as well as new predictions about the structure of the various MS44 defect cores in equilibrium and in simple shear. Electrostatically Induced Singular Dynamics in Long-Wave Annular Film Flows Xiaofeng Yang University of South Carolina We investigate the evolution and stability of a viscous, [email protected] leaky dielectric fluid layer wetting the surface of a cylindrical electrode, surrounded by a leaky dielectric gas and a concentric electrode. Electrostatic forces are induced at MS44 the interface in competition with surface tension and vis- Capillary Fracture of Soft Gels cous stresses. Asymptotic methods are used to derive a one dimensional long-wave system of evolution equations that A droplet of surfactant spreading on a gel substrate can exhibit a wide variety of dynamics including the formation fracture the gel surface and create a starburst pattern of fracture arms. We develop an elastic model to predict the number of fractures, consistent with experimental results. 94 MS13 Abstracts

of ﬁnite time touchdown singularities. with U. Salman.

Alexander Wray Lev Truskinovsky Department of of Mathematics Imperial College, London Laboratoire de Mechanique des Solides [email protected] Ecole Polytechnique [email protected] MS45 On the Nonlinear Dynamics of Granular Lattices MS46 Effective Behavior of Interfaces in a Random Elas- We investigate on the highly nonlinear propagation of soli- tic Medium tary waves in one and two dimensional granular lattices, with particular focus on the control of stress propagation We consider a model for the propagation of an interface in for the development of shock protecting devices. The anal- a random elastic medium. From a physical point of view, ysis included discrete particle approaches and the corre- we answer the question whether a microscopically viscous sponding continuum limits. The study discloses composite (force=velocity) dynamics transitions into a macroscopi- granular structures that enable forced energy confinement cally rate independent hysteresis through the interaction and transverse pulse-trapping within the granular mat- with the obstacles. mathematically, the problem consists ter. The granular medium converts transverse impacts into of finding a stationary supersolution to a fractional diffu- shifted superficial pulses with weak amplitude, thus acting sion equation which is coupled nonlinearly to a random as a pulse-trapping device and energy container. field. Fernando Fraternali Patrick Dondl Department of Civil Engineering Durham University University of Salerno Department of Mathematical Sciences [email protected] [email protected]

MS45 MS46 The p-Schrdinger Equation and Granular Crystals From Polymer Physics to Rubber Elasticity: a Stochastic Homogenization Approach We consider a Hamiltonian lattice consisting of a chain of particles in a local potential, coupled by fully-nonlinear Rubber materials are prototypical examples of hyperelastic nearest-neighbors interactions of order α>1. This system materials, best described at the continuum by the integral describes in particular a Newton’s cradle, i.e. a chain of of a frame-invariant and isotropic energy density of the beads attached to pendula and coupled by Hertzian con- strain gradient. On a microscopic scale, rubber materials tact. We show that the evolution of small initial data is are constituted by a network of interacting polymer-chains, governed by the discrete p-Schrödinger equation (involving best described by their Boltzmann free energy. The aim of a p-Laplacian with p = α + 1), which yields the existence this talk is to give the first steps towards a rigorous deriva- of breathers. tion of rubber elasticity from polymer-chain physics using a qualitative and quantitative discrete homogenization the- Brigitte Bidégaray-Fesquet ory of random graphs. I shall focus both on the theoretical Laboratoire Jean Kuntzmann, Université de Grenoble and computational aspects. high-level commands. and CNRS [email protected] Antoine Gloria Université Libre de Bruxelles Eric Dumas Département de mathématique Institut Fourier, Université Grenoble 1 and CNRS [email protected] [email protected] MS46 Guillaume James Laboratoire Jean Kuntzmann, Université de Grenoble Macro and Micro-Based Solutions for Random and CNRS Heterogeneous Microstructures [email protected] At small scale, material properties fluctuate randomly in space and are usually described by random functions. At MS45 the scale of the representative volume element, material properties are deterministic and independent of boundary Inertia-Induced Criticality in Martensites conditions under some assumptions. Quantities of interest, Intermittency and power law statistics of avalanches have Umicro(x)andUmacro(x), based on material properties at been recorded in several martensitic materials subjected to micro- and macro-scales are random fields and determin- cyclic loading. It implies long spatial and temporal corre- istic functions, respectively. We view Umacro(x)asanap- lations whose origin is still unclear. It has been proposed proximation for Umicro(x) and examine the quality of this previously that behind such self organization towards crit- approximation. icality is a limited dislocational activity. In this talk we Mircea Grigoriu discuss an alternative explanation based on an idea that Cornell University inertia may play an important role in marginally stable [email protected] systems. We consider a prototypical quasi-statically driven lattice system with double well energy and show that the power law correlations with realistic exponents can appear MS46 in this model if it is moderately under-damped. Joint work On a Class of weakly Stochastic Problems MS13 Abstracts 95

Amenable to Rapid Computational Approaches in second theorem, we find an explicit formula for the limit Stochastic Homogenization as the thickness of the scatterer vanishes for the operator associated to this surface integral. In our third and fourth We define and describe a class of problems in stochastic theorems, we demonstrate that under some uniform regu- homogenization that, in a sense made precise, are only larity assumptions, the normal trace of the electric field on “weakly” stochastic. Dedicated approaches can then be the object boundary goes to zero as the thickness of the applied, that significantly reduce the computational work- object goes to zero simultaneously as the contrast goes to load. We also mention how the approach can be useful infinity. This is joint work with David Ambrose. to reduce variance in actually fully (that is, non “weakly) stochastic problems. All the equations and examples are Shari Moskow issued from materials science. Drexel University Department of Mathematics Claude Le Bris [email protected] Ecole Nationale des Ponts et Chaussees [email protected] David Ambrose Drexel University MS47 [email protected] Model Reduction and Recovery of Structural In- formation in Heterogeneous Materials MS47 The talk discusses reconstruction of the spectral measure in The Underlying Analytical Links Between Various the Stieltjes integral representation of the effective proper- Effective Coefficients of a Poroelastic Medium: a ties of composite materials using Pade approximation. We Dehomogenization Approach consider a case of matrix valued measure corresponding Poroelastic materials are finely-structured composites of to anisotropic composites. Matrix Pade approximants are pore fluid and elastic solid, which are encountered very of- derived using matrix polynomials orthogonal with respect ten in geophysics and biophysics. This talk is based on our to the spectral function. We discuss applications to in- preliminary results on how to use the analytic properties verse homogenization theory and to numerical simulation of effective properties of poroelastic composites to quantify of propagation of waves in composites. the effect of microstructure on the dynamics of wave prop- Elena Cherkaev agation in poroelastic materials described by the Biot-JKD University of Utah model. Department of Mathematics Miao-Jung Yvonn Ou [email protected] University of Delaware [email protected] MS47 Approximation of DtN Map in a High Contrast MS48 Conductivity Problem A General Constitutive Framework for Model- A model of a composite material consisting of a matrix of ing Elasto-Visco-Plastic Behavior, Yielding and finite conductivity with ideally conducting almost touching Thixotropy in Waxy Crude-Oils, Microgels and particles is considered, and a discrete network approxima- Other Soft Solid Materials tion for the Dirichlet-to-Neumann map is constructed and Abstract not available at time of publication. justified. Gareth H. McKinley Yuliya Gorb Dept of Mechanical Engineering Department of Mathematics Massachusetts Institute of Technology University of Houston [email protected] [email protected]

Liliana Borcea, Yingpei Wang MS48 Rice University Mathematical Modeling of the Mucus Barrier in [email protected], [email protected] Human Lungs

The first line of defense of human lungs against inhaled MS47 pathogens is mucus. Foreign particles are cleared if flow of Scattering and Resonances of Electromagnetic the mucus layer toward the larynx dominates particle dif- Waves by Thin High Contrast Dielectric Structures fusion through the layer. Yet the flow and diffusive transport properties of mucus is poorly understood. Here we We study the scattered electric field from a thin, high- focus on progress understanding nonlinear phenomena in contrast dielectric volume. The space occupied by the the oscillatory flow of viscoelastic fluids, and explaining scatterer is the Cartesian product of a bounded two- why dynamic and spatial microstructural characterization dimensional region with a finite interval; that is, the scat- is essential in the understanding of mucus transport. terer is cylindrical, and of finite volume. The electric field is a solution of the time-harmonic Maxwell equations. We Paula A. Vasquez will discuss four theorems. In the first, we establish an in- Department of Mathematics tegral representation for the electric field which accounts University of North Carolina at Chapel Hill for the jumps in the index of refraction which occur at the [email protected] object boundary. This integral representation includes a surface integral over the boundary of the object. In our 96 MS13 Abstracts

Greg Forest MS49 Department of Mathematics The Wrinkle Patterns Caused by a Drop on a Sheet University of North Carolina, Chapel Hill [email protected] Recent interest in the behavior of thin sheets far beyond the buckling threshold was inspired by experiments wherein a David Hill liquid drop was placed on a thin elastic sheet. Compres- University of North Carolina at Chapel Hill sive forces due to surface tension effects created a wrinkle Cystic Fibrosis Center pattern near the contact line. We provide the first com- [email protected] pletely ”far-from-threshold” analysis of this configuration, and predict the measured extent of the wrinkles. We also Yuan Jin show that the liquid-solid contact angle is different from University of North Carolina at Chapel Hill the Young-Lapace angle. [email protected] Robert Schroll Departamento de Fisica MS48 Universidad de Santiago de Chile [email protected] Modeling and Simulation of Complex Biological Fluids Biofilms MS49 Biofilms are complex biological organisms ubiquitous almost everywhere in our daily life. Modeling and un- Plate and Shell Models in Elasticity Obtained derstanding the intricate biological, fluid mechanical, by Simultaneous Momogenization and Dimensional chemical-mechanical transduction of chemical signal and Reduction mechanical forces is a daunting task across multiple disci- We will give an overview of the models of plates and shells plines. In this presentation, we will present a systematic obtained by simultaneous homogenization and dimensional approach tooted in kinetic theory for complex fluids and reduction from 3D nonlinear elasticity, by means of Gamma expanded to include various biological and chemical mech- convergence. We will give the special emphasis on the ho- anistic models to investigate how the biofilm flows in vari- mogenized bending plate model. This is collaboration with ous geometry and boundary conditions. Hopefully, this will P. Hornung and S. Neukamm. shed light on how to treat biofilm infections in medical settings or take advantage of the biofilm’s barrier properties Igor Velcic in their beneficial applications. Models and 3-D numerical Max Planck Institute for Mathematics in the Sciences simulations will be discussed in a few selected applications. [email protected] Qi Wang,JiaZhao University of South Carolina MS49 [email protected], [email protected] Poking and Wrinkling of Thin Sheets and Shells

Poking an object is a useful way of testing its properties MS49 in a range of everyday applications from cooking meat to Wrinkles on Curved Surfaces for Aerodynamic inflating a bicycle tyre. It is also used quantitatively in sci- Drag Control ence to achieve the same thing. In this talk I will discuss what we can learn from poking pressurized elastic shells We present the results of an experimental investigation on and floating elastic sheets. Of particular interest is the the wrinkling of positively curved surfaces and explore their wrinkling pattern that forms in these scenarios. I will dis- use towards drag reduction applications. In our precision cuss these patterns from both the ’Near Threshold’ and model experiments we make use of rapid prototyping tech- ’Far From Threshold’ points of view. niques to cast samples with custom geometry and material properties out of silicone-based rubbers. Our structures Dominic Vella consist of a thin stiff shell that is chemically bonded to a Mathematical Institute thicker soft substrate. The substrate contains a spherical University of Oxford cavity that can be depressurized, under controlled volume [email protected] conditions, to compress the ensemble structure. Under this compressive loading, the initially smooth outer-shell develops complex wrinkling patterns. We systematically charac- MS50 terize and quantify the morphology of the various patterns A Boundary Integral Method for Computing the and study the phase diagram of the system. We consider Dynamics of An Epitaxial Island both geometric and material quantities in the parameter space. Moreover, since the wrinkling patterns can be actu- At the early stages of epitaxial growth, adatoms on the sub- ated dynamically using a pressure signal, we systematically strate often form small isolated islands. The morphological characterize the aerodynamic behavior of our structures in evolution (e.g. growth or shrink) of these islands is deter- the context of fluid drag reduction. An added advantage mined by many physical processes such as atom adsorp- of our novel mechanism is that it allows for both dynamic tion and desorption, adatom diffusion, adatom attachment switching and tuning of the surface morphology, thereby to island boundaries or detachment from the boundaries. opening paths for drag control. Mathematical formulation of the problem leads to a moving boundary/interface problem. In this talk, we present a Pedro M. Reis boundary integral method for computing the quasisteady Massachusetts Institute of Technology evolution of an epitaxial island. The problem consists of an [email protected] adatom diffusion equation (with desorption) on terrace and a kinetic boundary condition at the step (island boundary). The normal velocity for step motion is determined by a MS13 Abstracts 97

two-sided flux. Numerical tests on a growing/shrinking is- the shape changing phenomena observed in real experi- land are in excellent agreement with the analytical solution ments and other features of LCEs. However, due to the and demonstrate that the method is stable, efficient and complexity of governing equations, the simulation is very spectrally accurate in space.?Nonlinear simulations for the time-consuming. In this talk, we introduce a novel precon- growth of perturbed circular islands show that sharp tips ditioner for solving the velocity equation using Chebyshev and facet-like edge will form during growth instead of the spectral collocation method and present new simulations usual tip-splitting events for isotropic Laplacian growth. to show its efficiency. The numerical techniques presented here can be applied generally to a class of free/moving boundary problems in Wei Zhu physical and biological science. Mathematics, University of Alabama [email protected] Shuwang Li Department of Applied Mathematics Illinois Institute of Technology MS51 [email protected] Phase Field Crystal Models with Fast Dynamics

Abstract not available at time of publication. MS50 Multiscale Modeling and Computation of Nano Peter Galenko Optical Responses University of Jena Germany We introduce a new framework for the multiphysical [email protected] modeling and multiscale computation of nano-optical responses. The semi-classical theory treats the evolution of the electromagnetic ﬁeld and the motion of the charged MS51 particles self-consistently by coupling Maxwell equations Nonlocal Phase Field Models with Quantum Mechanics. To overcome the numerical challenge of solving high dimensional many body Schr Abstract not available at time of publication. odinger equations involved, we adopt the Time Dependent Maurizio Grasselli Current Density Functional Theory (TD-CDFT). In the Politechnico di Milano regime of linear responses, this leads to a linear system of [email protected] equations determining the electromagnetic eld as well as the current and electron densities simultaneously. A self- consistent multiscale method is proposed to deal with the MS51 well separated space scales. Numerical examples arepre- Some Equations with a Logarithmic Nonlinear sented to illustrate the resonant condition. Term

Di Liu Abstract not available at time of publication. Michigan State University Department of Mathematics Alain Miranville [email protected] University of Poitiers, France [email protected] MS50 Dislocation Dynamics in Thin Films Using Fast MS51 Multipole Accelerated Boundary Integral Equation Phase Field Models of Vacancy Mediated Deforma- Method tion

We develop an efficient numericalmethod based on the Abstract not available at time of publication. boundary integral equation formulation and new version of fast multipole method to solve the boundary value problem James Warren for the stress field associated with dislocations in a finite NIST medium. Numerical examples are presented to examine the Metallurgy Division influence from material boundaries on dislocations. Appli- [email protected] cations to dislocation dynamics in thin films will also be presented. MS52 Yang Xiang Magnetic Ratchet for 3-dimensional Memory and Hong Kong University of Science and Technology Logic [email protected] One of the major challenges for future electronic memory and logic devices is finding viable ways of moving from to- MS50 days 2-dimensional structures which hold data in an XY Simulation on Liquid Crystal Elastomers Using mesh of cells to 3-dimensional structures in which data are Spectral Methods with a New Preconditioner stored in an XYZ lattice of cells. This could allow a many- fold increase in performance. A suggested solution is the Liquid crystal elastomers (LCEs) are soft complex materi- shift register - a digital building block that passes data als of enormous technological importance because of their from cell to cell along a chain. In digital microelectron- remarkable responsiveness to excitations. In our previous ics, 2-dimensional shift registers are routinely constructed work, we proposed a non-local continuum model to study from a number of connected transistors. However, for 3- the dynamical behaviors of LCEs. The preliminary simula- D devices the added process complexity and space needed tion demonstrated that the model can successfully capture 98 MS13 Abstracts

for such transistors would largely cancel out the benefits of lize the steady state. moving into the third dimension. Physical shift registers, in which a low-level physical phenomenon is used to move Stavros Komineas data near-atomic distances, without requiring conventional University of Crete transistors, are therefore much preferred. We have discov- [email protected] ered a way of implementing a 3-dimensional spintronic unidirectional vertical shift register between sub-nanometer thickness perpendicularly magnetized CoFeB layers simi- MS52 lar to those used in MRAM. By carefully controlling the Analysis of Complex Domain Patterns in Bulk Fer- thickness of each magnetic layer and the RKKY exchange romagnets coupling between layers we form a ratchet which allows information in the form of a sharp magnetic kink soliton The rich world of magnetic domains, extending from vis- to be pumped unidirectionally from one magnetic layer to ible dimensions down to the nano-scale, forms the meso- another. In this talk I show experimental results from a scopic link between the fundamental physical properties of 44-layer sample in which digital bits are injected into the a magnetic material and its macroscopic properties typi- bottom layer and then progressively shifted from layer to cally measured in a hysteresis loop. Most challenging is layer before emerging from the top. This simple and ef- the analysis of hidden (internal) domains in bulk material, ficient shift-register demonstrates a route for spintronics which requires surface imaging in combination with domain to be used to create 3-dimensional microchips for memory modeling. In this presentation a review of (experimental) and logic applications. bulk domain analysis is given, based on surface domain observation by Kerr microscopy, metallographic domain anal- Russell P. Cowburn ysis and neutron imaging. Cavendish Laboratory University of Cambridge Rudolf Schäfer [email protected] Leibniz Institute for Solid State and Materials Research Dresden [email protected] MS52 The Spin-Cherenkov Effect MS53 We report on the Cherenkov-type excitation of spin waves Variational Analysis of Some Atomistic Systems in soft-magnet magnetic thin film elements. Our simula- Exhibiting Spatially-modulated Phases tions show that a point-like magnetic field source moving with sufficiently high velocity above the film surface gener- I will present some results concerning the continuum ates a spin wave ”boom”, propagating along a Mach-type Gamma-limit of a family of atomistic systems exhibiting conical wave front. This Spin Cherenkov Effect enables spatially-modulated phases the excitation of well-defined spin waves with velocity- Marco Cicalese dependent frequency by means of a linearly moving pertur- Technical University Munich bation, thereby providing a simple route towards tunable Germany spin-wave generation. [email protected] Riccardo Hertel Institute of Solid State Research IFF-9 Andrea Braides Forschungszentrum Jülich GmbH University of Rome II [email protected] [email protected]

Ming Yan MS53 Department of Physics Shanghai University Microstructures in Nematic Elastomers [email protected] Abstract not available at time of publication.

Attila Kakay Antonio DeSimone Institute of Solid State Research IFF-9 SISSA, Trieste, Italy Forschungszentrum J¨ulich GmbH 34014 Trieste, ITALY [email protected] [email protected]

MS52 MS53 Rotating Vortex-Antivortex Pairs in Ferromagnets Continuum Limit of Microscopic Models of Solids under Spin-Polarized Current Abstract not available at time of publication. A rotating vortex-antivortex dipole may be generated due to spin-polarized current ﬂowing through a magnetic ele- Jianfeng Lu ment. We study its dynamics within the Landau-Lifshitz- Mathematics Department Gilbert-Slonczewski equation. The rotation is due to two Duke University forces: the interaction between the two vortices and an [email protected] external in-plane magnetic ﬁeld. The nonzero skyrmion number of the dipole is responsible for both forces giving rise to rotational dynamics. The spin-torque acts to stabi- MS13 Abstracts 99

MS53 Role of Misfit and Volume Lattice Equivalent Models Abstract not available at time of publication. We investigate the macrocospic behavior of hexagonal lattices. We obtain a non explicit formula for the equivalent Barbara Zwicknagl energy density. Numerical computation tends to prove that University of Bonn this homogenized formula cannot be replaced by a simpler [email protected] expression. Additionnaly, numerical simulations show that in most cases Cauchy-Born rule fails to give the proper MS55 behavior. A Multiscale Atomistic-to-Continuum Method for Annie Raoult Atomic Monolayers Undergoing Bending MAP5, Université Paris Descartes [email protected] The framework of Objective Structures introduced by Richard James provides a method to systematically examine the behavior of various geometrically complex nanos- HervéLeDret tructures. These nanostructures include rod-like objects as Laboratoire Jacques-Louis Lions well as flat sheets. In this talk, we describe an extension of Université Pierre et Marie Curie this framework to sheets that undergo bending in complex herve.le [email protected] ways. We then apply the extended framework to develop a computational atomic multiscale method to understand MS54 the atomic structure of defects in these systems. Equilibrium vs. Kinetic Steady States in Epitaxial Kaushik Dayal Growth Civil and Environmental Engineering Carnegie Mellon University Abstract not available at time of publication. [email protected] Russel Caflisch Department of Mathematics Amin Aghaei University of California, Los Angeles Carnegie Mellon University cafl[email protected] [email protected]

MS54 MS55 Phase Field Modeling of Epitaxial Graphene Estimates for Two-phase Nonlinear Conductors via Growth Iterated Homogenization Abstract not available at time of publication. Estimates for the overall response of two-phase nonlinear conductors are derived via an iterated homogenization ap- Vivek Shenoy proach. The approach consists in the construction of se- University of Pennsylvania quentially laminated microgeometries for which the over- [email protected] all response can be determined exactly. The estimate depends on the one- and two-point microstructural correlations through the volume fractions of each constituent MS54 phase and the H-measures of the microstructure. Sample Lattice and Off-lattice KMC Models for Strained results for power-law random conductors are provided and Epitaxial Growth compared with earlier predictions. We conclude with a discussion on the possible extremal character of sequential We present weakly off-lattice and off-lattice kinetic Monte laminates in the nonlinear context. Carlo formulations for strained epitaxial growth. We have implemented the weakly off-lattice method in 2+1 dimen- Martin I. Idiart sions and it is capable of realizing many experimentally Universidad Nacional de La Plata observed features. The off-lattice method has been im- [email protected] plemented in 1+1 dimensions with a Lenard-Jones potential. This method is able to simulate Stranski-Krastanov Pedro Ponte Castaneda growth, and capture the formation of edge dislocations, University of Pennsylvania interstitials, and vacancies. [email protected] Peter Smereka, Henry A. Boateng Department of Mathematics MS55 University of Michigan Sharp Inequalities which Generalize the Diver- [email protected], [email protected] gence Theorem

Tim Schulze Subject to suitable boundary conditions being imposed, University of Tennessee sharp inequalities are obtained on integrals over a region Department of Mathematics Ω of certain special quadratic functions f(E)whereE(x) [email protected] derives from a potential U(x). This has application to bounding the response of bodies containing an inclusion, and inversely to estimating the volume of the inclusion. MS54 With E = ∇U it is known that such sharp inequalities can Analytical Study of Morphology of Strained Films: be obtained when f(E) is a quasiconvex function and when 100 MS13 Abstracts

U satisfies affine boundary conditions (i.e., for some matrix plex Patterns D, U = Dx on ∂Ω). Here we allow for other boundary conditions and for fields E that involve derivatives of a Experimental findings suggest that the compatibility of the variety orders of U. We also treat integrals over Ω of special highly symmetric austenite phase and the martensitic vari- quadratic functions g(J)whereJ(x) satisfies a differential ants is an important parameter controlling the width of the constraint involving derivatives with, possibly, a variety of thermal hysteresis in certain martensitic transformations. orders. The results generalize an example of Kang and the This observation forms the basis of a theory of hysteresis author in three spatial dimensions where J(x)isa3× 3 that assigns an important role to the energy of the transi- matrix valued field satisfying ∇·J =0.Wealsopresentan tion layer (Zhang, James, Mueller, Acta mat. 57(15):4332- algorithm for generating extremal quasiconvex quadratic 4352, 2009). Following this ansatz, we study analytically functions. the energy barriers leading to hysteresis and analyze the onset of complex microstructures in the transition layers Graeme W. Milton for low-hysteresis alloys. University of Utah Department of Mathematics Barbara Zwicknagl [email protected] University of Bonn [email protected]

MS55 Homogenization of Generalized Micro-Resonances MS57 and Coupled Properties Hybrid Continuum-Particle Thermostats based on Fluctuating Hydrodynamics : Dynamic Implicit- Abstract not available at time of publication. Solvent Coarse-Grained Simulations of Planar Lipid Bilayers and Vesicles Valery Smyshlyaev University College London Many coarse-grained models have been developed for ef- [email protected] ficient equilibrium studies of lipid bilayer membranes by treating implicitly interactions mediated by the solvent. However, for problems involving dynamics, such CG stud- MS56 ies require accounting for the momentum transfer through Energy Barriers for Interior Nucleation of Marten- the missing solvent degrees of freedom. We introduce site new thermostats for such CG models and computational methods based on fluctuating hydrodynamics. We show The phase transformation between martensite and austen- our momentum conserving approach yields results signifi- ite is typically accompanied by the creation and growth of cantly different than conventional Langevin dynamics. We small inclusions of the new phase. We consider geomet- then present a number of simulation results both for self- rically linear elasticity with sharp interface penalization assembled planar-bilayer sheets and vesicles. of phase boundaries. Following earlier work, we present matching upper and lower bounds for the elastic energy of Paul J. Atzberger these inclusions in terms of the volume. The methods are University of California-Santa Barbara based both on real and Fourier space representation of the [email protected] energy. Hans Knuepfer MS57 University of Bonn Regularization Method for the Numerical Solution [email protected] of Periodic Stokes Flow With Application to Cil- iary Beating MS56 In this talk, I will introduce a regularization method that Hysteresis in gives a smooth formulation for the fundamental solution Thermodynamically-Consistent Mesoscopic Model to Stokes flow driven by an infinite, triply-periodic array of the Ferro/paramagnetic Transition of point forces. With this formulation, the velocity at any spatial location may be calculated, including at and A continuum model for micromagnetics is presented that, very near the point forces; these locations typically lead beside the standard magnetic balance laws, includes to numerical difficulties due to the singularity within the thermo-magnetic coupling. Inspired by relaxation method Stokeslet when using other methods. For computational of static minimization problems, our model is mesoscopic efficiency, the current method is built upon previous meth- in the sense that possible fine spatial oscillations of the ods in which the periodic Stokeslet is split into two rapidly magnetization are modeled by means of Young measures. decaying sums, one in physical space and one in recipro- Existence of weak solutions is proved by backward Euler cal, or Fourier, space. I will show a few validation stud- time discretization. It is a joint work with B. Benesova and ies and then discuss a recent extension of the method to T. Roubicek. doubly-periodic flow. Finally, using the extended method, simulations of doubly-periodic arrays of beating cilia will Martin Kruzik be presented. Academy of Sciences Czech Technical University Prague Karin Leiderman [email protected] Applied Mathematics UC Merced [email protected] MS56 Mathematical Analysis of Microstructures in Low- Hysteresis Shape Memory Alloys: Onset of Com- MS13 Abstracts 101

MS57 can describe dislocations even in amorphous materials. We Modeling Neutralization Kinetics of HIV by provide explicit expression for edge dislocation, which is a Broadly Neutralizing Monoclonal Antibodies dipole of curvature. The model is supported with experimental results. Eliciting broadly neutralizing antibodies (bnAb) in cervi- covaginal mucus (CVM) is potentially a critical aspect of Michael Moshe an HIV vaccine that blocks initial vaginal HIV infections. Racah Institute of Physics To neutralize HIV in the vaginal lumen, bnAb must ac- The Hebrew University cumulate on virions at sufficient stoichiometry to inhibit [email protected] viral entry before virions penetrate CVM and infect target cells in the submucosa. Nevertheless, the relative rates of these competing processes remain poorly understood. In MS58 this talk I will highlight our existing work to model these Monge-Ampère Constraints in Thin Film Elastic dynamics with an eye toward some of the unsolved prob- Models lems that would benefit from an improved description of the basic particle-fluid coupling. We will review a few results and some open problems regarding the variational model of thin films consisting in |∇2 |2 Scott McKinley minimizing the bending energy Ω u of an out-of-plane University of Florida displacement u :Ω→ R under the Monge-Ampère con- 2 scott.mckinley@ufl.edu straint det ∇ u = f,wheref is a prescribed curvature function and Ω ⊂ R2 represents a thin plate. Alex Chen Marta Lewicka SAMSI/University of North Carolina at Chapel Hill Department of Mathematics [email protected] University of Pittsburgh [email protected] Feng B. Shi, Simi Wang University of North Carolina at Chapel Hill L Mahadevan [email protected], [email protected] Harvard University [email protected] Peter J. Mucha University of North Carolina Reza Pakzad [email protected] University of Pittsburgh [email protected] GregForest,SamuelLai University of North Carolina at Chapel Hill [email protected], [email protected] MS58 Growth-Induced Folding, Conformal Maps, and Optimal Design MS57 A Computational Model of Microtubule-Based Mo- I will discuss the growth-induced buckling of sheets with tion in the Single-Celled C. Elegans Embryo zero Gaussian curvature except at discrete points. This simplified problem already shows the hallmarks of more We present a model of microtubule-based pronuclear mo- complicated swelling patterns, yet appears to be tractable. tion in the Caenorhabditis elegans embryo. Microtubules This sheds some light on the problem of finding ”optimal” stochastically grow/shrink, encountering motor proteins swelling patterns for complex shapes that can be imple- in the viscous cytoplasm that attach and exert pulling mented experimentally. forces. Our computational method is based on an immersed boundary formulation that allows for the simul- Chris Santangelo taneous treatment of fluid flow and the dynamics of struc- Physics Department tures immersed within. Our simulations demonstrate nu- University of Massachusetts Amherst clear centration and rotation, while generating minus-end [email protected] directed flows along MTs similar to those observed in vivo.

MS58 Tamar Shinar Emergence of Spontaneous Twist and Curvature Computer Sciences in Non-Euclidean Rods: Application to Erodium UC Riverside Plant Cells [email protected] We present a limiting model for thin non-Euclidean elastic rods. Originating from the three-dimensional (3D) refer- MS58 ence metric of the rod, which is determined by its inter- Metric Description of Discontinuities in Amor- nal material structure, we derive a 1D reduced rod theory. phous Elastic Materials Specifically, we show how spontaneous twist and curvature of a rod are emerged from the reference metric derivatives. We suggest a description for dislocations using a torsion- Thus, the model allows calculating the unconstrained equi- free Riemannian manifold equipped with a reference met- librium configuration of a thin rod directly from its internal ric. This metric expresses the local equilibrium geome- structure. The model is applied to the study of stork’s bill try within the material. In this description, dislocations and cranesbill cells and their configurational response to are singularities in the intrinsic curvature structure. The dehydration. We show how the geometrical arrangement model is not based on a crystalline structure; therefore it of cellulose fibrils on the cell walls determines the helical 102 MS13 Abstracts

shapes of isolated cells. Our Covariant Universality Theory (CUT ) naturally sub- sumes the classical Dynamic Scaling Hypothesis. To exhibit Eran Sharon CUT ’s utility, a certain non-equilibrium, nano-faceting Racah Institute of Physics crystal growth model is considered. Combining the dis- The Hebrew University covery of exact thermo-kinetic translating solitons, which [email protected] violate the Wulff construction, with a novel, generally ap- plicable, asymptotic geometric methodology, we identify Hillel Aharoni an emergent Super-symmetric Lorentzian-Parabolic sym- The Racah Institute of Physics metry group G. The resulting G-covariant universal, 1- The Hebrew University of Jerusalem point length statistics are then completely characterized up [email protected] to a unique supra-universal, empirically determined distribution. MS59 Stephen J. Watson Nonequilibrium Processes for Current Reservoirs University of Glasgow [email protected] Stationary non equilibrium states are characterized by the presence of steady currents flowing through the system. Currents are produced by external forces and we are inter- MS60 ested in forces acting on the boundary trying to establish a Exponential Convergence to Equilibrium for Sub- given current. We model this process considering the sim- critical Solutions of the Becker-Dring Equations ple exclusion process in one space dimension with appropriate boundary mechanisms which create particles on the The Becker-Dring equations are a well-known model for one side (right) and kill particles on the other (left). The nucleation and growth. We show that solutions with mass system is then ”unbalanced” and in the stationary mea- under the critical one converge exponentially to equilib- sure there is a non-zero steady current of particles flow- rium. Our main tool is a study of the linearization of ing from right to left. The system is designed to model the equation close to equilibrium, for which we are able Fick’s law which relates the current to the density gra- to show a spectral gap. We use several techniques that dient. In statistical mechanics non-equilibrium is not as have been developed in the context of kinetic equations, well understood as equilibrium, hence the interest from a and find strong parallels with the study of the homoge- physical viewpoint to look at systems which are stationary neous Boltzmann equation. yet in non-equilibrium: in our case the stationary process is in fact non-reversible and the stationary measure not Jose A. Cañizo Gibbsian. In this presentation we give an overview of the School of Mathematics results we obtained in collaboration with Anna De Masi, University of Birmingham Errico Presutti and Maria Eulalia Vares. We prove that [email protected] the hydrodynamic limit is given by the linear heat equation with Dirichlet boundary conditions obtained by solving a Bertrand Lods non-linear equation which essentially fixes the values of the Dipartimento di Statistica e Matematica Applicata density at the boundary. Then we show that the rescaled Università degli Studi di Torino limiting density profile of the (unique) invariant measure of [email protected] the process coincides with the unique stationary solution of the hydrodynamic equation. Last, we obtain a spectral gap estimate in the (non equilibrium) stationary process MS60 uniformly on the system size. Coarsening for the Diffusive Carr-Penrose Model Dimitrios Tsagkarogiannis The Carr-Penrose (CP) model is a linear model of coars- Department of Applied Mathematics University of Crete ening which has many similar features to the non-linear [email protected] and physically important LSW model. In their original 1998 paper Carr and Penrose showed that their model has Anna De Masi a family of self similar solutions and that self-similar solu- Università di LAquila, LAquila tions are globally asymptotically stable in some sense. In [email protected] a 2008 paper Smereka considered solutions to a discrete approximation of the CP model with initial data of finite support. He proved that these solutions converge at large Errico Presutti time to a particular self-similar solution of the CP model. Università di Roma ”Tor Vergata” The result confirms the intuition that diffusion provides [email protected] a selection principle for the physically relevant self-similar solutions of this class of coarsening models. In the case Maria Eulalia Vares studied by Smereka effective diffusion is provided by the Universidade Federal do Rio de Janeiro discretization. This talk is concerned with the model ob- [email protected] tained by adding a second order diffusion term to the first order PDE of the CP model. The speaker will discuss some recent progress in understanding coarsening behavior for MS59 this model. The work is joint with Jingchen Wu. Covariant Statistical Theory of Phase-Ordering Ki- netics via Emergent Symmetries Joseph Conlon Department of Mathematics The emergent symmetry group of a non-equilibrium phase- The University of Michigan ordering system is shown to naturally provide a covari- [email protected] ant action on the associated universal coarsening statistics. MS13 Abstracts 103

Jingchen Wu mains in the Plane University of Michigan [email protected] We study the minimizers of the Dirichlet integral among (rank 1, orthogonal) projection valued maps in a perforated domain in the plane, subject to a Dirichlet condition MS60 on the outer boundary. We assume that the boundary con- Motion of Interfaces Under the Cahn-Hilliard dition represents a non-contractible curve on the set of such Equation with One or Two Sided Degenerate Dif- projections. When the size of the perforation (which is a fusion Mobility disk) goes to zero, we obtain an expression for the limits of the minimizers, which depends only on the location of the We use the asymptotic matching method to study the mo- perforation, and the boundary data. tion of interfaces in two phase systems governed by Cahn- Hilliard type equations with one or two-sided degenerate Alberto Montero diffusion mobilities. We find that there is a nonlinear diffu- Departamento de Matematica sion process that solves a quasi-stationary porous medium Pontificia Universidad Católica de Chile equation in the phase(s) where the mobility degenerates, [email protected] which is the mechanism for such systems to coarsen. When the mobility is disparate, scaling arguments suggests a Dmitry Golovaty crossover in the coarsening rate from t1/3 to t1/4. The University of Akron Department of Mathematics Shibin Dai [email protected] Michigan State University [email protected] MS61 Qiang Du Front Propagation in Stratified Media: A Varia- Penn State University tional Approach Department of Mathematics [email protected] We prove, under generic assumptions, that the special variational traveling wave that minimizes the exponentially weighted Ginzburg-Landau functional associated MS60 with scalar reaction-diffusion equations in infinite cylin- Self-similar Solutions to Coagulation Equations ders is the long-time attractor for the solutions of the initial value problems with front-like initial data. The con- In this talk I will describe some methods which allow to vergence to this traveling wave is exponentially fast. The obtain qualitative information about self-similar solutions obtained result is mainly a consequence of the gradient of the coagulation equations. For some specific kernels it is flow structure of the considered equation in the exponen- possible to derive very detailed asymptotics. General esti- tially weighted spaces and does not depend on the precise mates concerning the behaviour of the solutions for a large details of the problem. It strengthens our earlier generic class of kernels for small and large values of the argument propagation and selection result for ”pushed” fronts. of the solutions will be also discussed. Cyrill B. Muratov Juan Velazquez New Jersey Institute of Technology Institute of Applied Mathematics Department of Mathematical Sciences University of Bonn [email protected] [email protected] Matteo Novaga University of Padova (Italy) MS61 [email protected] Navigating Energy Landscapes in Ginzburg- Landau Problems with Long-Range Interactions MS62 Energy-driven pattern formation induced by competing Efficient Algorithms for (Di-)Atomic Basis Sets short and long-range interactions is common in many physical systems. A nonlocal perturbation (of Coulombic-type) We present to the well-known Ginzburg-Landau/Cahn-Hilliard free en- a fast algorithm to calculate Coulomb/exchange integrals ergy gives rise to a mathematical paradigm with a rich and of prolate spheroidal electronic orbitals, which are the ex- complex energy landscape. I will discuss some recent work act solutions of the single-electron, two-center Schrödinger on developing methods for (i) assessing whether or not a equation for diatomic molecules. Our approach employs particular state is a global minimizer and (ii) navigating Neumann’s expansion of the Coulomb repulsion 1/|x − y|, from metastable states to states of lower energy. solves the resulting integrals symbolically in closed form and subsequently performs a numeric Taylor expansion for Rustum Choksi efficiency. Thanks to the general form of the integrals, Department of Mathematics the obtained coefficients are independent of the particular McGill University wavefunctions and can thus be reused later. Key features [email protected] of our algorithm include complete avoidance of numeric integration, drafting of the individual steps as fast matrix operations and high accuracy due to the exponential con- MS61 vergence of the expansions. Application to the diatomic Projection Valued Functions on Perforated Do- molecules O2 and CO exemplifies the developed methods, which can be relevant for a quantitative understanding of 104 MS13 Abstracts

chemical bonds in general. the full CI space, but scales only polynomially w.r.t. the size of the basis set. Beside the alternating direction al- Christian B. Mendl gorithms, namely DMRG (density matrix renormalization TU Munich group), the dynamical treatment allow to apply first and [email protected] second order optimization methods. We try apply this approach to the compuation of transiton metal complexes, often considered as strongly correlated and hard problems. MS62 Higher-order Adaptive Finite-element Methods for Reinhold Schneider Large-scale Electronic Structure Calculations using Technische Universitat Berlin Kohn-Sham Density Functional Theory [email protected] Electronic structure calculations using Kohn-Sham density functional theory (DFT) have played a significant role in MS63 predicting wide range of material properties, yet simula- Macroscopic Interface Dynamics in Forward- tions of large-scale material systems with DFT are still backward Lattice Diffusion computationally very demanding. In this work, we present an efficient computational approach to perform real-space We consider a diffusive lattice equation with a non- electronic structure calculations using an adaptive higher- monotone non-linearity. The formal continuum limit of order finite-element discretization of DFT and show how such a problem is an ill-posed PDE, thus measure-valued the approach can be extended to develop a linear scaling solutions and hysteresis effects are to be expected. We dis- method for metals and insulators on the same footing. cuss the phenomena that occur for different types of initial data, paying particular attention to the case when inter- Phani S. Motamarri faces with non-trivial dynamics appear and persist in the University of Michigan macroscopic limit. [email protected] Michael Helmers Vikram Gavini Institute for Applied Mathematics Mechanical Engineering, University of Michigan University of Bonn [email protected] [email protected]

Michael Herrmann MS62 Saarland University, Department of Mathematics Finite Elements for Large-Scale Electronic Struc- [email protected] ture Calculations: From Classical to Enriched to Discontinuous MS63 Over the past few decades, the planewave (PW) pseu- Mesoscopic Peridynamics Derived from Mi- dopotential method has established itself as the method of crostructure choice for large, accurate, density-functional calculations in condensed matter. However, due to its global Fourier ba- We describe a method for deriving peridynamic constitu- sis, the PW method suffers from substantial inefficiencies in tive equations from the underlying molecular dynamics. parallelization and applications involving highly localized First, we obtain convolution integral representations for states. Here, we discuss recent enriched and discontinuous the average density and momentum. This establishes a finite element (FE) based methods for the solution of the connection between mesoscopic averages and certain recov- Kohn-Sham equations which have made possible order-of- erable fine scale functionals. Then we use regularization to magnitude reductions in basis size relative to PW and full, approximately invert convolutions, and thus represent the self-consistent calculations of 4000 atoms or more. recoverable functionals by operators acting on the averages. Next, the peridynamical force state is rewritten as a John Pask non-linear operator acting on the recoverable functionals. Lawrence Livemore National Lab The constitutive equations are obtained from this represen- [email protected] tation by replacing the exact recoverable functionals with their deconvoluted approximations. MS62 Alexander Panchenko Entanglement Based Algortihms for Electronic Washington State University Structure Computation of Strongly Correlated Sys- [email protected] tems

Based on an excitation number encoding for the Slater de- MS63 terminant basis functions, the full CI space could be eas- Travelling Waves in the Discrete FitzHugh- ily embedded into a (discrete) Fock space isomorphic to Nagumo Model d 2 F := i=1 C . These tensors can be represented and approximated in a hierarchical tensor (HT) format, known as While the theory of nonlinear waves in partial diﬀerential tree tensor network states (TTNS). An important example equations is very well developed, understanding travelling are tensor trains (TT) which are nothing but matrix prod- waves in systems posed on lattices is challenging, and many uct states (MPS). The ranks are measures for the entangle- basic questions remain open. Indeed, travelling waves on ment between corresponding parts. For given ranks these lattices can be found only by solving functional diﬀerential tensors form an analytic manifold and dynamics could be equations of mixed mode, which are ill-posed as initial- approximation by the Dirac-Frenkel variational principle. value problems. In addition, propagation failure or pinning The resulting variational wave function method permeates occurs frequently for waves with small speeds, which makes MS13 Abstracts 105

it hard to ﬁnd such waves using perturbation arguments. tinuum mechanics to allow for discontinuities In this talk, I will outline work on the existence and stability of travelling waves for the discrete FitzHugh-Nagumo Richard B. Lehoucq system using geometric singular perturbation theory. Sandia National Laboratories [email protected] Hermen Jan Hupkes University of Leiden Mathematical Institute MS64 [email protected] Peridynamic Instability and Damage

Bjorn Sandstede In this talk we explore connections between classic damage Brown University models and their relation to bond based peridynamics. bjorn [email protected] Robert P. Lipton Department of Mathematics MS63 Louisiana State University [email protected] Solitary Waves in the FPU Chain: A New Exact Solution MS64 We consider solitary wave solutions in the Fermi-Pasta- Ulam problem with piecewise linear nearest-neighbor in- Calibration and Ranking of Stochastic Peridynam- teractions. We show that in this case the problem reduces ics Models for Ring Fragmentation Phenomena to a Fredholm integral equation of the second kind, which Using Bayes’ formula and available uncertain experimental can be solved explicitly using Wiener-Hopf method. Taking data D related to the rapid expansion and fragmentation advantage of the availability of an exact solution, we test of metal rings, we quantitatively compare two stochastic the limits of applicability of the simplest quasicontinuum peridynamics modeling hypotheses proposed for simulating approximations of the discrete problem. We show that D. The methodology we discuss can be applied to any in agreement with the results of Friesecke and Matthies number of candidate hypotheses for simulating the same (2002), atomic-scale localization occurs in the high-energy data D, and it consists of (i) statistically calibrating the limit. Numerical simulations suggest stability of the ob- random parameters in each modeling hypothesis, and (ii) tained solutions above a certain velocity threshold. calculating the hypotheses’ plausibilities conditioned upon Anna Vainchtein D. Department of Mathematics Ernesto E. Prudencio University of Pittsburgh Institute for Computational Engineering and Sciences [email protected] University of Texas at Austin [email protected] Lev Truskinovsky Laboratoire de Mechanique des Solides Michael L. Parks Ecole Polytechnique Sandia National Laboratories [email protected] [email protected]

MS64 MS65 Intersonic Crack Propagation in Fiber-Reinforced Austenite As a Local Minimizer in a Model of Ma- Composites: a Peridynamic Approach terial Microstructure with a Surface Energy Term We present a homogenization-based anisotropic peridy- In this talk we present a simplified model of a single elastic namic model for unidirectional fiber-reinforced compos- crystal where the development of microstructure is influ- ites and we use it to model an experiment by Coker and enced by both potential and surface energies. In particular, Rosakis (2001) in which intersonic crack growth is observed we will show that (i) u = 0 (corresponding to austenite) is in asymmetrically loaded composites. We show that under a strict local minimizer of the energy in a suitable sense, sufficiently high amplitude loading, a splitting-type crack and (ii) provided the potential well-depths are sufficiently propagates intersonically, creating its own shock wave cone large, there is an energy barrier between the austenite state with an angle of about 18 degrees, very close to that seen and the global minimizer of the total energy. from experiments. Under symmetric loading, mode I cracks grow subsonically. Jonathan J. Bevan Department of Mathematics Florin Bobaru,YenanWang University of Surrey University of Nebraska-Lincoln [email protected] [email protected], [email protected]

MS65 MS64 Swell Induced Wrinkling and Creasing on the Sur- Peridynamic Balance Laws face of Hydrogel Bilayers

My talk introduces the peridynamic balance laws of mo- Upon swelling in a solvent, a thin hydrogel layer on a rigid mentum and energy. The nonlocal force and energy den- substrate may become unstable, developing various sur- sities are given by integral operators that are the nonlocal face patterns. Recent experimental studies have explored analogues for the classical force and energy densities. The the possibilities to generate controllable surface patterns resulting balance laws extend the classical theory of con- by chemically modifying the molecular structures of the 106 MS13 Abstracts

hydrogel near the surface. In this paper, we present a theo- localization will take place to finally generate cracks. This retical stability analysis for swelling of hydrogel layers with bifurcation is studied through a partial Fourier decompo- material properties varying in the thickness direction. As sition which leads to the study of a Rayleigh ratio. The a specialization of the general procedure, hydrogel bilayers determination of the time and mode of that bifurcation with different combinations of the material properties are allows us to explain the periodic distribution of the so- examined in details. For a soft-on-hard bilayer, the on- initiated cracks and to calculate the crack spacing in terms set of surface instability is determined by the short-wave of the material and loading parameters. We then discuss limit, similar to a homogeneous layer. In contrast, for a the stability of the fundamental and bifurcated solution. hard-on-soft bilayer, a long-wave mode with a finite wavelength emerges as the critical mode at the onset of sur- Jean-Jacques Marigo face instability, similar to wrinkling of an elastic thin film Ecole Polytechnique on a compliant substrate, and the critical swelling ratio is Palaiseau, France much lower than that for a homogeneous hydrogel layer. A [email protected] smooth transition of the critical mode is predicted as the volume fraction of the top layer changes, linking surface Paul Sicsic instability of a homogeneous layer to thin film wrinkling Laboratoire de Mecanique des Solides as two limiting cases. Numerical simulations by a nonlin- Ecole Polytechnique ear finite element method show that, while surface creases [email protected] form spontaneously in a soft-on-hard bilayer, surface wrinkles grow significantly before creases form in a hard-on-soft bilayer. MS66 Cytoskeletal Mechanics and Cell Motility Nikolaos Bouklas University of Texas at Austin Abstract not available at time of publication. [email protected] Antonio DeSimone Zhigen Wu SISSA, Trieste, Italy Hefei University of Technology 34014 Trieste, ITALY [email protected] [email protected]

Rui Huang MS66 University of Texas at Austin Lamellipodia Dynamics in Motile Cells [email protected] We develop a simple physical model that captures the large-scale lamellipodia dynamics in crawling cells and ex- MS65 plains the observed spectrum of fish keratocytes behavior. Stability Conditions for Constrained and Uncon- We deviate from existing theoretical works and consider strained Multi-Phase Elastic Solids the lamellipodium leading edge as a propagating front. The agreement of our model with experimental works suggests Inclusion of a non-positive-definite phase in an elastic com- that the large-scale migration features exhibited by kera- posite has the potential to give rise to greatly enhanced tocyte cells are a direct consequence of the closed feedback overall composite stiffness. While independent investiga- loop between the leading edge geometry and actin network tions have highlighted stability and effective properties of density such composites, no clear connection has been established between the two. Therefore, we here compare stability Sefi Givli and effective performance of elastic composites having non- Technion, Israel positive-definite phases, and we conclude that only the ef- [email protected] fective dynamic response can be positively affected by inclusion of a negative-stiffness phase. Yair Adler Dennis M. Kochmann,CharlesWojnar Technion - Israel Institue of Technology California Institute of Technology [email protected] [email protected], [email protected] MS66 MS65 Swimming Micro-organisms in Complex Fluids Thermal Shock Crack Initiation: a Non Local Dam- Swimming microorganisms commonly encounter non- age Model Stability Analysis Newtonian fluids such as mucus. In this talk I describe our This paper studies the initiation of cracks in the ther- work on swimming helices in polymeric liquids, in which mal shock problem through the variational analysis of the we use theory, computation, and scale-model experiments quasi-static evolution of a gradient damage model. We to determine how the swimming speed of a rotating helical consider a two-dimensional semi-infinite slab with an im- filament depends on frequency, polymer relaxation time, posed temperature drop on its free surface. The damage filament radius, and helical geometry. I also report on our model is formulated in the framework of the variational more recent work on swimming in anisotropic fluids and theory of rate-independent processes based on the princi- near flexible boundaries. ples of irreversibility, stability and energy balance. In the Thomas R. Powers case of a sufficiently severe shock, we show that damage Brown University immediately occurs and that its evolution follows first a Division of Engineering fundamental branch without localization. After a finite Thomas [email protected] time, it bifurcates into another branch in which damage MS13 Abstracts 107

MS66 characterize dislocation nucleation below the indenter in Cellular Pressure and Volume Regulation and Im- terms of bifurcations in atomic models. plications for Cell Mechanics and Cell Motility Ana Carpio In eukaryotic cells, small changes in cell volume can serve as Universidad Complutense de Madrid important signals for cell proliferation, death and migra- Departamento de Matemática Aplicada tion. Volume and shape regulation also directly impacts [email protected] mechanics of cells and tissues. Here we develop a quantitative mechanism of cellular volume and pressure regulation, incorporating essential elements such as water permeation, MS67 mechanosensitive channels, active ion pumps and active Plastic Strain Recovery in Nanocrystalline Nickel motor-driven stresses in the cell cortex. The model can predict the cellular volume and pressure for several mod- Grain refinement in crystalline materials leads to an en- els of cell cortical mechanics. Furthermore, we show that hancement of several materials properties including yield when cells are subjected to an externally applied load, such and fracture strength and superior wear resistance. These as in an AFM indentation experiment, active regulation of improved material responses benefit the reliability of micro volume and pressure leads to complex cellular response. In- and nano devices, including MEMS and NEMS with com- stead of the passive mechanics of the cortex, the observed ponents made of nanocrystalline materials. On the other cell stiffness depends on several factors working together. hand, this reduction in grain size is also responsible for new Finally, we examine the implications of volume regulation mechanisms that are not present in their coarse grained in cell motility, where polarized distribution of membrane counterparts. One of these mechanisms is plastic strain re- channels and pumps can lead to directed cell migration in covery. an actin-independent manner. Quantitative results from Even though, plastic deformation is not recoverable in experiments and modeling will be discussed. coarse grained crystalline materials, recent experiments in nanocrystalline aluminum, nickel and gold thin films and Sean Sun bulk nanocrystalline aluminum recovered more than 50% Whitaker Biomedical Engineering Institute of plastic strain after unloading. John Hopkins University We will present dislocation dynamics coupled to kinetic [email protected] Monte Carlo simulations that show plastic strain recovery in nanocrystalline metals with large scatter in the grain size distribution. Our results show that this phenomenon is MS67 driven by the inhomogeneous distribution of residual stress Strain and Rotation Fields of Dislocations in in the sample when the applied load is removed. We ana- Graphene lyze the effects of temperature, loading history, and grain size distribution on the time dependent plastic strain re- Recent experiments have revealed that the strain and rota- covery. tion fields about dislocations in suspended graphene sheets are qualitatively different from those provided by conven- Marisol Koslowski, Yuesong Xie tional elasticity. The observed fields are explained by Purdue University adding a term quadratic in the local rotation to the 2D [email protected], [email protected] isotropic elastic strain energy density and regularizing the singularity at the dislocation point in different ways. MS67 Luis Bonilla Kinematic Analysis of Finite Plasticity as the Limit Universidad Carlos III de Madrid of Dislocation Activity G. Millan Institute of Fluid Dynamics, Nanoscience & IndMath This talk will present a plasticity model in the finite kine- [email protected] matic framework that is directly obtained as the limit of the dislocation activity. The project intends to provide a Ana Carpio physically-based definition of the elastic and plastic defor- Universidad Complutense de Madrid mation gradient at the microscale that leads to the stan- Departamento de Matematica Aplicada dard multiplicative decomposition of the deformation gra- ana [email protected] dient in the continuum limit. Additionally, an expression for the dislocation density tensor is provided at both the discrete and continuum scale. The work is performed under Jamie Warner the auspices of the U.S. Department of Energy by Lawrence University of Oxford Livermore National Laboratory under Contract DE-AC52- Department of Materials 07NA27344. [email protected] Celia Reina Romo Graduate Aeronautical Laboratories MS67 California Institute of Technology Pattern Formation in Indentation Tests [email protected] Nanoindentation is currently used to explore the mechanical properties of solid surfaces. Controlled generation of Sergio Conti surface defects using indenters might render metallic sur- University of Duisburg-Essen faces stronger. Around each indentation mark, dislocation Duisburg, germany networks are formed. Patterns such as loops, terraces or [email protected] hillocks are commonly identified. The formation of terraces and hillocks involves glide and cross-slip mechanisms that we justify solving anisotropic Hertz contact problems. We 108 MS13 Abstracts

MS68 a more expensive, more accurate, model. We demonstrate Long-Time Simulation of Steady Nonequilibrium the effectiveness of this approach on several test problems. Flow Nonequilibrium molecular dynamics (NEMD) are widely Jonathan Weare employed in the study of molecular fluids under steady, University of Chicago homogeneous flow, such as in the computation of stress- Department of Mathematics strain constitutive relation using a microscopic stress for- [email protected] mulation. We will discuss the use of the Nonequilibrium Langevin Dynamics, a stochastic dynamics for sampling a Bo Qi, Seyit Kale molecular system with a homogeneous flow field ∇u = A. University of Chicago In such a simulation the unit cell moves with the flow, and [email protected], [email protected] we describe particular boundary conditions that allow for long-time simulation by avoiding extreme deformation of Aaron Dinner the unit cell. James Franck Institute University of Chicago Matthew Dobson [email protected] CERMICS - ENPC [email protected] MS69 MS68 Modeling Multiferroic Polycrystalline Materials Markov Model Reduction with Perturbed Test Multiferroics are materials that involve the coupling of elas- Functions ticity, magnetization and polarization. In systems that contain all three properties the elastic coupling can be used Abstract not available at time of publication. to control polarization with magnetic fields or magnetiza- Mathias Rousset tion with electric fields. The latter is particularly advan- INRIA Rocquencourt, France. tageous for memory applications. In this talk I would like [email protected] to discuss how these systems can be modeled efficiently by coupling the magnetization and polarization fields with a standard phase field crystal model. MS68 Ken Elder Local Hyperdynamics Dept Physics In hyperdynamics, a method for reaching long time scales Oakland U. in infrequent-event systems, the bias potential must be [email protected] zero everywhere on the dividing surface bounding the state, with the consequence that for large systems the boost fac- MS69 tor decays to unity, regardless of the form of the bias potential. I will describe a new, local form of hyperdynamics Phase Field Crystals - Modeling Structural Trans- that circumvents this problem, giving a constant boost fac- formations at Diffusive Time Scales and Atomic tor for arbitrarily large systems. Length Scales Arthur F. Voter Many different models have emerged in the past few Theoretical Division, T-1 decades to simulate phase transformations and the physi- Los Alamos National Laboratory cal mechanisms which govern them. Correspondingly, with [email protected] the increase in complexity, the demand on computational power has grown. Each transformation is broken down by its contributing physical components and an appropriate MS68 model is accordingly developed to simulate these compo- Using Coarse Grained Models to Speed Conver- nents. The phase field crystal methodology is a relatively gence to the Minimum Energy Pathway new model that attempts to incorporate many bulk and interface properties through an evolution of density fields The minimum energy pathway (MEP) is the most likely which simultaneously represents both the bulk phases, elas- transition pathway between reactant and product states in tic stresses and topological lattice defects. This method of a chemical reaction at low temperature and provides a con- simulation promises to provide atomic type simulations at venient, one dimensional, description of the reaction. For diffusive time scales allowing the investigation of slow mov- large complex systems interrogation of the reaction mecha- ing transformations and defect interactions. I will discuss nism by straightforward simulation is often impossible due some potential uses for the model and concepts behind it. to the presence of a vast range of time scales. For this rea- son, efficient techniques that focus on discovery of the MEP are important. Unfortunately in large complex systems Michael Greenwood discovery of the MEP can itself be prohibitively expensive. Natural Resources Canada In this work we develop a technique for discovery of the [email protected] MEP (and other pathwise descriptions of reactions) that uses inexpensive, coarse grained models to accelerate con- MS69 vergence. In most practical settings the reaction pathway corresponding to the coarse grained model does not accu- Fluctuating Nonlinear Hydrodynamics formalism rately describe the reaction of interest. Nevertheless, by of the Density Functional Theory of solidification. carefully arranging the calculation, the coarse grained sys- Recent developments in PFC modeling of crystalline pat- tem can be used to accelerate convergence to the MEP of MS13 Abstracts 109

tern formation in 2D and 3D are reviewed. This includes ground state is realized for charged molecules in the phys- various aspects of dendritic solidification and growth on ical parameter regions, which provides a reasonable expla- crystalline surfaces. Along these lines, we present results nation of local spins observed experimentally. In alkali- for the anisotropy of the solid-liquid interface free en- metal-doped dibenzopentacene, our results show that elec- ergy and kinetic anisotropy, including the respective Wulff tron correlation may produce an effective attraction be- shapes. Next, we compare dendritic patterns from atom- tween electrons for the charged molecule with one or three istic theory in 2D and 3D with those predicted by a quanti- added electrons, a necessary condition for superconductiv- tative phase-field model under similar conditions (driving ity. We further propose a different doping pattern which force and anisotropies), and discuss the validity range of may lead to higher transition temperature. Some results the latter approach. on the possible structure of PAH as functions of pressure and doing will also be discussed. Gyula Toth,György Tegze Wignes Research Centre for Physics H.Q. Lin Budapest, Hungary DEPARTMENT OF PHYSICS [email protected], [email protected] THE CHINESE UNIVERSITY OF HONG KONG [email protected] Laszlo Granasy Research Institute for Solid State Physics & Optics Budapest, Hungary MS70 [email protected] Application of Active Liquid Crystal Models to Complex Biological Systems

MS69 In order to model complex biological systems, we have to Two-Dimensional Crystals - the Interplay of Ge- treat the motility of their micro-constituents, cells in cel- ometry and Materials Defects lular systems, F-actins inside a cell, etc.. In this talk, I will discuss how active liquid crystal models can be used Using a phase ﬁeld crystal model on a curved surfaces al- to study the chemical-mechanical coupling in live cellular lows to investigate geometrical frustration on crystalline systems. Numerical simulations will be presented to simu- structures and the formation of defects. This will be stud- late a few selected cases. ies in detail for various geometries demonstrating the oc- curance of new defect structures, such as grain boundary Qi Wang scars and pleats. Possible applications for pliable sub- University of South Carolina strates will be discussed. [email protected]

Axel Voigt TU Dresden MS70 [email protected] Kinetic Theory and Simulations of Active Nematic Polymers

MS70 A kinetic model is proposed for active nematic polymers in Chiral Liquid Crystals in Poiseuille Flow a viscous solvent, by coupling particle-activation physics to the Doi-Hess theory for passive nematic polymers. Numer- Chiral liquid crystal (CLC) ordering occurs in solid bio- ical results are presented for the dilute regime where the composites such as insect cuticle, muscle, collagen and silk stable passive isotropic phase is driven from equilibrium by fibers. In this talk, we present a kinetic model for flow- activation physics, the nano-rod analog of non-Brownian, ing CLCs. The underlying microstructures and linear vis- non-polar, active pusher suspensions. Unsteady (periodic coelasticity of CLCs in Poiseuille oscillatory permeation and modulated periodic) and steady, 1D and 2D attrac- flows are presented and discussed, taking into account dy- tors are selected by varying active parameters, revealing namic couplings between orientation and velocity fields. rich diversity reminiscent of mesoscopic simulations of active semi-dilute nematics. Zhenlu Cui Department of Mathematics and Computer Science Ruhai Zhou Fayetteville State University Department of Mathematics and Statistics [email protected] Old Dominion University [email protected]

MS70 M. Gregory Forest Modeling and Simulation of Organic Superconduc- University of North Carolina at Chapel Hill tors Dept of Math & Biomedical Engr. [email protected] In this talk, I report our recent study on the magnetic and pairing properties of newly discovered polycyclic Qi Wang aromatic hydrocarbon (PAH) superconductors including University of South Carolina alkali-metal-doped picene, coronene, phenanthrene, and [email protected] dibenzopentacene. Systematic computer simulations were carried out so to gain understandings on magnetism and electron correlation in PAH. We model the p-electrons on MS71 the carbon atoms of a single molecule by a one-orbital Hub- Nonexistence Results for Energy Functionals with bard model, in which the energy diﬀerence ? between carbon atoms with and without hydrogen bonds is taking into account. Our results demonstrate that the spin polarized 110 MS13 Abstracts

Competing Attracting and Repelling Interactions uniformly bounded, radially symmetric nonnegative functions of fixed mass. Moreover we will show that in the case Abstract not available at time of publication. of a quadratic attraction the sharp interface version of this minimization problem admits a unique global minimizer, Jianfeng Lu namely the ball. This is a joint work with R. Choksi and Mathematics Department R. Fetecau. Duke University [email protected] Ihsan A. Topaloglu Indiana University [email protected] MS71 Existence and Qualitative Properties of Grounds States to the Non-Local Choquard-Type Equations MS72 Analyzing Capture Zone Distributions (CVDs) in The Choquard equation, also known as the Hartree equa- Growth: Theory and Applications tion or nonlinear Schrodinger-Newton equation is a stationary nonlinear Schrodinger type equation where the nonlin- We earity is coupled with a nonlocal convolution term given describe CZDs using the generalized-Wigner-distribution by an attractive gravitational potential. We present sharp (GWD): P (s)=asβ exp(−bs2), with s the normalized Liouville-type theorems on nonexistence of positive super- CZ area. Near the experimentally-accessible central re- solutions of such equations in exterior domains. We also gion, the GWD fits data well; β reveals physical infor- discuss existence, positivity, symmetry and optimal decay mation about nucleation. Careful simulations by Amar’s properties of ground state solutions under various assump- and Evans’s groups showed inadequacies in our mean-field tions on the decay of the external potential and the shape Fokker-Planck argument and for behavior in the tails. Dis- of the nonlinearity. In particular, we obtain a sharp decay cussing underlying reasons, we propose improved, more- estimate for the ground state solution which was discovered complicated descriptions of CZDs. We summarize appli- by E.Lieb in 1977. cations to various pure and impurity-encumbered growth (also to societal) systems. Vitaly Moroz Department of Mathematics Theodore L. Einstein Swansea University MRSEC, CMTC, and Physics Department [email protected] University of Maryland [email protected] MS71 Alberto Pimpinelli Verifying Global Minimizers for Ginzburg-Landau- Rice Quantum Institute type Problems: a Simple Approach via Convex Ap- Houston, TX proximation [email protected] Energy functionals of Ginzburg-Landau-type are promi- nent in modeling material phenomena. These function- DiegoLuis González als are non-convex and contain many local minima and Univ. del Valle metastable states. As a result, through standard meth- Cali, Colombia ods such as a gradient flow, it is easy to produce local [email protected] minimizers or metastable states, however difficult to verify whether a given state is also a global minimizer. In Rajesh Sathiyanarayanan our talk we present a new strategy for verifying candidate IBM Semiconductor Research & Development global minimizers. The approach relies on finding a good Bangalore, India lower bound quadratic functional through a convex opti- [email protected] mization procedure. Using a numerical method, we then solve the convex problem to obtain a bound on the order- Ajmi Hammouda disorder (ODT) transition curve. We apply this method Univ. of Monastir to the Ohta- Kawasaki functional. We conclude with a Monastir, Tunisia discussion of the verification for non-constant states. [email protected] David Shirokoff Mcgill university MS72 david.shirokoff@mail.mcgill.ca Nanocluster Self-assembly: Far-from-equilibrium Shapes and Composition Profiles

MS71 Self-assembly of nanoclusters often occurs far-from- Minimization of a Short-range Attractive and equilibrium in metallic systems. Consequently, shapes Long-range Repulsive Energy Related to a Non- and composition profiles for multi-component clusters can local Aggregation Model be exquisitely sensitive to the formation kinetics. First, we discuss general features for both diffusion-limited and In this talk I will consider an energy consisting of a short- attachment- or reaction-limited growth. Then, we present range attractive and a long-range repulsive term. This en- a detailed analysis for diffusion-limited growth of 2D epi- ergy is related to aggregation models given by the equa- ∇· −∇ ∗ taxial clusters by metal deposition on crystalline surfaces. tion ρt + (ρ( K ρ)) where ρ is the density of the We present examples for one- and two-component clusters aggregation and K is the interaction potential. Looking at − on simple fcc surfaces and on alloy surfaces. the energy E(ρ)= R3 R3 K(x y)ρ(x)ρ(y)dxdy we will establish the existence of minimizers among the class of Jim W. Evans MS13 Abstracts 111

Ames Laboratory USDOE and Iowa State University to some nonlocal balance laws in this talk. We use peridy- [email protected] namic materials models and nonlocal diffusion as examples to provide physical motivations and to illustrate mathematical challenges. We present a nonlocal vector calculus MS72 as an attempt to study related nonlocal variational prob- Kinetics in GaAs Thin-Film Growth with First- lems in more systematic and axiomatic ways. We also ex- Principles Local Superbasin Kinetic Monte Carlo plore connections and differences between nonlocal and local models and address questions concerning efficient and A significant challenge in rare-event simulations is deal- reliable numerical approximations. ing with superbasins, or groups of recurrent free-energy minima separated from the full phase space of the sys- Qiang Du tem by high barriers that can considerably reduce the Penn State University efficiency. We present a local superbasin kinetic Monte Department of Mathematics Carlo (LSKMC) method for identifying local superbasins [email protected] in KMC simulations containing both superbasins and non- superbasin events. We demonstrate aspects of LSKMC in several examples, which highlight the computational effi- MS73 ciency of this algorithm. Variational Analysis of Linearized Peridynamics for Heterogeneous Materials Kristen Fichthorn Penn State University We analyze the linearized state-based peridynamic model fi[email protected] of continuum mechanics. The focus of the analysis is on models of isotropic heterogeneous elastic materials. Using standard variational techniques we prove the well posed- MS72 ness of the system of equilibrium equations as well as the Directed Assembly of Nanoclusters on a Templated equations of motion, given as nonlocal equations with a Surface: Rumpled Graphene prescribed volumetric constraint. In the event of vanishing nonlocality solutions of the nonlocal system are shown to Deposition on templated surfaces can guide assembly of converge to the Navier-Lamé system of classical elasticity. periodic arrays of nanoclusters. This process involves nu- Our analysis is based on some nonlocal Poincaré-type in- cleation and growth in the presence of a periodically mod- equalities and compactness of the corresponding nonlocal ulated adsorption energy and diffusion barrier. Suitable operators. This is a joint work with Qiang Du. atomistic models are developed and analyzed by KMC simulation, and by coarse-graining. The model describes ar- Tadele Mengesha rays of mono- and bi-metallic nanoclusters formed by de- Louisiana State University position of Ru and Pt on a graphene sheet which exhibits Department of Mathematics a periodic moire structure when supported on Ru(0001) . [email protected]

Yong Han Ames Laboratory, U. S. Department of Energy MS73 Iowa State University Sparse Dynamics of Non-Local Evolution Equa- [email protected] tions

We investigate the approximate dynamics of several dif- MS73 ferential equations when the solutions are restricted to a Conditioning in Fractional Sobolev Spaces sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to We investigate the condition number of the stiffness matrix the coefficients of the basis approximation. By compressing arising from piecewise linear and constant finite element the information needed to represent the solution at every discretization of nonlocal integral operator with singular step, only the essential dynamics are represented. In many kernels. Depending on the singularity, we study the con- cases, there are natural bases derived from the differential dition number in respective fractional Sobolev spaces. We equations which promote sparsity. explicitly quantify mesh size and horizon dependence of extremal eigenvalues. We provide supplementary numerical Hayden Schaeffer results. UCLA Math Department hschaeff[email protected] Burak Aksoylu TOBB University of Economics and Technology, Dept of Stanley J. Osher Math University of California Louisiana State University, Dept of Math Department of Mathematics [email protected] [email protected]

Zuhal Unlu Russel Caﬂisch Louisiana State University Department of Mathematics [email protected] University of California, Los Angeles caﬂ[email protected] MS73 Mathematical and Numerical Analysis of Nonlocal Cory Hauck Models Oak Ridge National Laboratory [email protected] We discuss mathematical and computational issues related 112 MS13 Abstracts

MS74 Marcus Stiemer Rational Design of Molecular Materials: Piezo- Helmut-Schmidt-University of electrics and Organic Solar Cells Via Genetic Lgo- Federal Armed Forces Hamburg rithms [email protected] Abstract not available at time of publication. MS75 Geoffrey Hutchison Excitability and Chaos in Active Nematic Suspen- University of Pittsburg sions geoff[email protected] In this talk I will describe a model of mutually propelled filaments suspended in a two-dimensional solvent. The sys- MS74 tem undergoes a mean-field isotropic-nematic transition for Data Mining Big Materials Data large enough filament concentrations, and the nematic order parameter is allowed to vary in space and time. The Abstract not available at time of publication. interplay between nonuniform nematic order, activity, and flow results in spatially modulated relaxation oscillations, Shyue Ping Ong similar to those seen in excitable media. In this regime the Massachusetts Institute of Technology dynamics consists of nearly stationary periods separated [email protected] by bursts of activity in which the system is elastically dis- torted and solvent is pumped throughout. At even higher MS74 activity, the dynamics becomes chaotic. Taking Advantage of the Convexity of Chemical Luca Giomi Compund Space SISSA, Trieste, Italy. [email protected] Efficient exploration of enormous chemical spaces requires new optimization schemes that search directly for the property optimum, and in the process discover new molecu- MS75 lar architectures. We present an unbiased optimization The Metaphase Spindle As An Active Liquid Crys- paradigm that is free from preselected substitution frame- tal works. We propose directly optimizing on the space of possible compositions and structures subject to property con- Abstract not available at time of publication. straints such as visual clarity. We exemplify this algorithm with non-linear optical chromophores with a transparency Dan Needleman constraint in the visible spectroscopic region. School of Engineering and Applied Sciences Harvard University Berend C. Rinderspacher [email protected] Army Research Lboratory [email protected] MS75 Spontaneous Flow in Active Gels MS74 Numerical Algorithms for Identification of Opti- Abstract not available at time of publication. mal Parameters in Material Models for Industrial Forming Processes Tim Sanchez Physics Department Combining classical quasi-static forming with electromag- Brandeis University netic pulse forming can increase formability in a sheet [email protected] metal forming process. The numerical simulation of the combined forming process strongly depends on suitable material models. Recently proposed models take into account MS75 nonlinear kinematic and isotropic hardening. Fitting to Dynamical Structures in Active Nematics and experimental data identifies the model parameters. We Their Novel Behaviors present a second order optimization framework based on inner points to identify the model parameters by simulat- Abstract not available at time of publication. ing uniaxial tensile tests. Xia-qing Shi Marco Rozgic Center for Soft Condensed Matter Physics Helmut-Schmidt-Universitaet Hamburg Soochow University, China [email protected] [email protected]

Yalin Kiliclar MS76 RWTH AACHEN University Reformulation of Continuum Mechanics for Multi- [email protected] scale Simulation Abstract not available at time of publication. Ivaylo Vladimirov, Stefanie Reese RWTH Aachen University Youping Chen [email protected], University of Florida [email protected] ypchen2@uﬂ.edu MS13 Abstracts 113

MS76 Sampling From Atomistic to Continuum Boundary Value Problems in Nonlinear Elasticity The Multiple State Transition Interface Sampling (MSTIS) technique is a form of path sampling that can compute We study the passage from atomistic systems to an eﬀective rare event kinetics in complex systems exhibiting multi- continuum theory for boundary value problems in (mod- ple metastable states. I present a novel scheme combining erately) nonlinear elasticity: Under suitable assumptions MSTIS with a single replica exchange method based on we will show that discrete solutions of the Euler-Lagrange Wang-Landau sampling, that, in principle, can explore the equations converge to solutions of the continuum equations entire trajectory space starting from a single stable mini- of nonlinear elasticity. mum. The method is illustrated on simple models as well as more realistic biomolecular transitions. Bernd Schmidt Augsburg University Peter Bolhuis [email protected] University of Amsterdam [email protected]

MS76 Continuum Models for Dislocation Dynamics and MS77 Crystal Plasticity Recent Developments in Adaptive Kinetic Monte Carlo We present continuum models for dislocation dynamics and crystal plasticity. The continuum models are derived Adaptive kinetic Monte Carlo (AKMC) is a technique used from discrete dislocation dynamics models and incorpo- to study the long timescale dynamics of rare event systems. rate the long-range interaction of dislocations, local line AKMC is a type of kinetic Monte Carlo simulation where tension effect of dislocations, and dislocation multiplica- the events and their rates are calculated on-the-fly. The tion by Frank-Read source. We use the disregistry across reactive events are represented by saddle points on the po- the slip plane to represent the continuous distribution of tential energy surface and their rates are calculated using dislocations, which has the advantage of including the ori- harmonic transition state theory. Typically, saddles are entation dependence of dislocations in a very simple way. found in AKMC with single-ended min-mode following sad- Applications of two dimensional grain size effect and creep dle point searches. Here, I use high temperature molecular of metals are presented. dynamics trajectories, as is done in temperature accelerated dynamics, to discover the reactive events in AKMC. Yang Xiang In this approach, the error in the simulation can be esti- Hong Kong University of Science and Technology mated and controlled, little prior knowledge of the system [email protected] is required, and in favorable cases, the efficiency of AKMC simulations are substantially increased. Yichao Zhu Department of Mathematics Graeme Henkelman The Hong Kong University of Science and Technology Assistant professor at the University [email protected] of Texas at Austin [email protected]

MS76 Samuel Chill Continuum Limit of Discrete Motion of Interfaces The University of Texas at Austin Department of Chemistry & Biochemistry We will discuss some results on the motion of interfaces [email protected] in a discrete environment. The model takes into account nearest and next nearest neighbor interactions leading to interfaces between patterns. Intricate stick-slip phenom- MS77 ena also arises through diﬀerent spatial and temporal dis- Multiscale Modeling of Macromolecular Dynamics cretization. Abstract not available at time of publication. Andrea Braides University of Roma 2, Italy Cecilia Clementi Dipartimento di Matematica Rice University [email protected] [email protected]

Marco Cicalese MS77 Technical University Munich Germany An Infinite Swapping Approach to the Rare-Event [email protected] Sampling Problem Infinite swapping (INS) is a recently developed method to Aaron Yip overcome the rare-event sampling problem, Plattner et al., Purdue University 2011. The method is based on a mathematical analysis of Department of Mathematics parallel tempering (PT) by large deviation theory, Dupuis [email protected] et al., 2012. An expanded computational ensemble composed of a number of replicas at different temperatures is used for PT and for INS, but while the basic concept of PT MS77 is to sample various replicas of a system at different tem- Wang-Landau Multiple State Transition Interface peratures and exchange information between the replicas occasionally, INS uses the symmetrized distribution of con- 114 MS13 Abstracts

figurations in temperature space, which corresponds to the nology, live multicellular aggregates as bio-ink are used to infinite swapping limit of PT. INS is a general method and make tissue or organ constructs via the layer-by-layer de- therefore potentially useful for various application areas. position technique in biocompatible hydrogels; the printed So far it has been tested for Lennard-Jones clusters and dif- bio-constructs embedded in the hydrogels are then placed ferent biological systems. In biological systems, rare-event in bioreactors to undergo the self-assembly process to form sampling problems arise due to the different timescales on the desired functional tissue or organ products. Here we which biological processes occur and a number of chal- implement our model with an efficient KMC algorithm to lenges needs to be addressed due to the specific properties simulate the making of a set of tissues/organs in several of functional free energy landscapes characterizing biolog- designer’s geometries like a ring, a sheet and a tube, which ical macromolecules. can involve a large number of cells and various other support materials like agarose constructs etc. We also study Nuria Plattner the process of cell sorting/migration within the cellular ag- Freie Universitaet Berlin gregates formed by multiple types of cells with different [email protected] adhesivities. Yi Sun MS78 University of South Carolina A Hierarchy of Coarse-Grained Molecular Dynam- [email protected] icsModelsforMaterialDefects

I will present a systematic approach to coarse-grain molec- MS78 ular dynamics models for solids. The coarse-grained mod- Localized Bases for Numerical Homogenization of els are derived by Galerkin projection to a sequence of Heterogeneous Materials Krylov subspaces. On the coarsest space, the model corresponds to a finite element discretization of the continuum Homogenization Theory deals with mathematical models of elasto-dynamics model. On the other hand, the projection strongly inhomogeneous media with vastly different prop- to the finest space yields the full molecular dynamics de- erties. Traditionally, it is described by PDEs with rapidly scription. The models in between serve as a smooth tran- oscillating coefficients of the form A(x/), → 0. The sition between the two scales. I will also discuss some error homogenization of PDEs with periodic or ergodic coeffi- estimation and numerical experiments. cients and well separated scales is now well understood. We consider the most general case of arbitrary measurable Xiantao Li coefficients. Specifically, we study divergence-form scalar Department of Mathematics elliptic equations and vectorial equations with such coeffi- Pennsylvania State University cients. For these problems we establish finite-dimensional [email protected] approximations of solutions, which we refer to as finite- dimensional homogenization approximations. We introduce different constructions for the approximations and MS78 establish the error estimate with an explicit and optimal Fast Nanowire Simulations Using a Hash Table- error constant independent of the contrast and regularity Based Cache of the coefficients. A proper generalization of the notion of cell problem is the key technical issue in our consideration. We present an implementation of a rate cache designed to In the language of numerical analysis, we are answering the eliminate redundant calculations in Kinetic Monte Carlo following question: can we recover the typical O(h) error (KMC) simulations as well as applications of the imple- estimate for Laplace equation for PDEs with rough (L∞) mentation to simulating nanowire growth. We present nu- coefficients? and what is the optimal cost (localization) to merical evidence suggesting that the utilization of such a achieve this error estimate? cache is computationally advantageous. We further describe a simulated annealing technique to search for ef- Lei Zhang fective, system-specific hash functions. Equipped with an Shanghai Jiao Tong University efficient implementation, we are able to simulate nanowire [email protected] growth by the vapor-liquid-solid method as an example. An energy parameter study is presented. We show that the KMC model captures a wide range of observed phe- MS79 nomena, including faceting at the liquid-solid interface and The Cross-over from Symmetric to Asymmetric nanowire kinking. Domain Walls in Soft Ferromagnetic Films Kris Reyes We study the Landau-Lifshitz energy of domain walls in University of Michigan soft ferromagnetic films. At the cross-over from symmet- [email protected] ric Néel to asymmetric Néel and Bloch wall, we derive a reduced model that confirms an optimal splitting of the minimal energy into a numerically accessible contribution MS78 from a stray-field free wall-core, and an explicit contribu- Kinetic Monte Carlo Simulations of Multicellular tion from the logarithmic tails of a symmetric Néel wall Aggregate Self-Assembly in Biofabrication that complete the rotation.

We present a three-dimensional lattice model to study self- Lukas D¨oring assembly and fusion of multicellular aggregate systems by Max Planck Institute for Mathematics in the Sciences using kinetic Monte Carlo (KMC) simulations. This model Leipzig is developed to describe and predict the time evolution of [email protected] postprinting morphological structure formation during tissue or organ maturation in a novel biofabrication process Radu Ignat (or technology) known as bioprinting. In this new tech- MS13 Abstracts 115

Universite Paris 11 (Orsay) Arseni Goussev [email protected] Northumbria University [email protected] Felix Otto Max Planck Institute for Mathematics in the Sciences Leipzig, Germany MS80 [email protected] Numerical Simulation of Dewetting of Nan- odroplets

MS79 Abstract not available at time of publication. Boundary Vortices in Micromagnetics Shahriar Afkhami We study the asymptotic behavior of boundary vortices Department of Mathematical Sciences and their interaction energy in a certain regime of thin- New Jersey Institute of Technology film micromagnetics. The key tool relies on the notion of [email protected] “boundary Jacobian” which detects the topological defects at the boundary. The concentration of the energy around MS80 boundary vortices is proven via a Gamma-convergence result and we determine the renormalized energy that repre- Theoretical Modeling of Droplet Breakup and Gen- sents the interaction between the boundary vortices leading eration in Microfluidic Devices to their optimal position. The major difficulty consists in Abstract not available at time of publication. estimating the nonlocal part of the micromagnetic energy generated by the static Maxwell equation in order to detect Alexander M. Leshansky the exact terms corresponding to the topological defects Technion -IIT Department of Chemical Engineering Radu Ignat [email protected] Universite Paris 11 (Orsay) [email protected] MS80 Matthias Kurzke Assembly of Anisotropic Particles at Interfaces Institute for Applied Mathematics, University of Bonn Bonn, Germany Abstract not available at time of publication. [email protected] Kathleen Stebe University of Pennsylvania MS79 Department of Chemical and Biomolecular Engineering Ferromagnetism Modeling: from Micro-Scale to [email protected] Meso-Scale In this presentation we will focus on the link between the MS80 micro-scale and the meso-scale for ferromagnetic models. Self-Similar Rupture in Marangoni-Driven Thin The micro-scale designates a model where atom kernels are Fluid Sheets assimilated to point-wise magnetic charges and the mesoscale is the model of micromagnetism. Starting from the We derive a system of equations that govern the dynamics micro-scale description, we will give a stochastic descrip- of a symmetrically heated thin incompressible viscous fluid tion of heat effects. In the following, we will expose the sheet. We take surface tension to be temperature depen- link between the micro and meso-scale. dent and so the streamwise momentum equation includes thermocapillarity, inertia, viscous stresses and capillarity. Stéphane Labbé This system reduces to two of our previous models in the Université de Grenoble, France limit of large and small Reynolds number respectively. In [email protected] both limiting cases, we find conditions under which sufficiently large-amplitude initial temperature profiles induce film rupture in finite time, notably without the inclusion MS79 of disjoining pressures from van der Waals effects. In the Domain Wall Motion in Ferromagnetic Nanowires case of large Reynolds number, the similarity solution is governed by a balance of inertia and capillarity near the We study the dynamics of magnetic domain walls in ferro- rupture location, analogous to the isothermal case. In the magnetic nanowires under the influence of external mag- case of small Reynolds number, the thermocapillary tran- netic fields and currents. We investigate properties of the sients induce the same similarity solution over intermediate traveling wave and oscillating solutions of the Landau- times that is found for the drainage of lamellas in foams. Lifshitz-Gilbert equation. For O(1) Reynolds numbers, the dynamics are governed initially by the large Reynolds number evolution, and then Valeriy Slastikov a transition over several orders of magnitude in the sheet University of Bristol thickness needs to take place before the small Reynolds Bristol, UK number similarity solution is observed. [email protected] Burt S. Tilley Jonathan Robbins Mathematical Sciences Department University of Bristol Worcester Polytechnic Institute [email protected] [email protected] 116 MS13 Abstracts

MS81 Mariapia Palombaro Local and Non-Local Continuum Limits of Energies University of LAquila (Italy) for Spin Systems [email protected]

I will present some recent result about the asymptotic be- Anja Schlömerkemper havior, as the lattice size tends to 0, of a general class of University of Wuerzburg (Germany) energies of spin systems defined by mixing ferromagnetic [email protected] and antiferromagnetic type potentials accounting also for long-range interactions. Under very general assumptions on the potentials, the macroscopic limit is described by MS81 interfacial energies of perimeter type. I will also provide Asymptotic Analysis of Prestrained Materials some examples in which the macroscopic limit is a non local type functional. Abstract not available at time of publication. Roberto Alicandro Marta Lewicka Università di Cassino Department of Mathematics DAEIMI University of Pittsburgh [email protected] [email protected]

Nadia Ansini [email protected] MS82 Global Estimation of the Critical Time Step for Maria Stella Gelli Peridynamic Models UniversitàdiPisa Stability in explicit transient dynamic simulations is con- Dipartimento di Matematica tingent on a sufficiently small time step. While numer- [email protected] ous approaches have been explored for problems in classical solid mechanics, calculation of the critical time step MS81 for many peridynamic models remains unexplored. We present a global time step estimate for peridynamic models Atomistic Energy Minimization and Wulff Shapes based on the Lanczos method. Because the Lanczos-based In many situations, atoms self-assemble into specific value of the critical time step is derived from an eigenvalue shapes, governed by preferred solid-vapour interface ori- analysis of the stiffness matrix, its application to simula- entations. I will explain the recent rigorous results (joint tions involving arbitrary peridynamic constitutive models with Au Yeung and Schmidt, Calc.Var.PDE 44, 81-100, is straightforward. In the case of a bond-based elastic ma- 2012) that (i) atomistic ground states of 2D short-range terial model, this allows for direct comparison against the pair potentials form clusters of constant density whose in- critical time step derived by Silling and Askari [2005]. In dicator function belongs to the space BV of functions of addition to bond-based elastic models, we present an eval- bounded variation (ii) ground states of the 2D Heitmann- uation of the Lanczos estimate for state-based and non- Radin model form regular hexagons which are the optimiz- ordinary state-based material models. Analyses include a ers of a Wulff-Herring surface energy which emerges as the benchmark simulation of wave propagation in a bar, as well Gamma limit of the atomistic model. I will then discuss as a more complex simulation involving pervasive material difficulties, as well as some progress, regarding generalizing failure. The Lanczos global time step estimate is shown to these results to 3D. be a viable means for computing the critical time step in peridynamic simulations. Gero Friesecke Centre for Mathematical Sciences David Littlewood, Timothy Shelton, Jesse Thomas Technische Universität München, Germany Sandia National Laboratories [email protected] [email protected], [email protected], [email protected]

MS81 MS82 A Discrete-to-Continuum Model for Thin Rods Made from a Biphase Material Peridigm: A New Paradigm in Computational Peridynamics We discuss an atomistic model for heterogeneous nanowires, allowing for dislocations at the interface. We Peridynamics is a nonlocal extension of classical solid me- study the limit as the atomic distance converges to zero, chanics suitable for modeling the failure and fracture of considering simultaneously a dimensional reduction and engineering materials. The classical theory of continuum the passage from the discrete to the continuum. Employing mechanics is based on partial differential equations. These the notion of Gamma-convergence, we establish the mini- equations do not hold on crack surfaces and other singulari- mal energies associated respectively to an elastic (defect- ties, as partial derivatives are not defined at discontinuities. free) configuration and a configuration with dislocations In the classical theory, cracks are regarded as a pathological at the interface. This shows under which conditions the solution requiring special treatment. In contrast, the peri- dislocations are favoured. dynamic theory is based on integral equations, for which discontinuous functions present no difficulty. By utilizing Giuliano Lazzaroni integral equations, the peridynamic theory avoids the need Institute for Mathematics for the special techniques of fracture mechanics. In peridy- University of Wuerzburg namics, cracks are just another kind of solution and require [email protected] no special treatment. We provide an overview and intro- duction to Peridigm, a new open-source massively parallel MS13 Abstracts 117

code for computational peridynamics. We survey the capa- MS83 bilities of Peridigm, showing demonstration computations On the Computation of Optical Force and Stress in and highlighting several applications. We then discuss the Metamaterials numerical techniques used in Peridigm to solve the integro- differential equations of peridynamics, and end by present- We will talk about the theory of the light induced force ing our current and future development directions. and stress. We show that some non-diffracting beams can attract particles with simultaneous electric and magnetic Michael L. Parks, David J. Littlewood, John A. Mitchell responses. We will then address the question of light in- Sandia National Laboratories duced stress inside a metamaterial. We find that the ef- [email protected], [email protected], fective permittivity and permeability do not give sufficient [email protected] information to determine the force density inside a metamaterial and we show that how the required additional Stewart A. Silling parameters can be calculated semi-analytically. Multiscale Dynamic Material Modelling Sandia National Laboratories C. T. Chan [email protected] Dept. of Physics, HKUST, Clear Water Bay, Kowloon, Hong Kong, China [email protected] MS82 A Comparison of Concurrent Multiscale Methods in Peridynamics MS83 Amplitude Activated Acoustic Metamaterial The peridynamic theory of solid mechanics is a generalization of classical continuum mechanics. The governing The acoustic metamaterial structure contains an assem- equation in peridynamics is an integro-differential equation blage of bistable elastic links that loose stability when the without spatial derivatives of displacement fields, in con- amplitude of the acoustic signal reaches a threshold and trast to classical models based on partial differential equa- the excited inner high-frequency oscillations dissipate the tions. Discontinuous displacement fields do not represent a acoustic energy. The material transmits signals with low challenge in peridynamics; as a consequence, peridynamics magnitude but stops highamplitude signals: One can hear has been applied to the description of material failure and a whisper but not a roar. damage. As a nonlocal model, peridynamics is computationally more expensive than classical models; this moti- Elena Cherkaev vates the development of concurrent multiscale methods, University of Utah for which peridynamics is applied on regions where dis- Department of Mathematics continuities appear or may be generated, whereas classical [email protected] models are used elsewhere. A main challenge in concurrent multiscale modeling is how to couple different models Andrej V. Cherkaev without introducing spurious effects. We present different Department of Mathematics concurrent coupling methods for peridynamics and classi- University of Utah cal elasticity and compare these methods with respect to [email protected] different quantities of interest. Pablo Seleson MS83 ICES Wave Propagation in Multiple Scattering Media The University of Texas at Austin Near Resonances: Scaling and Universality [email protected] The propagation of electromagnetic waves in a medium made of parallel dielectric rods is studied in the vicinity of MS82 the Mie resonances of the rods. It is shown that in the low Variable Length Scale in a Peridynamic Body frequency domain the Maxwell equations can be homogenized, which leads to an equivalent permittivity and more In applications of peridynamics, it is sometimes desirable surprisingly to an effective permeability. It is demonstrated to have a different value of the horizon in different subre- that the magnetic resonance is a switch for the existence gions of a body. However, unintended effects can appear of a high density of states.The effect of spatial dispersion in solutions with a position-dependent horizon. This talk and the properties of universality and scaling are also in- will describe recent work on scaling the material model as vestigated a function of horizon to minimize these effects. It will also discuss a means for modifying the peridynamic nonlocal Didier Felbacq operator to minimize artifacts in regions where the hori- GES UMR CNRS 5650 zon is changing. [email protected] Stewart Silling Sandia National Laboratories MS83 [email protected] From Asymptotic Models of Structured Plates to Control of Seismic Waves Pablo Seleson University of Texas at Austin Abstract not available at time of publication. [email protected] Sebastien Guenneau Institut Fresnel, UMR CNRS 6133 [email protected] 118 MS13 Abstracts

MS84 Syracuse University Undulatory Swimming in Complex and Heteroge- Physics Department neous Media [email protected] Many fluids in which microorganisms move, feed, and reproduce are complex and possess an internal structure. MS85 Examples include wet soil, mucus, gels, and tissues. In Theory-Based Benchmarking of Blended Quasicon- this talk, we experimentally investigate the effects of poly- tinuum Methods mer concentration, spanning the dilute to the concentrated regimes, on the swimming behavior of the nematode Multiscale computational methods for materials need to be Caenorhabditis elegans. Results show a 40% increase in the validated by benchmark numerical experiments designed nematodes swimming speed once immersed in a concen- and evaluated on the basis of theoretical error analysis. We trated solution; that is, the propulsion speed is enhanced have shown that optimized blended quasicontinuum meth- by fluid viscosity. This enhancement seems to be related ods can be formulated and practically implemented for gen- to the dynamics of rod-like polymer networks formed in eral many-body interactions with a controllable error and concentrated solutions. with the same (or nearly the same) order of complexity as consistent methods. Paulo E. Arratia Mechanical Engineering and Applied Mechanics Mitchell Luskin University of Pennsylvania, Philadelphia. School of Mathematics [email protected] University of Minnesota [email protected]

MS84 Xingjie Helen Li Reverse Engineering the Euglenoid Movement Brown University xingjie [email protected] Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large am- Christoph Ortner plitude highly concerted deformations of the entire body University of Warwick (euglenoid movement or metaboly), poorly understood as [email protected] compared to cilliary or ﬂagelar locomotion. We investigate the kinematics and hydrodynamics of such motions with statistical learning and continuum mechanics. We ex- Alexander Shapeev amine the shape morphing mechanism of euglenids, which University of Minnesota could be extended to engineering systems. [email protected] Marino Arroyo Brian Van Koten Universitat Politecnica de Catalunya UCLA [email protected] [email protected]

Luca Heltai SISSA: International School for Advanced Studies MS85 Trieste, Italy The Failure of the Continuum Theory to Evaluate [email protected] the Elastic Energy of a Strained Alloy It is established by an exact solution of a ball and spring Daniel Millan model of a binary alloy that continuum theory fails to pre- Universitat Politecnica de Catalunya dict its elastic energy. This result also shows that ﬁnely [email protected] mixed alloys tend to have more elastic energy than segre- gated systems, which is the opposite of predictions made by Antonio DeSimone continuum theories. Results using density-functional the- SISSA, Trieste, Italy ory are in qualitative agreement. This work demonstrates 34014 Trieste, ITALY that it is critical to include the microscopic arrangements [email protected] in any elastic model to achieve even qualitatively correct behavior.

MS84 Peter Smereka Phase Separation and Jamming of Active Particles Department of Mathematics University of Michigan Experiments on conﬂuent layers of epithelial cells and self- [email protected] propelled colloids have motivated interest in the behavior of active matter at high density, where the interplay of Arvind Baskaran steric repulsion and activity can yield active glassy and Department of Mathematics solid states. In this talk I will discuss the behavior of University of California, Irvine dense collections of self-propelled particles in two dimen- [email protected] sions. I will show that the suppression of self-propulsion due to steric repulsion yields phase separation of a dense active ﬂuid in solid-like and gas phases in the absence of Christian Ratsch any aligning or attractive interaction and discuss the rele- UCLA vance of this phenomenon to recent experiments. Department of Mathematics [email protected] M. Cristina Marchetti MS13 Abstracts 119

MS85 Peter Smereka Atomistic and Continuum Simulation of Size Ef- Department of Mathematics fects in Polycrystalline Metal Deformation University of Michigan [email protected] Polycrystalline nanowires are interesting for exploring size effects in deformation. The three important length scales are grain size d, sample diameter D, and sample length MS87 L. I present very large scale molecular dynamics simula- Collision Rates for the Dynamics of Interacting tions of these materials and use these to develop an ana- Slipping Droplets lytical model for sample length effects, determine the role of these scales on deformation mechanism and failure and Reduced ODE models describing collision dynamics of use these to propose a new dislocation dynamics model for droplets in nanometric polymer film interacting on solid polycyrstalline materials. substrate in the presence of large slippage at the liquid/solid interface are derived from one-dimensional lu- David J. Srolovitz brication equations. In the limiting case of the infinite University of Pennsylvania slip length a collision/absorption model then arises and is [email protected] solved explicitly. The exact collision law is derived. Ex- istence of a threshold at which the collision rates switch Zhaoxuan Wu, Siu Sin Jerry Quek, YongWei Zhang from algebraic to exponential ones is shown. Institute of High Performance Computing [email protected], [email protected], Georgy Kitavtsev [email protected] Max Planck Institute for Mathematics in the Sciences Inselstrasse 22, 04103, Leipzig, Germany [email protected] MS85 A Continuum Model for Dynamics of Disloca- MS87 tion Arrays and Applications to Low Angle Grain Boundaries On the Coarsening Rates for Attachment-limited Kinetics We present a continuum model for dynamics of dislocation arrays. The continuum model is derived rigorously from We study the coarsening rates for attachment-limited ki- the discrete dislocation dynamics model using asymptotic netics during solidification processes which is mathemati- analysis. The obtained continuum model contains an in- cally modeled by volume-preserving mean-curvature flow. tegral over the dislocation array surface representing the Experiments, numerical simulations, and heuristics suggest long-range interaction of dislocations, and a local term that that the typical domain size of solid islands in an un- comes from the line tension effect of dislocations. We also dercooled liquid phase grow according to the power law ∼ 1/2 present numerical simulations using this continuum model t ,whent denotes time. We focus on the two- including applications to dislocation structures of low angle dimensional case. Using the Kohn–Otto method, we prove grain boundaries. a one-sided, time-averaged version of this coarsening rate, which is relevant and new for relatively sparse configura- Xiaohong Zhu tions. The bound is uniform in the sense that we do not Jinan University impose any explicit assumptions on the initial data. How- [email protected] ever, during the evolution, we have to assume that collisions of different islands are rare events. This is joint work Yang Xiang with Luca Mugnai. Hong Kong University of Science and Technology Christian Seis [email protected] University of Toronto [email protected] MS87 Simulations of Polycrystalline Grain Growth with MS87 Unequal Surface Energies Coarsening in Grain-boundary Networks and in a An extension of the distance function-based diffusion- Gradient Flow of Voronoi Diagrams generated motion algorithm for the simulation of polycrys- Many materials have polycrystalline structure – they con- talline grain growth is presented. Well-resolved simulations sists of many small crystallites (grains) of different shapes beginning with over 600,000 grains in two dimensions are and orientations. Under appropriate conditions the grain performed. The effect of the initial texture and the form of boundaries move to reduce the interfacial energy. This cur- the surface energy on the long-time evolution of the mis- vature driven evolution, causes some grains to grow, while orientation distribution is studied, and comparisons to ex- others get smaller and disappear. The typical grain size perimental data are presented. grows, while the number of grains is decreasing. One of the Matt Elsey immediate questions is to say what us the rate at which the Courant Institute grain-boundary network coarsenes. While there are heuris- New York University tic arguments that predict the rate of coarsening, obtaining [email protected] rigorous results that hold for arbitrary initial network has turned out to be difficult. Here we present rigorous upper bound on the rate of coarsening that holds under some mild Selim Esedoglu geometric assumptions on the network. We also introduce University of Michigan and study the coarsening of a gradient flow of Voronoi dia- [email protected] grams. For such systems we show a universal upper bound 120 MS13 Abstracts

on the rate of coarsening. Furthermore we carry out nu- ity. merical simulations that conﬁrm that the upper bound is sharp in terms of scaling. Jinhae Park Seoul National University Matthew Elsey Seoul, South Korea Max Planck Institut Leipzig [email protected] [email protected]

Dejan Slepcev MS89 Carnegie Mellon University Highly Accurate Numerical Solutions of Dirac [email protected] Equations Abstract not available at time of publication. MS88 Sihong Shao Phase Separation of Multiple Ginzburg-Landau Peking University Vortices Pinned by Small Holes [email protected] We consider a homogenization problem for magnetic GL functional in domains with a large number of small holes. MS89 For sufficiently strong magnetic field, a large number of vortices are pinned by the holes. We establish a scaling Coarse-Graining Density Functional Theory relation between sizes of holes and the magnitude of the We present a real-space formulation for coarse-graining external magnetic field when pinned vortices form a hier- Density Functional Theory that significantly speeds up archy of nested subdomains with different multiplicity that the analysis of material defects without appreciable loss manifests a physical phenomenon of vortex phase separa- of accuracy. The proposed technique consists of two steps. tion. First, we develop a linear-scaling method in terms of quan- Leonid Berlyand tities amenable to coarse-graining. Next, we introduce a Penn State University spatial approximation scheme which is adapted so as to Eberly College of Science furnish fine resolution where necessary and to coarsen else- [email protected] where. We validate the formulation through selected examples. Volodimir Rybalko Phanish Suryanarayana Institute for Low Temperature Physics and Engineering, Georgia Institute of Technology Kharkov, Ukraine [email protected] v [email protected]

MS89 MS88 Adaptive Regularized Self-Consistent Field Itera- Layer Undulations in 2D and 3D Smectic Liquid tion with Exact Hessian for Electronic Structure Crystals Calculation

We study the Landau-de Gennes free energy to describe We regularize the self-consistent field (SCF) iteration for the undulations instability in smectic A liquid crystals sub- minimizing the Kohn-Sham total energy functional subject jected to magnetic fields. If a magnetic field is applied to orthogonality constraints and establish rigorous global in the direction parallel to the smectic layers, an insta- convergence to first-order optimal solutions. The Hessian bility occurs above a threshold magnetic field. When the of the total energy functional is further exploited. By magnetic field reaches this critical threshold, periodic layer adding the part of the Hessian which is not considered in undulations are observed. We prove the existence and sta- SCF, our methods can obtain highly accurate solutions on bility of the solution to the nonlinear system of Landau-de problems for which SCF fails and achieve a better conver- Gennes model using bifurcation theory. We also perform gence rate than SCF in the KSSOLV toolbox. numerical simulations to illustrate the results of our analysis. An efficient numerical scheme for some free energy Michael Ulbrich containing the second order gradient will be presented. Un- Technische Universitaet Muenchen dulation instabilities on three dimensional systems will be Chair of Mathematical Optimization also discussed. [email protected]

Sookyung Joo Zaiwen Wen Old Dominion University Department of Mathematics [email protected] Shanghai Jiaotong University [email protected] MS88 Analysis of Ferroelectric Liquid Crystals Andre Milzarek Technische Universitaet Muenchen In this talk, we discuss some mathematical problems of Fer- Chair of Mathematical Optimization roelectric Liquid Crystals when the induced electric ﬁeld [email protected] appears to be in the system. we begin with a brief intro- duction and discuss existence theorem and partial regular- Hongchao Zhang Department of Mathematics and CCT Louisiana State University MS13 Abstracts 121

[email protected] this method using Langevin dynamics.

Richard James MS90 Department of Aerospace Engineering and Mechanics Imprimitivity in Non-Crystallographic Nets University of Minnesota [email protected] Periodic nets are commonly used to represent the topology of crystal structures. Some properties of non- Henrik van Lengerich crystallographic nets with non-trivial finite blocks of im- University of Minnesota primitivity for bounded automorphisms will be briefly dis- [email protected] cussed as well as the consequences for the respective la- belled quotient graphs. The concepts of equivoltage par- titions and correlation groups will be thoroughly worked MS90 out using the net associated to a newly reported sphere Why Topology Matters to Crystal Engineers packing as an example. The structure and properties of metal-organic materials Jean-Guillaume Eon (MOMs) have made them an attractive class of materi- Institute of Chemistry als for various applications including carbon capture and Universidade Federal do Rio de Janeiro methane storage. MOMs are amenable to design using the [email protected] “node and linker’ approach and they are typically classi- fied according to their connectivity or topology. This paper Montauban Moreira de Oliveira Jr will highlight why certain topologies are particularly salient Institute of Exact Sciences because they represent blueprints for families of porous Universidade Federal Rural do Rio de Janeiro MOMs, i.e. they enable materials scientists to think as [email protected] architects.

Mike Zaworotko MS90 Department of Chemistry Tangled Nets University of South Florida [email protected] Self-tangled nets have been reported in molecular frame- works. Knot theory allows us to explore the entanglement of loops. A corresponding toolkit for entangled nets is more MS92 subtle and far less developed. We define the ”untangled” Hysteresis in a Constrained Model for Magnetic ground state of nets via their barycentric embedding ion Shape Memory Alloys 3-space. These may contain knots. In contrast, knot-free net embeddings may be untangled. These ideas can be In a constrained model for magnetic shape memory alloys explored via simpler graphs, such as polyhedral graphs, we show loading paths where hysteresis cycles can be ob- whose simpler tangled versions can be enumerated from served. The occurrence of these cycles can be related to reticulations of the torus. Infinite three-periodic nets can the microstructures formed by the magneto-elastic phases. also be entangled. These can also be generated from reticulations of hyperbolic surfaces. Antonio Capella Kort Universidad Nacional Autónoma de México Stephen Hyde [email protected] RSPhysSE Australian National University [email protected] MS92 Geometric Compatibility, Quasiconvexity and Nu- Toen Castle cleation Australian National University Remarkable experimental observations of Hanus Seiner, [email protected] in which austenite is nucleated in martensite by localized heating in a rectangular specimen of a CuAlNi single crys- Myfanwy Evans tal, clearly demonstrate the important role of geometric Universitaet Erlangen-Nuernberg compatibility between phases in the nucleation process. [email protected] This talk proposes an explanation for the experimental observations in terms of quasiconvexity conditions in the interior and the boundary of a bar-shaped domain. This is MS90 joint work with John Ball. Self Assembly and the Structure of Matter Konstantinos Koumatos We describe recent work on a strategy for designing Oxford Centre for Nonlinear PDE molecules that leads to efficient self-assembly of nanos- Oxford University tructures. The method is based on the use of discrete [email protected] groups of isometries. The method has the potential to design molecules that assemble into structures of preassigned John Ball dimensions and functionality. The method is aided by a University of Oxford different classification of discrete groups of isometries than [email protected] the conventional one underlying the International Tables of Crystallography, that better reveals the dependence on parameters of the isometries. We present some preliminary results of a study of the kinetics of self-assembly based on 122 MS13 Abstracts

MS92 [email protected] Emergence of Rate Independence in Gradient Flows with Wiggly Energies Stefano Sacanna, David Pine, Paul Chaikin CSMR-NYU We show that continuum models for plasticity can be de- [email protected], [email protected], [email protected] rived as rigorous limit starting from a discrete microscopic model describing a visco-elastic chain with quenched disorder. The constitutive structure changes as a result of MS93 two concurrent limiting procedures: the vanishing-viscosity Analysis and Simulation of Model for Active Ne- limit and the discrete to continuum limit. References: matic Suspensions Mielke, Truskinovsky, From discrete visco-elasticity to continuum rate-independent plasticity. Archive for Ratio- In this presentation, I will give a brief report on the anal- nal Mechanics and Analysis 203, 2012; Mielke, Emergence ysis of a model for active nematic suspensions in various of rate-independent dissipation from viscous systems with material regimes. Numerical results on model predictions wiggly energies. Continuum Mechanics and Thermody- in more complicated regimes where analysis is not available namics 24, 2012. will be discussed. 2-D numerical simulation of interfacial instability in active nematic suspension fluids will be stud- Alexander Mielke ied using a high order numerical method. Different mode Weierstrass Institute for Applied Analysis and Stochastics of activities can significantly alter the classical capillary Berlin instability in droplet and filament of the active nematic [email protected] suspension material.

Leo Truskinovsky Qi Wang Ecole Polytechnique University of South Carolina [email protected] [email protected]

Xiaogang Yang MS93 Nankai University Hydrodynamic Suppression of Phase Separation in [email protected] Active Suspensions Xiaofeng Yang We simulate a suspension of active squirming disks over the University of South Carolina full range of volume fractions from dilute to close packed, [email protected] with full hydrodynamics in two spatial dimensions. By doing so we show that ”motility induced phase separation” (MIPS), recently proposed to arise generically in active MS93 matter, is strongly suppressed by hydrodynamic interac- Dynamics of Polyelectrolyte Gels tions. We give an argument for why this should be the case, supported by counterpart simulations of active Brownian Abstract not available at time of publication. disks in a parameter regime more closely akin to hydrodynamic suspensions than in previous studies. Lingxing Yao University of Minnesota Suzanne Fielding [email protected] Department of Physics Durham University, UK suzanne.fi[email protected] MS94 Quasiatomistic Method for Molecular Mechanics Model MS93 Out-of-Equilibriumness of Light Activated Colloids Quasiatomistic method (finite element approximation) is used for studying the molecular mechanics model. Two Self-propelled micro-particles are intrinsically out-of- efficiency issues are investigated. One is the optimal com- equilibrium. This renders their physics far richer than putational complexity in multigird with mesh refinement. that of passive colloids while relaxing some thermodynam- The other one is the good approximation accuracy by en- ical constraints and give rise to the emergence of com- riching bases from Krylov subspace. plex phenomena e.g. collective behavior, swarming We will present a new form of self-assembly originating from Jingrun Chen non-equilibrium driving forces. When activated by light, a University of California, Santa Barbara set of new self-propelled particles spontaneously assemble [email protected] into living crystals which behaves as ” self-propelled colloidal carpets” steerable with an external magnetic field. Carlos Garcia-Cervera We will show that this phenomenon is intrinsically out- Mathematics, UCSB of-equilibrium and originates in the competition between [email protected] self-propulsion, particles collisions and attractive interactions.The applications and the use of this system for col- Xiantao Li loidal cargo transportation in microfluidic will also be dis- Department of Mathematics cussed. Pennsylvania State University Jeremy Palacci [email protected] Department of Physics New York University MS13 Abstracts 123

MS94 disordered materials. Crack Initiation and Propagation: A Bifurcation Study Eric Cances Ecole des Ponts and INRIA, France Crack propagation and kinking are two important mech- [email protected] anisms for crack growth. In this talk I will present some results of bifurcation analysis based on a two-dimensional lattice model. In particular, I will show how the loading MS95 modes affects such mechanisms. A New Framework for the Interpretation of Mod- ulated Martensites in Shape Memory Alloys Xiantao Li Department of Mathematics Shape memory alloys (SMAs) are a class of materials Pennsylvania State University with unusual properties that have been attributed to the [email protected] material undergoing a Martensitic Phase Transformation (MPT). An MPT consists of the material’s crystal structure evolving in a coordinated fashion from a high symme- MS94 try austenite phase to a low symmetry martensite phase. The Climbing String Method for Saddle Point Often in SMAs, the austenite is a B2 cubic configura- Search tion that transforms a Modulated Martensite (MM) phase. MMs are long-period stacking order structures consisting The string method was originally designed for computing of [110]cubic basal planes. First-principles computational minimum energy paths between two minima of a potential results have shown that the minimum energy phase for energy. It evolves a continuous curve in the path space by these materials is not a MM, but a short-period structure the steepest descent dynamics. In this talk, we discuss how called the Ground State Martensite. It is commonly ar- the string method can be modified to find saddle points on gued that energy contributions associated with kinematic the boundary of the basin of a given minimum. Compared compatibility constraints at the austenite-martensite inter- to the existing algorithms, this new method has the advan- face explain the experimental observation of meta-stable tage that the computed saddle points are guaranteed to be MMs, as opposed to the expected Ground State Marten- directly connected to the minimum. We will also discuss site phase. To date, a general approach for predicting the how the convergence can be accelerated using an inexact properties of the MM structure that will be observed for Newton method in the late stage of the computation. a particular material has not been available. In this work, we develop a new framework for the interpretation of MMs Weiqing Ren as natural features of the material’s energy landscape (ex- National University of Singapore and IHPC, A-Star pressed as a function of the lattice parameters and indi- [email protected] vidual atomic positions within a perfect infinite crystal). From this energy-based framework, a new understanding of MMs as a mixture of two short-period Base Martensite MS95 phases is developed. Using only a small set of input data Non-Associated Plastic Flow in Crystalline Solids associated with the two Base Martensites, this MM Mix- ture Model (M4) is capable of accurately predicting the Experimental evidence that non-associated flow appropri- energy, lattice constants, and structural details of an arbi- ately characterizes dislocation glide has existed for some trary Modulated Martensite phase. This is demonstrated time, but not until atomistic simulations became suffi- by comparing the M4 predictions to computational results ciently refined have we been in a position to build rigorous from a particular empirical atomistic model. continuum theories for single and polycrystals. At all levels, non-associated flow is shown to persist and significantly Ryan S. Elliott affect strain localization. Under certain deformation his- University of Minnesota tories, intermittent bursts of strain are predicted, which [email protected] is somewhat surprising. Key features of the theory are in accord with experiments. MS95 John Bassani Modeling Plastic Flow at Interfaces and in Glassy Mechanical Engineering and Applied Mechanics Polymers University of Pennsylvania [email protected] The talk will first discuss contact of fractal surfaces with roughness on a wide range of scales. The amount of plastic deformation at the surface is strongly dependent on the MS95 detailed atomistic structure and the degree of adhesion. A The Supercell Method in Atomic Scale Simulation multiscale approach is applied with a fully atomistic treat- of Materials ment at the interface. Long range deformations in the bulk are captured using a Greens function based on the quasi- The supercell method is the standard approach in atomic harmonic approximation that provides seamless boundary scale simulation of bulk properties of materials in the con- conditions for the atomistic region. The second part of the densed phase. It consists in simulating a microscopic sam- talk will discuss coarse-grained models of glassy polymers. ple of the materials contained in a (typically) cubic box, Potentials derived from equilibrium simulations provide a called the supercell, with periodic boundary conditions in poor description of the plastic flow stress. The origins of order to get rid of surface effects. In some respects, it is this discrepancy and methods to correct for it by alternat- similar to the representative volume element (RVE) coming between coarse and fine grained simulations will be de- monly used in mechanics. In this talk, I will present some scribed. Supported by NSF Grant No. DMR-1006805 and mathematical and numerical results, and review some open questions, concerning the use of the supercell method to simulate perfect crystals, crystals with local defects, and 124 MS13 Abstracts

ARL/JHU Cooperative Agreement W911NS-12-2-0022. regions called interior and exterior. From this formulation and the comparison of interior and exterior sets between Mark Robbins sub- and super-solution we obtain the stability of a bunch Johns Hopkins University of spirals in the sense of Lyapunov. [email protected] Takeshi Ohtsuka Gunma University MS96 Graduate School of Engineering Threshold Dynamics for Networks with Arbitrary [email protected] Surface Tensions We present a new algorithm for simulating the mean curva- MS97 ture motion of multiple phases subject to arbitrary surface Asymptotic Analysis of Minimizers for the tensions. The departure point is the threshold dynamics Lawrence-Doniach Energy algorithm of Merriman, Bence, and Osher (MBO) in two phases. Our algorithm is based on a new energetic inter- We consider the behavior of minimizers for the Lawrence- pretation of the original MBO scheme. Doniach energy describing layered superconductors in perpendicular megnetic ﬁelds of modulus hex. Assuming that −2 Selim Esedoglu | ln | hex as → 0, where 1/ is the Ginzburg- University of Michigan Landau parameter, we prove an asyptotic formula for the [email protected] energy of a minimizer in terms of the measure of the domain, hex,and as and the interlayer distance s tend to Felix Otto zero. We also prove asymptotic estimates on the behavior Max Planck Institute for Mathematics in the Sciences of minimizers. Our work relies on Ginzburg-Landau the- [email protected] ory, pde estimates, and results on single layer potentials.

MS96 Patricia Bauman,GuanyingPeng On An Interfacial Motion by Surface Diﬀusion Purdue University [email protected], [email protected] The surface diﬀusion equation is one of the mathematical models which describe the thermal grooving in material science. It is a geometric evolution law and represented MS97 as a fourth order parabolic PDE. Also, it has the varia- The Hydrodynamic Limit of the Parabolic tional structure that the perimeter of an enclosed domain Ginzburg-Landau Equation decreases whereas the volume is conserved. In this talk, the stability analysis of equilibrium states on this geomet- We study the parabolic Ginzburg-Landau equation for a ric equation will be studied. complex-valued u, (PGL)

Yoshihito Kohsaka 1 1 2 Muroran Institute of Technology ∂tu =Δu + u(1 −|u| ) | log ε| ε2 Common Subject Division [email protected] for initial data corresponding to n vortices. For a bounded number of vortices, (PGL) induces a motion of vortices by MS96 the gradient flow of a renormalized energy. In the limit n → Stability and Bifurcation of Equilibria to Geomet- ∞, one obtains a hydrodynamic limit equation, formally ric Evolution Laws in the Axisymmetric Setting obtained by E in 1994. In this talk I will explain how one can use explicit estimates for (PGL) valid at fixed ε to We study the nonlinear qualitative structure of solutions rigorously connect (PGL) to E’s limit equation. near equilibria for the surface diffusion flow and averaged mean curvature flow. Working in the particular setting of Matthias Kurzke axisymmetric surfaces, satisfying periodic boundary con- Institute for Applied Mathematics, University of Bonn ditions, we characterize the equilibria of these flows. We Bonn, Germany further discuss how volume conservation and surface area [email protected] reduction, together with a maximal regularity setting, can be utilized to prove nonlinear stability, instability and bi- Daniel Spirn furcation of equilibria. University of Minnesota [email protected] Jeremy LeCrone Vanderbilt University, Nashville [email protected] MS97 Hydrodynamic limit of Gross-Pitaevksy vortices on the plane MS96 Stability of a Bunch of Spirals Evolving with An We consider detailed properties of Gross-Pitaevsky vortices Eikonal-Curvature Flow Equation on the plane. By renormalizing both the Ginzburg-Landau energy and the winding number at infinity, we establish We consider on stability of a bunch of spirals evolving by the vortex motion law for asymptotically large numbers an eikonal-curvature flow equation. In this talk we give of vortices. It is then shown that the vorticity measure a simple level set formulation for spirals and the covering converges to a weak solution to the Euler equations with space so that spirals divide the covering space into two vortex sheet initial data. This is joint work with Robert MS13 Abstracts 125

Jerrard. Brandeis University Department of Physics Daniel Spirn [email protected] University of Minnesota [email protected] John Lowengrub Department of Mathematics MS98 University of California Irvine [email protected] Modeling and Simulation of Nematic Liquid Crys- tal Films MS99 Abstract not available at time of publication. Aspects of Faceting in Epitaxial Relaxation Linda Cummings Department of Mathematical Sciences Below the roughening transition, crystal surfaces develop New Jersey Institute of Technology macroscopic facets. At the microscale, surface evolution is [email protected] driven by the motion of steps. In this talk, I focus on surface relaxation and present recent progress in analytically connecting step flow models in the presence of facets to MS98 continuum-scale variational principles and Partial Differ- Stability of Liquid Rings ential Equations. I address the evaporation-condensation and surface diffusion cases for radial structures. This is Abstract not available at time of publication. joint work with Kanna Nakamura and Joshua Schneider.

Lou Kondic Dionisios Margetis Department of Mathematical Sciences, NJIT University of Maryland, College Park University Heights, Newark, NJ 07102 [email protected] [email protected] MS99 MS98 Kinetic Monte Carlo Models for Nanoclusters and Directed, Liquid Phase Assembly of Patterned Dendrites Metallic Films by Pulsed Laser Dewetting Abstract not available at time of publication. Abstract not available at time of publication. Tim Schulze Philip D. Rack University of Tennessee Department of Material Science and Engineering Department of Mathematics University of Tennessee [email protected] [email protected] MS99 MS98 Symmetry-Breaking in Shape Transitions of Fingering Instability Down the Outside of a Verti- Epitaxially-Strained Islands cal Cylinder During heteroepitaxy, strained islands undergo a series of Abstract not available at time of publication. shape transitions with increasing size. We examine the transition pathway using a model free-boundary problem Linda Smolka and energy minimization, constructing the bifurcation di- Bucknell University agram of possible shapes including saddle-point barrier [email protected] states. We find that island shape transitions occur via sequential nucleation of facets and involve highly asymmetric transition states (eg half-dome) which can be metastable. MS99 In addition, we determine the effect of substrate miscut in Effect of Melt Flow on Morphological Evolution of promoting stable asymmetric shapes. Nanocrystal Nucleates Brian J. Spencer Self assembly of nano-scale structures are of great impor- University at Buffalo tance in modern day materials. This talk aims to address Department of Mathematics the effect of flow on crystallization kinetics of nano-crystals spencerb@buffalo.edu nucleated in a fluid. A Classical Density Functional Theory (CDFT) based hydrodynamic model for systems of inter- Jerry Tersoff acting particles will be discussed. A numerical study of IBM T.J. Watson Research Center the effect of flow on growth and morphological evolution of tersoff@us.ibm.com nano-crystal nucleates will be presented.

Arvind Baskaran MS100 Department of Mathematics Quasistatic Nonlinear Viscoelasticity and Gradient University of California, Irvine Flows [email protected] We study one-dimensional quasistatic viscoelasticity of rate Aparna Baskaran type under hard (Dirichlet) boundary conditions, which 126 MS13 Abstracts

can be expressed as a gradient ﬂow. There are continua of Giuseppe Savare’ equilibria and we prove convergence as time t →∞to one University of Pavia of these under a genericity assumption on the stress, which [email protected] we establish in some interesting cases.

John Ball MS100 Oxford Centre for Nonlinear PDE Mathematical Institute An Approach to Nonlinear Viscoelasticity Via Met- Oxford ric Gradient Flows [email protected] We formulate quasistatic nonlinear viscoelasticity as a gra- Yasemin Sengul dient system. Our focus is a new class of dissipation dis- Ozyegin University tances which are defined using weak diffeomorphisms keep- [email protected]] ing the boundary fixed and ensure frame-indifference of the viscoelastic stress. In order to pass from the time- discretized problem to the time-continuous limit, we need MS100 strong convergence for which we use evolutionary varia- Gradient Structures and Geodesic Convexity for tional inequalities for abstract gradient systems in a one- Reaction-Diffusion System dimensional setting. In this talk I consider systems of reaction-diffusion equa- Yasemin Sengul tions that can be written as gradient systems with respect Ozyegin University, Istanbul to an entropy functional and a dissipation metric. The lat- [email protected] ter is given in terms of a so-called Onsager operator, which is a sum of a diffusion part of Wasserstein type and a re- Alexander Mielke action part. I discuss methods for establishing geodesic Weierstrass Institute for Applied Analysis and Stochastics λ-convexity of the entropy functional by purely differential Berlin methods, thus circumventing arguments from mass trans- [email protected] portation. Christoph Ortner Matthias Liero University of Warwick Weierstrass Institute for Applied Analysis and Stochastics [email protected] [email protected]

Matthias Liero MS101 WIAS Bloch Waves Expansion for High Contrast Homog- [email protected] enization

Alexander Mielke Arrays of infinitely long dielectric rods can produce effec- Weierstrass Institute for Applied Analysis and Stochastics tive media with permeability and permittivity which are Berlin both negative. This has been evidenced in the case of [email protected] s-polarized light (electric field parallel to the axis of the rods) by numerical experiments and nicely explained by the appearance of magnetic and electric dipole resonances MS100 (Didier Felbacq, Physic review Letters 2009). However it Existence Results for Generalized Gradient Sys- seems difficult to deduce this phenomenum in a mathemat- tems with Applications to Finite-Strain Elasticity ical framework by performing the asymptotic analyis of a suitably scaled diffraction problem. The classical two-scale In this talk, we focus on a class of abstract doubly nonlin- method which uses periodic test functions fails and, pass- ear evolution equations in Banach spaces, with a gradient ing to the limit, we lose some important resonances of the structure. The driving energies are nonsmooth and non- system. In this talk I will present an attempt to substi- convex. We enucleate some general sufficient conditions on tute the two-scale approach with a developement in Bloch the dissipation potential and on the energy functional, for waves well adapted to the high contrast case. Let us no- existence of solutions to the related Cauchy problem. The tice that, in the case of classical homogenization without main existence result is obtained by passing to the limit in contrast, the link between this approach and the two-scale a time-discretization scheme with variational techniques, technique has been peformed by Allaire, Conca and Van- inspired by the theory of Minimizing Movements by E. De ninathan, but in their case, only the projection on the first Giorgi. Finally, we discuss an application to a material Bloch mode is useful in order to characterize the homoge- model in finite-strain elasticity. Based on joint work with nized limit. Alexander Mielke and Giuseppe Savaré. Guy Bouchitte Alexander Mielke Universite de Toulon et du Var Weierstrass Institute for Applied Analysis and Stochastics [email protected] Berlin [email protected] MS101 Riccarda Rossi Controlling the Phase and Power Flow of Electro- Department of Mathematics magnetic Fields with Metamaterials University of Brescia [email protected] A method for arbitrarily controlling the phase progression and power flow of electromagnetic fields within a region of space is introduced. Specifically, it is shown how a 2D MS13 Abstracts 127

inhomogeneous, anisotropic medium can be designed that of Lopez-Pamies et al. [Cavitation in elastomeric solids: I supports desired spatial distributions of the wave vector — A defect-growth theory. Journal of the Mechanics and and Poynting vector direction. Plane-wave relations in Physics of Solids 59 (2011), 1464–1487.] with a variety of anisotropic media are used in conjunction with an opti- cavitation experiments with the objective of establishing mization process to ﬁnd the required material parameters. whether the phenomenon of cavitation is an elastic instability (and hence depends only on the elastic properties of Anthony Grbic the rubber), or, on the other hand, a fracture process (and University of Michigan Ann Arbor hence depends on the fracture properties of the rubber). [email protected]

Gurkan Gok Oscar Lopez-Pamies University of Michigan, Ann Arbor University of Illinois at Urbana-Champaign [email protected] Civil and Environmental Engineering [email protected] MS101 Victor Lefevre Cloud Computing for Nanophotonics: Multi- University of Illinois at Urbana-Champaign physics and Ultra-Fast Solvers [email protected] Abstract not available at time of publication. MS102 Alexander V. Kildishev Birck Nanotechnology Center School of ECE Quasistatic Evolution of Cavities in Nonlinear Elas- Purdue University ticity [email protected] Starting with a variational static model for cavitation in nonlinear elasticity, we propose a quasistatic model for the MS101 evolution of the system also based on global minimization. We prove the existence of a quasistatic evolution, which Plasmonic Waves Allow Perfect Transmission of takes into account the non-interpenetration of matter, the Light Through Sub-Wavelength Holes irreversibility of the process of cavity formation, and the Optically active meta-materials can nowadays be con- growth of cavities. In the energy balance equation, a new structed as physical objects. They can have astonishing term appears involving the mean curvature of the cavity properties and can lead to striking effects, the key-words surface. are negative refraction, perfect imaging, and cloaking. This talk is concerned with a mathematical analysis that demon- Carlos Mora-Corral strates how the effect of a negative magnetic permeability Department of Mathematics of the effective material can occur, and how perfect light Univerisity Autonoma transmission through sub-wavelength holes in a metallic [email protected] structure is possible. Mathematically, we analyze the time- harmonic Maxwell equations in heterogeneous media, the MS102 coefficients of the equation can oscillate on a small spatial A Regularized Penalty-multiplier Method for the scale and the contrast can be very large. The heterogene- Computation of Fracture Surfaces in Strain Space ity of the optical medium is prescribed by the permittivity coefficient εη(x), where η>0 is a small parameter that If a body occupies the region Ω ∈ Rn, Ax for x ∈ ∂Ω stands for the typical dimension of spatial oscillations in represents an affine boundary displacement for such a body, ∈ the medium, and x R3 stands for the position in space. and E(·) represents an energy functional (defined on some The electric and the magnetic field Eη and Hη are given appropriate admissible set of deformations of Ω), then the as solutions of the Maxwell system volume derivative is given by:

∇×Eη = iωμ0Hη, E(uV) − E(Ax) ∇×Hη = −iωεηε0Eη, G(A) = lim , V0 V ∈ where ω R is a prescribed frequency and μ0 and ε0 are · given physical parameters. We analyze the weak limits E where uV is a minimizer of E( ) constrained to form a hole of volume V in Ω. For a large class of materials, the onset and H of Eη and Hη andderiveanequationforE and H, the so-called effective equation. The coefficients in the of cavitation–type instabilities can be characterized as the effective equation describe the behavior of the complex ma- zero level set of G. In this talk we describe a regularized terial. We present joint works with G. Bouchittéandwith penalty–multiplier method and its convergence properties A. Lamacz. for the computation of E(uV) above. This method together with a continuation method form the basis for a Ben Schweizer procedure for approximating the zero level set of G.We TU Dortmund present some numerical results that show the effectiveness Fakultät für Mathematik of this procedure versus the more direct approach of using [email protected] a contour finding routine. Pablo Negron MS102 University of Puerto Rico - Humacao Cavitation in Rubber: An Elastic Instability of a [email protected] Fracture Phenomenon? J. Sivaloganathan In this presentation, we will confront the cavitation theory University of Bath 128 MS13 Abstracts

[email protected] [email protected]

Marcello Ponsiglione MS102 Dipartimento di Matematica On the Global Stability of Elastic Cylinders under Universita‘diRomaI Tension [email protected] We consider the uniaxial extension of a three-dimensional, homogeneous, isotropic, hyperelastic cylindrical solid in MS103 which the length of cylinder is prescribed, the ends are as- Continuum Dislocation Theory for Modeling Size sumed to be free of shear, and the sides are left completely Effects in Crystal Plasticity free. We show that standard constitutive hypotheses on the stored-energy function imply that a homogeneous axisym- Experiments reveal ubiquitous size effects arising during metric deformation is the unique absolute minimizer of the plastic deformation of crystalline solids. At mesoscopic elastic energy. Therefore, such constitutive hypotheses are scales, such phenomena are accepted to predominantly incompatible with necks and shear bands. stem from dislocation interactions. We report a simple variational toy model that captures Bauschinger and Hall J. Sivaloganathan Petcheffectsaswellastypicalthin-filmsizeeffects.This University of Bath is accomplished by letting the energy of the microstruc- [email protected] ture enforce a physically-motivated dislocation saturation limit. The model has further been applied to deformation Scott Spector twinning. Southern Illinois University [email protected] Dennis M. Kochmann California Institute of Technology [email protected] MS103 Peierls Stress in Continuum Dislocation Mechanics Chau Le Ruhr-Univeristy Bochum From the time of Peierls’ (1940) classic paper and [email protected] Nabarro’s (1947) extension of that work, it is generally believed that a prediction of a threshold stress for dislocation motion is not possible within any ‘continuum’ pde model, MS103 without inducing the notion of lattice discreteness. We ex- Multiscale Problems in Dislocation Theory plore this conjecture within a pde model for dislocation dynamics. One of the hard open problems in mechanical engineering is the upscaling of large numbers of dislocations. The Xiaohan Zhang talk treats the derivation of continuum dislocation density Carnegie Mellon University models and strain-gradient plasticity models from discrete [email protected] and semi-discrete dislocations theories. The approach we use is Gamma-convergence. An important tool is a gen- Amit Acharya eralisation of the rigidity estimate of Friesecke, James & Civil and Environmental Engineering Müller to fields that are not gradients. We will also dis- Carnegie Mellon University cuss progress and open problems in modelling dislocation [email protected] interactions. Lucia Scardia MS103 School of Mathematics and Statistics Asymptotic Analysis and Dynamics of a System of University of Glasgow Straight Dislocations [email protected]

We consider a discrete variational model for screw disloca- Mark Peletier, Ron Peerlings, Marc Geers tions and exploit the relation with an XY model for spins Technische Universiteit Eindhoven systems. In the passage from discrete to continuum, in [email protected], [email protected], terms of Gamma-convergence, we get a leading term that [email protected] behaves logarithmically in the lattice spacing, while the next order is given by a function of the positions of the dislocations. This function is used to study the dynamics Caterina Zeppieri of a system of screw dislocations. Universität Münster [email protected] Adriana Garroni Universita’diRoma Stefan Müller [email protected] University of Bonn [email protected] Roberto Alicandro Università di Cassino DAEIMI MS104 [email protected] Title Not Available at Time of Publication Abstract not available at time of publication. Lucia De Luca Universita’ Sapienza di Roma Markos A. Katsoulakis MS13 Abstracts 129

UMass, Amherst MS105 Dept of Mathematics Convex Splitting Methods for Nonlocal Models of [email protected] Phase Separation Abstract not available at time of publication. MS104 Title Not Available at Time of Publication Zhen Guan Mathematics Department Abstract not available at time of publication. University of California, Irvine [email protected] Ben Leimkuhler University of Edinburgh School of Mathematics MS105 [email protected] Two Phase Flow in Porous Media Abstract not available at time of publication. MS104 Title Not Available at Time of Publication Xiaoming Wang FSU Abstract not available at time of publication. [email protected] Yiannis Pantazis University of Massachusetts, Amherst MS106 Department of Mathematics and Statistics Energy Driven Pattern Formation in a Non-local [email protected] Ginzburg-Landau/Cahn-Hilliard Energy

This describes joint work with Sylvia Serfaty and Cyrill MS104 Muratov. We study the asymptotic behavior of the Title Not Available at Time of Publication screened sharp interface Ohta-Kawasaki energy in dimension 2 using the framework of G-convergence. In that Abstract not available at time of publication. model, two phases appear, and they interact via a nonlocal Coulomb type energy. We focus on the regime where one TBD TBD,TBDTBD of the phases has very small volume fraction, thus creating TBD “droplets” of that phase in a sea of the other phase. We TBD, TBD consider perturbations to the critical volume fraction where droplets first appear, show the number of droplets increases MS105 monotonically with respect to the perturbation factor, and describe their arrangement in all regimes, whether their Gpu Parallelized Spectral Methods for Phase-Field number is bounded or unbounded. When their number is and Phase-Field-Crystal Models unbounded, the most interesting case we compute the G Abstract not available at time of publication. limit of the ‘zeroth’ order energy and yield averaged information for almost minimizers, namely that the density of Feng Chen droplets should be uniform. We then go to the next order, Brown University and derive a next order G-limit energy, which is exactly the feng chen [email protected] “Coulombian renormalized energy W” introduced in the work of Sandier/Serfaty, and obtained there as a limiting interaction energy for vortices in Ginzburg-Landau. The MS105 derivation is based on their abstract scheme, that serves to A Numerical Analysis of the Cahn-Hilliard Equa- obtain lower bounds for 2-scale energies and express them tion in a Domain with Non Permeable Walls through some probabilities on patterns via the multipa- rameter ergodic theorem. Without thus appealing at all In this talk, I will present a joint work with Madalina Petcu to the Euler-Lagrange equation, we establish here for all (University of Poitiers, France), concerning a numerical configurations which have “almost minimal energy,” the analysis of the Cahn-Hilliard equation, for a binary ma- asymptotic roundness and radius of the droplets as done terial in a bounded domain. We assume that the walls by Muratov, and the fact that they asymptotically shrink bordering the material are permeable, which leads us to to points whose arrangement should minimize the renor- consider the non usual dynamic boundary conditions re- malized energy W, in some averaged sense. This leads to cently introduced by G. Goldstein et al. The equation is expecting to see triangular lattices of droplets. discretized, using a finite element method for the space and the backward Euler scheme for the time discretiza- Dorian Goldman tion. I will discuss different convergence and stability re- Courant Institute (NYU) sults, and obtain errors estimates (between the solutions of [email protected] the discretized and of the continuous problem), depending on whether we assume or relax diffusion along the walls. MS106 Laurence Cherfils On the Shape of Charged Drops: an Isoperimetric Universitè de la Rochelle Problem with a Competing Non-local Term. Laboratoire MIA et département de Mathématiques laurence.cherfi[email protected] I will give an overview of my recent work with C. Mu- ratov on the analysis of a class of geometric problems in the calculus of variations. I will discuss the basic questions of existence and non-existence of energy minimizers 130 MS13 Abstracts

for the isoperimetric problem with a competing non-local Elastomers term and for space dimensions n ¡ 8. A complete answer will be given for the case of slowly decaying kernels in two Abstract not available at time of publication. space dimensions. Kaushik Bhattacharya Hans Knuepfer Howell N. Tyson Sr. Professor of Mechanics University of Bonn California Institute of Technology [email protected] [email protected]

MS106 MS107 Minimality via Second Variation for a Nonlocal From Wrinkles to Scars: Universality of Stress Col- Isoperimetric Problem lapse in Confined Crystalline Sheets We discuss the loca lminimality ofcertain configurations Imposing curvature on crystalline sheets leads to distinct for a non local isoperimetric problem used to model mi- types of structural instabilities. The first type involves the crophase separation in diblock copolymer melts. We show proliferation of localized defects that disrupt the crystalline that critical configurations with positive second variation order, whereas the second type consists of elastic modes, are local minimizers of the nonlocal area functional and, such as wrinkles and crumples, which are common also in in fact, satisfy a quantitative isoperimetric inequality with amorphous sheets. Here we propose a profound link be- respect to sets that are L1- close. The link with local min- tween these types of patterns, encapsulated in a universal, imizers for the diffuse-interface Ohta-Kawasaki energy is compression-free stress field, which is determined solely by also discussed. As a byproduct of the quantitative esti- the macro-scale confining conditions. mate, we get also new results concerning periodic local minimizers of the area functional. Benjamin Davidovich Physics Department Massimiliano Morini University of Massachusetts Amherst Universita degli Studi di Parma [email protected] Parma, Italy [email protected] Gregory M. Grason Polymer Science and Engineering University of Massachusetts Amherst MS106 [email protected] A Double Bubble Solution in a Ternary System with Inhibitory Long Range Interaction MS107 We consider a ternary system of three constituents, a model Asymptotics of a Prototype Lattice Energy under motivated by the triblock copolymer theory. The free en- an Impenetrability Constraint ergy of the system consists of two parts: an interfacial energy coming from the boundaries separating the three We consider the prototype model of particles parameter- constituents, and a longer range interaction energy that ized on a 2-d triangular lattice linked with mearest neigh- functions as an inhibitor to limit micro domain growth. bouring Lennnard-Jones type interactions in presence of We show that a perturbed double bubble exists as a stable an additional incompenetrability constraint. The positive- solution of the system. Each bubble is occupied by one determinant constraint indeed mimics the effect of long- constituent. The third constituent fills the complement of range interactions and, as we focus on a surface scaling of the double bubble. Two techniques are developed. First the associated energies as the lattice size goes to zero, it one defines restricted classes of perturbed double bubbles. limits the ground states to piecewise rigid configurations, Each perturbed double bubble in a restricted class is ob- i.e. piecewise rotations with an underlying partition of the tained from a standard double bubble by a special pertur- domain into sets of finite perimeter. We push forward our bation. The second technique is the use of the so called analysis to determine whether this constraint turns into a internal variables. The advantage of the internal variables (possibly anisotropic) ”opening crack” condition along the is that they are only subject to linear constraints, and per- interfaces. The variational analysis turns out to be rich of turbed double bubbles in each restricted class represented features, among these: an opening crack constraint of novel by internal variables are elements of a Hilbert space. A type that take into account both the gradient of the defor- local minimizer of the free energy in each restricted class mation on both sides of the fracture and the orientation is found as a fixed point of a nonlinear equation. This per- of the fracture sites in the reference configuration; addi- turbed double bubble satisfies three of the four equations tional positive-determinant request on points where more for critical points of the free energy. The unsolved equation fractures meets (triple points); possible overtaking of the is the 120 degree angle condition at triple junction points. previous conditions by adding ”fictitious” micro-fractures. Perform another minimization among the local minimizers from all restricted classes. A minimum of minimizers emerges and solves all the equations for critical points. Maria Stella Gelli UniversitàdiPisa Xiaofeng Ren Dipartimento di Matematica The George Washington University [email protected] Department of Mathematics [email protected] Andrea Braides University of Roma 2, Italy Dipartimento di Matematica MS107 [email protected] Effective Behavior of Thin Films of Liquid Crystal MS13 Abstracts 131

MS107 uum Method Homogenization of the Kirchhoff Bending Theory for Plates The energy-based Blended Quasicontinuum method (BQCE) is an atomistic-to-continuum coupling used to We carry out the spatially periodic homogenization of simulate defects such as cracks and vacancies in crystalline Kirchho?s plate theory. The derivation is rigorous in the materials. I will present a numerical analysis of BQCE. I sense of Gamma-convergence. In contrast to what one nat- will then explain how the analysis can be used to choose urally would expect, our result shows that the limiting optimal approximation parameters for the implementation functional is not simply a quadratic functional of the sec- of BQCE. I will also explain how the analysis leads to novel ond fundamental of the deformed plate. The limiting func- continuum models which can be used in versions of BQCE tional distinguishes between whether the deformed plate is for materials which have multi-lattice structure. locally shaped like a cylinder or not. For the derivation we investigate the oscillatory behavior of sequences of sec- Brian Van Koten ond fundamental forms associated with isometric immer- UCLA sions, using two-scale convergence. To do so, we have to [email protected] treat two-scale convergence in connection with a nonlinear di?erential constraint. Joint work with Stefan Neukamm MS108 (MPIS Leipzig, WIAS Berlin.) Consistent Atomistic/Continuum Coupling Meth- Heiner Olbermann ods Hausdorff Center for Mathematics & Institute for Appl. Math. Atomistic/continuum coupling methods are a class of University of Bonn coarse-graining techniques for the efficient simulation of [email protected] atomistic systems with localized defects. I will show that for general simple crystal lattices, patch test consistency is a necessary and sufficient condition for the first-order con- MS108 sistency of an energy based coupling method. We will con- An Optimization Based Atomistic-to-Continuum struct consistent coupling energy functional by geometric Coupling Method reconstruction on the interface in 2D and 3D. I will remark on the stability of the method. Atomistic-to-continuum (AtC) coupling methods aim to combine the efficiency of continuum models with the ac- Lei Zhang curacy of the atomistic models necessary to resolve local Shanghai Jiao Tong University features. We present a new AtC method which seeks to [email protected] minimize the error between the atomistic and continuum displacement fields over a suitably defined overlap region. Christoph Ortner We provide an error analysis of the method in the context University of Warwick of a 1D linear system with next-nearest neighbor interac- [email protected] tions. Derek Olson PP1 School of Mathematics Algorithm for Linear Programming Involving In- University of Minnesota terval Constraints [email protected] In real optimization, we meet the criteria of useful out- Pavel Bochev comes increasing or expenses decreasing and demands of Sandia National Laboratories lower uncertainty. Therefore, we usually formulate an op- Computational Math and Algorithms timization problem under conditions of uncertainty. In this [email protected] paper, a new method for solving linear programming problems with Interval coefficients in the objective function and the constraints based on preference relations between in- Mitchell Luskin, Alexander V. Shapeev tervals is investigated. To illustrate the efficiency of the School of Mathematics proposed method, a numerical example is presented. University of Minnesota [email protected], [email protected] Ibraheem Alolyan King Saud University [email protected] MS108 Energy-Based Atomistic-to-Continuum Coupling PP1 I will discuss the recent advances in the construction and Constitutive Models for the Macroscopic Re- analysis of the energy-based atomistic-to-continuum cou- sponse and Microstructure Evolution in Particle- pling. Reinforced Elastomers at Finite Strains Alexander V. Shapeev This study presents the application of recently proposed, School of Mathematics homogenization estimates (Avazmohammadi and Ponte University of Minnesota Castañeda; J. Elasticity, 2012) for hyperelastic compos- [email protected] ites consisting of an incompressible matrix and aligned, rigid spheroidal particles, subjected to general (3-D), finite- MS108 deformation loadings. The major results of this study include: (1) the particles tend to orient themselves with the Numerical Analysis of the Blended Quasicontin- largest tensile loading axis, (2) the rotation of particles has 132 MS13 Abstracts

a significant impact on the macroscopic response and can free discontinuity problem, in the context of a variational lead to loss of strong ellipticity. model for epitaxial growth of strained elastic films. We generalize previous results to the three dimensional case and to Pedro Ponte Castaneda nonlinear elastic energies, deriving a minimality criterion University of Pennsylvania expressed in terms of a suitable notion of second variation [email protected] of the functional involved. Applications to the study of stability of flat morphologies are shown. Reza Avazmohammadi Department of Mechanical Engineering and Applied Marco Bonacini Mechanics SISSA - International School for Advanced Studies University of Pennsylvania [email protected] [email protected] PP1 PP1 A Quantitative Second Order Minimality Criterion Multi Stage Approach to Extract Microstructural for Cavities in Elastic Bodies Information in X-Ray Microtomography Images: Case Study of Fully Lamellar Titanium Alloy We consider a functional which models an elastic body with a cavity. We show that if a critical point has positive second (α+β) titanium alloys are widely used in the industry. An variation then it is a strict local minimizer. We also provide important materials science aspect is the understanding of a quantitative estimate. their microstructural properties in relation to damage. No other nondestructive 3D techniques than X-ray microto- Giuseppe Maria Capriani mography can provide these information, provided the use Applied Mathematics Münster of 3D image processing. The current work concentrates University of Münster, Germany on the fully lamellar microstructure and uses directional [email protected] filter bank, edge preserving smoothing combined with discrete geometry analysis to separately segment α-lamellar Vesa Julin colonies and β grain boundaries. Department of Mathematics and Statistics University of Jyvaskyla, Finland Laurent Babout, Lukasz Jopek, Michal Postolski, Marcin vesa.julin@jyu.fi Janaszewski Lodz University of Technology Giovanni Pisante [email protected], [email protected], Dipartimento di Matematica [email protected], [email protected] Seconda Università degli Studi di Napoli, Italy [email protected] PP1 Quasi-Equilibrium Off-Lattice Kinetic Monte Carlo PP1 of Heteroepitaxy Morphological and Mechanical Properties of En- tangled Triblock Copolymer Gels We present an off-lattice kinetic Monte Carlo algorithm in (1 + 1)-dimensions that drives surface diffusion by a chem- A novel dissipative particle dynamics model which includes ical potential gradient. Interactions between atoms are de- a modified segmental repulsive potential was used to elu- fined by the Lennard-Jones potential which removes the cidate the morphological/mechanical properties of triblock lattice restriction on atomic positions enforced by lattice copolymer gels. The micelle size, distance between mi- based models. The method is validated by simulations of celles, and the bridge fraction were calculated as a func- heteroepitaxial growth, annealing of strained bilayer sys- tion of concentration, where only a strong dependence on tems and a qualitative verification of Stoney’s formula. concentration was observed for micelle size. The cross-link and entanglement contribution to the modulus were ex- Henry A. Boateng tracted from deformation simulations and were found to Department of Mathematics qualitatively agree with theoretical predications. University of Michigan [email protected] Tanya L. Chantawansri, Timothy Sirk, Yelena Sliozberg US Army Research Laboratory Tim Schulze [email protected], timo- University of Tennessee [email protected], [email protected] Department of Mathematics [email protected] PP1 Peter Smereka Use of Sensitivity Analysis and Error Analysis to Department of Mathematics Implement Recursively Self-Consistent Programs University of Michigan [email protected] To conquer slowly and unstably oscillatory phenomena produced by stimulating recursively self-consistent calculation, invented scaling approaches, which stop the propagation PP1 errors of the recursive iterations, eliminate or reduce the A Second Order Minimality Criterion for Free Dis- possibilities of producing the oscillatory calculations. To continuity Problems grant a better practical solution at the next step of optimization processes, exploring primary errors is helpful to We present a sufficient condition for local minimality for a understand the sensitive mechanisms of the invented scal- MS13 Abstracts 133

ing approaches. of fibrous EAPCs. We also study the effect of electromechanical instabilities and dielectric breakdown on the Che-Sheng Chung, Sheng-Lyang Jang performance of such actuators. Department of Electronic Engineering National Taiwan University of Science and Technology Morteza Hakimi Siboni [email protected], [email protected] Univercity of Pennsylvania Department of Mechanical Engineering and Applied Mechanics PP1 [email protected] A Quasistatic Evolution Model for Perfectly Plastic Plates Derived by Gamma Convergence Pedro Ponte Castaneda University of Pennsylvania The subject of this poster is the rigorous derivation of a [email protected] quasistatic evolution model for a linearly elastic - perfectly plastic thin plate. As the thickness of the plate tends to zero, we prove via G-convergence techniques that solu- PP1 tions to the three-dimensional quasistatic evolution prob- Electron Transport in Thin Semiconductor Gas lem of Prandtl-Reuss elastoplasticity converge to a qua- Sensors sistatic evolution of a suitable reduced model. In this limiting model the admissible displacements are of Kirchhoff- The aim of this work is to derive, from a kinetic descrip- Love type and the stretching and bending components of tion, a SHE model (for Spherical Harmonics Expansion) for the stress are coupled through a plastic flow rule. electron transport in semiconductor gas sensor. Electron transport in the thin semiconductor gas sensors is modeled Elisa Davoli by a collisionless Boltzman equation subject to a periodic Carnegie Mellon University array of localized scatters modeling the periodic hetero- Department of Mathematical Sciences geneities of the semiconductors material. The localized [email protected] scatters may not conserve the electron number, and then a localized electronic charge have been manifested to re- Maria Giovanna Mora veal the localized absorption phenomenon. The limit of Università degli Studi di Pavia a large number of periodicity cells combined with a large Dipartimento di Matematica time asymptotics leads to a homogenized diffusion equa- [email protected] tion (SHE model) with a non vanishing second term which represents the absorption term. The rigorous proof relies on fine estimates on the operator modeling the localized PP1 scatters. Modeling Collective Chemical Effects in Carbon Nanotube Growth Hechmi Hattab ENIT-LAMSIN - Tunis TUNISIA We model and simulate collective chemical effects in the [email protected] growth of populations of carbon nanotubes. When carbon deposits on the catalyst during growth, growth-enhancing gases are produced. We model the partial pressure of these PP1 gases using a diffusion equation and couple with a growth Spectra of Functionalized Operators Arising from model developed by Puretzky, et al. [Applied Physics A, Hypersurfaces 2005]. We fit parameters to our model by comparing computer simulations with experimental results for growth of Functionalized energies, such as the Functionalized Cahn- patterned carbon nanotube ”forest” microstructures. Hilliard, model phase separation in amphiphilic systems, in which interface production is limited by competition Brittan A. Farmer for surfactant phase, which wets the interface. This is in Department of Mathematics contrast to classical phase-separating energies, such as the University of Michigan Cahn-Hilliard, in which interfacial area is energetically pe- [email protected] nalized. In binary amphiphilic mixtures interfaces are characterized by bilayers, which divide the domain of the dom- Mostafa Bedewy, John Hart inant phase, A, via thin layers of phase B formed by ho- Department of Mechanical Engineering moclinic connections. We characterize the center-unstable University of Michigan spectra of the second variation of the Functionalized energy [email protected], [email protected] and obtain resolvent estimates to the operators associated with gradient flows of the Functionalized energies. This is an essential step to a rigorous reduction to a sharp-interface PP1 limit. Electro-active Polymer Composites at Finite De- formations: Effective Behavior and Stability Anal- Gurgen Hayrapetyan ysis Carnegie Mellon University [email protected] In this poster we present homogenization estimates for theeffectiveresponseofelectro-activepolymercompos- Keith Promislow ites (EAPCs), consisting of a family of aligned rigid fibers Michigan State University firmly embedded in an ideal dielectric matrix and undergo- [email protected] ing finite strains. Using such homogenization estimates, we investigate the effect of microstructural parameters on the electro-mechanical response of dielectric actuators made 134 MS13 Abstracts

PP1 [email protected] A Density Result for GSBD and Its Application to the Approximation of Fracture Energies Charles Sonnenberg University of Bristol We present an approximation result for functions u :Ω→ [email protected] Rn belonging to the space GSBD(Ω)∩L2(Ω,Rn)withe(u) n−1 square integrable and H (Ju) finite. The approximating functions uk are piecewise continuous functions such PP1 2 n 2 n×n that uk → u in L (Ω,R ), e(uk) → e(u)inL (Ω,Msym ), Tubes of Maximal Probability and Transition Path- n−1 → | ± − ±|∧ n−1 → H (Juk Ju) 0, and J ∪J uk u 1dH 0. way Sampling uk u As an application, we provide the extension to the vector- We are studying how a collection of atoms, governed by valued case of the Γ-convergence result in SBV (Ω) proved Brownian dynamics, undergoes a conformational change. in [Ambrosio L., Tortorelli V.M., On the approximation When the encountered energy barrier is much larger than of free discontinuity problems, Boll. Un. Mat. Ital. 6, the thermal energy of the atoms, the transition is a rare 105-123]. event. We probe the free energy landscape and directly Flaviana Iurlano sample such rare transition paths in an efficient manner us- SISSA/ISAS - International School for Advanced Studies ing a Hybrid Monte Carlo method. This method includes [email protected] thermal fluctuations and thus conserves the sample’s thermodynamic significance. To interpret the data generated by direct sampling of the paths, we explore a novel method PP1 that approximates the physical measure with a Gaussian Zero Transmission in Waveguides with Thin Struc- measure that can be viewed as a tube that encloses the vast tured Membranes majority of the paths. The optimal parameters are then determined by minimizing the asymmetric KullbackLeibler Structured membrane devices, sometimes known as mem- divergence between the two measures. The extracted pa- brane metamaterials, can exhibit unusual and surprising rameters define the tube center and its width. We present wave scattering properties. I will present resent work on a results for a particle moving in several multi-welled two- particular such device consisting of a waveguide in which dimensional potentials. sound waves interact with a thin elastic membrane. With a proper choice of membrane structure the device will com- Patrick Malsom, Frank Pinski pletely reflect incoming waves for certain frequencies. Us- University of Cincinnati ing a new simplified model, this effect can be understood [email protected], [email protected] in a precise way.

Jens B. Jorgensen PP1 Courant Institute of Mathematical Sciences mystic and Uncertainty Quantification in Materials [email protected] Design, Analysis, and Failure We have developed a rigorous mathematical framework PP1 for quantifying uncertainty (OUQ), and a robust software Domain Wall Motion in Magnetic Nanowires: An (mystic) for solving high-dimensional global optimization Asymptotic Approach problems. Mystic provides tools for constraining design space and targeting unique solutions, including suites of We study the motion of domain walls in a magnetic standard and statistical constraints, and constraints for nanowire under the influence of small applied magnetic legacy data and coupled or surrogate models. Mystic has fields, material anisotropy, and applied electric current. been used in large-scale calculations of materials failure un- The Landau–Lifshitz–Gilbert equation is linearized about der hypervelocity impact and elasto-plastic failure in struc- a static solution and the magnetization dynamics investi- tures under seismic ground acceleration, among others. gated via a perturbation expansion. We compute leading order behaviour, propagation velocities, and first order cor- Michael McKerns rections of both travelling waves and oscillatory solutions, California Institute of Technology and find bifurcation points between these two types of so- [email protected] lutions. Houman Owhadi Ross Lund Applied Mathematics University of Bristol Caltech [email protected] [email protected]

Arseni Goussev Tim Sullivan Northumbria University University of Warwick [email protected] [email protected]

Jonathan Robbins Alta Fang University of Bristol Princeton University [email protected] [email protected]

Valeriy Slastikov Michael Aivazis University of Bristol California Institute of Technology Bristol, UK [email protected] MS13 Abstracts 135

PP1 els to study anti-plane strain fracture. Using asymptotic Mathematical and Compu- analysis of the model near the tip of crack, they showed tational Methods for the Analysis of Low-Energy that both stress and strain vanish at the crack-tip, and the Electron Microscopy/Diffraction of Graphene and crack separation displacement has a cusp-shaped profile. Other Semiconductors The purpose of present study is to extend this previous analysis to the setting of plane-strain fracture. In joint We present a computational method, using density- work with K. Gou, K. R. Rajagopal and J. R. Walton, we functional theory (DFT), to calculate low-energy electron employ a combination of asymptotic and numerical tech- microscopy (LEEM) spectra of semiconductor thin-films, niques to show that both stress and strain vanish at the including graphene. We solve Schrodinger equation bound- tip of the crack. ary value problems with a Bloch wave matching approach using self-consistent potentials via DFT to approximate Mallikarjunaiah S. Muddamallappa LEEM spectra better than previous model-potential meth- Department of Mathematics ods in the lowest energy range. We compare results to Texas A&M University experiment and discuss well-posedness and associated is- [email protected] sues in obtaining the solution sets needed for matching at higher-energies. PP1 John F. Mcclain Connection of Kinetic Monte Carlo Method for University of New Hampshire Surfaces to the Burton-Cabrera-Frank Model jfi[email protected] There are many questions concerning the underlying phys- Jiebing Sun ical processes and theoretical assumptions that yield the Michigan State University Burton- Cabrera-Frank (BCF) model of step-flow. We for- [email protected] mally derive the BCF theory from an atomistic, kinetic Monte Carlo model of the surface in 1+1 dimensions with one step. Our analysis (i) shows how the BCF theory de- James Hannon scribes a surface with a low density of adsorbed atoms, and IBM Thomas J Watson Research Center (ii) establishes near-equilibrium conditions ensuring that [email protected] the theory remains valid for all times. Karsten Pohl, Jian-Ming Tang Paul Patrone University of New Hampshire Department of Physics, University of Maryland, College [email protected], [email protected] Park NIST Gaithersburg [email protected] PP1 Renormalized Energy and Dynamics of Screw Dis- Dionisios Margetis locations with Antiplane Shear University of Maryland, College Park [email protected] We describe the dynamics for a system of screw dislocations subject to anti-plane shear. Variational techniques allow us to find minimizers for the energy functional asso- PP1 ciated with the system of dislocations in an elastic medium. Evolution Results for Epitaxially Strained Thin Building on a model due to Cermelli and Gurtin, a weak Films notion of solutions (in the sense of Filippov) to ordinary differential equations is used to solve the dynamics prob- We consider the evolution equation with curvature regular- lem. Some examples of interesting scenarios complement ization that models the motion of a two-dimensional thin the presentation. film by evaporation-condensation on a rigid substrate. The film is strained due to a mismatch between the crystalline Marco Morandotti, Timothy Blass lattices of the two materials and the film surface anisotropy Carnegie Mellon University is taken into account. The author established short time [email protected], [email protected] existence, uniqueness, and regularity of the solution using De Giorgi’s minimizing movements to exploit the L2- Irene Fonseca gradient flow structure of the fourth order parabolic equa- Carnegie Mellon University tion. This seems to be the first analytical result for the Center for Nonlinear Analysis evaporation-condensation case in the presence of elasticity. [email protected]

Giovanni Leoni Paolo Piovano Carnegie Mellon University CNR-IMATI, Pavia, Italy [email protected] [email protected]

PP1 PP1 On Modeling Plane-Strain Fracture Using Strain- A Model for Crack Growth with Branching and Limiting Theory of Elasticity Kinking In this work we study the problem of plane-strain fracture We study an evolution model for fractured elastic materials in the setting of a strain-limiting theory of elasticity. Re- in the 2-dimensional case, for which the crack path is not cently Rajagopal and Walton used a new class of such mod- known a priori. We introduce some general assumptions 136 MS13 Abstracts

on the fracture sets structure suitable to allow for kink- PP1 ing and branching to develop. We define the front of the Nonlinear Solvers for Dislocation Dynamics fracture and its velocity. By means of a time-discretization approach, we prove the existence of a continuous-time evo- We present results of applying accelerated fixed point and lution that satisfies an energy inequality and a stability Newton nonlinear solvers for implicit integration of dislo- criterion. cation dynamics simulations in the ParaDiS code. In particular, we compare performance of fixed point and Ander- Simone Racca son accelerated fixed point methods for large-scale, parallel SISSA-ISAS International School for Advanced Studies simulations looking at parallel efficiency, algorithmic scala- [email protected] bility, and robustness. Preliminary results show significant speedup using the acceleration methods. These methods will also be compared with a Newton iteration. PP1 Behavioral Modeling of Corundum under the Ef- Carol S. Woodward fect of Porosity Rate Lawrence Livermore Nat’l Lab [email protected] Corundum Known for its relatively high hardness, its other characteristics depend on the rate of porosity that varies Athanasio Arsenlis, Sylvie Aubry, Gregg Hommes, Moono depending on the manufacturing process. One of the char- Rhee acteristics to consider is the value of the tensile stress in a Lawrence Livermore National Laboratory standard test to failure as a function of the force applied [email protected], [email protected], and the rate of porosity. In this study, to analyze the si- [email protected], [email protected] multaneous effect of two parameters, we used the statistical method of design of experiments. PP1 Bendaoudi Seifeddine Djillali LIABES university of Sidi Bel Abbes Collective Behavior of Walls of Dislocations [email protected] We try to understand plastic behavior of metals by upscaling the micro-mechanics of dislocations. We consider Bounazef Mokhtar, Adda Bedia El-Abbes a highly simplified dislocation network, which leads to our Djillali LIABES University microscopic model being a one dimensional particle system, corundum known for its relatively high hardness, i, in which the interactions between the particles are singular [email protected] and non-local. Finally, we derive the effective equations by means of Gamma-convergence on the space of probability measures. PP1 Practical Modelling of Statistical Nanocomposite Patrick van Meurs Optical Coating Materials for Filter and Absorber Eindhoven University of Technology, The Netherlands Specifications: Oscillator Model, Mixing Model [email protected] and Spectral Moments Approaches Metal-dielectric nanocomposites are candidate materials for applications in optical coatings when in the specifi- cation tailored optical absorption behaviour is required. In order to make such nanocomposite coatings accessible to commercial coating design and characterization software, reliable mathematical modelling of the dispersion of the composites effective optical constants is essential. We present different possible approaches and discuss their relative use for optical characterization or design tasks at practically relevant examples (beamsplitters, color filters, decorative coatings). Olaf Stenzel Fraunhofer IOF Jena [email protected]

Steﬀen Wilbrandt Fraunhofer IOF steﬀ[email protected]

Karen K¨ohler Bonn University [email protected]

Norbert Kaiser Fraunhofer IOF [email protected]