50 MS10 Abstracts

IP1 because of physical requirements like objectivity and plas- Diffusion Generated Motion for Large Scale Simu- tic indifference. The latter leads to the multiplicative de- lations of Grain Growth and Recrystallization composition of the strain tensor and asks to consider the plastic tensor as elements of multiplicative matrix group, A polycrystalline material consists of many crystallites which leads to strong geometric nonlinearities. We show called grains that are differentiated by their varying ori- how polyconvexity and time-incremental minimization can entation. These materials are very common, including be used to establish global existence for elastoplastic evo- most metals and ceramics. The properties of the network lutionary systems. of grains making up these materials influence macroscale properties, such as strength and conductivity. Hence, un- Alexander Mielke derstanding the statistics of the grain network and how it Weierstrass Institute for Applied Analysis and Stochastics evolves is of great interest. We describe new, efficient nu- Berlin merical algorithms for simulating with high accuracy on [email protected] uniform grids the motion of grain boundaries in polycrystals. These algorithms are related to the level set method, but generate the desired geometric motion of a network IP4 of curves or surfaces (along with the appropriate bound- Gels and Microfluidic Devices ary conditions) by alternating two very simple operations for which fast algorithms already exist: Convolution with a Gels are materials that consist of a solid, crosslinked sys- kernel, and the construction of the signed distance function tem in a fluid solvent. They are over-whelmingly present to a set. Motions that can be treated with these algorithms in biological systems and also occur in many aspects of include grain growth under misorientation dependent sur- materials applications. Some gels are mostly characterized face energies, and various models of recrystallization. We by their mechanical properties whereas for the large class will present simulations with hundreds of thousands of fully of hydrogels, the electric effect of ions is the signature fea- resolved grains in 3D. Joint work with Matt Elsey and Pe- ture. In the biomedical industry, mechanical properties of ter Smereka. gels are relevant to the prediction of the life-cycle of body implantable devices such as pacemaker, bone-replacement Selim Esedoglu systems and artifcial skin. Upon body implantation, de- Department of Mathematics vices swell due to the moisture of the environment, result- University of Michigan ing in stress concentrations that may cause failure of the [email protected] device. A main goal is to determine the time evolution of stresses at interfaces between different materials of the device, and controlability conditions that ensure that the IP2 stress values will remain below an allowed threshold. The Accurate and Efficient Atomistic-to-Continuum proposed governing equations involve transport, diffusion, Coupling Methods elasticity and dissipation. To study hydrogels, we explore the coupling of the mechanics of gels with the Poisson- Many materials problems require the accuracy of atomistic Nernst-Planck equations governing the transport and dif- modeling in small regions, such as the neighborhood of a fusion of ions in the solvent, and in the presence of the crack tip. However, these localized defects typically inter- electric potential of the system. We focus on two types of act with a much larger region through long-ranged elastic microuidic models that emerge from such a setting, cyclic fields. These regions are too large to be computed atom- drug-delivery devices and microvalves. istically. Materials scientists have proposed many methods to compute solutions to these multiscale problems by cou- M. Carme Calderer pling atomistic models near a localized defect with contin- University of Minnesota uum models where the deformation is nearly uniform. The [email protected] development of coupling methods for crystalline materials that are reliable and accurate for configurations near the onset of lattice instabilities such as dislocation formation IP5 has been particularly challenging. I will present theory Predictive Atomistic and Coarse-Grained Model- developedwithMathewDobsonandChristophOrtnerto ing of Epitaxial Thin Film Growth assess currently utilized methods and to propose more reliable, accurate, and efficient methods. Thin film deposition provides a pathway to create a variety of complex surface nanostructures with diverse functional- Mitchell Luskin ity. Atomistic modeling of homoepitaxial film growth (A on School of Mathematics A) on single-crystal surfaces, when combined with kinetic University of Minnesota Monte Carlo (KMC) simulation, has achieved remarkable [email protected] predictive accuracy in describing far-from-equilibrium evolution*. This includes both initial submonolayer 2D island formation and subsequent multilayer growth and kinetic IP3 roughening (i.e., formation of 3D mound-like stacks of 2D Approaches to Finite-strain Elastoplasticity islands). Less progress has been made for heteroepitaxy on single-element substrates (A on B) or on alloys (A on BC), Elastoplastic material models involve a decomposition of where strain and quantum size effects can be significant. the strain tensor into an elastic and a plastic part. The As an alternative to atomistic treatments, coarse-grained latter is driven by a nonsmooth evolution law, the flow modeling is appealing from the perspective of algorithmic rule. Small-strain elastoplasticity, which is based on the efficiency, and also to provide deeper insight into funda- additive decomposition of the strain tensor, has developed mental issues such as development 2D island distributions significantly over the last decades, since techniques from or 3D mound coarsening dynamics. We review recent suc- convex analysis and variational inequalities are applicable. cesses and open challenges for modeling. *Evans et al., For finite-strain elastoplasticity, convexity is unacceptable MS10 Abstracts 51

Surf. Sci. Rep. 61 (2006) 1-128. applied stress results in a deformation close to the critical strain, the gel slowly creeps for an extended incubation Jim W. Evans time at which point it catastrophically fails and flows. In Ames Laboratory USDOE and Iowa State University fact, there is a power-law relationship between the applied [email protected] stress and the incubation time. Although similar behavior is reported in materials ranging from ketchup to waxy crude oil, surprisingly little is understood about the creep- IP6 ing behavior of materials close to their critical strain. We Symmetries Broken by Electrostatics in Nanoscale have looked to structural kinetic models, which balance the Ionic Assemblies rate of structure formation and stress-induced structure break down, as a way to generalize the problem. These Electrostatic interactions are essential in the structure and approaches should have broad application to a variety of function of biological assemblies since most biomolecules industries and technologies. are charged. Oppositely charged molecules often co- assemble into units with some inherent asymmetry that Matthew Lynch renders functionality. Symmetric electrostatic interactions Proctor & Gamble Company alone are shown to spontaneously break symmetries at the [email protected] nanometer scale, such as the formation of helical ionic patterns on fibers and the buckling of ionic shells into icosa- Alan Graham hedra. Through varying the strength of the electrostatic Los Alamos National Laboratory interactions we control the pitch of the helical patterns of [email protected] the surface of virus-like fibers or of aqueous channels. In ionic spheres, correlations may lead to faceting into icosa- hedra without rotational symmetry. This buckling appears IP9 on vesicles of cationic-anionic molecules, as well as on co- Mathematical Modelling of Hydrogen Fuel Cells adsorbed charged molecules that form ionic rafts. Hydrogen Fuel Cells can efficiently convert Hydrogen fuel Monica Olvera De La Cruz and air to electrical power with zero emissions. This Northwestern University talk concerns Polymer Electrolyte Membrane Fuel Cells [email protected] (PEMFC). A general overview of how these devices are constructed and how they work is given. PEMFCs are IP7 fundamentally multi-scale. The central component of a PEMFC (the Membrane Electrode Assembly or MEA) has Polycrystalline Materials: Greater Than the Sum micron scale. The MEA is made of composite layers which of Their Crystals must facilitate selective multiphase transport of reactants Polycrystalline materials are pervasive in nature and en- to and products from catalyst sites. The need for com- gineering, and have long been studied as a collection of posite materials with these selective transport properties individual crystalline grains. Mathematical tools to repre- is a recurring theme in energy conversion and storage ap- sent the statistics of many individual grains and to more plications. MEAs are built into unit cells which are then intuitively visualize the grain structure were developed long arranged in stacks. The micro-components have behaviour ago, and have greatly facilitated advances in understand- determined by their structure on the nano-scale. Modelling ing and designing these materials. However, it is not the stack level behaviour from component models and compo- crystals themselves, but the boundaries between crystals, nents from their nano-scale structure are both of interest that frequently dominate the properties of polycrystalline and are illustrated with examples. materials. Unfortunately, the population of these bound- Brian R. Wetton aries is more difficult to measure, visualize, and represent University of British Columbia statistically. This talk will highlight our recent work to- Department of Mathematics wards quantitatively understanding the population of grain [email protected] boundaries in materials. Beginning from an understanding of the topology of the group space for grain misorientations, we develop new methods of mapping and visualizing IP10 boundary character, representing their statistics with con- Nonlinear Mechanics of Elastic Plates tinuous functions, and understanding the rules that govern their connectivity as a network. The mechanics of thin elastic or viscous objects is critical to our understanding of e.g. the buckling of engineering struc- Christopher Schuh tures, the spinning of polymer fibers, or the crumpling of MIT plates and shells. During the past decade, the mathemat- [email protected] ics, mechanics and physics communities have witnessed an upsurge of interest in those issues. Yet, fundamental ques- IP8 tions are still open. For example, the exact nature of the singularities in crumpled plates remains a topic of passion- Failure of Polymer Gum Gels Close to their Critical ate debate. My talk will address this problem, focussing Strain specifically on the internal structure of conical singularities. Polymer gels prepared from synergistic blends of xanthan I will propose an explicit construction which is amenable and konjac gums exhibit remarkable flow characteristics. to analytical calculations, and is at odds with scaling ar- Creep measurements indicate that when the applied stress guments usually assumed in the literature. results in a deformation of the gel in excess of the criti- Basile Audoly cal strain, the gel rapidly fails and flows; when the applied University Paris VI, France stress results in a deformation far less than the critical Paris, France strain, the gel only slowly creeps. Remarkably, when the 52 MS10 Abstracts

[email protected] cloaking devices are studied in weighted Sobolev spaces with singular weights. We describe the behavior of the ﬁ- nite energy solution in the cloaking medium, in the cloaked IP11 region, and at the interface between the two regions. A spe- Modeling the Plastic Deformation of Crystals and cial ﬁnite element method is proposed for simulating these Glasses with Colloids devices.

Dense colloidal systems form crystalline, liquid and glassy Ulrich Hetmaniuk phases similar to those observed in simple atomic systems. University of Washington Confocal microscope makes it possible to track the indi- Department of Applied Mathematics vidual particles in space and time, which allows a unique [email protected] look at the mechanisms of deformation on the particle level. Dislocations in colloidal crystals can also be visualized by Hongyu Liu laser diffraction microscopy. Measurements of the geom- University of Washington etry and dynamics of these dislocations agree remarkably Department of Mathematics well with the classical predictions for atomic-scale crystals. [email protected] In glasses, the technique has allowed direct measurments of the size, strain and concentration of the local shear trans- Gunther Uhlmann formations that govern the macroscopic flow. University of Washington Frans Spaepen [email protected] Harvard University [email protected] CP1 A Long Wave Approximation for a Model Describ- CP1 ing the Self-Assembly of Quantum Dots Higher Order Phase Field Equation for Direct Cal- Evolution equations for the self-assembly and coarsening of culation of Surface Tension Anisotropy nano-crystals are of growing interest since two decades and Recently, it was shown [Caginalp and Esenturk, accepted in particular heteroepitaxial systems leading to quantum in DCDS] that for interfaces of symmetric microscopic in- dot growth have been considered in many works. We ex- teractions (4-fold or higher), one needs to go to higher or- tend a model that captures the effects of surface diffusion, ders (in derivatives) in the phase field equation to capture elasticity, wetting and isotropic surface energy to one that the anisotropy of the surface tension. For a given type additionally reflects preferred orientations as minima in the of molecular interactions one can find a explicit formula surface energy. A long wave reduction allows to simplify for the surface tension in terms of the phase field. As an the equation such that it can be simulated efficiently by example we will start with an an anisotropic interaction a pseudospectral method on large domains. The evolving potential, seek numerical solutions to the differential equa- dots indeed show faceting and an Ostwald ripening process tion and calculate the surface tension anisotropy. can be observed. The island density obeys a power law and the ripening is accelerated in comparison to the isotropic Emre Esenturk case. A linear stability analysis shows that the anisotropy University of Pittsburgh destabilizes flat films and that above a critical number all [email protected] wave numbers are unstable. Maciek D. Korzec CP1 WIAS Berlin Diffusion and Homogenization Approximation for [email protected] Semiconductor Gaz Sensor Boltzmann Equation Peter L. Evans The aim of this work is to derive, from a kinetic discription, Humboldt University in Berlin a drift-diffusion model for electron transport in semicon- [email protected] ductor gaz sensor, by using diffusion and homogenization approximation. An homoenized absorption term appears in the fluid model. In the presence of a self-consistent spa- CP1 tially oscillating electrostatic potential, the right hand side Computations of Asymptotic Scaling for the Kohn- of the Boltzmann equation presents, an absorption term Müller and Aviles-Giga Functionals added to the electron-phonon operator collision. This absorption term has the periodicity of the oscillating electro- We report on computations using spectral methods which static potential. capture asymptotic behavior for the Kohn-Müller model for branching in martensitic materials and on the Aviles- Hechmi Hattab Giga functional. The simulation results show that by solv- ENIT-LAMSIN - Tunis TUNISIA ing evolutionary partial differential equations, it is feasible [email protected] to explore the energy landscape of these non-convex model energies and to provide conjectures for the behavior of the global energy minimising solutions as the parameters in the CP1 models are changed. Finite Element Simulations for Active Acoustic Cloaking Devices Benson K. Muite Department of Mathematics We investigate a class of active acoustic cloaking devices University of Michigan where the device and the cloaked region can be mapped [email protected] into two nested balls. Finite energy solutions for these MS10 Abstracts 53

CP1 Victoria Gamez-Garcia Design of the Potential in a Parametrically Forced Universidad Autonoma Metrpolitana Azcapotzalco Schroedinger Equation to Minimize Radiative Loss [email protected]

We consider a micro-cavity governed by the Schroedinger Eusebio Bolaños-Reynoso equation with a potential. When the system is paramet- Instituto Tecnologico de Orizaba rically forced, the eigenfunction becomes a resonant state [email protected] and decays according to Fermi’s Golden Rule. We pose the Design Problem: what potential maximizes the lifetime of this resonant state? This is formulated and studied as CP2 a constrained optimization problem. Optimal potentials The Rapid Advance and Slow Retreat of a Mushy emerge which are periodic with a localized defect. Quality Zone factors improve from O(102)toO(109). Mushy zones are regions of intermixed liquid and solid Braxton Osting which result from instability due to the build-up of solute Columbia University during solidification of multispecies materials. If solute dif- [email protected] fusion is ignored there is a steady-state mushy zone representative of what is observed over typical laboratory time Michael I. Weinstein scales, but even a small amount of diffusion dramatically Columbia University alters the eventual steady state. We discuss the evolution Dept of Applied Physics & Applied Math of a mushy zone where diffusion of the solute is not ignored. [email protected] Nicholas Gewecke University of Tennessee CP2 [email protected] Convective Instabilities During the Solidification of An Ideal Ternary Alloy in a Mushy Layer Tim Schulze University of Tennessee We consider a model for the solidification of an ideal Department of Mathematics ternary alloy in a mushy layer that incorporates the effects [email protected] of thermal and solutal diffusion, convection and solidification. Our results reveal that the system admits double- diffusive modes of instability. Additionally, modes of in- CP2 stability exist even in situations in which the thermal and Molecular-Dynamics Calculation of Thermody- solute fields are each individually stable from a static point namic Melting Point of view. We show both numerical and analytical solutions. We tried to bring closer mechanical melting to thermo- Daniel Anderson dynamic melting by incorporating an extra energy con- Department of Mathematical Sciences stant corresponding to thermodynamics energy gap into George Mason University the Tight-Binding potential of Molecular Dynamic (MD) [email protected] simulation. The calculated melting point of single elements was 0.5 to 9.8% deviated from the experimental ones in- Geoffrey McFadden, Sam Coriell stead of 20 to 30% in conventional simulation. The method National Institute of Standards and Technology works especially well for elements with a low ratio between [email protected], [email protected] Debye temperature and melting temperature.

Bruce T. Murray Pee-Yew Lee Department of Mechanical Engineering Institute of Materials Engineering, National Taiwan SUNY at Binghamton Ocean Un [email protected] [email protected]

CP2 CP2 Controlling Nonlinear Dynamics in Continuous Nonlinear Convection in a Mushy Layer: Chimney Crystallizers Spacing and Optimal Solute Fluxes Crystallization is a process widely used in industry for the The rapid solidification of any binary alloy leads to the for- production of many particle products. Continuous crystal- mation of a chemically reactive porous medium, or mushy lizers typically exhibit oscillatory dynamics. We are ad- layer. Convection and dissolution generate drainage chan- dressing the suppression of oscillatory behavior in contin- nels devoid of solid, or chimneys, with a spacing that uous crystallizers via a feedback control approach. Two evolves over time. We consider a numerical model of non- controllers are applied and compared, a control based on linear convection within a mushy layer and investigate the modeling error compensation ideas, and high-order slid- spacing mechanism for fully developed chimneys. This ing mode control. Numerical simulations on a dynamical yields insight into the evolution of solute fluxes and com- model described by integro-differential equations are used position in growing mushy layers. to illustrate the control performance. Andrew J. Wells, Steven Orszag, John Wettlaufer Hector F. Puebla Yale University Universidad Autonoma Metropolitana Azcapotzalco [email protected], [email protected], [email protected] [email protected] 54 MS10 Abstracts

CP3 [email protected] Euler-Poisson System for Leo Spacecraft Charging David Wu Not available at time of publication. Institute of High Performance Computing, Singapore [email protected] Saja Borghol Universite des Sciences et Technologies de Lille1-batiment [email protected] Ramanarayan Hariharaputran Institute Of High Performance Computing [email protected] Christophe Besse Universite des Sciences et Technologies de Lille [email protected] CP3 Nonlinear and Fractal Analysis of Electrochemical Thierry Goudon Noise Time Series in the Corrosion of 304 Steel INRIA Lille Nord Europe Research Centre with Heat Treatment Villeneuve d’Ascq, France [email protected] Electrochemical noise (EN) signals are widely used to characterize corrosion parameters and mechanisms of corroding Ingrid Violet materials. The highly irregular behavior of EN motivates Universite Lille 1 Cite scientiﬁque the application of time series analyses that derive from sta- [email protected] tistical physics. In this work we have applied three fractal methods to EN data of 304 steel discs with diﬀerent heat treatment in presence of NaCl. For completeness, stan- CP3 dard non-linear analysis, such as delayed phase-plane re- New Augmented Primal-Mixed Finite Element construction and lyapunov exponents, is also performed. Methods in Elasticity

We introduce a new augmented variational formulation William Sanchez-Ortiz, Manuel Palomar-Pardave for the linear elasticity problem based on the Hu-Washizu Universidad Autonoma Metropolitana Azcapotzalco method. The resulting problem is well posed for appro- [email protected], [email protected] priate values of a stabilization parameter. We establish suﬃcient conditions for the well posedness of the corre- Jorge Uruchurtu sponding Galerkin scheme and give concrete examples of Universidad Autonoma del Estado de Morelos discrete spaces satisfying these conditions. Error estimates [email protected] are also provided. The application of the method to the case when the stress-strain relation is given by a nonlinear Hector F. Puebla or semilinear operator is also discussed. Universidad Autonoma Metropolitana Azcapotzalco [email protected] Maria Gonzalez Taboada Departamento de Matematicas Universidad de La Coru˜na CP3 [email protected] Upscaling Multiscale Flows in Highly Porous Me- dia Gabriel Gatica Universidad de Concepcion An iterative two-scale ?nite element method for solving Departamento de Ingeniera Matematica Brinkmans equations is presented. These equations model [email protected] ?uid ?ow in highly porous media. The method uses a DGFEM for Stokes equations by Wang and Ye and the Luis Gatica concept of subgrid approximation developed by Arbogast Universidad Catolica de la Santisima Concepcion for Darcys equations. The method is put in the framework (Chile) of alternating Schwarz iterations to reduce boundary layer [email protected] errors and to ensure convergence to the global ?ne solution.

CP3 Joerg Willems An Unbiased Method for Estimating Stationary Texas A&M University Transition Rates of Markov Processes [email protected] The dynamics of phenomena such as nucleation, diffusion, Raytcho Lazarov or coarsening may be modeled as Markov processes if the Math Department/Inst. for scientific Computattion transition rates between states are known theoretically or Texsas A&M University empirically. These transition rates can be estimated from [email protected] simulation or experiment results via a formula proposed by Reiss et al. We show that Reiss’ formula gives a bi- Yalchin Efendiev ased estimate and propose an unbiased alternative. We Dept of Mathematics demonstrate an efficient implementation of our formula for Texas A&M University molecular dynamics simulation of nucleation. [email protected] Yang Hao Lau Institute of High Performance Computing Oleg Iliev Fraunhofer ITWM MS10 Abstracts 55

[email protected] CP4 Effects of Wetting and Anisotropy on Stability and Morphological Evolution of Ultrathin Solid Films CP3 A Robust, Practical, and General Method for Cou- The combined effects of stress, two-layer wetting potential pled Iterations of Black Box Nonlinear Solvers by and strong surface energy anisotropy on linear stability of An Approximate Block Newton Method wetting epitaxial thin film on elastic substrate are analyzed within the framework of longwave approximation. The im- We have developed an approximate block Newton-Krylov pacts of perturbation wavenumber, strain, film thickness, method to couple arbitrary black box nonlinear solvers. shear modulus ratio, and anisotropy strength are studied. The ABN method preserves the quadratic approximation Detailed stability diagrams are plotted, revealing some sur- properties of exact Newton iteration. The notion of a solver prising linear responses of the film which were not previ- is completely abstract, encompassing any interpolations or ously noted in the studies of film stability. In the non- other transformations of data exchanged between solvers. wetting, stress-free situation which may be appropriate for We demonstrate the method on a modular coupling of the surface-energy driven dewetting of silicon-on-insulator, be- radiation heat transfer code CrysMAS to our multi-physics sides linear stability, the fully nonlinear evolution of an CFD code Cats3D. Application to other problem types will anisotropic surface pit in the attractive field of the sub- also be discussed. strate is studied numerically. Andrew Yeckel, Jeffrey J. Derby Mikhail V. Khenner University of Minnesota Department of Mathematics [email protected], [email protected] Western Kentucky University [email protected] CP4 Effect of Stress on the Growth of Concentric Grains CP4 andPoresEmbeddedinaMatrix Dislocation Propagation in Phase Field Dislocation Dynamics The isothermal growth of a spherical grain from its melt filling a spherical pore embedded in a binary alloy ma- We find analytical solutions of the Guinzburg Landau equa- trix under stress is theoretically investigated as well as the tion describing the evolution of dislocations in a single crys- dissolution of the matrix, assuming solute diffusion only tal. The solutions include estimations of the yield stress proceeds in the liquid phase. The stress has been found to and stacking fault energy relations as well as the criti- be responsible for the destabilization of both fronts leading cal source size. For the dynamical solutions we are able in particular to the development of a delayed roughness on to compute the dependency of the velocity on the applied the stress-free grain interface. stress with very good agreement with molecular dynamics simulations Jerome Colin university of poitiers Dong-Wook Lee [email protected] School of Mechancial Engineering Purdue University [email protected] CP4 Continuum Simulations of Lipid Membranes Using Marisol Koslowski a Phase-Field Method Coupling Composition with Purdue University Membrane Mechanical Properties [email protected] Ternary lipid membranes are used extensively as a model for the plasma membrane of biological cells. They contain CP4 phase-separated domains and exhibit deformation. The morphologies of these systems provide information about Mathematical Modeling of Fluid Flow Through a the thermodynamics and kinetics of multicomponent mem- Porous Deformable Arterial Wall branes. We examine the formation and evolution of do- We model a problem of fluid flow interactions within a de- mains in lipid vesicles using a phase-field model coupling formable arterial wall. We have used mixture theory to composition with deformation, and find that the composi- compute both the structural displacement of the solid and tional and shape evolutions are significantly altered when fluid motion. The coupled system of equations is solved this coupling is present. numerically. We compare the mixture theory model to Chloe M. Funkhouser a hierarchy of models including simple spring models as Biomedical Engineering well as elastic deformation models. The applications of the University of Michigan model are to understand the deformation of the wall as a [email protected] function of its material properties and the relation of this deformation to the growth and rupture of aneurysms. Francisco Solis Javed Siddique Arizona State University Penn State York [email protected] [email protected]

Katsuyo Thornton Daniel Anderson Department of Materials Science and Engineering Department of Mathematical Sciences University of Michigan George Mason University [email protected] [email protected] 56 MS10 Abstracts

Padmanabhan Seshaiyer [email protected] George Mason University [email protected] CP5 Stochastic Simulation for Self-Organization in Ma- CP5 terials Scaling States of an Aggregating, Ballistic Particle (ABP) Model Self-organization of components of two phase mixtures through diffusion is known as Ostwald ripening. This phe- We study a class of continuous in time, aggregating 1D par- nomenon can be described using mesoscopic models which ticle models, namely aggregating, ballistic particle (ABP) are stochastic partial differential equations that were de- models, motivated by material science applications. We rived from the underlying microphysics of the system. In numerically validate the dynamic scaling hypothesis, and this talk, results from simulations using spectral schemes in particular identify the associated scaling functions that for stochastic partial differential equations are described characterize the self-similar 1-point statistics of the coars- andnewresultsonimprovingthe accuracy and efficiency ening ensemble. Interesting links to the scaling state of of this method are given. Finally, simulation results for the ‘Min-driven Clustering’ model (Menon, Niethammer the mesoscopic model are compared with theoretical re- and Pego, 2008) are obtained in the ‘infinite-speed’ limit. sults such as the Lifshitz-Slyozov growth law.

Craig K. Chapman,StephenJ.Watson David J. Horntrop University of Glasgow Dept of Mathematical Sciences, Center for Applied Math [email protected], [email protected] New Jersey Institute of Technology [email protected] Steven M. Roper Glasgow [email protected] CP5 A Generalized Space-Time Poisson Voronoi Con- struction Applied to Crystal Nucleation and CP5 Growth Moments of the Grain Size Distribution Formed Via Nucleation and Growth in 3D We present a generalization of the Poisson Voronoi construction in space-time that provides a mathematical A common characteristic of a cellular structure is the cell- framework for studying crystal nucleation and growth. We size distribution, which can be expressed as a series involv- show that the construction naturally leads to a very effi- ing the moments. For the formation of domains via nucle- cient simulation technique that provides information about ation and growth, we show that the leading order moments the crystallization history without a need for explicit time are exactly solvable. We present a procedure to approxi- marching during the simulation. The excellent efficiency of mate the cell-size distribution using the first few moments. the method enables us to perform large ensemble calcula- The procedure is validated by comparison with simulation tions to obtain reliable statistics of various microstructural results for selected nucleation and growth schedules in 3D. characteristics. Jerry Quek Marcelo F. Ciappina Institute of High Performance Computing Institute of High Performance Computing Singapore [email protected] [email protected]

David Wu Kevin Chu Institute of High Performance Computing, Singapore Serendipity Research [email protected] [email protected]

David Wu CP5 Institute of High Performance Computing, Singapore A Stochastic Approach to Coarsening of Cellular [email protected] Networks

We prove existence for a system of master equations mod- CP6 eling grain growth proposed by K. Barmak, D. Kinder- Building Effective Models from Scarce But Precise lehrer, I. Livshits and S. Ta’asan. The method used to Data prove existence for these nonlinear, integro-partial differential equations employs tools from both functional analy- Large-scale models in materials science are generally pa- sis and probability. The stochastic interpretation for the rameterized by least-squares fitting. To fit arbitrarily pre- evolution of the mesoscopic properties of this large scale cise ab initio data, however, we argue that it is more appro- metastable system we provide here is general enough to priate to begin with a ensemble of models that overfit the apply to other cellular networks. This approach leads to data. Within a Bayesian framework, a most likely model an internally consistent theory, and opens a new discus- can be defined that incorporates physical knowledge, pro- sion on asymptotics for the distribution of grains in a two vides error estimates for configurations not included in the dimensional network, which is the subject of future work. fit, and reproduces the original data exactly. We apply this approach to the Ca[Zr,Ti]O3 solid solution. Albert Cohen Visiting Research Instructor Eric Cockayne Michigan State University NIST MS10 Abstracts 57

[email protected] the surrounding normal tissue. None of the non-invasive, imaging techniques used by clinicians to find and diagnose Axel Van De Walle tumors provides the critical information about the stiffness California Institute of Technology of the imaged tissues. We propose a novel technique of dif- [email protected] ferentiating between benign and malignant tumors based on their corresponding Youngs moduli obtained using information provided by image mass spectroscopy. CP6 Image-Based Analysis of Microstructures with Anthony Palocaren OOF Engineering Science and Mechanics Penn State Univeristy Material scientists have access to a wealth of image data [email protected] on microstructures from various sources, such as micro-CT, serial sectioning and various forms of microscopy, and of- Corina Drapaca ten their interest is in inferring the relevant physics from Department of Engineering Science and Mechanics these images. The software, Object-Oriented Finite Ele- Pennsylvania State University ment Analysis for Microstructures (OOF), has been devel- [email protected] oped at NIST for this purpose; it enables users to segment microstructure images, create high-quality meshes for computation and simulate the physical behavior of the mate- CP7 rial. In this talk, we will describe the capabilities of OOF Effective Properties of Random Elastic Media and and demonstrate OOF’s power with challenging examples. Their Isotropy Valerie Coffman, Gunay Dogan We present sufficient conditions on a symmetry group of a Mathematical and Computational Sciences Division random elastic medium that ensure isotropy of the homog- National Institute of Standards and Technology enized limit. These conditions involve the irreducibility of valeria.coff[email protected], [email protected] certain representations of the group in question. Our results also lead to an alternative proof of the representation Stephen Langer theorem for an isotropic elasticity tensor. Information Technology Laboratory National Institute of Standards and Technology Alen Alexanderian, Muruhan Rathinam, Rouben [email protected] Rostamian University of Maryland, Baltimore County [email protected], [email protected], Andrew Reid [email protected] Center for Theoretical and Computational Materials Science National Institute of Standards and Technology CP7 [email protected] Homogenization of a Weakly Randomly Perturbed Periodic Material CP6 We present an approach aiming at computing the first- Methods for Obtaining True Grain Size Distribu- order homogenized behavior of a randomly perturbed pe- tions from Cross Section Measurements riodic material. More precisely, we are interested in the homogenization limit as → 0 of the field Sectioning methods are frequently used to measure grain sizes in materials. These methods do not provide accurate x x x x A ,ω A b ,ω C grain sizes, however, because random sections are always η = per + η per smaller than the true sizes of solid objects, as noted by Wicksell, [Biometrika, 17 (1925), pp. 84-99]. We present where Aper and Cper are deterministic periodic matrices a method for deducing true grain size distributions from and bη is a “small’ stochastic perturbation. Our approach, those determined from specimen cross sections, either by which is rigorously founded in a certain class of settings, measurement of equivalent grain diameters or mean linear proves to be very efficient from a computational point of intercepts. view for even more general settings. Kristina A. Lord Arnaud Anantharaman Iowa State University ENPC-CERMICS Ames Laboratory [email protected] [email protected] Claude Le Bris Alexander King ENPC/CERMICS The Ames Laboratory [email protected] Ames, IA 50011 [email protected] CP7 Numerical Simulation of Wave Propagation in Ma- CP6 terials with Microstructure A Study of Elastography Based on Image Mass Spectroscopy Results of numerical simulations of one-dimensional wave propagation in microstructured solids are compared with Palpation is an important medical diagnostic tool which corresponding results in given layered media. A linear mi- is based on the fact that tumors tend to be stiffer than crostructure model based on Mindlin theory is adopted in 58 MS10 Abstracts

the framework of the internal variable theory. Fully cou- Frederic Legoll pled systems of equations are rewritten in the form of con- LAMI, ENPC servation laws. A modification of wave propagation algo- [email protected] rithm is used. It is shown how the initial microstructure model can be improved to match the better result. CP7 Mihhail Berezovski, Arkadi Berezovski, Juri Engelbrecht Correctors and Field Fluctuations for the p(x)- Institute of Cybernetics at Tallinn University of Laplacian with Rough Exponents Technology [email protected], Properties of local fields inside mixtures of two nonlinear [email protected], [email protected] power law materials are studied. This simple constitutive model is frequently used to describe several phenomena ranging from plasticity to nonlinear dielectric media. This CP7 work addresses a prototypical problem in the scalar set- Two-Scale G-Convergence and Its Applications ting. We provide the corrector theory for the strong ap- to Homogenisation of Non-Linear High-Contrast proximation of fields inside composites made from power Problems. law materials. These results are applied to deliver new multiscale tools for bounding the local singularity strength It is a resent results of Bouchitte, Felbacq, Zhikov and inside micro-structured media in terms of the macroscopic others that passing to the limit in high-contrast elliptic applied fields. PDEs may lead to non-classical effects, which are due to the two-scale nature of the limit problem. These have so Silvia Jimenez,RobertP.Lipton far been studied in the linear setting, or under the assump- Department of Mathematics tion of convexity of the stored energy function. It seems of Louisiana State University practical interest however to investigate the effect of high- [email protected], [email protected] contrast in the general non-linear case, such as of finite elasticity. With this aim in mind, we develop a new tool to study non-linear high-contrast problems, which may be CP8 thought of as a hybrid of the classical Γ-convergence (De Nanostructure Instability Induced by Anisotropic Giorgi, Dal Maso, Braides) and two-scale convergence (Al- Epitaxial Stresses laire, Briane, Zhikov). We demonstrate the need for such a tool by showing that in the high-contrast case the mini- The morphological evolution of an initially straight stripe mizing sequences may be non-compact in Lp space and the lying on a semi-infinite substrate is studied in the linear corresponding minima may not converge to the minimum regime when the mass transport mechanism is the diffusion of the usual Γ-limit. We prove a compactness principle of ad-atoms along stripe edges and when the heteroepi- for high-contrast functionals with respect to the two-scale taxy between the line and the substrate is anisotropic. It Γ-convergence, which in particular implies convergence of is found that anti-phase fluctuations grows faster than in- their minima. phase ones for selected values of epitaxial stress components such that a pinched shape preferentially emerges. Mikhail Cherdantsev, Kirill Cherednichenko Cardiff University Jerome Colin cherdantsevm@cardiff.ac.uk, [email protected] university of poitiers [email protected]

CP7 Jean Grilh´e Variance Reduction Methods for Stochastic Ho- PHYMAT-CNRS, University of Poitiers mogenization [email protected]

The homogenized matrix of a random material is known Pierre Muller from the solutions of the so-called corrector problems, CINaM-CNRS, UPR 3118, University of Aix-Marseille which, in the stochastic framework, are stochastic equa- [email protected] tions posed on the whole space Rd. In practice, these equations are solved numerically on a truncated domain. Because of this truncation, the approximated homogenized CP8 matrix is random. In this work, we explain how to reduce Micromechanics Model for Debonding of Elliptical its variance, using antithetic variables. Numerical simula- Particles tions illustrate the eﬃciency of the approach. A primary failure mode for particulate composites is the Ronan Costaouec dewetting of particles from the surrounding matrix. This CERMICS, ENPC nonlinear process in an inherently multiscale system results INRIA Rocquencourt, MICMAC Project team in complex physical behaviour. A cohesive law is incorpo- [email protected] rated into a micromechanics formulation to investigate the debonding of elliptical particles, for which the macroscopic Xavier Blanc response depends strongly on the misalignment between Universite Paris 6 the loading direction and the major axis of the ellipse. [email protected] Helen M. Inglis Claude Le Bris Department of Mechanical and Aeronautical Engineering ENPC/CERMICS University of Pretoria [email protected] [email protected] MS10 Abstracts 59

CP8 due to incident plane transverse wave at a plane inter- A Mathematical Tool for Investigating the Struc- face between two dissimilar thermo-elastic materials has tural Response of Composites Subjected to Impact been analyzed. The theory developed by Iesan (1986) for Loading thermo-elastic materials with voids has been used. There exist three sets of reflected and refracted coupled longi- A tool for analyzing the propagation of a wave in composite tudinal waves and transverse waves in the half-spaces of material due to an impact load is described. It consists of a thermo-elastic materials with voids when a transverse wave micromechanical model of wave propagation in composite is incident at the plane interface. The formulae for ampli- material using a lattice structure of a two dimensional plate tudes and energy ratios of various reflected and refracted divided into subcells. The top of the plate is impacted waves have been obtained. The amplitude and energy ra- by a wave (input) and a propagated wave is recorded at tios of various reflected and refracted waves are computed the bottom. The tool can allow the study of transmission numerically and the results are presented graphically for a loss due to impact of an acoustical wave or dissipation of specific model a mechanical impact. Examples of specific materials and composites will be illustrated and mathematical problems Sanasam S. Singh associated with the current version will be discussed. Pachhunga University College, Mizoram University Aizawl -796 001, MIZORAM: INDIA James A. Pennline [email protected] NASA Glenn Research Center [email protected] CP9 Jacob Aboudi Multiscale Modeling of Flow-Induced Semicrys- Tel Aviv University talline Morphologies in Polymer Fiber Spinning [email protected] A systematic multiscale approach is developed to model the flow-induced semicrystalline morphologies in polymer fiber Steve Arnold, Brett Bednarcyk spinning processes. It combines a non-equilibrium lattice- NASA Glenn Research Center based microscopic Monte Carlo simulation of the polymer [email protected], [email protected] chains, implemented efficiently using a lattice subdivision technique, with a non-equilibrium thermodynamics con- CP8 tinuum flow model of the polymer amorphous phase. We showed that as the extensional rate increases, the lamellar Maximization of Fracture Energy by Variation of semicrystalline morphology becomes less favored than the Shapes of Inclusions fibrillar, in agreement with what has been observed exper- Our goal is to design shapes of inclusions inside brittle imentally. composite materials yielding maximal fracture energy for a Antony N. Beris given load case. For each design the resulting crack pattern University of Delaware is computed as solution of an energy minimization prob- Newark, DE lem. The uncracked domain is modeled by linear elasticity [email protected] while the area close to the crack is described on a smaller scale taking into account non-linear cohesive effects. Nu- merically, this problem is solved by the FEM with cohesive Joydeep Mukherjee elements. The Dow Chemical Company Freeport, TX 77541 Marina Prechtel [email protected] Chair of Applied Mathematics II FAU Erlangen-Nuremberg [email protected] CP9 Adaptive Free Energy Computations for Crys- Günter Leugering talline Materials University Erlangen-Nuremberg Several processes in the thermo-mechanical behavior of Institute of Applied Math. crystalline materials arise from microscopic interactions be- [email protected] tween constituent atoms. As a result molecular dynamics simulations have become a valuable tool as they allow de- Paul Steinmann tailed resolution of such phenomena. Despite their accu- Chair of Applied Mechanics racy, atomistic simulations at the engineering space/time Friedrich-Alexander-University Erlangen-Nuremberg scales are impossible with current or forseeable compua- [email protected] tional capabilities. On the other hand, continuum theories are computationally efficient but their accuracy can be lim- Michael Stingl ited unless they are somehow informed from the atomistic Institut für Angewandte Mathematik properties. Important steps in this direction are a variety Universität Erlangen-Nürnberg, Germany of sequential or hierarchical multiscale methods which com- [email protected] bine atomistic models with coarse-graining schemes. The critical issue in coarse-graining equilibrium atomistic descriptions amounts to the computation of the free energy CP8 with respect to the collective variables of interest. Ex- Refraction of Transverse Wave at a Plane Interface isting efforts along these lines frequently employ (local) in Thermo-Elastic Materials with Voids (quasi)harmonic approximations to get a semi-analytic expression of the free energy. This approach however under- The problem of reflection and refraction of elastic waves estimates the temperature dependence, fails for tempera- 60 MS10 Abstracts

tures greater than half the melting point and is sensitive to the local atomic configurations. We developed computer unharmonicities of the interatomic potential which become algorithms and relevant software that enable simultaneous prominent at transitions between microscopic equilibrium fitting of multiple types of experimental data under vari- states. In order to connect atomistic and continuum de- ous bespoke restraints on atomic moves. Applications of scriptions we make use of the Cauchy-Born rule. At fi- this method to several practical material systems will be nite temperature, we consider a representative cell of the discussed to highlight the capabilities of this approach and crystal and impose boundary displacements according to the challenges that still need to be resolved. the macroscopic deformation gradient of the contiuum description. The problem therefore reduces to calculating the Victor Krayzman free energy landscape as a function of the nine (in three- National Institute of Standards and Technology dimensions) components of the deformation gradient (or [email protected] six-components of the Cauchy-Green strain tensor due to frame indifference). The core contribution of this paper is a Igor Levin novel, adaptive technique for calculating such free-energy NIST surfaces. The proposed procedure combines elements of [email protected] adavanced Monte Carlo sampling and statistical learning. We utilize an extended-space formulation where sampling is performed with respect to the macroscopic variables (or CP9 reaction coordinates). The free energy is estimated from Coarse Variables As Adapted Projections an evolving ensemble of non-equilibrium atomistic simulations. This estimate is used to bias the dynamics until Given an autonomous ODE system we aim to define (non- the whole free energy landscpe is identified. In contrast to trivial) scalar state functions that evolve autonomously. If existing techniques that employ dynamical arguments, we possible, such functions can be useful as candidates for un- are motivated from statistical learning theories and provide ambiguously initializable coarse dynamics in physical ap- rigorous bounds for convergence. We investigate the use of plications. The question motivates a mathematical restate- Bayesian sparseness priors that favor the discovery of free ment in terms of a first-order PDE. A computational ap- energy surfaces in high-dimensional domains. proximation is developed and tested on the Lorenz system and the Hald Hamiltonian system with promising results Phaedon-Stelios Koutsourelakis and intriguing questions. School of Civil and Environmental Engineering & Center for Applied Mathematics, Cornell University Likun Tan [email protected] Carnegie Mellon University [email protected] Ilias Bilionis Center for Applied Mathematics Amit Acharya, Kaushik Dayal Cornell University, Ithaca Civil and Environmental Engineering [email protected] Carnegie Mellon University [email protected], [email protected]

CP9 Lucio Soibelman In Silico Structure and Nanomechanics of Interme- Carnegie Mellon diate Filaments [email protected]

Intermediate filaments (IFs) are a major component of the cytoskeleton in eukaryotic cells, playing a vital role in pro- CP9 viding structural stability. Here we utilize an in silico ma- Coupled Atomistic-Continuum Study of Inertial teriomics approach to develop a structural model of IFs Effects for Brittle Cracks through the use of a multi-scale simulation. We report experimentally validated atomistic-level models of IF dimer A coupled method is proposed which employs the contin- and tetramer structures, and examine their response to me- uum elastodynamics model to introduce loading conditions chanical stress. A comparison with experimental nanome- and capture elastic waves, and uses molecular dynamics to chanics results shows good agreement. resolve the local structures at the atomic scale. A consistent coupling condition with special treatment of the Markus J. Buehler atomistic boundary condition is introduced at the inter- Civil and Environmental Engineering face. Application to the dynamics of a brittle crack under Masachussets Institute of Technology various loading conditions is presented, with a focus on the [email protected] inertial effects of the crack tip. Zhijian Yang CP9 Rochester Institute of Technology Reverse Monte Carlo Refinements of Local Atomic [email protected] Structure in Crystalline Materials

Exploitable properties of many functional crystalline mate- MS1 rials, such as ferroelectrics, high Tc superconductors, mul- Bounds on the Rate of Coarsening for the LSW and tiferroics, etc., are controlled by the local atomic order- Diffusive LSW Models ing (i.e. chemical ordering in solid solutions or correlated atomic displacements from the average lattice sites). Re- The Lifschitz-Slyozov-Wagner (LSW) model is one of the verse Monte Carlo refinements of local structure, which rely simplest models describing the phenomenon of domain on the Metropolis algorithm to fit the experimental data, coarsening. The talk is concerned with the problem of provide an opportunity for quantitative determination of estimating in a mathematically rigorous way the rate of MS10 Abstracts 61

coarsening for this model and its related diffusive (DLSW) cally Complex Mixtures version. Point-wise in time upper and lower bounds on the rate of coarsening are obtained for the classical LSW model Coarsening of three-dimensional two-phase structures is ex- with fairly general initial data. These bounds complement amined using nonconserved and conserved dynamics. For the time averaged upper bounds previously obtained by systems with 50% volume fraction evolving via both dy- Dai and Pego, and the point-wise in time upper and lower namics and 36% and 40% mixtures evolving via conserved bounds obtained by Niethammer and Velasquez for solu- dynamics, we find that the domains are bicontinuous, and tions with initial data close to a self-similar solution. Cur- have time-invariant scaled morphologies and topologies. rent work of the speaker and Mohar Guha to extend these We will discuss the evolution equation for the principal results to the DLSW model will also be summarized. curvatures of the interface, and the resulting flux of probability of finding a patch of interface with a given pair of Joseph Conlon principal curvatures. Department of Mathematics The University of Michigan Peter Voorhees [email protected] Northwestern University Dept. of Material Science and Engineering [email protected] MS1 Coarsening Rates for the Degenerate Cahn-Hilliard Equations MS2 A Boundary Integral Approach and Its Applica- Upper bounds on coarsening rates at long times are ob- tions to Crystal Growth tained for the degenerate Cahn-Hilliard equation, for all temperatures below the critical temperature and for all In this talk, we will develop a boundary integral method concentrations within the miscibility gap. These results for solving the quasi-steady crystal growth and epitaxial generalize the results of Kohn & Otto (2001). Additionally, thin film growth problem within the context of classical upper bounds on coarsening are obtained that are valid BCF model. We compare our numerical results with linear from early times, based on bounds from below on the free stability analysis and show that there exist critical condi- energy. Various time dependent transitions between vari- tions such that the evolving morphology can be controlled ous coarsening rates are shown to be possible. by the mass flux and related boundary conditions. This enables us to develop effective ways to control the evolving Amy Novick-Cohen morphologies. Department of Mathematics Technion IIT, Haifa, Israel Shuwang Li [email protected] Department of Applied Mathematics Illinois Institute of Technology Andrey Shishkov [email protected] Institute of Applied Mathematics and Mechanics Donetsk, Ukraine Xiaofan Li [email protected] Illinois Institute of Technology [email protected]

MS1 Crossover in the Coarsening Rates in Demixing Bi- MS2 nary Viscous Liquids A Phase Field Simulation of Step Flow Problem

We consider the demixing process of a binary mixture of Abstract not available at time of publication. two liquids after a temperature quench. In viscous liquids, the demixing is mediated by diffusion and convection. John Lowengrub The typical particle size grows as a function of time t,a Department of Mathematics phenomenon called coarsening. Simple scaling arguments University of California at Irvine based on the assumption of statistical self-similarity of [email protected] the domain morphology suggest the coarsening rate: from ∼ t1/3 ∼ t for diffusion-mediated to for flow-mediated. MS2 In joint works with Yann Brenier, Felix Otto, and Dejan A Level Set Simulation for Ordering of Quantum Slepcev, we derive the crossover of both scaling regimes. Dots The mathematical model is a Cahn-Hilliard equation with convection term, where the fluid velocity is determined by We present level set simulations for the ordering and self- a Stokes equation. The analysis follows closely a method organization of quantum dots. In particular, we will discuss proposed by Kohn and Otto, which is based on the gradient how variations of the potential energy surface for adatom flow structure of the evolution. diffusion affects ordering. Our results are compared to recent experiments that use the cleaved edge overgrowth Christian Seis technique, which is a promising technique to obtain or- Institut fuer Angewandte Mathematik dered arrays of quantum dots, where the size and position Universitaet Bonn of the dots can be controlled very well. Our results then [email protected] suggest what type of variations of the potential energy surface can potentially improve the uniformity of quantum dot MS1 arrays. Self Similarity During Coarsening of Morphologi- Christian Ratsch UCLA 62 MS10 Abstracts

Department of Mathematics elasticity, and in computation. [email protected] Stuart Antman Dept of Mathematics, Inst. Phys. Sci & Tech, Inst. MS2 Systems R Simulating Surface Energy Anisotropy Using Ex- UMCP tended Cahn-Hilliard Model [email protected]

We study the influence of surface and strain energies on heteroepitaxial thin-film growth. We propose an alternate MS3 way of simulating anisotropy for the surface energy by us- Nucleation of Austenite in Martensite ing the higher order terms in the free energy. To the second order, the system only have isotropic properties. We can In recent experiments of H. Seiner, austenite was nucle- produce different anisotropy by adding higher order terms ated via localized heating in a single crystal of CuAlNi to the energy. By choosing the right parameters, we can mechanically stabilized as a single martensitic variant. It study the behavior SiGe/Si thin film. This type of ex- was observed that the shape recovery process was always tended Cahn-Hilliard model has been previously studied initiated at a corner irrespective of the point of contact of to the 4th order, but to our knowledge no one has ever the localized heat source with the specimen. We present implemented all the terms in this system. One advantage an analysis of this phenomenon in terms of quasiconvexity of this energy is that it has the intrinsic regularization. properties of the energy density. We present numerical results using an adaptive, nonlinear multigrid finite-difference method. John Ball University of Oxford, United Kingdom Solmaz Torabi [email protected] Department of Materials Science and Engineering University of California, Irvine Konstantinos Koumatos [email protected] Oxford Centre for Nonlinear PDE Oxford University Zhengzheng Hu [email protected] North Carolina State University Math Department [email protected] MS3 An Iterated Homogenization Method to Study John Lowengrub Cavitation in Hyperelastic Solids Department of Mathematics We propose a novel formulation to study cavitation in University of California at Irvine solids that: (i) is applicable to large classes of nonlinear [email protected] elastic materials, (ii) allows for 3D general loading conditions with arbitrary triaxility, (iii) incorporates direct in- MS2 formation on the initial shape, spatial distribution, and mechanical properties of the underlying defects at which Smoothed Boundary Method for Problems in Ma- cavitation can initiate, and (iv) is, at the same time, com- terials Science putationally tractable. The proposed framework is based In this presentation, we will describe an approach for on an iterated homogenization method that allows for the solving partial differential equations with general bound- construction of exact solutions for the mechanical response ary conditions imposed on arbitrarily shaped boundaries, of nonlinear elastic materials containing random distribu- along with the mathematical derivation. To demonstrate tions of initially infinitesimal cavities (or defects). The the general applicability of this approach, we provide four relevant analysis reduces to the study of Hamilton-Jacobi examples: the diffusion equation with both Neumann equations in which the initial size of the cavities plays the and Dirichlet boundary conditions, the diffusion equation role of time and the applied load plays the role of space. with surface diffusion, the mechanical equilibrium equation Oscar Lopez-Pamies and the equation for phase transformation with additional S.U.N.Y. Stony Brook boundaries. Stony Brook, USA Hui-Chia Yu, Hsun-Yi Chen, Katsuyo Thornton [email protected] Department of Materials Science and Engineering University of Michigan Martin Idiart [email protected], [email protected], [email protected] Universidad Nacional de La Plata [email protected]

MS3 Structured Elastic Media MS3 On the Symmetry of Energy Minimising Deforma- This lecture treats a variety of properly invariant dissi- tions in Nonlinear Elasticity pative and regularizing mechanisms for the dynamics of nonlinearly elastic rods and of 3-dimensional nonlinearly We present a new symmetrisation procedure applicable to elastic bodies. The constitutive equations for the resulting deformations of spherically symmetric, nonlinearly elastic, structured media play a central role in stability studies, compressible shells. The procedure can be used to prove the treatment of incompressibility, the theory of shocks in the symmetry of energy minimisers obtained using the direct method of the Calculus of Variations in the case when symmetric boundary conditions are imposed. Our meth- MS10 Abstracts 63

ods apply to classes of polyconvex stored energy functions motors where the shape change is a bend, rather than an and involve use of the isoperimetric inequality to obtain elongation or contraction. We analyze in detail the physical lower bounds on the energy of deformed spheres in terms mechanisms which bring about the motion, and discuss the of their deformed area. These bounds turn out to be sharp origins and path of the momentum current which is gen- in the case of the symmetrised deformation. erated. We present the results of numerical simulations, and compare these with experimental observations. Some J. Sivaloganathan novel approaches to motor design will be discussed. University of Bath (UK) [email protected] Peter Palffy-Muhoray Liquid Crystal Institute Scott Spector Kent State University Southern Illinois University mpalff[email protected] [email protected] Xiaoyu Zheng Dept of Mathematics MS4 Kent State University Energy Minimizers for a Class of Incompressible [email protected] Liquid Crystal Elastomers Mark Warner We present results on existence of minimizers and qualita- Cavendish Laboratory tive behavior for the Warner-Terentjev energy in a certain University of Cambridge material regime. [email protected] Patricia Bauman Purdue University MS4 [email protected] The Mechanics of Nematic Glasses with Topolog- ical Defects - How to Develop a Non-developable MS4 Surface The Effects of Strain on the Orientational Distri- Nematic solids suffer considerable elongations and contrac- bution of Particles on a Rubber Surface tions along or perpendicular to a uniform director on temperature change or illumination. Gradients of director in- We discuss the effect of strain on the orientational distribu- stead lead to bend or curl. More subtle response occurs tion of particles on a surface of a rubber sheet. Both exper- when topological defects in the director field cause flat imental and modeling results will be presented for particles sheets of nematic glass to thermally or optically develop with various aspect ratios and strengths of attachement to localised Gaussian curvature. Reversibly inducing non- the rubber. developable surfaces offers a new mechanics paradigm for Dmitry Golovaty actuation and for adaptive surfaces. The University of Akron Carl Modes, Mark Warner Department of Theoretical and Applied Mathematics Cavendish Laboratory [email protected] University of Cambridge [email protected], [email protected] Peter Palffy-Muhoray Kent State University Kaushik Bhattacharya mpalff[email protected] Professor of Mechanics and Materials Science California Institute of Technology Xiaoyu Zheng [email protected] Dept of Mathematics Kent State University [email protected] MS4 A Nonlocal Model and Its Simulation of Liquid Ines Busuladzic Crystal Elastomers University of Akron [email protected] We consider a nonlocal model describing the dynamic behavior of nematic liquid crystal elastomers (LCEs) and Jeremy Neal solve the governing equations numerically. The model gives Kent State University dynamics for the material displacement, the scalar order [email protected] parameter and the nematic director, the latter two of which correspond to the order parameter tensor. The simulation shows that our model can successfully capture the shape MS4 changing phenomena of LCEs observed in experiments, and Motors Based on Shape Change: See How They also track the dynamics of the order parameter tensor. Run Wei Zhu Motors are devices which produce motion due to the trans- Mathematics, University of Alabama fer of energy, but not of momentum, to the device. Recent [email protected] advances in materials science have allowed the construction of motors where the motion is produced via changes Michael J. Shelley in the shapes of solid objects. In this talk, we consider New York University Courant Inst of Math Sciences 64 MS10 Abstracts

[email protected] terials

Peter Palffy-Muhoray This work considers materials whose microstructure is ran- Liquid Crystal Institute dom. Effective constitutive relations and associated varia- Kent State University tional principles are derived via ensemble averaging. The mpalff[email protected] form of the relations is preserved even if effective relations are expressed via “weighted averages’ of the displacement (for elasticity) or the vector potential (for electromagnet- MS5 ics). Even for elasticity, this form is invariant under arbi- Selected Features of Plasmonic Cloaking trary coordinate transformations. The variational principles have stationary character; related minimum principles, One of the exciting topics in the field of metamaterials is applicable to dissipative media, will be mentioned briefly. the concept of cloaking and invisibility. There have been various different methods and techniques for cloaking sug- John Willis gested in the recent years. Among those, we have been de- Department of Applied Mathematics and Theoretical veloping the scattering-cancellation-based plasmonic cloak- Physics ing. In this method, the induced dipole moment (and University of Cambridge possibly any of the higher-order relevant multipoles) in a [email protected] moderately-sized object when illuminated by electromagnetic waves can be canceled by the dipole moments gen- MS5 erated in the metamaterial shells around the object. The material parameters, the geometry,andthesizeofsuch Optical Cloaking and Transformation Optics metamaterial invisibility cloaks can be judiciously selected Metamaterials are artificially designed subwavelength com- in order to make the total induced dipole (or higher order) posites that possess extraordinary properties not existing moments in the cloak and the object together vanish, re- in naturally occurring materials. They can alter the prop- sulting in significant reduction of total scattering cross sec- agation of electromagnetic waves resulting in negative re- tions. Such plasmonic cloaking does not require anisotropy, fraction, subwavelength focusing and even in cloaking of inhomogeneity nor a specific geometry in the metamaterial macroscopic objects. Such unusual properties can be ob- cloaks, since the integrative effects of dipolar cancellation tained by a careful design of dielectric or metal-dielectric is the main mechanism behind such invisibility. We have composites on a deep sub-wavelength scale. Metamateri- studied numerous features of this plasmonic cloaking in als can now be designed with spatially-varying properties the past several years, and have obtained exciting results using coordinate transformation for new range of appli- that exhibit the advantages and constraints of this cloaking cations. I will discuss a few recent experiments demon- method. In this talk, we will present an overview of our strating intriguing phenomena associated with Metamate- work in this area, and highlight key features of plasmonic rials and transformation optics including 3D negative-index cloaking. metamaterials, carpet cloak and other transformation op- Nader Engheta tics applications. Department of Electrical and Systems Engineering Xiang Zhang University of Pennsylvania University of California at Berkeley [email protected] [email protected] Andrea Alu University of Texas at Austin MS6 Electrical and Computer Engineering Physical Models for Describing the Forced Separa- [email protected] tion of a Molecular Bond Over the past decade, direct measurements of the mechan- MS5 ical strengths of bio-protein bonds have been reported, and Cloaking vs. Shielding in Transformation Optics the data provide an glimpse into the realm of material structure and its evolution. The data also offer a chal- It is generally believed that transformation optics based lenge to develop a quantitative description of the molec- cloaking, besides rendering the cloaked region invisible to ular phenomena being interrogated. In particular, a uni- detection by scattering of incident waves, also shields the fying theme in the study of these phenomena has been to region from those same waves. We exhibit a coupling be- extract microscopic characteristics of the bonds from the tween the cloaked and uncloaked regions, and as one ap- macroscopic data obtained, with a view toward compar- plication, show how to hide sensors in the cloaked region ing bond structures based on behavior or controlling bond and yet enable them to efficiently measure the waves inci- behavior through control of environmnent. The process dent on the exterior of the cloak, an effect similar to the of protein-protein debonding can be described function- plasmon-based approach of Alú and Engheta. ally as a transition from one stable configuration of the system to another, with passage through an unstable in- Allan Greenleaf termediate configuration. Accessible configurations are de- Department of Mathematics fined by means of a landscape surface in a space spanned University of Rochester by both random coodinates and external coordinates rep- [email protected] resenting loading. For the case of time dependent loading, the landscape itself is time-dependent, pushing the frame- MS5 work beyond the direct application of Kramers’ theory and similar models for calculating bond reaction characteristics Effective Constitutive Relations and Variational from physical properties of the landscape. In this contri- Principles for Waves in Composites and Metama- bution, we use the established picture of bond behavior for MS10 Abstracts 65

time-indenpendent landsapes as the point of departure for 3D Viscous Flows considering resisting force probablity distribtions and interaction energy landscapes with multiple dimensions for Vesicles are locally-inextensible closed membranes that transient bond separtion processes. possess tension and bending energies. Vesicle flows model numerous biophysical phenomena that involve deforming Ben Freund particles interacting with a Stokesian fluid. We will present Brown University new schemes for simulating the three-dimensional hydrody- Division of Engineering namic interactions of large number of vesicles. They incor- [email protected] porate a stable time-stepping scheme, high-order spatio- temporal discretizations, spectral preconditioners, and a new reparameterization scheme capable of resolving ex- MS6 treme mesh distortions in dynamic simulations. The Non-equilibrium Thermodynamics and Kinet- ics of Focal Adhesion Dynamics Shravan Veerapaneni Courant Institute We present focal adhesion dynamics via a non-equilibrium New York University thermodynamics treatment, which is derived from har- [email protected] monic transition state theory. For this purpose we consider several competing thermodynamic driving forces that are both chemical and mechanical in origin. Crucially, we MS7 have found a work-based symmetry-breaking mechanism Dynamic Homogenization of a Non-linear Lattice that enables the dominant treadmilling mode of focal adhesion dynamics. Our findings hold for a variety of models, The talk deals with a problem of dynamic homogenization suggesting that the underlying mechanisms are are widely which accounts for kinetic energy of phase transition in a applicable to the dynamics of a broad class of biological bi-stable lattice. In the course of dynamic transition, a soft matter. part of the energy is radiated and dissipated due to high frequency oscillations and waves. It is necessary to ac- Krishna Garikipati count for the dissipated high frequency part of energy in Mechanical Engineering order to construct an adequate description of the behavior University of Michigan, Ann Arbor. of the microstructured material or dynamically homoge- [email protected] nized model. We derive a macrolevel description of a model problem, analyze the solution at the micro-level, and ob- Joseph Olberding tain consistent equations for the homogenized system. The University of Michigan computed on the micro-level quantities such as energy loss Department of Biomedical Engineering which accompanies the waves of transitions are used in the [email protected] derivation. Elena Cherkaev Michael Thouless University of Utah University of Michigan Department of Mathematics Depts of Mech. Engr. and Materials Sci & Engr. [email protected] [email protected] Andrej V. Cherkaev Ellen Arruda Department of Mathematics University of Michigan University of Utah Dept of Mech. Engr. and Prog. in Macromol. Engr. [email protected] [email protected]

MS7 MS6 Hysteresis Due to Non-monotone Material Be- Cytoskeletal Dynamics Simulations: A Minimalis- haviour Inside Many Particle Systems tic Approach We study storage problems of the following kind. A many- We discuss about coarse-grained approaches to modeling particle system is used to reversibly store and release a for- cytoskeletal dynamics in a living cell (Biophys. J. 88 (2005) eign substance. Examples are the storage of hydrogen in 3707; PNAS 104 (2007) 4937), using the red blood cell small magnesium particles, the storage of lithium in small as example. The fundamental distinction between living iron phosphate particles and the storage of air in elastic matter such as tissues and cells with traditional engineer- rubber balloons. The three storage systems have in com- ing materials is that living matter consumes high-quality mon: 1. Non-monotone constitutive behavior of the indi- energy non-stop. The eﬀect of such metabolic energy con- vidual particles and spherical rubber balloons. 2. Phase sumption on cytoskeletal structural evolution and mechan- transition and hysteresis of the particle ensemble during ical properties are investigated by computer simulations. loading and unloading. Ju Li University of Pennsylvania We describe the evolution of the processes of loading and [email protected] unloading by a kinetic equation of Fokker-Planck type. There are two small parameters that control whether those processes run in the vicinity of the Maxwell line or whether MS6 they exhibit strong hysteretic behavior. Large Scale Simulations of Vesicles Suspended in Wolfgang Dreyer Weierstrass Institute for Applied Analysis and Stochastics 66 MS10 Abstracts

Berlin, Germany MS8 [email protected] Self Assembly of Colloidal Spheres

Clemens Guhlke We present an analytical method, using graph theory and Weierstrass Institute for Applied Analysis and Stochastics geometry, that is capable of deriving all structures into B which N colloidal particles can self-assemble in thermody- [email protected] namic equilibrium. We derive such structures up to N =10 and present conjectures for N>10. We also present a method for directing the self-assembly of the particles such MS7 that any N particle equilibrium structure self-assembles Wave Propagation and Thermalisation in Hamilto- with 100% yield. nian Lattices Natalie Arkus Hamiltonian lattices provide simple models for crystals and Rockefeller University solids but obey a quite complex dynamical behaviour, in [email protected] particular when studied on a macroscopic scale. A key phenomenon in this context is the onset of dispersive shocks, in which a Hamiltonian lattice self-thermalises via modulated MS8 travelling waves. In this talk we present some new results Growth of Objective Structures by Self-assembly about several types of travelling waves in FPU chains. In particular, we discuss the existence of action-minimising The ideas of Caspar and Klug (Physical principles in heteroclinic waves and show that their existence is closely the construction of regular viruses, Cold Spring Harbor related to a geometric area condition for the interaction po- Symp. Quant. Biol. 27 (1962), 1–24) on equivalence and tential. Afterwards we use these results and describe sev- quasi-equivalence of viral capsids suggest a precise con- eral macroscopic Riemann solvers for FPU chains which cept, termed “objective structures’, that summarizes an involve dispersive shocks, conservative shocks, and com- essential feature about their construction. An objective posite waves. structure is a collection of identical molecules for which corresponding atoms in each molecule see the same envi- Michael Herrmann ronment up to orthogonal transformation. Objective struc- Oxford Centre for Nonlinear PDE tures include many of the most widely studied structures Mathematical Institute, University of Oxford in science today, including carbon nanotubes, the other [email protected] parts of viruses like necks, tails and baseplates, the cilia of some bacteria, DNA octahedra, buckyballs, actin and Jens Rademacher collagen and many other common proteins, and typical CWI, Amsterdam, NL nonrods, nanosprings and nanowires being synthesized by [email protected] methods of self-assembly. We discuss quantitative mathematical theory for the self-assembly process, and present some experiments suggested by this theory. MS7 Richard James,YanivGanor Coherent Structures in Granular Crystals: from Department of Aerospace Engineering and Mechanics Traveling Waves to Discrete Breathers and Beyond University of Minnesota In this talk, we intend to give an overview of our recent the- [email protected], [email protected] oretical, numerical and experimental activity in the theme of solitary nonlinear waves that arise in granular crystals MS8 made up of elastically interacting spherical beads subject to Hertz’s law. We start by examining beads of a sin- Minimal Energy Polymer Packings gle type, reviewing the theory of highly localized (nearly We study the structural and mechanical properties of compact) solitary traveling waves that exist therein and model collapsed polymers using tangent, ‘sticky’ hard- we consider the possibility of discrete breathers in the 1d sphere chains. For small chains, using analytical tech- granular chain. We then insert a single or multiple de- niques, we enumerate all low-energy packings. For larger fect beads (e.g. of different mass) and examine how this chains, we employ molecular dynamics simulations to study insertion modifies the underlying linear spectrum and the how the quench rate affects the structure of packings and nonlinear states emanating from it. We find interesting transitions from one low-energy packing to another. These bifurcation phenomena especially when inserting multiple studies will elucidate how chain connectivity affects the defects, such as next-nearest-neighboring ones. We illus- packing and dynamics of adhesive hard spheres. trate how to generalize this paradigm of “defect insertion’ to an infinite limit of the so-called dimer lattice. In that Corey S. O’Hern limit, we consider both solitary traveling waves and discrete Yale University breathers. Time permitting, generalizations to other het- Departments of Mechanical Engineering and Physics erogeneous or even disordered chains, as well as to higher [email protected] dimensional examples will also be given.

Panayotis Kevrekidis Robert Hoy UMass, Amherst Yale University [email protected] Department of Physics [email protected]

MS8 Particle Packing Problems: From Kepler and Be- MS10 Abstracts 67

yond MS9 Predictive Theory for the Grain Boundary Char- Packing problems, such as how densely nonoverlapping acter Distribution particles fill d-dimensional Euclidean space Rd are ancient. We provide the putative exponential improvement on a Most technologically useful materials are polycrystalline 100-year-old lower bound on the maximal sphere-packing d microstructures composed of a myriad of small grains sepa- density due to Minkowski in R in the asymptotic limit rated by grain boundaries. The energetics and connectivity d →∞. Our study suggests that disordered (rather than of the grain boundary network plays a crucial role in de- ordered) sphere packings may be the densest for sufficiently termining the properties of a material across a wide range large d. We also conjecture that the densest packings of the of scales. Cellular structures coarsen according to a local Platonic and Archimedean solids with central symmetry evolution law, a gradient flow or curvature driven growth, are given by their corresponding densest lattice packings. for example, limited by space filling constraints, which give This is the analogue of Kepler’s sphere-packing conjecture rise to changes in the configuration. There are two aspects for these solids. of coarsening, geometric growth and texture development. The main objective of this presentation is to show that they Salvatore Torquato may be decoupled and characterized by different types of Chemistry and Princeton Center for Theoretical Science evolution processes, leading to statistically different types Princeton University of coarsening rates. We consider the grain boundary char- [email protected] acter distribution, the GBCD, a basic texture measure, and outline a possible entropy based theory for it which MS9 suggests that the GBCD statistic satisfies a Fokker-Planck equation. For this, we introduce and study a simplified Phase-field Model of Stress Effect on Grain Growth critical event model which is driven by the boundary con- We report an efficient phase field formalism to compute ditions and reflects the dissipation principle present in the the stress distribution in polycrystalline materials with ar- real system. The proposed theory is consistent with the bitrary elastic inhomogeneity and anisotropy. The depen- numerical simulations and experiments. dence of elastic stiffness tensor on grain orientation is taken Yekaterina Epshteyn, Katayun Barmak into account, and the elastic equilibrium equation is solved Carnegie Mellon University using a spectral iterative perturbation method. We discuss [email protected], [email protected] its applications to computing residual stress distribution in systems containing arbitrarily shaped cavities and cracks (with zero elastic modulus) and to determining the effec- Eva Eggeling tive elastic properties of polycrystals and multilayered com- Fraunhofer InstitutComputer Graphics Research IGD posites. We implemented this approach in a grain growth [email protected] model to study the stress-driven grain boundary migration and grain growth in two and three dimensions. Maria Emelianenko George Mason University Saswata Bhattacharya [email protected] Penn State University Department of Materials Science and Engineering David Kinderlehrer [email protected] Carnegie Mellon University [email protected] Long-Qing Chen Materials Science and Engineering Shlomo Ta’asan Penn State University Department of Mathematical Sciences [email protected] Carnegie Mellon University [email protected] MS9 Simulations of Anisotropic Grain Growth MS9 Experimental Studies of Grain Boundary Migra- We describe a new method for simulating anisotropic grain tion growth in which the interface between each pair of grains is permitted an arbitrary, constant surface tension. This Grain boundary motion constitutes the microstructural algorithm is an extension of diffusion generated motion, mechanism of recrystallization and grain growth and is usu- with significant modifications made to ensure that the Her- ally accompanied by a dramatic change of material proper- ring angle conditions are satisfied at triple junctions. Pre- ties. This contribution reports on experimental efforts and liminary results are shown for simulations of analytically- quantitative results of grain boundary migration mainly known three-phase evolutions and for large-scale simula- in aluminum. Various driving forces and different grain tions of anisotropic grain growth beginning from thousands boundary geometries were chosen to study grain boundary of grains. mobility of flat and curved grain boundaries. Besides single boundaries also systems of grain boundaries were investi- Matt Elsey, Selim Esedoglu, Peter Smereka gated to reveal the effect of grain boundary junctions on Department of Mathematics grain growth. The measurements were complemented by University of Michigan molecular dynamics simulations of grain boundary motion [email protected], [email protected], and vertex simulations of grain growth. [email protected] Gunter Gottstein University of Aachen [email protected] 68 MS10 Abstracts

D. A. Molodov MS10 RWTH Aachen University Simulation of Dendritic Growth in Melt Flows [email protected] We simulate the evolution and free particle motion of an L. S. Shvindlerman individual nucleus. The melt ﬂow and the convective heat Russian Academy of Sciences transfer around the dendrites are simulated using a phase- [email protected] ﬁeld model. Di Yana MS10 Institute of Computational Mathematics, Ferroelectric Phase Transitions, Domain Evolution Chinese Academy of Sciences and Switching in Thin Films [email protected]

This presentation will discuss the applications of the phase field approach to predicting phase transitions, domain MS11 structures, and properties of ferroelectric thin films. In this Quasistatic Evolution for Cam-Clay Plasticity approach, a nanoscale domain structure is described using a set of spatially inhomogeneous distributions of order Cam-Clay nonassociative plasticity exhibits both harden- parameters such as polarization and strains. Their tem- ing and softening behavior, depending on the loading. For poral evolution toward equilibrium is obtained by solving many initial data the classical formulation of the qua- the coupled time dependent Ginzburg-Landau equations as sistatic evolution problem has no smooth solution. We well as the electrostatic and mechanical equilibrium equa- propose here a notion of generalized solution, based on a tions. In particular, it will be shown that one can use viscoplastic approximation. To study the limit of the vis- it to not only help interpreting experimental observations coplastic evolutions we rescale time, in such a way that but also provide guidance to achieve desirable transition the plastic strain is uniformly Lipschitz with respect to temperatures, specific domain states, domain wall orienta- the rescaled time. The limit of these rescaled solutions, tions, and domain wall mobility. It will also be shown that as the viscosity parameter tends to zero, is characterized mechanical boundary conditions and stress distributions through an energy-dissipation balance, that can be written may be manipulated to tune the coercive field and dramat- in a natural way using the rescaled time. We can also give ically enhance piezoelectric responses of ferroelectric thin a differential characterization of the limit, based on a gen- films. Examples to be discussed are drawn from recent col- eralization of the flow rule in the rescaled time. It turns laborations between the authors group in continuum and out that the proposed solution may be discontinuous with mesoscale modeling and a number of experimental groups respect to the original time, and our formulation allows on oxide film growth and characterizations. to compute the amouunt of viscous dissipation occurring instantaneously at each discontinuity time. Long-Qing Chen Materials Science and Engineering Gianni Dal Maso Penn State University SISSA, Trieste, Italy [email protected] [email protected] Antonio DeSimone MS10 SISSA, Trieste, Italy Phase-Field Modeling of Grain-Boundary Premelt- 34014 Trieste, ITALY ing [email protected]

Abstract not available at time of publication. Francesco Solombrino SISSA Alain Karma Trieste, Italy Distinguish Professor [email protected] Northeastern University [email protected] MS11 MS10 Non Associative Plasticity Modeling and Simulation of Two Phase Flow on In this joint work with JFB and MGM we uncover a vari- Rough Surface ational structure for a large class of materials that behave plastically, but with a flow rule which is unrelated to the In this talk, I will first describe a newly developed phase yield surface. This is of special significance when studying field model for two phase fluid flow based on Cahn Hilliard various soil or rock-like materials. Navier Stokes equation with generalized Navier boundary condition. Efficient numerical method for the model will be Gilles Francfort discussed. We then present some numerical results on two UniversitédeParisNord phase flow on rough and patterned surfaces. Issues related Villetaneuse, France to drop formation, dripping to jetting transition will also [email protected] be discussed.

Xiao-Ping Wang MS11 Hong Kong University of The Wigner-Fokker-Planck Equation and the Size Science and Technology Eﬀect on Resistivity in Polycrystalline Materials [email protected] Recent experimental results attribute increased resistivity MS10 Abstracts 69

in small conductors to grain boundary scattering. The namics of isotropic membranes is presented. Based on the Wigner-Fokker-Planck equation yields a temperature de- membrane’s force and torque balance equations and the pendent open quantum kinetic model of electron flow in a fiber’s balance of molecular fields, the model provides the polycrystalline wire. The equation models electron scatter- governing equations for the membrane’s velocity and cur- ing from an electric potential representing the lattice and vature and the fiber structure (fiber orientation and order). grain boundaries, and diffusive electron-phonon scattering with a Fokker-Planck operator. Resistivity is extracted from steady-state solutions computed with the discontinu- Alejandro D. Rey, Yogesh Kumar Murugesan ous Galerkin method. Department of Chemical Engineering McGill University Richard Sharp [email protected], Department of Mathematical Sciences [email protected] Carnegie Mellon University [email protected] MS12 Kinetic Modeling of Biological Systems MS12 Pressure Driven Flow of a Wormlike Micellar Mix- I will present a kinetic theory for a biofilm system with ture in a Straight Mircrochannel active polymeric components. The networked biopolymers and bacteria interact with the surrounding nutrient and The inhomogeneous (shear-banding) response of the VCM background fluid to produce the biofilm material system. I model (Vasquez, Cook, McKinley 2007) in steady rectilin- will give a detailed discussion on the structure of the gov- ear pressure-driven channel flow is examined. The VCM erning system of equations, growth modes, and nonlinear model is a microstructural network model developed to interaction among the fluid components. Finally, rheolog- describe flows of concentrated solutions of wormlike mi- ical implication will be discussed as well. celles. The model comprises of a set of coupled, nonlinear partial differential equations, which incorporate breakage Qi Wang and reforming of two micellar species (a long species A University of South Carolina and a shorter species B) in addition to reptative and Rou- [email protected] sian stress-relaxation mechanisms. We report on results for pressure-driven flow in microfluidic devices with rect- angular cross-sections. The velocity profile predicted in MS12 a straight channel deviates from the parabolic profile ex- Maier-Saupe Theory in 4D pected for a constant viscosity fluid and exhibits strong shear bands near channel walls. This (nonlocal) model in- Maier-Saupe theory is the canonical mean field description volves diffusive terms both through Brownian motion and of thermotropic nematic liquid crystals. In this talk, we ex- through the finite length of the worms. The relevant di- amine the predictions of the theory in four spatial dimen- mensionless (diffusive) parameter controlling the width of sions. Representations of the order parameter tensor and the transition region is a Peclet number; i.e. a microstruc- the existence of new phases will be discussed. The phase tural diffusion length scaled by a typical device length diagram, based on numerical solution of the self-consistent scale. Recent experiments have shown that relative mag- equations and Landau theory will be presented. nitude of such terms become increasingly important in mi- Xiaoyu Zheng crofludic devices. Simulations with the VCM model show Dept of Mathematics that decreasing the characteristic size of the diffusive cou- Kent State University pling between the stress and fluid microstructure results in [email protected] pronounced non-local effects felt across the flow channel.

Pamela Cook Peter Palﬀy-Muhoray Dept of Mathematical Sciences Liquid Crystal Institute UofDelaware Kent State University [email protected] mpalﬀ[email protected]

Michael Cromer MS13 University of Delaware [email protected] The Continuum Mechanics of Liquid Crystal Elas- tic Fluids with Line Defects

Gareth McKinley We develop the continuum mechanics of nonlinear vis- Dept of Mechanical Engineering coleastic fluids with disclination and dislocation defects. Massachusetts Institute of Technology Driving forces on the defects (under no dynamical restric- [email protected] tion) are a natural outcome of our analysis. Both types of defect motion are dissipative, following rigorous kinematic conservation laws for line densities that allow the MS12 independent specification of defect kinetics. With appro- Structure and Rheology of Fiber-Laden Mem- priate restrictions on kinematic ingredients, the nematic, branes Via Integration of Nematodynamics and smectic (A and C), and cholesteric liquid crystal phases, Membranodynamics the solid nematic and smectic elastomers and the nematic glass can all be modeled by our theory. A primary feature A study of the structure and dynamics of rigid fiber-laden of this approach is the feasibility of numerical calculations deformable curved fluid membranes based on an viscoelas- of the interaction of multiple dynamic defects. tic model that integrates the statics of anisotropic membranes, the planar nematodynamics of fibers and the dy- Amit Acharya,KaushikDayal 70 MS10 Abstracts

Civil and Environmental Engineering Mitchell Luskin Carnegie Mellon University School of Mathematics [email protected], [email protected] University of Minnesota [email protected] Shelley Anna Carnegie Mellon University Christoph Ortner [email protected] University of Oxford [email protected]

MS13 Mathematical Analysis for the Peridynamic Non- MS14 local Continuum Theory A Field Theoretical Approach to the Quasi- Continuum Method We develop a functional analytical framework for the nonlocal peridynamic models. Various properties of the nonlo- We present a field formulation for the quasi-continuum cal peridynamic operators are examined. The connections method based on the following ideas: (i) reformulation of to the classical elastic models are also provided. the extended interatomic interactions into a local variational problem that describes the energy of a system via Qiang Du potential fields; (ii) quasi-continuum reduction of these po- Penn State University tential fields using an adaptive finite-element discretization Department of Mathematics of the formulation. We demonstrate that the present for- [email protected] mulation resolves inconsistencies present in previous formulations of the quasi-continuum method, and show using Kun Zhou numerical examples the remarkable improvement in the ac- Penn State University curacy of solutions. [email protected] Vikram Gavini,MrinalIyer Mechanical Engineering, University of Michigan MS13 [email protected], [email protected] Tight Bounds on Failure Surfaces for Random Elastic-Plastic Composites MS14 The failure of load bearing structures made from composite Analysis of Quasicontinuum Methods: Introduc- materials is a multiscale phenomena. It involves quantify- tion and Overview ing force transfer from the structural length scale down to the microscale. In this talk we provide new tools for quan- In the first half of the talk I will give a point-of-view- in- tifying the effects associated with force transfer from struc- troduction and overview to the development of the quasi- tural length scales to the length scale of the heterogeneity continuum method, with particular emphasis on the anal- of the reinforcement phase. We report on new tight bounds ysis in the zero- temperature static case. I will conclude for the strength domains for elastic-plastic composite mate- this part with some remarks on the most important open rials when only the volume fractions of the constituent ma- questions. In the second half of the talk, I will present a terials are known. These calculations provide bench marks new force-based quasicontinuum formulation, developed in that can be used to validate phenomenological models and joint work with E. Süli and C. Makridakis. Our motivation numerical computations. and starting point are the unusual and potentially damag- ing stability properties of the ”classical” force- based QC Robert P. Lipton method (described in recent work with M. Luskin and M. Department of Mathematics Dobson). By formulating a variational form of the atom- Louisiana State University istic equilibrium equations and coupling stress tensors in- [email protected] stead of pointwise forces we obtain an alternative force- based coupling scheme that has superior stability proper- Bacim Alali ties. Department of Mathematics University of Utah Christoph Ortner [email protected] University of Oxford [email protected]

MS14 MS14 Convergence of Quasicontinuum Approximations Atomistic-to-Continuum Coupling Methods Based The quasicontinuum method reduces the computational on Domain Decomposition cost of approximating the solution of atomistic equilibrium equations by directly coupling the atomistic model with a The atomistic-to-continuum coupling problem has similari- continuum approximation. We present numerical analy- ties with the classical continuum-to-continuum domain de- sis for a one-dimensional model problem and evaluate the composition problem. We will explore some of these simi- accuracy and eﬃciency of quasicontinuum approximations larities and address the extent to which both problems can with a focus on the choice of coupling at the atomistic-to- be placed within the same mathematical and algorithmic continuum interface. framework. We will address domain decomposition methods that can be harnessed when solving the atomistic-to- Matthew Dobson continuum coupling problem, and provide some analysis CERMICS - ENPC giving guidance about when the scheme will produce a sat- [email protected] MS10 Abstracts 71

isfactory answer. boundaries with eigenstrain, both spherical and plane (by a limiting procedure), are also obtained, and the analogy Michael L. Parks of the Peach-Koehler forces of dislocations and inclusions Sandia National Laboratories is shown. [email protected] Xanthippi Markenscoff, Luqun Ni University of California, San Diego MS15 [email protected], [email protected] Beating the Clock with Atomistic Simulation of Dislocations MS15 Atomistic simulation is uniquely suited to study the inter- A Continuum Model for Dislocation Dynamics in action of dislocations with each other and with surfaces and a Slip Plane interfaces. However, the accessible timescale is often a se- vere challenge. In this talk I will discuss about theoretical We derive a continuum model for the PeachKoehler force and numerical issues associated with predicting elementary on dislocations in a slip plane. To represent the disloca- dislocation behavior at anthropological timescales, namely tions, we use the disregistry across the slip plane, whose seconds to hours. For strongly driven systems where the gradient gives the density and direction of the disloca- saddle-point is far from the ending equilibrium, a so-called tions. The continuum model is derived rigorously from the free end modification to the Nudged Elastic Band method PeachKoehler force on dislocations in a region that con- (PNAS 104 (2007) 3031; Phys. Rev. Lett. 100 (2008) tains many dislocations. The resulting continuum model 025502) has proven to be quite effective. canbewrittenasthevariationofanelasticenergythat consists of the contribution from the long-range elastic in- Ju Li teraction of dislocations and a correction due to the line University of Pennsylvania tension effect. We validate our model by performing linear [email protected] stability analysis and numerical simulation and compar- ing the results with those of discrete dislocation dynamics model. MS15 Magnetism-induced Dislocation Mobility and Yang Xiang Cross-slip in NiAl: A Multiscale Modeling Hong Kong University of Science and Technology [email protected] Can magnetism be responsible for dislocation mobility and cross-slip, thus the mechanical strength of materials? The answer is yes. With intermetallic NiAl alloy as an example, MS16 we perform multiscale simulations to study how magnetic Ab Initio Enumeration of 3-periodic Weavings and impurities could affect dislocation mobility and cross-slip. Catenated Nets from 2D Hyperbolic Tilings. Re- More specifically, we examine the effect of 3d-transition sults, Applications and Open Questions metal impurities (Ni, Fe and Co) on the core structure, Peierls energy and stress of a screw dislocation in NiAl. A variety of nets and weavings can be formed in 3D The multiscale approach combines quantum mechanical de- (euclidean) space by folding patterns created in 2D hy- scription of the dislocation core with DFT and empirical perbolic space onto triply-periodic minimal surfaces em- atomistic simulations of long-range strain field with EAM. bedded in 3D space (see S. J. Ramsden, V. Robins and Both spin-polarized and non-spin-polarized DFT calcula- S. T. Hyde, ActaCryst. (2009). A65, 81–108; see also tions are carried out and compared against each other. We epinet.anu.edu.au). The ”epinet” project offers a multi- find that Fe impurities can introduce local magnetic mo- tude of structures available for materials modelling. A ments at the dislocation core and enhance dislocation mo- number of fundamental questions arise from these patterns, bility. Depending on concentrations, Ni and Co impurities some answerable, other not (yet). can either dissociate the dislocation or render spontaneous dislocation cross-slip. Stephen Hyde RSPhysSE Gang Lu Australian National University California State University Northtridge [email protected] [email protected] Myfanwy Evans Yi Zhao Applied Maths, Australian National University California State University Northridge [email protected] [email protected] Stuart Ramsden RSPhysSE MS15 Australian National University Self-forces of Moving Dislocations and Inclusion [email protected] Boundaries with Inertia Effects

On the basis of Noether’s theorem and the dynamic J in- Vanessa Robins tegral, the self-forces of Volterra dislocations moving in Australian National University generally accelerating motions are calculated with regular- [email protected] ization in the sense of distributions. A particular analysis involves the singularity at the forming Mach cone as MS16 the dislocation crosses the shear-wave-speed (with Surong Huang).The self-forces of dynamically expanding inclusion Three-periodic Tilings, Nets and Designed Synthe- 72 MS10 Abstracts

sis of Materials to create uniform arrays of nanostructures.

Crystal structures can be abstracted as nets (periodic con- Kristen Fichthorn, Yogesh Tiwary nected simple graphs). Such nets are carried by face-to-face Penn State University tilings of space by generalized polyhedra (cages)andmuch fi[email protected], [email protected] of our knowledge of nets has come from systematic enumeration of tilings. Particularly interesting to chemistry are edge-transitive nets which are carried by the duals of MS17 face-transitive tilings. The taxonomy of such structures Hierarchical Coarse-graining Methods for Complex and their relevance to the designed synthesis of targeted Stochastic Lattice Systems materials will be described. We will discuss a variety of coarse-graining methods for Michael O’Keeffe many-body microscopic lattice systems and in particular Department of Chemistry & Biochemistry systems dominated by the competition of short and long Arizona State University, Tempe, AZ 85287 range interactions. We focus on mathematical, numerical mokeeff[email protected] and statistical methods allowing us to assess the parameter regimes where such approximations are valid. Finally, motivated by related problems in the simulation of macro- MS16 molecular systems, we discuss mathematical strategies for The Mathematics and (Mathematical) Physics of reversing the coarse-graining procedure. The principal pur- Zeolites pose of such a task is recovering local microscopic information in a large system by first employing inexpensive I will discuss problems we face when designing algorithms coarse-grained solvers. to design zeolites. The problems range from purely combi- natorial (how to explore the space of four-regular graphs?) Markos Katsoulakis to group theoretic and topological (how to represent such UMass structures in a compact yet expressive way?) to physical [email protected] (how to find a good model for the energy of such a structure). MS17 Igor Rivin An Energy Localization Principle and Its Appli- Department of Mathematics cation to Fast Kinetic Monte Carlo Simulation of Temple University Heteroepitaxial Growth [email protected] Simulation of heteroepitaxial growth using kinetic Monte Carlo (KMC) is often based on rates determined by differ- MS16 ences in elastic energy between two configurations. This From Enumerated Graphs to Zeolites; The Mathe- is computationally challenging due to the long range na- matical Challenges of Identifying the Real Among ture of elastic interactions. A new method is introduced the Fanciful in which the elastic field is updated using a local approximation technique. This involves an iterative method that Zeolites are an important class of materials because of their is applied in a sequence of nested domains until a conver- microporosity. They contain sub-nanometer sized pores gence criteria is satisfied. These localized calculations yield and channels that allow small molecules to enter. By mod- energy differences that are highly accurate despite the fact eling zeolites as periodic, corner-connected, regular tetra- that the energies themselves are far less accurate: an ef- hedra (i.e. as periodic 4-valent graphs), we have been fect referred to as the principle of energy localization. This able to enumerate over 5 million hypothetical zeolite struc- is explained using the continuum analogue of the discrete tures. However, in nature, there are fewer than 200 known model and error estimates are found. In addition, a rejec- structures. In this talk, I will discuss some of the subtle, tion algorithm that relies on a computationally inexpensive and perhaps surprising, mathematical differences between estimate of hopping rates is used to avoid a substantial a real zeolite and many of the relaxed 4-valent periodic fraction of the elastic updates. These techniques are ap- graphs in our database. plied to 1 + 1 and 2 + 1 dimensional KMC simulations in physically interesting regimes. The simulations in 2 + 1 di- Michael Treacy mensions introduce additional approximations in order to Department of Physics further improve the performance of the simulations. Arizona State University, Tempe, AZ 85287 [email protected] Tim Schulze University of Tennessee Department of Mathematics MS17 [email protected] Kinetic Monte Carlo Simulation of Nanohut As- sembly on Al(110) Peter Smereka Al(110) homoepitaxy exhibits nanoscale self-assembly into Department of Mathematics huts with well-defined (100) and (111) facets. We used University of Michigan density-functional theory (DFT) to identify the mecha- [email protected] nisms needed to describe this three-dimensional assembly and incorporated these into a kinetic Monte Carlo MS17 (KMC) model. Our model predicts experimentally observed trends for this system. To achieve precise placement Extending the Computational and Phenomenolog- of Al nanohuts, we simulated thermal-field-directed assembly. Our results indicate that this technique can be used MS10 Abstracts 73

ical Scope of Kinetic Monte Carlo Simulations MS18 Phase-field Modeling of Reactive Wetting Two approaches are presented for extending the application horizon of kinetic Monte Carlo (KMC) simulations. During reactive wetting the fluid and solid substrate can re- First, a coarse-graining methodology is discussed in which act together chemically, so that the solid undergoes further lattice KMC simulations are mapped onto coarser grids. phase transitions. Such intermetallic formation introduces Using properly formulated rate averaging, the coarse- an additional free boundary into the problem description, grained simulations are shown to retain essential ingre- which becomes even more challenging than the classical dients of the full-resolution model that are required to problem of droplet spreading on an inert substrate. A four- capture dynamical and equilibrium properties. Secondly, phase, diffuse interface model for a ternary alloy system approaches for incorporating convective flow into lattice has been formulated, and numerical solutions describing KMC simulations of particle transport and clustering are the dynamics of the interface motion are being computed. discussed.

Talid Sinno Geoffrey McFadden Department of Chemical and Biomolecular Engineering National Institute of Standards and Technology University of Pennsylvania [email protected] [email protected] Walter Villanueva MS18 NIST [email protected] Phase-Field Studies of Crystal Cohesion during Late-Stage Solidification William Boettinger, James Warren This talk will discuss recent progress made in using both NIST conventional phase-field and phase-field-crystal simulations Metallurgy Division to characterize the complex interaction between solid- [email protected], [email protected] liquid interfaces that come into close contact during the late stages of solidification. When interfaces belong to different crystal grains, this interaction can be either attrac- MS18 tive or repulsive depending on the br¿the two grains. For Phase Field Models of Grain Boundaries: The strong repulsion, crystal cohesion is retarded and interface Good and the Bad bridging only occurs substantially below the liquidus temperature, thereby promoting hot cracking. Results will be Over the years, there have been many different approaches presented that shed light on various factors that control in- to modeling the dynamics of grain boundaries. In partic- terface bridging and the mechanical response of bicrystals ular, over the past two decades, a number of phase field in between the liquidus and bridging temperatures. models of grain boundary evolution have been developed, all with particular short-comings. In this talk I will review Alain Karma these approaches, discuss their advantages and disadvan- Distinguish Professor tages, and finally suggest a possible ”way” out. Northeastern University [email protected] James Warren NIST Metallurgy Division Ari Adland [email protected] Northeastern University [email protected] MS19 MS18 Electroactive Polymers Calculation of Interfacial Free Energies from Atom- This talk is motivated by soft dielectric elastomer actu- istic Simulation with Thermodynamic Integration ators. In these materials, deformation is obtained by an γ applied electric field mediated by the Maxwell stress. The The solid-liquid interfacial free energy, sl,playsacentral low electro-mechanical coupling efficiency has given rise to role in understanding a number of technologically impor- various attempts to improve the underlying materials. Of tant phenomena in physics, chemistry and materials sci- particular interest is heterogeneous media which can show ence, such as crystal nucleation and growth, dendritic solid- an unexpectedly large increase in coupling. This talk will ification, liquid-metal embrittlement, and wetting. In this γ describe the basis of this increase, and potential instabili- talk, I will review our work on the direct calculation of sl ties which can give rise to even larger deformation. for a number of model systems using molecular-dynamics simulation and thermodynamic integration. This discus- Kaushik Bhattacharya sion will highlight recent work where we use Cahn’s re- Professor of Mechanics and Materials Science formulation of Gibbs’ interfacial thermodynamics to deter- California Institute of Technology mine γsl along a solid-liquid coexistence curve by integra- [email protected] tion of data for the excess interfacial energy and stress, with specific application to the Lennard-Jones system. MS19 Brian Laird Material Instabilities in Nematic Elastomers University of Kansas [email protected] We discuss material instabilities in nematic elastomers, which are crucial for the interpretation of their mechanical response. These are mostly in the form of reversible, 74 MS10 Abstracts

elastic shear bands and they underlie the unusually soft MS20 response of these materials to imposed stretches. Dynamics of Colloidal Particles in Liquid Crystals Antonio DeSimone We employ 3D microscopy to study electrically-controlled SISSA, Trieste, Italy dynamics of colloidal particles in a liquid crystal. Particles 34014 Trieste, ITALY create defects of a dipolar type (hyperbolic hedgehogs) in [email protected] the otherwise homogeneous director field. The particles levitate in the nematic bulk thanks to the elastic repulsion from the bounding plates. By applying electric field one MS19 causes three dynamic effects: (1) backflow of the nematic A Micromechanical Approach of Localization Phe- and bidirectional motion of particles; (2) electrophoresis of nomena in SMAs the particles; (3) electrorotation. Localization phenomena are frequently observed in poly- Oleg Lavrentovich crystalline SMAs, and are known to be partly related to Liquid Crystal Institute material instabilities. Common micromechanical models Kent State University of SMAs result in convex estimation of the free energy and [email protected] therefore are not able to capture all the complexity of the localization phenomena. Using tools of quasiconvex analysis and homogenization, a non convex lower bound on the MS20 free energy of polycrystalline SMAs is proposed. That re- Stable States in a Coupled Energetic Model for In- sult is a step towards a better understanding of localization compressible Nematic Elastomers aspects in SMAs. We investigate an energetic model for incompressible ne- Michael Peigney matic elastomers. A unit-length molecular director and Laboratoire Central des Ponts et Chaussées an incompressible deformation are the unknown functions, Paris, France minimizers of a proposed coupled energy in R3.Working [email protected] in Sobolev spaces, we prove lower semi-continuity and existence of minimizers for the energy. Keeping incompressibility, we derive weak Euler Lagrange equations. Addition- MS20 ally, we consider 2-dimensional models with non-convex en- Mathematical Differences and Similarities Between ergy densities involving terms related to the volume con- High-TC and Low-TC Superconductors straint, and deduce existence and partial regularity results. We present recent results on the behavior of the Lawrence- Doniach system for layered superconductors occupying a Andrea C. Rubiano, Patricia Bauman bounded domain in three dimensions. The Lawrence- Purdue University Doniach system is the Euler-Lagrange system for a corre- [email protected], [email protected] sponding anisotropic Ginzburg-Landau energy used to describe anisotropic high-temperature superconductors. We prove that applied magnetic fields in a direction parallel MS21 to the layers do not produce vortices in energy minimiz- Flux Norm in a Finite-demensiona Homogenization ers, in contrast to the behavior of low-temperature three- Approximation with Non-separated Scales dimensional superconductors or the anisotropic ”effective mass” model in three dimensions. For nonparallel (tilted) The homogenization of PDEs with periodic or ergodic co- applied fields, vortices do form at a sufficiently large field, efficients and well separated scales is now well understood. and we characterize the critical modulus of this field in In a joint work with H. Owhadi (Caltech) we consider the terms of the angle it makes with the layers. We also present most general case of arbitrary bounded coefficients. Specif- results on the behavior of minimizers in parallel or slightly ically, we study divergence-form scalar elliptic equations tilted magnetic fields. and vectorial equations with such coefficients. For these problems we establish two finite-dimensional approxima- Patricia Bauman tions of solutions, which we refer to as finite-dimensional Purdue University homogenization approximations. We introduce a flux norm [email protected] and establish the error estimate in this norm with an explicit and optimal error constant independent of the contrast and regularity of the coefficients. A proper general- MS20 ization of the notion of cell problem is the key technical Patterns in Two-dimensional Nematics issue in our consideration.

I will present an extension of Onsager’s variational theory Leonid Berlyand of nematic liquid crystals to spatially inhomogeneous sys- Penn State University tems. Concentrating on the two-dimensional model I will Eberly College of Science provide a detailed description of vortex-like patterns and [email protected] their evolution induced by the diﬀusive transport (Doi) dynamics. MS21 Ibrahim Fatkullin Pade Approximations for Composites with Evolv- University of Arizona ing Structure Department of Mathematics [email protected] The talk discusses a problem of approximation of eﬀec- tive transport properties of a two-phase composite with slowly changing structure. The Stieltjes integral represen- MS10 Abstracts 75

tation is used to describe the effective properties of the Institute for Computational Engineering and Sciences composite. This representation relates the n-point corre- University of Texas at Austin lation functions of the microgeometry to the moments of [email protected] the spectral measure, which contain all information about the microstructure. Pade approximation of the spectral Graeme Henkelman function can be used to construct a minimal lattice whose Assistant professor at the University effective properties approximate the properties of the com- of Texas at Austin posite. The moments of the spectral measure character- [email protected] izing the structure, are exactly calculated using poles and residues of Pade approximation; this allows us to monitor Gregory Rodin the changes in the microgeometry using a small number of Aerospace Engineering and Engineering Mechanics parameters. University of Texas at Austin Elena Cherkaev [email protected] University of Utah Department of Mathematics MS22 [email protected] Bridging Fluctuating Hydrodynamics and Molecu- lar Dynamics Simulations Dali Zhang University of Calgary We devise a scheme to map the atomic representation of a Department of Mathematics fluid to field variables and show that field fluctuations in [email protected] FHD and all-atom MD simulations and their equation of state and transport coefficients can be matched quantitatively. We also show that the FHD equations can be gener- MS21 alized to use a viscoelastic rheological model with colored Electromagnetic Circuits noise. Finally, we develop a coupling scheme based the Lum- Chandler-Week theory of hydrophobicity to enable Maxwell’s equations bear a close resemblance with those combined particle/ field simulations. of linear elastodynamics. So a natural question to ask is: what is the electromagnetic analog of a mass-spring net- Nikolaos Voulgarakis work in elastodynamics? We assume the frequency is fixed UC Berkeley and construct such an analog, which we call an electro- Chemical Engineering Department magnetic circuit. By interchanging the roles of epsilon and [email protected] mu we also obtain magnetoelectric circuits. Then one can join electromagnetic and magnetoelectric circuits to obtain Jhih-Wei Chu hybrid circuits. Their response is measured in terms of Chemical Engineering the electric or magnetic field along or across the terminal UC Berkeley edges of the circuit. This response is governed by a sym- [email protected] metric matrix with negative semidefinite imaginary part. Conversely given any such matrix a recipe is given for constructing a hybrid circuit which has that matrix as its re- MS22 sponse matrix. A Hybrid Particle-continuum Method for Hydro- Graeme W. Milton dynamics of Complex Fluids University of Utah We describe a hybrid method coupling a fluctuating com- Department of Mathematics pressible Navier-Stokes solver with the I-DSMC particle [email protected] method. The continuum provides state boundary conditions to the particle subdomain, which in turn provides Pierre Seppecher fluxes to the continuum subdomain. We study the Brow- Institut de Math nian motion of a large spherical bead, as well as the relax- ’ematiques de Toulon ation of an adiabatic piston, and we find that the hybrid Universit correctly reproduces the particle simulations only if the ’e de Toulon et du Var continuum solver includes thermal fluctuations. [email protected] Aleksandar Donev Luis W. Alvarez Postdoctoral Fellow MS21 Lawrence Berkeley National Laboratory Controlled Self-assembly of Charged Particle [email protected] Monolayers John B. Bell Recently, self-assembly has emerged as an efficient method CCSE to create scale-independent regular structures. A problem Lawrence Berkeley Laboratory commonly encountered in experiment is little or no control [email protected] over the kinetics of structure formation. In this work, an optimal choice of macroscopic control parameters is identified. Using Molecular Dynamics, kinetics of self-assembly Alejandro Garcia is evaluated in systems proposed by Whitesides et. al.An San Jose State University idealized model is put forward to rationalize the results [email protected] observed in simulations. Berni Alder Nickolay Shestopalov Lawrence Livermore National Labs 76 MS10 Abstracts

[email protected] plex Ginzburg-Landau, the XY spin system and the screw dislocation energy functionals are variationally equivalent. Exploiting such an equivalence between dislocations and MS22 vortices, we can show new results concerning the asymp- Constrained Polymer Dynamics in a Mesoscale Sol- totic behavior of screw dislocations in the | log ε|2 energetic vent regime.

While modeling polymer solutions, the presence of multi- Marco Cicalese ple time scales, such as the intermolecular bond potentials, Universita’diNapoliFedericoII makes quantitative analysis of results difficult, and simu- Dipartimento di Matematica e Applicazioni lations costly. Here, we show how these degrees of free- [email protected] dom can be replaced by rigid bond constraints—as commonly done in Brownian dynamics—for polymers embed- Roberto Alicandro ded in a recently introduced hydrodynamic solvent known Università di Cassino as Stochastic Rotation Dynamics (SRD) (or Multi-Particle DAEIMI Collision Dynamics - MPCD). [email protected] Erkan Tuzel Department of Physics Marcello Ponsiglione Worcester Polytechnic Institute Dipartimento di Matematica [email protected] Universita‘diRomaI [email protected] Daniel Kroll Department of Physics, North Dakota State University MS23 [email protected] Gradient Theory for Plasticity via Homogenization of Discrete Dislocations MS23 We derive, in a mathematically rigorous way, a strain gra- Patterning and Intermittency in a PDE Model of dient theory for plasticity as a mesoscopic limit of systems Dislocation Plasticity of discrete dislocations, where only the elastic energy is taken into account and the presence of dislocations is de- An exact 1-d reduction of a 3-d, time-dependent PDE termined by a topological constraint. This is joint work model of dislocation mechanics will be discussed. The 1-d with A. Garroni and M. Ponsiglione. model takes the form of a level set equation whose velocity is the driving force of a Ginzburg-Landau equation. Com- Giovanni Leoni putation of pattern formation and time-dependent behav- Carnegie Mellon University ior will be presented, including the formation of near-static [email protected] dipolar dislocation wall and cell structures observed within persistent slip bands in bulk single crystals under fatigue loading. MS23 Coarse-graining in Atomistic Models of Disloca- Amit Acharya tions Civil and Environmental Engineering Carnegie Mellon University Dislocations and their dynamics play a major role in the [email protected] response of materials to mechanical and thermal loading. Extensive work has been done on different scales of the Amit Das problem from atomistic level, to dislocation level to macro- Carnegie mellon University scopic level. Yet the behavior of material under plastic [email protected] deformation is still a source of many challenging mathematical problems. In this talk we focus on models at the Johannes Zimmer atomistic level and deal with questions of coarse graining Bath where higher level models are sought. We focus on dis- [email protected] tribution functions characterizing the atomic arrangement and discuss energy representation and dislocation motion in terms of these statistical properties. The evolution is MS23 formulated as a gradient flow. Variational Equivalence Between Ginzburg-Landau, XY Spin Shlomo Ta’asan Systems and Screw Dislocation Energies Department of Mathematical Sciences Carnegie Mellon University We introduce and discuss discrete two-dimensional mod- [email protected] els for XY spin systems and screw dislocations in crystals. We prove that, as the lattice spacing ε tends to zero, the Dmitry Golovaty relevant energies in these models behave like a free energy The University of Akron in the complex Ginzburg-Landau theory of superconduc- Department of Theoretical and Applied Mathematics tivity, justifying in a rigorous mathematical language the [email protected] analogies between screw dislocations in crystals and vortices in superconductors. To this purpose, we introduce a notion of asymptotic variational equivalence between MS24 families of functionals in the framework of Γ-convergence. Coarsening of Surface Patterns in Growth and Ero- We then prove that, in several scaling regimes, the com- MS10 Abstracts 77

sion MS24 Step Dynamics: Deterministic and Stochastic Ef- Surface patterns like ripples, mounds or pits are a ubiqui- fects in Mound Decay and Growth tous feature of thin film deposition and erosion processes. In many cases such patterns are observed to coarsen, in the Thistalkfocusesonaclassofmodelsforthedynamics sense that the typical feature scale increases as a power law of line defects (steps) on crystal surfaces in homoepitaxy. with growth or erosion time. Nonlinear continuum equa- Two topics to be discussed are: (i) The homogenization tions have played an important role in classifying possible of microscale effects and resulting properties of effective coarsening laws as a function of the symmetries and conser- deterministic partial differential equations for the surface vation laws of the system. The typical scenario suggested height profile. (ii) Analytical aspects of adding noise to by these studies is that coarsening is driven by the min- Burton-Cabrera-Frank-type models for steps under growth, imization of some energy-like quantity (more generally, a with some emphasis on the variance of terrace widths and Lyapunov function of the process). After outlining this the comparison to ‘mean-field’ theories. general framework, the talk will focus on recent experiments on the rapid coarsening of ripples by ion erosion Dionisios Margetis under near-glancing incidence. In this system coarsening University of Maryland, College Park appears to be a purely kinematic phenomenon, which can [email protected] be consistently described in terms of the ion-driven motion of pattern defects. The analogy to the evolution of wind- driven sand ripples is emphasized, and it is argued that a MS25 full quantitative theory of this type of coarsening dynamics Phase-Field Crystal Modeling of Morphology Evo- poses an interesting challenge to the continuum modeling lution in 2D and 3D of surface structures. The talk is based on joint work with H. Hansen, A. Redinger, S. Messlinger, G. Stoian and T. Crystallization kinetics and morphological evolution are Michely (Phys. Rev. Lett. 102, 146103, 2009). addressed using the phase-field crystal approach. We show that at low thermodynamic driving forces continuously de- Joachim Krug celerating diffusion-controlled growth is observed, while University of Cologne (Germany) at large enough driving forces a steady-state diffusionless Institute for Theoretical Physics mode occurs. This is associated with dynamic broadening [email protected] of the crystal-liquid interface that influences the anisotropy of interfacial properties. Consistently with experiments, this leads to a transition from faceted dendrites to curved MS24 dendrite tips in 2d and 3d. Effects of Additives on Restructuring of Two- dimensional Islands on Metal Surfaces Laszlo Granasy, Gyorgy Tegze, Gyula I Toth, Tamas Pusztai Addition of chalogen atoms (O, S, ...) generally enhance Research Institute for Solid State Physics & Optics the rates of coarsening of nanostructures on coinage met- Budapest, Hungary als (Cu, Ag, Au, ...). While some metal-chalogen complex [email protected], [email protected], [email protected], pusz- are found to be stable and can be observed through scan- [email protected] ning tunneling microscope, surfactant assisted surface dynamics involves structures that could be highly transient and unstable. Using density functional theory, we calcu- MS25 late the formation energy of various Ag-S and Cu-S clus- Multi-Scale Modeling of Phase Transformations: ters on Ag(111) and Cu(111) surfaces. Some clusters has From Classical Density Functional Theory to Phase significantly lower energies than Ag and Cu adatoms, and Field Methods can serve as more efficient carriers for mass transport on surfaces. A continuum model utilizing those calculated en- We review recent mathematical and numerical innovations ergies is developed to modeling the effect of additives on in quantitative modeling microstructure formation using relaxation of surface nanostructures. phase field methods. Their success in predicting steady state and transient spacing selection in solidification is re- Da-Jiang Liu viewed. The new phase field crystal (PFC) methodology, Iowa State University and some of its variants, is then discussed as a simple yet dajiang@fi.ameslab.gov fundamental method of addressing some of the shortcomings of traditional phase field theory. The PFC methodology is demonstrated by reviewing new research on the MS24 effects of elasto-plasticity, polycrystalline interactions and Self-assembled Superlattice Patterns multiple phases on microstructure formation. Finally, new work on connecting phase field crystal models to density On a solid surface a binary thin film may separate into functional theory (DFT) is reviewed. Two applications two phases. The phases can self-assemble into nanoscale that exploit this connection are discussed. The first deals domains. We show that directed self-assembly via sub- with interfacing PFC models with molecular dynamics for strate elasticity, surface strain field and surface chemistry more quantitative simulations than have been possible thus can produce a variety of patterns. Our study also reveals far. The second discusses new uses of course graining the important role of diffusion dynamics, and how a locally strategies, aimed at projecting out free energies, the forms ordered seeding pattern propagates to the neighboring re- of which are more fundamental than those used in tradi- gions to form a large uniform supperlattice structures. tional phase field modeling.

Wei Lu Nikolas Provatas University of Michigan McMaster University [email protected] [email protected] 78 MS10 Abstracts

MS25 the neighborhood of critical points. The softening of vari- Nucleation Barriers: Using a String Method for ous material moduli is commonly reported, and the smooth the Phase Field Crystal Model change of homogeneous states into complex multiphase microstructures is possible. For solids, the analysis of this Phase Field Crystal (PFC) is a well established model to behavior is complicated by the fact that the full notion study solid state phenomena in metals and colloids on an of stress and deformation gradient (as tensors), including atomistic scale. It can be connected to time dependent shearing, must be considered, rather than simply the clas- classical density functional theory. We will use PFC to sical effects associated with pressure, specific volume, and study nucleation. This requires to explore the transition temperature. In this work, I consider sequences of equilib- path between two (meta)stable states. The nucleation bar- rium coexistent phases, induced by thermal and mechan- rier is then defined by the most probable transition path, ical loading, and the asymptotic limits and relations be- which is equivalent to the minimum energy path (MEP) tween the thermodynamic fields of deformation gradient, in configuration space. We use a simplified string method temperature and the specific heat at constant deformation proposed by E, Ren and Vanden-Eijnden in order to cal- for elastic solids in the neighborhood of critical points. culate MEP based on PFC. Nucleation barriers as well as A generalized form of the famous Rushbrooke inequality the morphology of minimal stable nuclei and the influence from physical chemistry is obtained. Also, a generalized of walls on nucleation will be discussed. Clausius-Clapeyron equation is obtained. Axel Voigt, Rainer Backofen Roger Fosdick TU Dresden University of Minnesota [email protected], [email protected] Dept. of Aerospace Engineering and Mechanics [email protected]

MS25 Energy Stable Schemes for the Phase Field Crystal MS26 Equation Metastable Elastic Equilibria with Surfaces of Dis- continuity The PFC and MPFC equations decribe crystals at the atomic scale in space but on diffusive scales in time. The We consider non-linearly elastic equilibrium configurations, models account for the periodic structure of a crystal lat- that are smooth away from a a smooth phase boundary. We tice through a free energy functional of Swift-Hohenberg ask for conditions that would be necessary for such configu- type that is minimized by periodic functions. The models rations to be strong local minimizers. We discuss classical naturally incorporate elastic and plastic deformations, mul- necessary conditions and derive new ones from a unified tiple crystal orientations and defects and have been used point of view. We also discuss interrelations between all to simulate a wide variety of microstructures. In this talk necessary conditions. Open questions remain, highlight- I describe energy stable and convergent finite difference ing the fundamental difference between configurations with schemes and their effcient solution using nonlinear multi- and without phase boundaries. grid methods. A key point in the numerical analysis is the convex splitting of the functional energy correspond- Yury Grabovsky ing to the gradient systems. In more detail, the physical Temple University energy in both cases can be decomposed into purely convex [email protected] and concave parts. The convex part is treated implicitly, and the concave part is updated explicitly in the numer- Lev Truskinovsky ical schemes. I will discuss both first- and second-order Laboratoire de Mechanique des Solides accurate convex splitting schemes. The proposed schemes Ecole Polytechnique are unconditionally stable in terms of the physical energy [email protected] and unconditionally solvable, which allows for arbitrarily large time step sizes. This property is vital for coarsening studies that require very long time scales. MS26 Twisting Elastic Annuli, SO(n) and the Lifting of Steven M. Wise Stationary Loops to the Spinor Groups Mathematics Department University of Tennessee In this talk I will consider the equilibrium equations of elas- [email protected] ticity for an incompressible material having the geometry of an annulus (in any dimension) and examine a family Cheng Wang of maps rooted in geometry and topology, i.e., generalised University of Massachusetts twists, as possible solutions. The analysis leads to a sur- Dartmouth, MA prising multiplicity versus non-existence result depending [email protected] on the dimension being even or odd. I will then move on to discussing some qualitative features of the solutions in John Lowengrub particular introduce and evaluate an associated topological Department of Mathematics invariant namely their spin degree. University of California at Irvine Ali Taheri [email protected] University of Sussex, UK Department of Mathematics MS26 [email protected] Coexistent Phases and Critical Points in Thermoe- lasticity MS27 Materials are known to behave in strange and novel ways in Effective Properties of Polydomain Liquid Crystal MS10 Abstracts 79

Elastomers ement phase field framework. The effects of nonequilibrium domain structure evolution under mechanical loading The talk concerns polydomain liquid-crystal elastomers, and light exposure are modeled. Computational results il- materials are not homogeneous with each mesoscale region lustrating nonlinear microstructure evolution during finite having a distinct preferred director orientation. We present deformation and photoisomerization are presented. a theoretical analysis of the overall or collective behavior of this heterogeneous medium starting from the neo-classical William Oates soft and semi-soft free energies for LCEs. We show that Department of Mechanical Engineering, Florida State there is a significant difference between polydomains cross- Universi linkedinhomogeneoushighsymmetrystatesthencooled [email protected] to low symmetry polydomain states and those cross-linked directly in the low symmetry polydomain state. Hongbo Wang Florida State University John Biggins [email protected] University of Cambridge [email protected] MS27 Kaushik Bhattacharya Modeling Shape Change and Microstructural Evo- Professor of Mechanics and Materials Science lution in Nematic Elastomers via Finite Element California Institute of Technology Elastodynamics [email protected] When a nematic elastomer is subject to external strain, Mark Warner the sample’s shape and microstructure may both evolve Cavendish Laboratory over time. To model the resulting mechanical response University of Cambridge of these fascinating materials, we have developed a three- [email protected] dimensional finite element elastodynamics simulation technique. We apply this method to study the mechanical response and microstructural evolution of nematic elas- MS27 tomers as a function of the sample’s initial state, geometry, Recent Results on the Mechanical Response of Ne- and applied strain rate. For initially monodomain sam- matic Elastomers ples under external strain, simulations show the formation of striped textures accompanied by a pronounced plateau We present recent analytical and numerical results on the in the force-displacement curve. For polydomain nematic mechanical response of nematic elastomers. These are elastomers, simulation shows that applied strain drives a based on two fully nonlinear elastic energies and on their polydomain to monodomain transition, but the resulting small strain expansions in the regime of small strains and mechanical response depends sensitively on the sample’s large director rotations. We compare the behavior they thermomechanical history. In particular, we explore the predict with the currently available experimental evidence, role of the ”crosslink memory” effect, in which the local and discuss their relation with other models recently pro- preferred nematic director orientation is patterned in the posed in the theoretical literature. polymer network upon crosslinking. Our results suggest that this memory effect is far more pronounced in polydo- Antonio DeSimone main samples crosslinked in the nematic phase (N-PNE) SISSA, Trieste, Italy than in those crosslinked in the isotropic phase (I-PNE). 34014 Trieste, ITALY Our simulation results are in good qualitative agreement [email protected] with observed differences in the stress-strain behaviors of N-PNE and I-PNE materials, as seen in recent experiments (K. Urayama, Macromolecules 2009). MS27 A Phase Field Approach to Modeling Nonequilib- Robin Selinger rium Liquid Crystal Elastomer Behavior Liquid Crystal Institute, Kent State University [email protected] Liquid crystal elastomers exhibit a number of fascinating and important material characteristics for a number of en- Badel Mbanga, Jonathan Selinger gineering applications including for aerospace applications, Liquid Crystal Institute adaptive optics, and robotics. This class of materials is Kent State University characterized by unusual nonlinear, anisotropic mechanics [email protected], [email protected] and field-coupled material behavior including light or pH induced deformation, flexoelectricity, shape memory behavior, and electrostriction. The constitutive behavior is Fangfu Ye strongly dependent on the interactions between liquid crys- Dept. of Physics tal domain structure evolution and deformation of the host Univ of Illinois elastomer during electrical or mechanical loading, applica- [email protected] tion of heat, or exposure to light or chemical constituents. This has motivated an analysis of the interplay between MS27 microscopic liquid crystal domains and the host elastomer network to fully utilize these materials in various artificial Angular Momentum Transport in Complex Fluids muscle and sensor applications. A phase field description In dye doped nematics, the threshold intensity for the op- of liquid crystals is developed and coupled to photoiso- tical Freedericksz transition can be dramatically reduced merization behavior and nonlinear mechanics of the host due to an optical ratchet mechanism. Dye molecules ab- elastomer. This provides a relatively simple computational sorb light and rotate; angular momentum is transported modeling strategy that is implemented within a finite el- from the cell walls via shear flow generated by the rotation 80 MS10 Abstracts

[P. Palffy-Muhoray, T. Kosa and Weinan E, “Brownian Mo- Bounds for Multiphase Composites tors in the Photoalignment of Liquid Crystals’, Appl. Phys. A 75, 293-300 (2002)]. We describe the transport of angu- This paper addresses the attainability of the Hashin- lar momentum caused by singular vortices which generate Shtrikman (HS) bounds for multiphase composites, includ- flow, and which are transported by the flow which they gen- ing those of conductive materials and elastic materials. It erate. We provide analytic and numerical solutions for the presents a novel derivation of these bounds and a neces- vorticity distribution in simple and non-Newtonian fluids. sary and sufficient condition for attainment. A key idea is to focus on the optimal gradient field and the associated gradient Young measures. In particular we find a series of Xiaoyu Zheng sufficient conditions such that the HS bounds are attain- Dept of Mathematics able or not attainable. Kent State University [email protected] Liping Liu U. Houston Peter Palffy-Muhoray [email protected] Liquid Crystal Institute Kent State University MS28 mpalff[email protected] Complete Characterization and Synthesis of the Dynamic Response of Spring-mass Networks Mike Shelley Courant Institute The response function of a network of springs and masses, New York University an elastodynamic network, is the matrix valued function [email protected] W (ω), depending on the frequency ω, mapping the displacements of some accessible or terminal nodes to the net Mark Warner forces at the terminals. We give necessary and sufficient Cavendish Laboratory conditions for a given function W (ω) to be the response University of Cambridge function of an elastodynamic network, assuming there is no [email protected] damping. In particular we construct an elastodynamic network that can mimic a suitable response in the frequency or time domain. Our characterization is valid for networks MS28 in three dimensions and also for planar networks, which are Evolution of Brittle Damage with Multiple Dam- networks where all the elements, displacements and forces aged States are in a plane. Additionally, we prove stability of the network response to the addition of springs with small spring We present a variational formulation for the evolution of constants, which may serve to eliminate floppy modes. brutal brittle damage for isotropic materials which extends the earlier work of Garroni and Larsen by permitting mul- Fernando Guevara Vasquez tiple damaged states. If time permits we shall also present University of Utah results for anisotropic and continuous (ie. non-brutal) [email protected] damage. Graeme W. Milton Isaac V. Chenchiah University of Utah University of Bristol Department of Mathematics UK [email protected] [email protected] Daniel Onofrei MS28 Department of Mathematics Exact Results for Effective Tensors of Fiber- University of Utah reinforced Elastic Composites via General Theory [email protected]

Exact relations, or cases when effective tensors of composites satisfy certain equalities regardless of the microstruc- MS29 ture, are well-known in the literature. The general the- Dynamic Modeling of Lipid Bilayer Membranes: ory of exact relations developed by Graeme Milton, Daniel Simulation Studies Relating Molecular Level Inter- Sage and Yury Grabovsky permits a complete description actions and Bulk Material Properties of all such cases. In this talk I will report on my recent work on exact relations for fiber-reinforced elastic composites. A model is developed for lipid bilayer membranes which takes into account microscopic interactions and dynam- Meredith Hegg ics at the level of individual lipid molecules. The model Department of Mathematics also takes into account hydrodynamic coupling between Temple University the lipid molecules, bilayer embedded particles, and the [email protected] surrounding solvent fluid. To carry out the studies, new stochastic computational methods are introduced which Yury Grabovsky utilized a mixed Eulerian and Lagrangian description of the Temple University physical system. Stochastic forcing terms are introduced [email protected] to account for thermal fluctuations in a manner consistent with statistical mechanics. Dynamic simulations studies are carried out for the bilayer which relate molecular level MS28 interactions and kinetics to bulk material properties. Spe- The Attainability of the Hashin-Shtrikman’s cific results are presented which characterize how molecular MS10 Abstracts 81

level interactions contribute to bilayer mechanics (stiffness, lar mechanics, such as the determination of the shape of a tension, compressibility), bilayer rheology (shear viscosity, model rotating flagellum, and how hydrodynamic interac- normal stress differences), and the mobility of bilayer em- tions lead to synchronization of nearby beating cilia. bedded particles (single and pair diffusivity tensors). Ap- plications of the bilayer model and computational methods Thomas R. Powers to problems in cell biology are also discussed. Brown University Division of Engineering Paul J. Atzberger Thomas [email protected] University of California-Santa Barbara [email protected] MS30 Frank Brown Domain Decomposition for Nonlocal Problems Department of Chemistry and Biochemistry University of California Santa Barbara We generalize iterative substructuring methods to nonlocal fl[email protected] settings and characterize the impact of nonlocality upon the scalability of these methods. We present a nonlocal variational formulation and establish spectral equiva- MS29 lences to characterize conditioning of the underlying stiff- Studying the Thermodynamic Folding Characteris- ness matrix and the Schur complement by proving a nonlo- tics of Peptides Using Coarse-grained Simulations cal Poincare inequality. Furthermore, we introduce a nonlocal two-domain variational formulation utilizing nonlocal One of the central problems of computational biology is transmission conditions, and prove equivalence with the to predict the three-dimensional shape of proteins starting single-domain formulation, a first step in establishing rig- from their primary sequence of amino acids. I will show orous theory for nonlocal domain decomposition methods. how one can use coarse-grained simulations to address certain aspects of this problem which are amenable to a sim- Burak Aksoylu plified biophysical analysis, and how well-known (but not Louisiana State University, Department of Mathematics widely used) thermodynamic principles can be employed to Center for Computation & Technology shed further light on it. I will also point out the problems [email protected] and suggest ways to overcome them. Michael L. Parks Markus Deserno Sandia National Laboratories Department of Physics [email protected] Carnegie Mellon University [email protected] MS30 Tristan Bereau A Nonlocal Vector Calculus with Application to Department of Physics Nonlocal Boundary Value Problems Carnegie Mellon University [email protected] We develop a calculus for nonlocal operators that mimics Gauss’ theorem and the Green’s identities of the classical vector calculus for scalar functions. The operators we MS29 treat do not involve the gradient of the scalar function. An Implicit Interface Formulation of the Stochastic We then apply the nonlocal calculus to define variational Immersed Boundary Method formulations of nonlocal “boundary’ value problems that mimic the Dirichlet and Neumann problems for second- We present the derivation and some mathematical analysis order scalar elliptic partial differential equations. For the of the recently proposed stochastic implicit interface mod- nonlocal variational problems, we derive fundamental so- els for an elastic interface immersed in a background fluid lutions, show how one can derive existence and uniqueness subject to fluctuation forces. This provides an implicit in- results, and state conditions under which the solution is a terface formulation of the stochastic immersed boundary member of a fractional Sobolev space. methods. We discuss the implication of the fluctuation- dissipation theorem and present suitable a priori estimates Richard B. Lehoucq and the well-posedness of pathwise solutions for a couple of Sandia National Laboratories different elastic energy functionals and an incompressible [email protected] Stokes fluid. Qiang Du Qiang Du, Manlin Li Penn State University Penn State University Department of Mathematics Department of Mathematics [email protected] [email protected], [email protected] Max Gunzburger Dept. of Scientific Computing MS29 Florida State University Fluid-structure Interactions in Flagella and Cilia [email protected] Flagella and cilia are used by microorganisms to swim. A complete understanding of the mechanics of flagella re- Kun Zhou quires integrating the physics from the molecular scale of Penn State University the driving motors with the fluid mechanics of flagella. [email protected] In this talk I will describe several problems from flagel- 82 MS10 Abstracts

MS30 MS31 Length Scales and Time Scales in Peridynamics Model Development and Analysis of Granular Avalanches The peridynamic theory of continuum mechanics is based on integro-differential equations that model interactions A model developed by Gray and Thornton (2005) is used within groups of particles over finite distances. These dis- to describe the phenomen of particle-size segregation in tances provide a length scale within the theory. The bound- granular avalanches. In my presentation, we study the for- edness of the dispersion curves for peridynamic materials mation of shocks, which are jumps in the concentration of results in a time scale that emerges naturally from a given dissimilar particles, as well as the mixing zone that results length scale. This talk will explore the origins and signifi- from a shock breaking. Finally, I will talk about the lab cance of peridynamic length and time scales in numerical experiment that has been run to show how well the model discretization and predictions of physical phenomena. performs in reality. Stewart Silling Nicholas Giffen Sandia National Laboratories North Carolina State University Mathematics [email protected] Department njgiff[email protected]

MS30 Michael Shearer Green’s Functions in Non-local Three-dimensional North Carolina State Univ. Linear Elasticity [email protected] In this talk small deformations due to the presence of point loads in a linear locally elastic body are compared to the MS31 corresponding deformations in the peridynamic, non-local Analysis of Preisach and Homogenized Energy formulation. Owing to the linearity of the problem, the Models for Ferroic Compounds response to a point load can then be used to obtain the response to general body force loading functions by super- There presently exist a number of modeling frameworks to position. Using Laplace and Fourier transforms, an integral quantify hysteresis in ferromagnetic, ferroelectric and fer- representation for the dynamic three-dimensional peridy- roelastic (ferroic) compounds including Preisach, Prandtl- namic solution is obtained with the help of Greens func- Ishlinskii and homogenized energy models. Whereas the tions. This new theoretical result is illustrated by dynamic formulations differ, all are comprised of kernels integrated and static examples in one and three dimensions. It is against density functions quantifying the distributions of demonstrated that the non-local peridynamic formulation various parameters. In this talk, we will discuss the similar- regularizes the singular response encoutered in local elas- ities and differences between these models and indicate the ticity. degreee to which unifying frameworks can be constructed. Attributes of the models will be illustrated through com- Olaf Weckner parisonwithexperimentaldata. The Boeing Company Mathematics and Computing Technology David Pate [email protected] North Carolina State University [email protected] Stewart A. Silling Multiscale Dynamic Material Modelling Ralph C. Smith Sandia National Laboratories North Carolina State Univ [email protected] Dept of Mathematics, CRSC [email protected] MS31 Modeling Thermal Based Damage Detection in MS31 Porous Materials A Fast Quadrature Method for the Continuous Spectrum Biphasic Poroviscoelastic Model of Car- We use the heat equation to simuate a thermal interro- tilage gation method for detecting damage in porous materials, which is being developed in collaboration with scientists The talk presents a new fast numerical method for the con- at NASA Langley Research Center. We first use prob- tinuous poroviscoelastic model of soft tissue. The reduced ability schemes to randomly generate pores in a sample continuous stress-relaxation function is approximated with material; then we simulate flash-heating of the compart- high accuracy by a Gauss-Legendre integration formula. ment along one of the boundaries with and without dam- This leads to an update rule for the stress-strain integral age due to oxidation which is represented with a large el- with similar accuracy compared to the full method but a lipse. We will discuss the computational complexity from reduction of the computational cost from O(N 2)toO(N). the complicated geometry of the porosity. We then inves- Numerical results and comparison to other methods are tigate techniques from homogenization theory to alleviate presented. this problem by approximating the thermal effect of the porosity with a matrix AΩ in the conductivity term of the Michael Stuebner, Mansoor Haider heat equation. We compare this approximation with the North Carolina State University results of the simulations. [email protected], [email protected] Amanda Criner,H.T.Banks North Carolina State University MS32 [email protected], [email protected] Is Step-flow Epitaxial Growth Ever Stable Against MS10 Abstracts 83

Bunching and Meandering? Yukio Saito Keio Univ., Yokohama, Japan Recent experiments have established that bunching and [email protected] meandering instabilities coexist during step flow, in contrast to the predictions of existing Burton–Cabrera–Frank Matthieu Dufay models. Indeed, in the BCF framework, meandering LPMCN, UNiv-Lyon1 is predicated on an Ehrlich–Schwoebel barrier whereas [email protected] bunching requires an inverse ES effect. The two appear therefore to be mutually exclusive. Herein, an alternative theory is presented that resolves this apparent paradox. MS32 Its main ingredient is a generalized Gibbs–Thomson rela- Linear Stability Analysis and Phase-Field Simula- tion, derived via an energy-rate calculation and resulting tions of Step Flow Dynamics in jump conditions that couple adjacent terraces. Special- ization to a periodic step train reveals a competition be- We examine the dynamics of step flow growth using a lin- tween the stabilizing ES kinetics and a destabilizing ener- ear stability analysis and a phase-field model that include getic correction that leads to step collisions. This can be the effects of the Ehrlich-Schwoebel Barrier and elastic understood in terms of the tendency of the thin film to stress. We summarize the instabilities observed from the minimize its total grand canonical potential. linear stability analysis, including the transition between patterned and random morphologies. The full simulations Michel E. Jabbour using the phase-field model provide the evolution of the Department of Mathematics step morphologies beyond the linear regime. University of Kentucky [email protected] Dong-Hee Yeon Department of Materials Science and Engineering University of Michigan MS32 [email protected] Anti-coarsening of Step Bunches with Non- conserved Dynamics Pil-Ryung Cha Step bunching is a ubiquitous morphological instability of The School of Advanced Materials Engineering vicinal crystal surfaces that occurs during nonequilibrium Kookmin University processes such as growth, sublimation or surface electro- [email protected] migation. In the standard scenario, bunching is initiated at a small length scale determined by the linear instabil- Axel Voigt ity and proceeds by the unlimited coarsening of bunches, TU Dresden often characterized by a power law growth of the mean [email protected] bunch size. Here we point out that the reverse process, the breakup of a large bunch into several smaller bunches, John Lowengrub occurs generically in situations (such as sublimation with Department of Mathematics or without electromigration) where the step dynamics is University of California at Irvine coupled to the change of the total volume of the film. Ex- [email protected] tensive simulations of a discrete step model are presented in combination with a phenomenological continuum the- Katsuyo Thornton ory. The talk is based on joint work with Marian Ivanov Department of Materials Science and Engineering and Vladislav Popkov. University of Michigan [email protected] Joachim Krug University of Cologne (Germany) Institute for Theoretical Physics MS33 [email protected] Localized and Propagating Oscillation Modes for Spin-torque Induced Magnetic Excitations in Structures with Different Dimensionalities MS32 Dewetting of Ultra-Thin Solid Films In this talk we present an overview of localized and propagating magnetization oscillation modes, excited in The dewetting dynamics of ultra-thin solid films is dis- magnetic elements of various dimensionality (nanodots, cussed. The dynamics is found to be controlled by atomic nanowires, extended films) due to the torque induced by step formation and motion. Two regimes are found: layer- spin injection. The mode nature qualitatively depends by-layer dewetting, and a regime with a facetted rim. A on the system dimensionality, current strength, current- analytical model is obtained, which is in quantitative agree- flooded area size, stray field from other layers, Oersted ment with Kinetic Monte Carlo Simulations. The stability field. Qualitatively different localized modes (relatively ho- of the dewetting fronts is also discussed. Finally we discuss mogenous ’bullet mode’, highly inhomogeneous vortex and the relevance of these results for experiments. vortex-antivortex pair modes) can be excited when these parameters are varied. Olivier Pierre-Louis Université J. Fourier Grenoble 1 Dmitry Berkov [email protected] INNOVENT Technology Development [email protected] Anna Chame UFF-Niteroi, Rio, Brasil [email protected]ff.br 84 MS10 Abstracts

MS33 Elzbieta Jaromirska Nonlinear Magnetization Dynamics and Spin-wave University of Salamanca Instabilities in Magnetic Nanostructures [email protected]

The discovery that large-amplitude magnetization mo- Giancarlo Consolo tions can be induced by spin-polarized electron currents University of Messina through spin-transfer torques has generated renewed at- [email protected] tention on Landau-Lifshitz equation for magnetization dynamics. The analysis of the stability of magnetization motions induced by time-dependent magnetic fields or by MS33 spin-transfer torques leads to the introduction of a general- The Effect of Disorder on Domain Wall Propaga- ized notion of spin-wave, applicable to far-from-equilibrium tion in Magnetic Wires conditions. On this basis, analytical predictions are obtained for the onset of spin-wave instabilities in large mag- The dynamics of magnetic domain wall structures driven netization motions. These instabilities can be viewed as byfieldsorcurrentsisasubject of practical importance the far-from-equilibrium generalization of Suhl’s instabili- related to possible schemes for nanoscale magnetic mem- ties occurring in ferromagnetic resonance. These results are ory devices. Experimental results are typically interpreted compared with numerical simulations of Landau-Lifshitz in comparison to ideal models that ignore the effects of dynamics in sub-micron magnetic elements. extrinsic disorder and internal dynamics of domain wall structures. To understand the effect of disorder and inter- Giorgio Bertotti nal dynamics, we study the dynamics of vortex wall propa- INRIM - Istituto Nazionale di Ricerca Metrologica gation driven by fields or currents, and vortex wall gyration [email protected] driven by an external magnetic field pulse in the presence of extrinsic random potential. We analyze micromagnetic Roberto Bonin simulations using ideal models and observe that effective Politecnico di Torino, sede di Verres damping increases due to the disorder. Verres (AO), Italy [email protected] Hongki Min NIST, Center for Nanoscale Science and Technology Massimiliano d’Aquino University of Maryland, Maryland NanoCenter Università Parthenope [email protected] Napoli, Italy [email protected] Robert D. McMichael NIST Claudio Serpico Center for Nanoscale Science and Technology Università Federico II [email protected] Napoli, Italy [email protected] Jacques Miltat UniversitéParis Isaak Mayergoyz Laboratoire de Physique des Solides University of Maryland [email protected] College Park, MD, USA [email protected] Michael J. Donahue NIST Mathematical and Computational Sciences Division MS33 [email protected] Modelling Spin Transfer Induced Dynamics in Point Contact Devices Mark D. Stiles NIST Micromagnetic modelling of point contact devices is not Center for Nanoscale Science and Technology straightforward because the computational region one can [email protected] realistically consider is typically one order of magnitude smaller than the lateral dimensions of the real device. Therefore, depending on the features of the dynamics un- MS34 der study, some ad-hoc techniques are to be developed in Some Problems in Heterogeneous Griffith Fracture order to avoid unphysical effects due the computational boundary. For instance, if a propagating linear mode is We describe some examples of Griffith fracture in a mi- excited, spin wave reflections at the boundaries need to crostructured material, and how the effective macroscopic be minimized. On the other hand, if a localized vortex is behavior can be very different from what might be ex- oscillating around the point contact in a well defined or- pected. In particular, considering Griffith fracture in a bit, the charges in the boundaries need to be removed. I material with elastic properties obtained by homogenizing will discuss how with these ad-hoc techniques one can sat- the elastic properties of the microstructured material, and isfactorily simulate point-contact devices. The results are fracture toughness obtained as a function of only the tough- compared to some recent experimental data. nesses of the microstructured material, will not in general produce the correct behavior. Luis Lopez-Diaz University of Salamanca Christopher Larsen Department of Applied Physics Worcester Polytechnic Institute [email protected] Math Dept [email protected] MS10 Abstracts 85

MS34 E.M. Lauridsen, S.O. Poulsen Strong Deformations of and at Soft Interfaces Riso National Laboratory Technical University Denmark I will discuss some simple examples of how soft interfaces [email protected], stefan othmar poulsen behave when strongly deformed. I will start by considering ¡[email protected]¿ how a thin film peels off from a substrate to which it is adhered in the presence and absence of a fluid. I will then M. Stampanoni move to the question of how creases form on soft interfaces, Swiss Light Source and then close with the question of how cracks and cuts Paul Scherrer Institut, Switzerland appear at such an interface. In each example, geometry [email protected] and physics meld with each other interestingly and lead to a rich variety of mathematical problems. Peter Voorhees L. Mahadevan Northwestern University Harvard University Dept. of Material Science and Engineering [email protected] [email protected]

MS34 MS35 The Time-dependent von Kármán Plate Equation Linear Stability and the Role of Rotational Diffu- as a Limit of 3d Nonlinear Elasticity sion for Active Suspensions

In this talk we discuss the asymptotic behaviour of solu- The dynamics of active suspensions has been modeled tions of three-dimensional nonlinear elastodynamics in a through a modification of Doi rod theory. We investi- thin plate, as the thickness of the plate tends to zero. Un- gate the structure of this system linearized near a state der appropriate scalings of the applied force and of the of isotropy and uniformity. We show that while long-wave initial values, we prove existence of strong solutions for instability depends upon the swimming mechanism, short- large times and sufficiently small thickness and we show wave stability does not. Further, we find a critical volume their convergence to solutions of the time-dependent von concentration or system size for the onset of instabilities in Kármán plate equation. the presence of both rotational and translational diffusion. Helmut Abels Universit Christel Hohenegger ”at Regensburg New York University Regenburg, Germany [email protected] [email protected] MS35 Maria Giovanna Mora Hydrodynamics of Active Suspensions: Instabili- Sissa,Trieste,Italy ties and Rheology [email protected] Bacterial suspensions and extracts of cytoskeletal filaments Stefan Müller and motor proteins are examples of assemblies of interact- Hausdorff Center for Mathematics ing self-driven units that form active fluids. These systems Bonn, Germany exhibit fascinating collective behavior, including nonequi- [email protected] librium phase transitions and pattern formation. In this talk I will review our work on using nonequilibrium statistical physics to derive a continuum description of active MS34 suspensions from specific models of single particle dynam- Universal Interfacial Morphologies near Topologi- ics, highlighting the role of physical interactions in control- cal Singularities in Materials ling the large-scale behavior. It is well known that interfacial energy will induce a rod of M. Cristina Marchetti one phase embedded in another to develop undulations by Syracuse University the well-known Rayleigh instability. We show that suffi- Physics Department ciently close to the pinching event the interfacial morphol- [email protected] ogy for systems evolving by interface-energy-driven bulk diffusion becomes universal, independent of the initial morphology and material system. We find an excellent agree- MS35 ment between theory and experiment in both the morphol- Hydrodynamics of Active Fluids: Pattern Forma- ogy and the kinetics of the pinching process tion and Phase Transitions in Bacterial Suspen- sions L.K. Aagesen, A.E. Johnson, J.L. Fife Dept. of Material Science and Engineering I will present simulations of the hydrodynamics of active Northwestern University bacterial fluids. Firstly, I will discuss concentrated active [email protected], gels, which undergo a transition between a passive and a [email protected], j-fi[email protected] spontaneously flowing phase at high enough density. Sec- ondly, I will consider a run-and-tumble bacterial colony M.J. Miksis with logistic growth, where the swimming speed decreases Engineering Science and Applied Mathematics with density. If the velocity decrease is strong enough, the Northwestern University system forms patterns usually attributed to chemotaxis, [email protected] 86 MS10 Abstracts

but in the absence of any diffusing chemical. and School of Physics, University of Sydney [email protected] Davide Marenduzzo The University of Edinburgh N.A. Nicorovici [email protected] School of Physics, University of Sydney,Australia . MS35 Active Films, Drops and Filaments L.C. Botten, C.G. Poulton, A.A Asatryan Department of Mathematical Sciences The study of self-driven particles, such as cytoskeletal fil- University of Technology Sydney, Australia aments with motors, pumps in biomembranes, or swim- ., ., . ming organisms, is a new frontier in the hydrodynamics of suspensions. In my talk I will focus on the unique phenomena engendered by the presence of active contractile MS36 or tensile force dipoles in Stokesian fluids, in thin-film, Limits to Cloaking and Optical Devices strand and droplet geometries. The results I will present include waves, surface-undulation instabilities, and anoma- For cloaking, we show that causal cloaking is generally im- lous spreading laws. possible, regardless of the material used. It is easily dis- coverable by pulsed probing. We also show how perfect Sriram Ramaswamy cloaking can be approached. For optical devices, we prove Indian Institute of Science, India a fundamental bound that depends only on the maximum [email protected] variation of dielectric constant and the physical volumes involved, independent of the design details, and show applications to slow light, dispersion and volume holography. MS35 Modeling and Simulation of Biologically Active Suspensions David A. Miller Ginzton Laboratory Active suspensions, of which a bath of swimming bacteria Standford University is a paradigmatic example, are fluid systems whose mi- [email protected] crostructure is motile, and constitute a fundamental example of nonequilibrium pattern-forming systems. In this work, we apply a kinetic theory previously developed by MS36 Saintillan and Shelley (Phys. Fluids 20, 123304, 2008) Cloaking Via Change of Variables for the to study the nonlinear dynamics and pattern formation in Helmholtz Equation in the Whole Spaces active suspensions in a variety of situations. We first consider the case of a uniform isotropic suspension, where we In this talk, I will discuss a cloaking device which is com- show using a linear stability analysis that long-wavelength posed of a standard near cloak based on a regularization of fluctuations are unstable as a result of hydrodynamic in- the transformation optics, and a fixed lossy-layer, for the teractions. The long-time dynamics and pattern formation Helmholtz equation in the whole space of dimension 2 or 3. are studied using large-scale three-dimensional numerical Two important features of this problem will be presented: simulations, where we report results on the coherent struc- i) degree of near invisibility, ii) necessity of the lossy-layer. tures that are seen to appear and their relation to the dis- A similar problem for a bounded domain was previously turbance flows driven by the particles. Second, we extend studied by Kohn-Onofrei-Vogelius-Weinstein. this study to investigate the effects of an external shear Hoai-Minh Nguyen flow: in this case, it is found using a stability analysis that Courant Institute of Mathematical Sciences the external flow is stabilizing at high shear rates, and [email protected] nonlinear simulations demonstrate the existence of several regimes of instability at low and moderate shear rates. MS36 David Saintillan, Amir Alizadeh Pahlavan Department of Mechanical Science and Engineering Approximate Cloaking for the Helmholtz Equation University of Illinois at Urbana-Champaign I shall give a brief review of the estimates that may ob- [email protected], [email protected] tained for the effect of a very natural approximate cloaking scheme. The particular cloaking scheme is of the ”cloaking- MS36 by-mapping” type, and efficacy estimates have been obtained at all frequencies. This represents joint work with Ideal Cloaking and Local Density of States Kohn, Onofrei, Weinstein and Nguyen. We discuss cloaking or hiding the objects from detection Michael S. Vogelius by electromagnetic probes, and means of detecting cloaked Rutgers University, New Brunswick objects. Among these are passive schemes, whereby radia- [email protected] tion absorbed and then reradiated at different wavelengths is detected. To study these, we calculate the Local Den- sity of States (LDOS) of the cloaking system as a function MS37 of position and frequency, which quantifies the radiative Some Recent Progress on Quantum Simulations ability of sources. We derive LDOS from Green’s functions and illustrate its properties. Abstract not available at time of publication. Ross McPhedran Roberto Car CUDOS ARC Centre of Excellence Princeton University MS10 Abstracts 87

[email protected] orientations, elastic anisotropy and dislocation collisions.

Vasily Bulatov MS37 Lawrence Livermore National Labs Continuue Limit for the Electronic Structure Mod- [email protected] els

We analyze the electronic structure of smoothly or elasti- MS38 cally deformed crystals by studying various quantum me- Dislocation Dynamics in Micro-Pillars and Thin chanics models at different levels of complexity, including Films the Kohn-Sham density functional theory, Thomas-Fermi type of models and tight-binding models. Our overall ob- Understanding plasticity and strength of crystalline ma- jective is to establish the microscopic foundation of the terials in terms of the dynamics of microscopic defects continuum theories of solids, such as the nonlinear elas- has been a goal of materials research in the last seventy ticity theory and the theory of piezoelectric or magnetic years. The size-dependent yield stress observed in recent materials, in terms of quantum mechanics and to examine experiments of sub-micrometer metallic pillars provides a the boundary where the continuum theories break down. unique opportunity to test our theoretical models, allow- This is joint work with Jianfeng Lu of NYU. ing the predictions from defect dynamics simulations to be directly compared with mechanical strength measure- Weinan E ments. The balance between the dislocation multiplication Princeton Univesity rate and exhaustion rate (at the surface) may be the key Department of Mathematics to understand the observed size effect in flow stress. Here [email protected] we report two counterintuitive observations from Molecular Dynamics and Dislocation Dynamics simulations. In body- centered-cubic (BCC) metals, the surface itself is sufficient MS37 to induce dislocation multiplication as a single disloca- Heuristics for Accelerating Electronic Structure tion moves across the pillar. In face-centered-cubic (FCC) Calculation metal pillars and thin films, however, even jogs of the Lomer-Cottrell type are not strong enough pinning points Under the Kohn-Sham density functional theory frame- to cause dislocation multiplication. These results highlight work, the electron density ρ associated with a ground state the need for better calibration of Dislocation Dynamics atomistic system can be obtained by solving the nonlinear models against the more fundamental atomistic models. equation ρ = f(H(ρ)) where f is the Fermi-Dirac distribution function and H is the Kohn-Sham Hamiltonian. One Wei Cai way to solve this nonlinear equation is to apply a Broy- Department of Mechanical Engineering den type of method. I will discuss a number of heuristics Stanford University for constructing an effective Jacobian approximation and [email protected] efficient ways to evaluate f(H(ρ)).

Chao Yang MS38 Lawrence Berkeley National Lab Ginzburg-Landau-type Energy of a Crystalline Lat- [email protected] tice with Defects

We propose a Ginzburg-Landau-type energy functional MS37 that describes a crystalline lattice with defects. The mo- Some Recent Progress in Fast Algorithms for DFT tion of dislocations can be described as a gradient ﬂow for Calculation this energy; we show that the predicted dynamics corresponds to the known results for the standard models. Abstract not available at time of publication. Dmitry Golovaty Lexing Ying The University of Akron University of Texas Department of Theoretical and Applied Mathematics Dept. of Mathematics [email protected] [email protected] Shlomo Ta’asan MS38 Department of Mathematical Sciences Carnegie Mellon University Dislocation Mobility and Stiﬀness in Dislocation [email protected] Dynamics

Crystal’s ability to withstand applied loads is ultimately MS38 defined by the behavior of lattice dislocations. The method of Dislocation Dynamics (DD) seeks to compute plastic re- Atomic Diffusion in Dislocation Cores Studied by sponse of a crystalline material directly from the motion Molecular Dynamics of interacting dislocations lines. This is achieved by for- We report on molecular dynamics simulations of self- ward integration of coupled equations of motion (ODE) diffusion along screw and edge dislocations, both isolated for dislocation segments and/or nodes. The resulting set and assembled in low-angle grain boundaries. While va- of equations can be more or less stiff depending on the cancy migration is confirmed to be the most important dif- type of material and dislocation motion mechanisms. This fusion mechanism, the unexpected finding is that diffusion presentation will describe several physical sources of ODE can occur without pre-existing point defects. This intrin- stiffness in Dislocations Dynamics, including anisotropy of sic diffusion mechanism is mediated by dynamic vacancy- dislocation mobility as a function of line and slip plane 88 MS10 Abstracts

interstitial pairs whose activation can be assisted by ther- MS39 mal jogs. The dislocation interactions in low-angle bound- The Theory of Herring Crystals: Morphology, aries result in acceleration of dislocation diffusion. Morphometrics, and Emergent Symmetries Yuri Mishin Herring’s model of crystal interface energy combines the George Mason University (non-convex) orientation-dependant Wulff energy with a Physics curvature penalisation. Herring crystals evolve when in [email protected] contact with their melt through a fourth order hyperbolic- parabolic geometric evolution equation (GE). We demon- Ganga P. Purja Pun strate, contrary to expectation, that such Herring inter- George Mason University faces generally violate the classical Wulff construction. [email protected] Further, we characterise the singular limit of GE, identify the associated scaling laws and scaling functions (morphometrics), and close with a curious emergent symmetry. MS39 On a Mean Field Model for 1D Thin Film Droplet Stephen J. Watson Coarsening University of Glasgow [email protected] A thin liquid film coating a solid substrate is unstable and the late stage morphology is essentially quasiequilibrium droplets connected by an ultra thin film. Droplets ex- MS39 change mass and coarsening occurs – the total number of Transient and Self-similar Dynamics in Thin Film droplets N(t) decreases while the average size of droplets Coarsening increases. It is predicted that N(t)obeysapowerlaw N(t) ∼ t−2/5 in the 1D case. We study a mean field model The dynamics of arrays of droplets formed by the dewet- proposed by Gratton and Witelski for the one-dimensional ting of viscous thin films on hydrophobic substrates can be thin film coarsening and prove a universal one-sided bound reduced to a coarsening dynamical system (CDS) consist- on N(t) that partially justifies the power law. A corre- ing of a set of coupled ODEs and deletion rules for when sponding bound on the average drop size is also obtained. droplets vanish. We write a Lifshitz-Slyozov-Wagner-type Then we study the relation of this model and the mean (LSW) continuous mean-field model for the drop size dis- field model for Ostwald ripening and show that they are tribution and compare it with simulations of discrete mod- equivalent after a nonlinear rescaling of time. Finally we els derived from the CDS. Large transient deviations from present some further estimates on the coarsening rates for self-similar LSW dynamics are shown to conform to bounds the Ostwald ripening. given by Kohn and Otto. Shibin Dai Thomas P. Witelski Worcester Polytechnic Institute Duke University [email protected] Department of Mathematics [email protected]

MS39 Michael Gratton Novel Coarsening Kinetics for Islands on Surfaces: Dept of Engineering Sciences and Applied Mathematics Eﬀects of Anisotropy, Quantum Size Eﬀects, and Northwestern University Additives [email protected]

Metal islands on surfaces in homoepitaxial fcc(111) systems often provide ideal examples of 2D Ostwald ripen- MS40 ing limited by isotropic terrace diffusion. LSW theory de- Dynamics of Faceted Solid-liquid Interfaces Probed scribes such details as the decay of individual small islands by Atomistic Simulations [Thiel et al., J. Phys. Chem. C 113 (2009) 5047]. We describe the refinement of LSW theory to treat more com- This talk will discuss recent work involving the application plex situations: (i) Introducing trace amounts of chem- of molecular dynamics simulations in the study of the dy- ical additives can dramatically accelerate coarsening due namics of faceted solid-liquid interfaces in both bulk and to facile mass transport via metal-additive complexes. (ii) nanometer-scale confined geometries. We discuss examples For homoepitaxial fcc(110) systems, diffusional and ener- highlighting the ways in which the structural, thermody- getic anisotropies exist, and deviations from expected equi- namic and kinetic information derived from such simula- librated island shapes occur. (iii) In heteroepitaxial sys- tions can be used both to parametrize and refine continuum tems, quantum size effects (QSE) can impact island struc- theories for growth of faceted bulk and nanoscale crystals ture and coarsening kinetics. from the liquid state. Jim W. Evans M. Asta Ames Laboratory USDOE and Iowa State University University of California, Berkeley & [email protected] University of California, Davis [email protected] M.Shen,D.-J.Liu,Y.Han,D.Jing,P.A.Thiel Iowa State University Dorel Buta [email protected], dajiang@fi.ameslab.gov, University of California - Davis [email protected], [email protected], [email protected] [email protected] Tomorr Haxhimali University of California, Davis & MS10 Abstracts 89

Northwestern University curvature, roughness, and orientation distribution as well [email protected] as the net line length of step edges or triple lines. Fur- thermore, thermodynamics also suggests an important link Jeff Hoyt between surface mechanics and reactivity. McMaster University, Hamilton, ON, Canada [email protected] Joerg Weissmueller Karlsruhe Institute of Technology [email protected] MS40 Utilizing MD-based Information on Interfacial Dy- MS41 namics to Understand Microstructure Evolution Step Evolution for Crystals of Finite Size Molecular dynamics can determine interfacial properties for specific boundaries. We discuss two modes of using mo- We study the step evolution of crystal structures relax- bility results. Interpolation in the 5-dimensional space of ing toward flat surface when the number of steps is finite. grain boundaries allows their incorporation into mesoscale The model is 1-dimensional and the rate limiting transport models, but requires an appropriate metric and a sufficient process is attachment-detachment limited (ADL). Starting with the step equations, we write down ODE’s for the dis- density of data. The results can also be used to infer the l2 presence of classes of values, in this case fast and slow crete slope of the profile. These are the -steepest descent boundaries. The presence of these classes provides insight of an energy functional. Using this structure, we prove into grain growth stagnation. existence, uniqueness, and stability of the self-similar solution for profiles with “monotone’ initial data. S. M. Foiles,E.A.Holm We then propose a fourth order PDE whose natural dis- Sandia National Laboratories cretization is the slope ODE’s. We prove existence and [email protected], [email protected] uniqueness of a positive self-similar solution this continuum setting. Moreover, we give some qualitative features D. L. Olmsted of the self-similar solution and the corresponding height Northeastern University profile. linked puff[email protected] Michael Brenner Division of Engineering and Applied Science MS40 Harvard University [email protected] The Composition Dependence of the Anisotropy in the Crystal-melt Interfacial Free Energy: A Progress Report Hala Al Hajj Shehadeh Courant Institute Recent phase field simulations have shown that the varia- NYU tion in the crystallographic growth direction of dendrites as [email protected] a function of increasing solute concentration arises from an interplay between the four-fold and six-fold anisotropy pa- Jonathan Weare rameters, which characterize the orientation dependence of NYU the solid-liquid interfacial free energy. In this talk we will [email protected] summarize several molecular dynamics simulation studies of the dependence of interfacial energy anisotropy on so- Robert V. Kohn lute additions. Systems discussed include: Lennard-Jones, Courant Institute of Mathematical Sciences hard sphere, Al-Mg and Cu-Ag-Au. New York University [email protected] J. J. Hoyt McMaster University, Canada [email protected] MS41 Understanding the Shape Evolution of Nanoscale M.J.Rahman,A.A.Potter Objects: Continuum Models from the Atomistics McMaster University of Jets, Menisci, Catalyst Particles and Protective [email protected], [email protected] Coatings

Mark Asta Abstract not available at time of publication. University of California, Berkeley [email protected] Michael Moseler Fraunhofer Institute for Mechanics of Materials [email protected] MS40 Surface Mechanics and its Coupling to Electronic MS41 Structure and Chemical Reactivity Multi-scale Modeling of Ion-beam Irradiation: Surface stress quantiﬁes the elastic interaction of the mat- Linking Atomistic Simulation to Continuum PDEs ter at solid surfaces and interfaces with the adjacent regions of bulk solid. From a materials point of view, surface stress Energetic particle irradiation of solids – long used in indus- is relevant since balance equations for stress and chemical try for surface ultra-smoothening – can lead to nanoscale potential couple the simultaneous mechanical and chemi- pattern formation under the right environmental condi- cal equilibrium in the material to its capillary parameters tions. The widespread use of this technology in current and to microstructural quantities such as surface net area, industrial settings for smoothening suggests the promise of 90 MS10 Abstracts

harnessing spontaneous pattern formation to create novel MS42 devices. However, existing theoretical models of ion ir- Near Boundary Vortices in a Magnetic Ginzburg- radiation fail to agree broadly with experiment even in Landau Model: Their Locations via Tight Energy the linear regime. To investigate this dilemma, we con- Bounds duct molecular dynamics simulations of the average crater shape caused by ion bombardment of an initially flat silicon Given a bounded doubly connected domain G ⊂ R2,we surface, and develop a multi-scale framework that directly consider a minimization problem for the Ginzburg-Landau predicts a parameter-free continuum PDE for the surface energy functional when the order parameter is constrained topography. Analysis of the PDE yields a parameter-free to take §1-values on ∂G and have degrees zero and one phase diagram for pattern formation and the characteris- on the inner and outer connected components of ∂G,cor- tic wavelength as the incidence angle is varied. The re- respondingly. We identify intervals of the GL parameter sults agree remarkably well with the pattern wavelength where the minimizers always exist and never exist. For the and transition angle between patterns and smoothening ob- critical values of the GL parameter we show limited loca- served in experiments on silicon. In addition, they overturn tions of vortices (that correspond to the singularities of the the long-held assumption that pattern formation is due to limiting currents) by deriving tight upper and lower energy the removal of target atoms by sputter erosion; instead, bounds. These locations are described via a scalar linear these phenomena are dominated by the impact-induced re- PDE problem in the entire domain G and therefore they distribution of target atoms that are not sputtered away. are not determined by local characteristics of the boundary such as maximal curvature of of ∂G (as conjectured previously). Scott Norris School of Engineering and Applied Sciences Leonid Berlyand Harvard University Penn State University [email protected] Eberly College of Science [email protected] Juha Samela University of Helsinki Volodymyr Rybalko juha.samela@pivotal.fi Institute for Lower Temperature Physics and Engineerin [email protected] Charbel Madi Harvard University Oleksandr Misiats [email protected] Penn State University [email protected] Michael Brenner Harvard Univ. Cambridge, MA MS42 [email protected] Gauge Uniqueness of Solutions to the Ginzburg- Landau Equations of Superconductivity in Small Kai Nordlund Samples University of Helsinki In this talk, we present some results on the solutions of the [email protected].fi Ginzburg-Landau system for small two-dimensional superconducting samples. We show that up to a gauge, the sys- Michael Aziz tem has only two solutions: the normal and the vortex-less Harvard University superconduting states. Additionally, we identify a criti- [email protected] cal field below which the vortex-less solution is the global minimizer and above which the normal solution is the only possible state. MS41 Continuum Model for the Long-range Elastic In- Tiziana Giorgi teraction on Stepped Epitaxial Surfaces Department of Mathematics New Mexico State University In heteroepitaxy, the mismatch of lattice constants between [email protected] the crystal film and the substrate causes misfit strain and stress in the bulk of the film, driving the surface of the Robert Smits film to self-organize into various nanostructures. Below New Mexico State University the roughening transition temperature, an epitaxial sur- [email protected] face consists of facets and steps and changes its morphology by lateral motion of steps. We present a 2+1-dimensional continuum model for the long range elastic interaction on MS42 stepped surface of a strained film. The continuum model Some Remarks Regarding a Ginzburg-Landau is derived rigorously from the discrete model for the inter- Type Model for Liquid Crystals action of steps; thus it incorporates the discrete features of thesteppedsurfaces.Wevalidateourmodelbyperform- We will discuss some results regarding the Landau De ing linear stability analysis and numerical simulation in the Gennes energy, often used to model liquid crystals, in the nonlinear regime. framework developed by Bethuel, Brezis and Helein for the Ginzburg-Landau energy of superconductivity. Our even- Yang Xiang tual aim is to describe the types of singularities allowed by Hong Kong University of Science and Technology this model. [email protected] Alberto Montero MS10 Abstracts 91

Departamento de Matematica ground states. We introduce a new set of phases and a Pontificia Universidad Católica de Chile phase transition energy to describe such a phenomenon. [email protected] Finally, we briefly compare this model with its continuous counterpart.

MS42 Marco Cicalese Order Parameter Models for Problems from Liquid Universita’diNapoliFedericoII Crystals Dipartimento di Matematica e Applicazioni [email protected] In this talk I will describe our work on order parameter models for liquid crystals where we investigate the struc- Andrea Braides ture of solutions and their defects. University of Roma 2, Italy Dipartimento di Matematica Daniel Phillips [email protected] Department of Mathematics, Purdue University [email protected] MS43 Patricia Bauman Sub-Wavelength Plasmonic Crystals: Dispersion Purdue University Relations and Effective Properties [email protected] Plasmonic crystals are representative of a class of mi- Jinhae Park crostructured dielectrics known as meta-materials. The University of Minnesota period of the meta-material crystal lies below the wave- [email protected] length of illumination and the propagation of light is in- fluenced by local electromagnetic field resonances on the length scale of the period. In this talk we report on recent MS42 work that develops a new type of power series expansion Variational Characterization of the Abrikosov Lat- for the first branch of the dispersion relation for plasmonic tice crystals. The expansion parameter is given by the product kd where k is the wave number and d is the period of the The Abrikosov Lattice is the name of the hexagonal lattice crystal. Explicit error estimates show that a good approx- in the context of superconductivity, where superconducting imation to the true dispersion relation is obtained using vortices arrange themselves in this way. In a joint work only a few terms of the expansion. with S.Serfaty we derive from the Ginzburg-Landau model an energy for configurations of points in the plane for which Santiago Fortes, Robert P. Lipton, Stephen P. Shipman the optimal lattice is the Abrikosov lattice. The question Department of Mathematics of minimization among all possible configurations remains Louisiana State University open. [email protected], [email protected], [email protected] Etienne Sandier UniversitéParis-EstCréteil Creteil, France MS43 [email protected] A Geometric Approach to Bounds of Discrete Com- posites

MS43 Cherkaev and Rogora proposed a discrete approach to com- Discrete Inhomogeneous Materials posites based on the concept of monad, A discrete composite is an arrangement of monads, glued together at their We study lattice models of inhomogeneous materials, deriv- boundary points. The associated simplicial complex of a ing compatibility conditions, phase equilibrium and eigen- discrete composite covers the composite and each of its 2- deformation, effective properties of discrete composites and dim simplexes contains one and only one monad. On the their lower bound, and discrete polyconvexity. We discuss associated simplicial complex, discrete forms and the basic similarity and difference of discrete and continuum models, operators of exterior calculus can be define. The discrete homogenization, and lower limit of the size of a material wedge product allows one to define translators . We shall grain. discuss for which kind of monads these translators can be used to get translation bounds as in continuum theory. Andrej V. Cherkaev Department of Mathematics Enrico Rogora University of Utah universita’ di Roma I [email protected] [email protected]

MS43 MS44 Patterns in Ferromagnetic Anti-ferromagnetic Spin Multiscale Science of Protein Materials in Extreme Systems Conditions and Disease

We consider a simple variational model for a ferromagnetic Protein materials feature hierarchical structures, ranging anti-ferromagnetic spin system with nearest-neighbors and from the atomistic, molecular to macroscopic scales to form next-to-nearest-neighbors interactions. By tuning the in- functional biological tissues as diverse as silk, bone, skin, teraction parameters the system develop, in the continuum hair or cells. I will present integrated theoretical, compu- limit, interfacial energies parameterized on the set of the tational and experimental multiscale materiomics studies, 92 MS10 Abstracts

focused on how protein materials deform and fail due to of these networks. extreme mechanical conditions, disease and injuries. Spe- ciﬁc focus is on collagenous tissues including tendon and L. Mahadevan bone, where we investigate the mechanisms of brittle bone Harvard University disease osteogenesis imperfecta. [email protected]

Markus J. Buehler Civil and Environmental Engineering MS44 Masachussets Institute of Technology Mesoscale Modeling of Cell Membrane-Mediated [email protected] Trafficking Trafficking of receptors and nanocarriers on cell membranes MS44 regulate important intracellular processes governing cell Mechanics of Adhesion Between Elastic Mediua growth and hold promise in targeted drug delivery, but Via Molecular Bond Clusters: Implications on Cell their optimization require accurate descriptions of hydro- Adhesion dynamics as well as dynamics of cell membranes. We will describe our computational approach for modeling protein- Cell adhesion depends on the collective behavior of a large mediated membrane deformation as well as energy land- number of molecular bonds. While the behavior of a single scapes and hydrodynamic interactions in nanocarrier bind- molecular bond is governed by statistical mechanics, con- ing to cell membranes. The method consists of employing tinuum mechanics should be valid at a large scale. How to the time-dependent Ginzburg Landau approach for confor- model this transition and can this tell us something about mational sampling, flat histogram methods for defining the mechanics of cell adhesion? With a long-term objective to- free energy landscape, and fluctuating hydrodynamics for wards quantitative understanding of cell adhesion, we con- quantifying the hydrodynamic interactions. From a bio- sider an idealized theoretical model of a cluster of molecular logical standpoint, we describe the importance of coopera- bonds between two dissimilar elastic media subjected to an tivity and spatial order in curvature inducing proteins and applied tensile load. In this model, the distribution of inter- the effect of flexure, bond-stiffness in receptor-ligand interfacial traction is assumed to obey classical elastic equations actions as well as the effect of shear force and resistance while the rupture and rebinding of individual molecular due to glycocalyx in binding and trafficking mechanisms. bonds are governed by stochastic equations. Monte Carlo simulations that combine the elastic and stochastic equa- Ravi Radhakrishnan tions are conducted to investigate the lifetime of the bond Bioengineering cluster as a function of the applied load. We show that University of Pennsylvania, Philadelphia. the interfacial traction is generally non-uniform and for a [email protected] given adhesion size, the average cluster lifetime asymptot- ically approaches infinity as the applied load is reduced to below a critical value, defined as the strength of the cluster. MS45 The effects of elastic moduli, adhesion size and rebinding Defect Dynamics in Graphene rate on the cluster lifetime and strength are studied under strongly non-uniform distributions of interfacial traction. We have proposed a nonlinear lattice model for defects While overly simplified in a number of aspects, our model in graphene (single sheet of carbon atoms arranged in seems to give predictions that are consistent with relevant a hexagonal lattice) with overdamped or conservative experimental observations on focal adhesion dynamics. dynamics. Solving numerically our model with initial and boundary conditions corresponding to edge disloca- Huajian Gao tions and dislocation dipoles, we study the associated de- Solid Mechanics fect cores. Stable cores include pentagon-heptagon pairs Brown University, Providence, RI. and shuffle dislocations (octagons with a dangling bond). huajian [email protected] Stone-Wales defects are dynamically unstable, collapse and disappear. Recent experiments agree with our predictions. Jin Qian Luis Bonilla Georgia Institute of Technology Universidad Carlos III de Madrid [email protected] G. Millan Institute of Fluid Dynamics, Nanoscience & IndMath MS44 [email protected] Elasticity of Random Networks MS45 We study the role of connectivity on the linear and nonlinear elastic behavior of amorphous systems using a two- Nucleation of Defects and Incipient Plasticity in dimensional random network of springs as a model system. Crystals A natural characterization of these systems arises in terms By performing a bifurcation analysis in a lattice model of of the network coordination relative to that of an isostatic two dimensional nanoindentation we show that disconti- network δz; a floppy network has δz < 0, while a stiff net- δz > nuities in the load versus penetration depth curve corre- work has 0. We use numerical simulations to compute spond to the nucleation of dislocation loops. Another pre- the exponents which characterize the onset of elasticity in diction of the model is the possibility of reversible homo- these networks and also determine the scaling exponents for geneous nucleation and annihilation of dislocation loops as the shear modulus, the heterogeneity of the response, and δz the stress is released. Recent experiments confirm these the network stiffening as a function of . We also derive predictions. these theoretically and consider the effect of the probability distribution of the random network on the properties Ana Carpio Universidad Complutense de Madrid MS10 Abstracts 93

Departamento de Matemática Aplicada Y. Han, B. Unal, D. Jing, P.A. Thiel [email protected] Iowa State University [email protected], [email protected], [email protected], [email protected] MS45 Lattice Models in Fracture MS46 Mass-spring and bending beam lattices are considered, Patterns in Strained Epitaxial Layers: Beyond the and lattice fracture phenomena and the analytical tech- Frenkel-Kontrova Model nique are discussed. Crack resistance and continuum limit. Discrete and continuum fields coupling. Discrete versus Although the structures of strained layers have been under- continuum stress distributions. Lattice trapping and the stood in terms of the classical Frenkel-Kontorova model, local-to-global energy release ratio. Dynamic factor and our work shows that these structures can have a quan- crack speeds. Green’s functions, causality principle, remote tum mechanical origin. We consider the striped phases of load and homogeneous equations. Dynamic-to-static crack Ag on Pt(111). Using Monte Carlo simulations based on growth transition and the related continuous-to-discrete substrate-mediated Ag-Ag pair interactions obtained up to transition of the Fourier transform. the 53rd neighbor with DFT, we find striped phases with all the experimental characteristics. Angular variations in Leonid Slepyan the potential are important in producing these phases. Tel Aviv University, Israel [email protected] Kristen Fichthorn Penn State University fi[email protected] MS45 Continuum Linear Elasticity Theory with a Set of Joshua Howe Internal Length Scales University of California - Berkeley [email protected] We propose a method of constructing a series of nested continuum models, which describe linear elastic behavior of crystal lattices at successively smaller scales. The rel- MS46 evant scales are dictated by the interatomic interactions Nucleation, Growth, and Self-assembly of Strained and are not arbitrary. The essence of the model is a de- Islands on Patterned Surfaces composition of the displacement field into the coarse part and the micro-level corrections. The coarse contribution Abstract not available at time of publication. is the conventional homogenized displacement field used in classical continuum elasticity. The micro-level corrections Feng Liu are sub-continuum fields representing the fine structure of Dept. Materials Science & Engineering the boundary layers exhibited by the discrete equilibrium University of Utah configuration. The model is based on a multi-point Pad fl[email protected] approximation in the Fourier space of the Greens function for discrete problem. Joint work with M. Charlotte MS46 Lev Truskinovsky Compositional Patterning in Alloy Nanostructures Laboratoire de Mechanique des Solides Ecole Polytechnique Knowledge of composition profiles within alloy nanostruc- [email protected] tures such as heteroepitaxial nanowires, alloy nanocrystals/quantum dots and self-assembled surface patterns is critical for applications in electronic, photonic and mem- MS46 ory devices as variations in composition at the nanoscale Far-from-equilibrium Growth of Multicomponent can substantially influence electronic and optical proper- Films: Ni+Al/NiAl(110) ties. Obtaining a quantitative description of composition profiles in these small-scale structures is a challenging task Homoepitaxial growth of single-element films (A on A) has due to the complex coupling between composition varia- provided an ideal testing ground for assessing the funda- tions, shape and long-range elastic interactions. In addi- mentals of crystal growth. Equilibrated films have simple tion, differences in the bulk and surface transport proper- structure, but deposited films display complex morpholo- ties of the alloy components can lead to rich pattering phe- gies reflecting kinetic limitations [Evans et al. Surf. Sci. nomena that cannot be observed in single-component sys- Rep. 61 (2006) 1]. For homoepitaxial growth of binary tems. In this talk I will present efficient numerical schemes alloys (A+B on AB), an additional issue is the interplay to study both equilibrium and far-from equilibrium com- between growth morphology and alloy ordering. Several position profiles in alloy nanostructures. I will illustrate studies explored these issues using generic models with an application of our methods for 1) determination of com- idealized treatment of diffusion. However, morphology and positional patterning in strained alloy quantum dots, 2) ordering in systems driven out of equilibrium depends sen- analysis of the morphology and instabilities of heteroepi- sitively on the details of the diffusion kinetics. This mo- taxial nanowires and 3) the formation of compositionally tivated our development of a realistic atomistic model for modulated ripples during sputtering of alloy surfaces. deposition of Ni+Al on NiAl(110). Vivek Shenoy Jim W. Evans Division of Engineering, Brown University Ames Laboratory USDOE and Iowa State University Providence RI-02912 [email protected] vivek [email protected] 94 MS10 Abstracts

MS47 MS47 Ultrafast Micromagnetics at Elevated Tempera- Mathematical Treatment of Nanoscale Multilayer tures Materials: Is a Continuum Limit Useful? It has recently been shown experimentally that magneti- Micromagnetic methods are well established for the treat- zation reversal can occur following the application of cir- ment of homogeneous materials described by a bulk ex- cularly polarised laser light. The reversal mechanism (K. change constant A, and for discrete grains or layers cou- Vahaplar et al, Phys. Rev. Lett., 103, 117201 (2009)) in- pled at their boundaries by a surface energy σ. In the latter volves a strongly non-uniform magnetization state achieved case, magnetization variation within a grain is ignored. We by heating close to Tc. We will describe a micromagnetic have developed a consistent scheme involving both A and model based on the Landau-Lifshitz-Bloch equation. The σ,inwhichA →∞gives the usual discrete theory, and model will be applied to the prediction of laser assisted σ →∞gives the continuum theory. reversal processes including opto-magnetic reversal. Pieter Visscher Roy Chantrell University of Alabama The University of York [email protected] [email protected]

Denise Hinzke, Uli Nowak MS48 University of Konstanz Energy-minimizing Weak Solutions in Second- [email protected], gradient Nonlinear Elasticity [email protected] We consider a class of second-gradient nonlinear elasticity models in which the stored energy density is assumed MS47 to grow unboundedly as the local volume ratio approaches Strategies for the Efficient and Accurate Micro- zero. We provide a general setting in which the determi- magnetic Modeling of Static Hysteresis Loops nant of any admissible deformation with bounded energy is strictly positive on the closure of the domain. We ob- The attention is focused on the computation of equilib- tain energy-minimizing weak solutions for a wide variety of rium states for the determination of static hysteresis loops mixed boundary conditions on bounded Lipshitz domains. of submicron samples. Starting from the space-time integration of the Landau-Lifshitz-Gilbert equation, the magnetization is time-updated by means of a norm-conserving Tim Healey algorithm based on Cayley transform. The analysis gives Cornell University hints for the definition of a correct criterion of convergence Universidad de Los Andes towards equilibrium states and for the improvement of the [email protected] numerical efficiency, exploring the possibility of reducing the simulation duration. MS48 Alessandra Manzin, Oriano Bottauscio A Quantitative Rigidity Result for the Cubic to Istituto Nazionale di Ricerca Metrologica (INRiM) Tetragonal Phase Transition in the Geometrically [email protected], [email protected] Linear Theory with Interfacial Energy We are interested in the cubic to tetragonal phase transi- MS47 tion in a shape memory alloy. We consider geometrically The Magnetic Effect of Dislocations in Small Fer- linear elasticity. In this framework, Dolzmann and Müller romagnetic Minerals have shown the following rigidity result: The only stress- free configurations are (locally) twins (i.e. laminates of just Dislocations have a major effect on magnetic hysteresis in two of the three Martensitic variants). However, configura- large ferromagnetic crystals, but very little is known about tions with arbitrarily small elastic energy are not necessar- their effect in nanocrystals. Any effect arises from the ily close to these twins: The formation of microstructure coupling between the magnetization and the strain field allows to mix all three Martensitic variants at arbitrary around the dislocation. Strain fields in finite crystals are volume fractions. In this paper, we take an interfacial en- difficult to calculate because of the boundary conditions. ergy into account and establish a (local) lower bound on A new method is presented that solves the boundary value elastic + interfacial energy in terms of the Martensitic vol- problem. Magnetic hysteresis curves are calculated for ume fractions. The introduction of an interfacial energy nanocrystals with screw and edge dislocations. introduces a length scale and thus, together with the linear dimensions of the sample, a non-dimensional parame- Andrew Newell ter. Our lower Ansatz-free bound has optimal scaling in North Carolina State University this parameter. It is the scaling predicted by a reduced andrew [email protected] model introduced and analyzed by Kohn and Müller with the purpose to describe the microstructure near an inter- Meijie Tang face between Austenite and twinned Martensite. The op- Lawrence Livermore National Laboratories timal construction features branching of the Martensitic meijie tang ¡[email protected]¿ twins when approaching this interface. Felix Otto Joshua Feinberg University of Bonn University of Minnesota Germany joshua feinberg ¡[email protected]¿ [email protected] MS10 Abstracts 95

MS48 [email protected] Everting Elastic Spherical Caps It is common experience that a half tennis ball or a contact MS49 lense can be made to snap from a load-free and stress- Transient Rheological Responses in Sheared Biax- free configuration into another loqd-free but not stress-free ial Liquid Crystals equilibrium configuration, characterized by a macroscopic change in sign of the mid-surface’s curvature and a further We study the rheological response of monodomain ellip- curvature flipping localized about the rim. Such a snap soidal biaxial liquid crystal polymers as well as bent-core instability is called eversion. A mathematical model that or V-shaped liquid crystal polymers subject to steady and accounts for eversion is discussed. time-dependent small amplitude oscillatory shear. Tran- sient shear stresses and normal stress differences corre- Paolo Podio-Guidugli sponding to steady and small amplitude oscillatory shear Università degli Studi di Roma are investigated. Dipartimento di Ingegnera Civile [email protected] Sarthok K. Sircar University of Utah [email protected] MS48 Title Not Available at Time of Publication MS49 Abstract not available at time of publication. Physical-Chemical Based Modeling of Biofilm In- duced Mineralization Phoebus Rosakis Professor, Dept of Theor. and Appl. Mechanics We consider the following biomineralization problem. Urea Cornell University hydrolysis catalyzed by biofilm increases the pH value and [email protected] produces carbonate ions. In the presence of calcium ions, calcite (CaCO3) will precipitate and form crystal once its saturation index exceeds certain critical value. We MS49 present a mathematical model including the important Hydrogels and Microfluidic Devices chemical, physican and biological processes (Ureolysis and pH value change, advection, diffusion and crystal precip- Hydrogels consist of crosslinked polymeric networks, hold- itation, biofilm growth and deformation) involved in the ing fluid able to sustain ions. We propose a model based on problem. Some computation results and discussion will mixture theory that the couples equations of elasticity and also be given. Navier Stokes that account for the mechanical properties of gels with the Nearst-Planck equations for ion transport. Tianyu Zhang We apply the model to the design of a microfluidic valve Mathematics activated by an alternating current. Montana State University [email protected] M. Carme Calderer University of Minnesota [email protected] MS49 Kinetic Structure Simuations of Nematic Polymers in Shear MS49 Undulation Instability in Smectic Liquid Crystals We numerically simulate the structure formation of nematic rigid-rod liquid crystalline polymers confined in a We study layer undulations of smectic A liquid crystals Couette cell using the kinetic model equations coupled with when a magnetic field is applied in the direction parallel the Navier-Stokes equation. The transient defect cores as- to smectic layers. Using the Landau-de Gennes model of sociated with the flow for large Erickson number will be smectic A liquid crystals, we characterize the critical field examined in detail. and obtain the asymptotic expression of unstable modes using the Γ-convergence theory. Under the assumption that Ruhai Zhou the layers are fixed at the boundaries, the maximum un- Department of Mathematics and Statistics dulation occurs in the middle of the cell and the displace- Old Dominion University ment amplitude decreases as approaching the boundaries. [email protected] We also obtain the estimate of the critical field, which is consistent with Helfrich-Hurault theory. With the natural boundary condition, however, the displacement amplitude MS50 weakly depends on the vertical z-coordinate and the criti- Phase-Field Modelling of Bi-Crystal Grain Bound- cal field is reduced compared to the one calculated in the aries via an Orientation Parameter classic theory. This is consistent with the experiment done by Laverentovich. Numerical simulations will be presented Grain Boundaries are of paramount importance in Mate- to confirm the predictions of the analysis. rials Science; they influence the macroscopic properties of materials in very profound ways such as tensile strength Sookyung Joo and creep. Thus, the ability to accurately describe their be- University of California, Santa Barbara havior and extract material properties from their behavior [email protected] is important. In this talk, we present a phase-field model that incorporates the effect of temperature of the structure Carlos Garcia-Cervera and free energy of grain boundaries in order to describe Mathematics, UCSB the behavior of grain boundaries. The model was obtained 96 MS10 Abstracts

numerically using a copper bicrystal with symmetrical tilt the system, and employ sampling techniques that do not grain boundaries of different misorientaion angles. To eval- require a uniform domain discretization. Specifically, we uate the accuracy of this phase-field model, its solutions employ adaptive search methods, and sample the domain will be compared with molecular dynamics simulations of using low-discrepancy sequences. Various combinations of the same set of grain boundaries. these methods will be compared with each other and with conventional techniques. Michael R. Atkins George Mason University Thomas Stephens [email protected] George Mason University [email protected] MS50 A Level Set Simulation of Theta Phase Dissolution MS51 in Al-Cu Alloys Multiscale Modeling and Simulation of Multi- walled Carbon Nanotubes (MWCNTs) A common approach to particle dissolution is the phase- field approach which is based on the minimization of a free We will review recently developed models for multiwalled energy function over a diffuse interface. Although recent carbon nanotubes, hierarchically built from the atom- studies have shown agreement between a phase-field ap- istic interactions up to mesoscopic scales. These include proach and sharp interface approach, the diffuse interface surface models, foliation models, and non-linear phase- is unrealistic and the free energy function parameters are transforming elastica models. These models serve as the difficult to obtain. The level set method is one of the sev- basis for efficient simulations, which are able to make a eral numerical methods available for solving Stefan prob- direct connection with the experimental observations. lems with a sharp interface. It is also capable of handling complex topological changes that allow particle break-up Marino Arroyo, Irene Arias, Susanta Ghosh in a natural way. The goal is this study is to replicate Universitat Politecnica de Catalunya the sharp interface diffusion obtained from the software [email protected], [email protected], package DICTRA for theta phase particle dissolution in [email protected] Al-Cu alloys. The results from two-dimensional and three- dimensional models using the level set method are then compared with experimental data. MS51 Finite-Temperature Extension of the Quasicontin- Wren Chan uum Method based on Langevin Dynamics Carnegie Mellon University [email protected] The concurrent bridging of molecular dynamics and continuum thermodynamics remains one of the most challenging problems in multi-scale material modeling. The challenge MS50 lays in being able to derive an accurate description of the Modeling Phase Separation in Ternary Alloys energy transfer across all length-scales involved. We propose a framework for simulating coarse-grained dynamic Alloys have many desirable properties and numerous ap- systems in the canonical ensemble using the Quasicontin- plications, however sometimes nature combats their use uum method (QC). The equations of motion are expressed with phenomena known as phase separation. Specifically, in reduced QC coordinates and are derived from dissipative we examine a type of phase separation called nucleation Lagrangian mechanics. The derivation naturally leads to which occurs after an alloy is quenched. Nucleation is a classical Langevin implementation where the time-scale characterized by the formation of discrete droplets of an is governed by vibrations emanating from the finest length individual material speckled throughout the otherwise ho- scale occurring in the computational cell. The equations of mogeneous domain; this process weakens the composition motion are integrated by recourse to Newmark’s method, and diminishes the value of the material. We model this which is parametrized to ensure over-damped dynamics. phenomenon using the Cahn-Morral system by employing Thus, spurious heating due to reflected vibrations is sup- numerical continuation via AUTO. We discuss the model, pressed, leading to stable canonical trajectories. To esti- associated numerical techniques, and comparison of non- mate the errors introduced by the QC reduction in the linearities. resulting dynamics, we quantify the vibrational entropy losses in Al uniform meshes by calculating the thermal ex- James O’Beirne pansion coefficient for a number of conditions. The limita- George Mason University tions of the method and alternatives to mitigate the errors [email protected] introduced by coarsening will also be discussed.

Jaroslaw Knap MS50 U.S. Army Research Laboratory Toward Accurate Computation of Ternary Phase [email protected] Diagrams Using Low-discrepancy Sequences The eﬀective and accurate computation of phase diagrams MS51 plays a critical role in allowing materials scientists to fully Finite Temperature Coarse-graining of Atomistic exploit the potential of cutting-edge manufacturing tech- Models: Some Simple Cases nology. It is currently possible to compute satisfactory phase diagrams for simple materials, however multi- com- Molecular dynamics is a classical method to simulate mate- ponent materials are provingtobelesstractable.Our rials at constant temperature. For instance, the evolution work focuses on these complicated systems, and in sce- of an atomistic system according to the Langevin equation narios where existing techniques fail. We explore methods is simulated, while some relevant observables are averaged that do not require diﬃcult-to-obtain a priori knowledge of along the trajectory. On the basis of such a microscopic MS10 Abstracts 97

model, macroscopic quantities can be computed. It is of- ture Calculations ten the case that interesting observables actually do not depend on all the particles, but only on the position of The electronic structure calculations based on Kohn-Sham some of them. In this case, it is natural to try and de- density functional theory is limited to small systems due sign a strategy to compute more efficiently the quantities to its expensive computational cost. By coupling with con- under study. We will review some recent progress on that tinuum theory derived from the Kohn-Sham density func- question. Efficient methods will be described, that are sup- tional theory, we develop a sublinear scaling algorithm for ported by rigorous error analysis. Numerical simulations electronic structure calculations. This extends the solution will illustrate the obtained theoretical results. of density functional theory to macroscopic systems with local defects. Joint work with Weinan E (Princeton) and Xavier Blanc Carlos Garcia-Cervera (UCSB). Universite Paris 6 [email protected] Jianfeng Lu Courant Institute of Mathematical Sciences Claude Le Bris New York University ENPC/CERMICS [email protected] [email protected] MS52 Frederic Legoll Fem for Geometric Problems: Application to Bio- LAMI, Ecole Nationale des Ponts et Chaussees Membranes and Shape Optimization in Continuous [email protected] Mechanics Carsten Patz A parametric FEM for free boundary problems is discussed. WIAS Berlin Some applications include geometric and fluid-membrane [email protected] interaction in bio-membranes. With slight modification the method can be successfully applied in shape optimization problems such the design of an obstacle with minimal drag MS51 or a cantilever with minimal compliance. The last in the Multiscale Modeling of Surface-Induced Instabili- context of inexact sequential quadratic programming. In- ties in Nanomaterials exactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state equation, up- The objective of the present work is to investigate the date the boundary, and compute the geometric functional. recently-developed Wallace instability criterion with a particular emphasis on studying defect nucleation and instabil- Miguel S. Pauletti ities arising from the failure of nanomaterial surfaces. We Texas A&M University study this within the context of FCC metals using both a [email protected] mode Lennard-Jones potential, as well as a realistic embedded atom (EAM) potential. Ricardo Nochetto Department of Mathematics Harold Park University of Maryland, College Park Boston University [email protected] [email protected] Marco Verani Geng Yun MOX (Milano) University of Colorado [email protected] [email protected] Pedro Morin MS52 IMAL (Argentina) Simulating Fracture Interfaces with Curvature De- [email protected] pendent Surface Tension

The classical theory of linear elastic fracture mechanics for MS52 static cracks in an infinite linear elastic body has two signif- The Effect of Surface Tension in Modeling Fracture icant defects: it predicts unbounded crack-tip stresses and elliptical crack opening profiles. A new model of fracture The talk will focus on the analysis of a class of fracture based on extending continuum mechanics to the nanoscale models based on a new approach to modeling brittle frac- corrects these anomalous effects, predicting finite crack-tip ture which incorporate molecular scale effects. Ascribing stresses and cusp-like opening profiles. We describe how curvature-dependent surface tension to the fracture sur- this new fracture modeling paradigm can be implemented faces and using the appropriate crack surface boundary in a finite element analysis. condition, given by the jump momentum balance, leads to bounded stresses. This allows for a fracture criterion based Lauren Ferguson on Critical Crack Tip Stress, in addition to an energy based Department of Mathematics criterion. Texas A&M University [email protected] Tsvetanka Sendova Institute for Mathematics and Its Applications University of MInnesota MS52 [email protected] Sublinear Scaling Algorithms for Electronic Struc- Jay Walton 98 MS10 Abstracts

Department of mathematics Cardiff University Texas A&M University cherednichenkokd@cardiff.ac.uk [email protected] Andreas Burgmann Cardiff School of Mathematics MS52 Cardiff University Debonding of a Material Interface burgmanna@cardiff.ac.uk We discuss mixed mode de-bonding of a material interface within the context of a new theory of fracture incorporat- MS53 ing curvature dependent crack surface tension and a mu- Focussing Bending Waves via Negative Refraction tual force correction to the balance of linear momentum in Perforated Thin Plates within a thin region enveloping the interface. It is shown that once chemical bonds are broken, neither pure mode We propose a design of a periodically perforated thin plate III (anti-plane shear) nor mode II (in-plane shear) defor- leading to a lensing effect of bending waves via negative mations are possible even under pure anti-plane or in-plane refraction. To achieve this goal, we first analyse the band shear loading leading to new crack growth criteria. spectrum of the bi-harmonic operator for an array of freely vibrating square voids using both numerical (finite ele- Jay R. Walton ments) and asymptotic methods. We then find some point Department of Mathematics in the reciprocal space where the acoustic dispersion sur- Texas A&M face displays a convex isofrequency contour shrinking with [email protected] frequency. Sebastien Guenneau MS53 Institut Fresnel, UMR CNRS 6133 Resonant [email protected] Properties of Complementary Filled Nanospheres and Nanocylinders: Optical Nanoswitch, Focusing Mohamed Farhat and Extreme Anisotropy Institut Fresnel We discuss here the closed-form analytical solution for in- Marseille homogeneous spheres and cylinders partially filled by plas- [email protected] monic materials. We show that under proper conditions these nanoparticles may constitute optical nanoswitches, Stefan Enoch characterized by extremely anisotropic scattering behav- CNRS ior, or focusing devices. In our talk, we will provide math- Institut Fresnel ematical details and physical insights into the anomalous [email protected] optical response of these 2-D and 3-D nanostructures, and its interpretation in terms of optical nanocircuit theory. Alexander Movchan Department of Mathematical Sciences Andrea Alu University of Liverpool, UK Department of Electrical and Computer Engineering [email protected] University of Texas at Austin [email protected] MS53 Nader Engheta More Defective Knowledge About Photonic Crys- Department of Electrical and Systems Engineering tals University of Pennsylvania [email protected] This talk describes recent progress in deriving semi- analytic models for defects created in photonic crystals, such a resonant cavities and waveguides. The presence MS53 of the defect modifies Bloch states of the perfect crystal, One-dimensional High-contrast Models and the As- giving them an envelope function which gets broader and sociated Defect Modes broader as the defect weakens. We derive analytic expressions for the envelope function, using perturbation ideas Several recent works made an advance on the rigorous anal- and the Luttinger-Kohn model from solid state physics. ysis of localised, or “defect’, modes in mathematical mod- The semi-analytic results are verified using accurate elec- els of photonic crystal fibres. One of the key geometric tromagnetic theory numerical methods. assumptions for the validity of the related results is that the “matrix’ component of the high-contrast fibre cladding Ross McPhedran be a connected set. In the present talk we focus on the CUDOS ARC Centre of Excellence analogous 1D setting, where the above assumptions can and School of Physics, University of Sydney not be fulfilled. We study the limit S of the spectra of the [email protected] associated differential operators. One of the marked differences of our results from those in 2D is that, in the case of Sahand Mahmoodian a fibre whose cross-section is bounded, the limiting set S CUDOS and School of Physics, University of Sydney contains a union of disjoint intervals. We also discuss the [email protected] conditions under which defect modes emerge in this kind of 1D model. Martijn de Sterke CUDOS and School of Physics Kirill Cherednichenko University of Sydney MS10 Abstracts 99

[email protected] important effect on macroscopic behavior, yet they are not stationary and may evolve as a result of loading. There- Lindsay C. Botten fore, it is important to understand their evolution on the CUDOS and Department of Mathematical Sciences proper time scales under relevant thermal and mechani- University of Technology, Sydney cal conditions. In this talk we will review some aspects of [email protected] well studied distribution functions and discuss challenges in constructing theories for their evolution and their place Kokou Dossou in a macroscopic theory of material behavior. We will CUDOS and Department of Mathematical Sciences use simulation combined with analysis in our discussions University of Technology Sydney of challenges and possible solutions. [email protected] Shlomo Ta’asan Department of Mathematical Sciences MS54 Carnegie Mellon University [email protected] Towards a Unified Statistical Theory of Texture EvolutioninPolycrystals MS54 We present an account of recent developments in mesoscale theory of texture evolution in polycrystalline materials. Are Grain Boundaries Like Glass? The talk will demonstrate how a carefully chosen combi- It has long been hypothesized that GBs have features in nation of simulation, theory and modeling techniques can common with glass-forming liquids based on the process- bring a deeper understanding to coarsening processes gov- ing characteristics of polycrystalline materials. We ?nd erned by the motion of triple junctions. By means of mod- remarkable support for this suggestion, as evidenced by ulated stochastic process characterization and kinetic evo- string-like collective atomic motion and transient caging of lution equations, we will quantify the rates of grain bound- atomic motion, and a non-Arrhenius GB mobility describ- ary disappearance events and predict the influence of these ing the average rate of large-scale GB displacement. Time events on macro-level materials properties. Comparison permitting, I will also discuss a new model of creep in grain with large-scale 2D and 3D simulations will provide the boundaries. necessary validation and reveal similarities and differences between these approaches. James Warren NIST Maria Emelianenko Metallurgy Division George Mason University [email protected] [email protected] Hao Zhang MS54 U. Alberta Grain Boundary Pore Interaction [email protected]

The talk will focus on large-scale simulations of grain David Srolovitz boundary pore interaction in three dimensions to capture The Institute for High Performance Computing in the drag on grain boundaries when the pores move due to Singapore the presence of a temperature gradient. The simulations [email protected] will be extended to three-dimensional grain structures to identify the path of a moving pore as a function of pore Jack Douglas size, grain boundary character distribution and grain mor- NIST phology. The application of the simulations to ﬁssion gas [email protected] bubble evolution in nuclear fuels will be discussed.

Balasubramaniam Radhakrishnan MS55 Oak Ridge National Laboratory A Grid Based Particle Method for Moving Inter- [email protected] face Problems

We propose a novel algorithm for modeling interface mo- MS54 tions. The interface is represented and is tracked using Challenges in Interpretation of Statistical Proper- quasi-uniform meshless particles. These particles are sam- tiesofGrainGrowthModels pled according to an underlying grid such that each particle is associated to a grid point which is in the neighborhood of Polycrystalline materials are composed of small grains the interface. The underlying grid provides an Eulerian ref- interconnected through a network of grain boundaries. erence and local sampling rate for particles on the interface. Macroscopic properties of such materials including their It also renders neighborhood information among the mesh- response to mechanical and thermal loading are aﬀected less particles for local reconstruction of the interface. The by the structure of the network of grains. It is expected resulting algorithm, which is based on Lagrangian tracking that predictive macroscopic theories of such materials must using meshless particles with Eulerian reference grid, can include some features of the mesoscopic structure, yet the naturally handle/control topological changes. Moreover, precise details are still unknown. Extensive work has been adaptive sampling of the interface can be achieved easily done on some statistical properties characterizing these through local grid reﬁnement with simple quad/oct-tree networks. These include the well studied grain size distri- data structure. bution function, the grain orientation distribution function (texture), and more recently the grain boundary character Shingyu Leung distribution function. These functions are known to have Hong Kong University of Science and Technology 100 MS10 Abstracts

[email protected] ble) phases of the crystal are identified and this information is used to predict the strain-rate dependent material behavior. Molecular dynamics simulations at various de- MS55 formation rates are performed and the results are compared Phase Field Models of Fluids with Evaporation and and contrasted with the BFB predictions. Condensation Vincent Jusuf, Ryan S. Elliott I will present phase field models of fluids undergoing evapo- University of Minnesota ration and condensation with inhomogeneous temperature, [email protected], [email protected] where latent heat transport is crucial. I will also discuss Marangoni effect arising from the surface tension inhomogeneity in binary fluid mixtures. Evaporation, spreading, MS56 and boiling are examples of simulation. Entropic Stabilization of Austenite in Shape Mem- ory Alloys Akira Onuki Department of Physics Recent calculations have revealed that the observable Kyoto University high temperature austenite structure in shape memory [email protected] alloys (SMAs) is entropically stabilized by nonlinear dynamic effects. The phenomenon of entropic stabilization in SMAs will be explicitly demonstrated with a realistic MS55 three-dimensional all-atom model using Molecular Dynam- Phase Field Modeling and Simulation for Contact- ics (MD). Additionally, some observations about the transi- Line Motion in One-Component Liquid-Gas Sys- tion pathways for the martensite to austenite and austenite tems to martensite transformations are discussed. The dynamic van der Waals theory has recently been pre- Daniel Karls, Ryan S. Elliott sented for the study of hydrodynamics in liquid-gas sys- University of Minnesota tems. We derive the boundary conditions at the fluid-solid [email protected], [email protected] interface by introducing two dissipative processes on the solid surface and requiring the surface entropy production rate to be positive definite. We then carry out numer- MS56 ical simulations to investigate the quantitative effects of Cavitation in Nonlinear Elastic Solids Under 3D the boundary conditions on contact-line motion, with an Loading Conditions with Various Triaxilities emphasis on the fluid slip at solid surface. In this work, we study the problem of a single vacuous Tiezheng Qian cavity of initially spherical shape embedded in a nonlinear Department of Math elastic solid of infinite extent that is subjected to affine Hong Kong University of Science and Technology displacement loading conditions on its boundary, i.e., at [email protected] infinity. By means of the Finite Element Method (FEM), we generate solutions for a variety of materials (including incompressible Neo-Hookean solids) and loading conditions MS55 (with various triaxilities) and analyze in detail the onset of A New Phase-field Model for Incompressible Two- cavitation corresponding to the event at which the size of phase Flows with Large Density Ratios the cavity grows unbounded. We present a new phase-field model for the incompress- Toshio Nakamura ible two-phase flows with variable density which admits S.U.N.Y. Stony Brook an energy law. We also construct weakly coupled time dis- [email protected] cretization schemes that are energy stable. Efficient numerical implementations of these schemes are also presented. Oscar Lopez-Pamies The model and the corresponding numerical schemes are S.U.N.Y. Stony Brook particularly suited for incompressible flows with large den- Stony Brook, USA sity ratios. Ample numerical experiments are carried out [email protected] to validate the correctness of these schemes and their accuracy. MS56 Jie Shen Shear Localization Instabilities in Porous Metals Department of Mathematics Purdue University Making use of a recently developed homogenization model [email protected] for porous metals with evolving microstructure, we investigate the possible development of shear localization and cavitation instabilities. In particular, we explore the de- MS56 pendence of these different types of instabilities on the ap- Branch-following and Bifurcation Methods for plied loading conditions, as characterized by the triaxiality Crystals: A Study of Stability and Meta-stability (i.e., the ratio of the hydrostatic and deviatoric stresses) in a One-dimensional Crystal Model and the Lode angle (i.e., the third invariant), as well as on the elastic and plastic properties of the material. Branch-following and bifurcation (BFB) techniques are used to explore a one-dimensional crystal model of a phase Kostas Danas transforming material. At bifurcation points group-theory Ecole Polytechnique methods are combined with an asymptotic analysis to de- [email protected] termine all bifurcating branches. Multiple observable (sta- MS10 Abstracts 101

Pedro Ponte Castañeda magnetic field and applied current, we construct some spe- Dept Mech. Engng cial solutions which, up to a constant shift of phase in time, & Appl. Mech are the stationary solutions of the model equation. Our University of Pennsylvania result provides partial justification to the existence of a [email protected] critical applied current.

Qiang Du MS57 Penn State University Transition Layers from the Normal to the Super- Department of Mathematics conducting State in the Preence of Electric Cur- [email protected] rents Juncheng Wei Abstract not available at time of publication. Department of Mathematics Chinese University of Hong Kong Yaniv Almog [email protected] Lousiana State University Department of Mathematics [email protected] Chunyi Zhao Chinese University of Hong Kong chunyi [email protected] MS57 Meissner States of 3-Dimensional Superconductors MS58 and a Quasilinear System Involving Curl Nonequilibrium Molecular Dynamics of Complex Meissner state of bulk superconductors of type II loses its Structures using Objective Structures stability as the applied magnetic field increases to a critical field H S. The Meissner states are described by the solu- The method of Objective Structures generalizes the notion tions of a partial differential system in 3-dimensional space, of crystallinity to important non-crystalline nanostructures which are called Meissner solutions. In this talk we shall such as carbon nanotubes. This allows the calculation of show the existence of the Meissner solutions, and exam- properties of these nanostructures through efficient tech- ine the convergence of the Meissner solutions to a solution niques developed for crystals. We apply the method to of the limiting system as the Ginzburg-Landau parameter the non-equilibrium deformation and failure of carbon nan- increases to infinity. Our results suggest that in order to otubes at an imposed strain rate, using the Tersoff potential for carbon. Simulations with different strain rates determine the critical field H S one needs to measure the 4/s − 8/s maximum value of the tangential component of the induced (10 10 ), temperatures and unit cells show that magnetic field on the surface of the superconductor. Stone-Wales defects play no role in the failure (though par- tials are sometimes seen just prior to failure), a variety of Xingbin Pan failure mechanisms is observed, and most simulations give East China Normal University a strain at failure of 15–20%, except those done with initial [email protected] temperature above about 1200 K and at the lower strain rates. The latter have a strain at failure of 1–2%.

MS57 Kaushik Dayal Ginzburg-Landau Vortex Dynamics Driven by an Civil and Environmental Engineering Applied Boundary Current Carnegie Mellon University [email protected] This talk concerns recent results on the time-dependent Ginzburg-Landau equations on a smooth, bounded 2-D do- Richard James main, subject to both an applied magnetic field and an Department of Aerospace Engineering and Mechanics applied electrical current on the boundary. The energy of University of Minnesota such solutions does not dissipate, but it is possible to esti- [email protected] mate the growth of the energy in time. This estimate then allows for the derivation of the dynamics of the vortices in the limit as the Ginzburg-Landau parameter vanishes. MS58 In an appropriate time scale, we show that the vortex mo- A Quasicontinuum for Multilattice Crystals Ex- tion is driven by a novel Lorentz drift term induced by the hibiting Martensitic Phase Transformations: Cas- presence of the applied boundary current. cading Cauchy-Born Kinematics Ian Tice The quasicontinuum (QC) method is a multiscale method Division of Applied Mathematics coupling atomistic regions with a surrounding continuum Brown University modeled within a nonlinear finite element formulation. Ap- [email protected] plication of QC to multilattice crystals is straightforward in principle, however a question arises as to which description of the crystal structure should be used with Cauchy-Born MS57 kinematics. Here a methodology referred to as Cascading Quantized Vortices in Ginzburg-Landau Models Cauchy-Born kinematics is developed to detect deforma- with an Applied Current tions that require an increase in the periodic size of the 1 unit cell. Applications to one- and 2 2 -dimensional test We study the single-vortex solutions of a two-dimensional problems that highlight the salient features will be pre- high-κ high-field Ginzburg-Landau model of superconduc- sented. tivity with a constant applied current. Under a nondegen- eracy condition and for appropriate ranges of the applied Ryan S. Elliott 102 MS10 Abstracts

University of Minnesota MS58 [email protected] Waves in Lattice Models for Moving Interfaces and Macroscopic Implications Ellad B Tadmor U. of M. We study the motion of interfaces on the atomic (lattice) [email protected] scale and seek to obtain related macroscopic information, for example kinetic relations. As the microscopic model, we consider a one-dimensional chain of atoms with near- MS58 est neighbour interaction, with the dynamics governed by A Relation Between Compatibility and Hysteresis Newton’s law. To describe phase transitions, the elastic and its Role in the Search for New Active Materials potential is chosen to be nonconvex in the discrete elastic strain. Travelling waves are particularly simple instances We present some recent measurements of hysteresis, in ma- of moving interfaces. The topic of the talk is the existence terials undergoing big first order phase transformations, and non-existence of travelling waves for ’heteroclinic’ so- that resulted from a systematic program of tuning of the lutions, that is, solutions which explore both wells of the lattice parameters by changing composition. The lattice energy and thus have an interface moving with the speed parameters were tuned so that a certain non generic con- of the wave. We will discuss the existence of waves and dition of compatibility between phases was satisfied. An sketch a mathematical setting for the proof. exceptionally sharp drop of size of the hysteresis of the transformation was observed at the special lattice parame- Johannes Zimmer ters. The data has some fascinating features, including an Bath apparent singularity. We re-examine the origins of hystere- [email protected] sis in light of these measurements, commenting also on the role of defects and pinning, and the use of this kind of tun- Hartmut Schwetlick ing to discover ”unlikely” new materials. These thoughts University of Bath lead us to consider hysteresis as arising from an elastic en- Department of Mathematical Sciences ergy barrier associated with the failure of certain conditions hartmut schwetlick ¡[email protected]¿ of compatibility. We calculate this barrier based on methods of Gamma-convergence, where the small parameter is related to the near satisfaction of this non-generic condi- MS59 tion of compatibility. A recent study suggest suggests a Friction in F-actin Knots tantalizing relation between the emerging alloys with minimum hysteresis and stability of the transformation under We use existing data of force-extension experiments on F- cycling. Joint work with Stefan Mueller, Nick Schryvers actin molecules tied into knots to compute a value of 0.15 and Jerry Zhang. for the static friction coefficient for contact between different parts of the same molecule with itself. This estimate Richard James for protein-protein friction is relevant for the stabilization Department of Aerospace Engineering and Mechanics of the 273 known proteins with knots, one percent of the University of Minnesota structures deposited in the Protein Data Bank. [email protected] Sebastien Neukirch Stefan Mueller Institut Jean Le Rond d’Alembert University of Bonn CNRS. France. [email protected] [email protected]

Dominique Schryvers Nicolas Clauvelin University of Antwerp Rutgers University, New Jersey. [email protected] [email protected]

MS58 MS59 Moving Interfaces in Rod-like Molecules as Agents Mechanics of Myosin VI Molecular Motor and its of Conformational Change Reverse Directionality

We model coiled-coil molecules in viscous fluids as one- Myosin VI moves toward the (-) end of actin filaments, de- dimensional continua with a multi-well free energy. These spite sharing extensive sequence and structural homology molecules suffer a conformational change in response to with (+) end directed myosins. We designed a range of large forces. We assume that the conformational change myosin VI constructs with artificial lever arms to identify proceeds via a folded/unfolded interface that represents a key structural elements dictating its reverse directional- jump in strain and is governed by the Abeyaratne-Knowles ity. Using molecular dynamics simulation, we examined theory. The model agrees with experimental data on the the mechanics in the converter domain of myosin VI. The melting transition in DNA and is able to predict the speed results demonstrate that an alpha helix of 18 amino acids at which the interface moves. are enough to change the directionality. Ritwik Raj,PrashantK.Purohit Jung-Chi Liao Mechanical Engineering and Applied Mechanics Mechanical Engineering University of Pennsylvania Columbia University, New York. [email protected], [email protected] [email protected] MS10 Abstracts 103

MS59 ulus goes through a maximum and creep rate goes through Heterorgeneous Fluctuating Rod Models for Un- a minimum at intermediate water activity that depends on folded Proteins and Application to Fibrin Networks temperature. Below 50C Nafion is plasticized by water, its modulus decreases and creep strain increase with in- We present a theory to efficiently calculate the thermo- creasing water activity. Above 80C water stiffens Nafion, mechanical properties of fluctuating heterogeneous rods its modulus increases and creep strain decreases with in- and chains and their networks. The central problem is to creasing water activity. The mechanical properties show evaluate the partition function and free energy of a general the existence of structural transitions in Nafion. In this heterogeneous chain/network under the assumption that talk we shall examine the recent experimental results for its energy can be expressed as a quadratic function in the the mechanical and transport properties of Nafion, relate kinematic variables that characterize the configurations of them to structure and structural transitions and discuss the chain. The results from the model are verified through the implications for PEM fuel cell operation. Monte Carlo simulations. Jay Benziger Prashant K. Purohit Chemical Engineering Mechanical Engineering and Applied Mechanics Princeton University of Pennsylvania [email protected] [email protected]

Tianxiang Su MS60 University of Pennsylvania Fan the Flame with Water: Operation of PEM Fuel [email protected] Cells with Dry Feeds Water management is a major technological problem with MS59 Polymer Electrolyte Membrane (PEM) Fuel Cells. Bad Mechanics of the Power Stroke in Myosin II performance is seen with membranes operating at low relative humidity or with liquid water flooding the fuel cell. Power stroke in skeletal muscles is a result of a confor- Employing model fuel cell reactors that elucidate the basic mational change in the globular portion of the molecular physics of Polymer Electrolyte Membrane (PEM) fuel cell motor Myosin II. We show that the fast tension recovery reactors we have been able to demonstrate that the water data reflecting the inner working of the power stroke mech- produced at the cathode can auto-humidify the fuel cell and anism can be quantitatively reproduced by a Langevin dy- operate with dry feeds to 130C. PEM fuel cells reactors are namics of a simple mechanical system with only two struc- shown to be conceptually identical to exothermic reactions, tural states. The proposed model is a generalization of the e.g. flames! Current ignition in PEM fuel cells is analo- two state model of Huxley and Simmons. The main idea gous to thermal ignition in flames. Current density fronts which dates back to Eisenberg and Hill is to replace the propagate in fuel cells resulting from a balance between rigid bi-stable device of Huxley and Simmons with an elas- convection and diffusion, this is analogous to flame fronts tic bi-stable snap-spring. In this new setting the attached that propagate resulting from a balance between convec- configuration of a cross-bridge is represented not only by tion and heat conduction. Our model fuel cells have been the discrete energy minima but also by a continuum of in- employed to elucidate the mechanism of liquid water mo- termediate states where the fluctuation induced dynamics tion through the PEM fuel cell. These experiments have of the system takes place. Joint work with L. Marcucci illustrated the importance of gravity of PEM fuel cell operation. We have also exploited gravity to facilitate liquid Lev Truskinovsky water removal in the channel-less self-draining PEM fuel Laboratoire de Mechanique des Solides cell, which operates with operates with current densities > Ecole Polytechnique 1 A/cm2 with dry feeds and T >120C and high current [email protected] densities. This design has facilitated control and fuel utilization; we have been able to directly control power output to fixed load impedance with 100% fuel utilization with a MS60 system that requires no temperature control. In this talk Mechanical and Transport Properties of Polymer we shall review the use of reaction engineering principles Electrolytes for PEM Fuel Cells to arrive at improved PEM fuel cell design.

Water and temperature alter the mechanical and trans- Jay Benziger port properties of the Nafion, and in turn the operation of Chemical Engineering Polymer Electrolyte Membrane (PEM) fuel cells. Sorption Princeton and permeation involve interfacial mass transport, diffu- [email protected] sion and polymer swelling. Water is transported through the hydrophilic phase of Nafion. The volume fraction of the hydrophilic phase increases with water activity, which in- MS60 creases permeation. At high water activity, interfacial mass Electrodes for Energy Applications Including Ef- transport at the membrane/vapor interface is the limiting fects of Diffuse Space Charge: Microscopic vs. resistance to permeation. Water absorption into Nafion is Phenomenological Modeling initially limited by interfacial mass transport; above critical water content water sorption is limited by polymer relax- To describe charge transfer at porous and planar electrodes ation dynamics associated with swelling. The dynamics of in energy systems, the structure of the nanoscopic space water absorption show that at room temperature it takes charge region which forms at the electrode/electrolyte in- more than 105 s for Nafion to equilibrate to changes in wa- terface is generally not considered, even though details of ter activity. The mechanical properties of Nafion (elastic this layer are of utmost importance for correct and self- modulus and creep rate) show complex behavior as func- consistent microscopic modeling of electrochemical pro- tions of water activity and temperature. The elastic mod- cesses. We show how these effects can be included in an 104 MS10 Abstracts

insightful, comprehensive and transparent framework and [email protected] present numerical examples both for planar and porous electrodes. Peter Smereka University of Michigan P. Maarten Biesheuvel [email protected] Department of Environmental Technology Wageningen University, The Netherlands [email protected] Jason Devita Arete Associates [email protected] Martin Z. Bazant Department of Mathematics Massachusetts Institute of Technology MS61 [email protected] Accurate Acceleration of the Kinetic Monte Carlo Method MS60 While kinetic Monte Carlo (KMC) is a powerful materials Ion Conduction in Polymer Electrolytes modeling tool, it is computationally expensive when rare- events are present. We present a novel method called the Polymer electrolyte membranes play a central role in en- accelerated superbasin KMC (AS-KMC) method, that energy conversion. By spontaneously forming pore networks ables a more efficient study of rare-event dynamics than then preferentially conduct ions of prescribed charge. For KMC, while maintaining control over the error. In AS- applications to PEM fuel cells, dye-sensitized solar cells, KMC, the rate constants of frequent processes are lowered. and lithium ion batteries, it is desirable to have membranes We show that AS-KMC can provide large CPU savings with high conductivity, as well as robust structural char- over KMC without significant loss in accuracy. acteristics. One method to achieve this is by dissolving a functionalized and a crystallizable polymer in solvent, and Abhijit Chatterjee evaporating off the solvent. We present a class of mod- Department of Chemical Engineering els for the phase separation which occurs within the cast- Indian Institute of Technology, Kanpur ing process of these blended membranes, as well as for the [email protected] pore network created when the membranes are exposed to water. Arthur Voter Keith Promislow Theoretical Division, T-1 Michigan State University Los Alamos National Laboratory [email protected] [email protected]

Andrew J. Christlieb MS61 Michigan State Univerity Numerical Methods for Stochastic Bio-chemical Department of Mathematics Reacting Networks with Multiple Time Scales [email protected] Multiscale and stochastic approaches play a crucial role in faithfully capturing the dynamical features and making MS61 insightful predictions of cellular reacting systems involv- The Theory of Stranski Krastanov Transition: ing gene expression. Despite their accuracy, the standard What We Truly Understand stochastic simulation algorithms are necessarily inefficient for most of the realistic problems with a multiscale nature The self assembly of quantum dots in the Hetero-epitaxial characterized by multiple time scales induced by widely growth occurs though the Stranski Krastanov transition. disparate reactions rates. In this talk, I will discuss some This refers to the process where the flat surface of a recent progress on using asymptotic techniques for proba- strained thin film of a certain thickness (critical thickness) bility theory to simplify the complex networks and help to becomes unstable. This unstable film forms islands (quan- design efficient numerical schemes. tum dots) that sit on top of a strained film known as the wetting layer. This transition is understood theoretically Di Liu as a strain driven instability known as the Grinfeld insta- Department of Mathematics bility. The Grinfeld instability however fails to predict a Michigan State University non-zero critical thickness or a wetting layer. Thus the re- [email protected] lation between the Critical thickness and Wetting layer is also not understood. In this talk using a Kinetic Monte Carlo approach the Stranski Krastanov Transition in the MS61 epitaxial growth of strained alloy films is explored. It will Connections Between Kinetic Monte Carlo and be shown that the intermixing of the film and substrate Continuum Models material is entropy driven at the cost of increasing the energy of the system. The importance of entropy and inter- In this talk the connections between traditional continuum mixing and its role in stabilizing the initial layers will be models and kinetic Monte Carlo, as applied to heteroepi- discussed. The Stranski Krastanov transition and the exis- taxy will be explored. The advantage and disadvantages tence of a wetting layer, is then understood in the context of both approaches will be outlined. One crucial aspect of of the competition between entropy and energy. kinetic Monte Carlo is that it naturally captures the discrete and stochastic nature of heteroepitaxial growth at the Arvind Baskaran atomistic scale. Some examples will be shown where this Institute for Pure and Applied Mathematics, UCLA University of California, Irvine MS10 Abstracts 105

has consequences on bigger scales. for atomistic simulations. The new relations are illustrated by several examples of calculation of interface thermody- Peter Smereka namic properties in solid-liquid coexistence systems us- Department of Mathematics ing Monte Carlo and molecular dynamics methods with University of Michigan embedded-atom potentials. [email protected] Timofey Frolov Tim Schulze George Mason University University of Tennessee [email protected] Department of Mathematics [email protected] Yuri Mishin George Mason University Arvind Baskaran Physics Institute for Pure and Applied Mathematics, UCLA [email protected] University of California, Irvine [email protected] MS62 Thermodynamics and Atomistic Modeling of Solid- MS62 solid Interfaces: An Overview Generalized Thermodynamics of Solid Surfaces with Application to Nucleation We discuss interfacial thermodynamics of coherent and in- coherent solid-solid interfaces, deriving an adsorption equa- When considering the thermodynamics of solid-fluid sur- tion with additional terms representing the effect of applied faces, Gibbs restricted attention to single-component mechanical stresses on excess quantities. This equation solids. Attempts to generalize Gibbs approach for mul- predicts a number of stress-strain, stress-segregation and ticomponent solids are problematic because the chemical other cross effects that do not exist in fluids. New thermo- potentials for substitutional components are not well de- dynamic integration schemes are proposed, which are use- fined at the surface. It is proposed that this difficulty can ful in atomistic simulations of interfaces. We demonstrate be overcome by using the concept of thermodynamic avail- applications to atomistic simulations of grain boundaries ability (exergy). It will be discussed how this method can and other interfaces subject to applied stresses. be used in the thermodynamics of nucleation and other applications. Yuri Mishin George Mason University Robert C. Cammarata Physics Johns Hopins University [email protected] Materials Science and Engineering [email protected] Tim Frolov George Mason University [email protected] MS62 Cleaving Method for Determining Solid-liquid In- terfacial Free Energy in Molecular Systems: Re- MS63 sults for Simple Models of Water Bifurcations, Instabilities and Localizations of De- formations in Gradient Damage Models with Soft- The cleaving method for computing solid-liquid interfa- ening cial free energy has been very successful in atomic systems (hard and soft spheres, Lennard-Jones). The challenge for This work is devoted to the mathematical study of soften- molecular systems is to take into account the rotational ing damage models which are regularized by gradient dam- degrees of freedom of a molecule. I will present an ex- age terms. We first give the variational formulation of the tension of the cleaving method to molecular systems and damage evolution problem. Then we analyze the stability results for several simple models of water, TIP4P, TIP4P- of homogeneous responses and we propose a construction Ew, TIP5P-Ew, also elucidating the effect of including full of localized solutions when the homogeneous states are no electrostatic interactions. more stable.

Ruslan L. Davidchack, Richard Handel, Jamshed Anwar, Jean-Jacques Marigo Andrey Brukhno Ecole Polytechnique University of Leicester Palaiseau, France [email protected], [email protected], [email protected], [email protected] [email protected] Kim Pham, Corrado Maurini Institut Jean le Rond d’Alembert MS62 [email protected], [email protected] Interface Thermodynamics for Strongly Non- hydrostatic Solids MS63 We derive thermodynamic relations for the free energy, A Variational Model for Cavitation and Fracture interfaces stress tensor, segregation and other excess in Nonlinear Elasticity properties of interfaces between ﬂuids and strongly non- hydrostatically stressed solid phases in multi-component We propose a variational model for cavitation and fracture systems. These relations lead to various thermodynamic in the context of nonlinear elasticity. The energy to mini- integration schemes and are presented in forms convenient mize is the sum of the elastic energy plus a surface energy 106 MS10 Abstracts

accounting for the creation of surface. We prove the ex- two immiscible ﬂuids are maintained in a rigid state, by a istence of minimizers that are one-to-one and orientation- jammed layer of colloidal particles at their interface. We preserving. We explain the connections with the theory of derive a model for such a system which combines a Cahn- Cartesian currents and with the regularity of inverses of Hilliard-Navier-Stokes model for the macroscopic two- weakly diﬀerentiable functions. This is a joint work with phase system with a surface Phase-Field-Crystal model for Duvan Henao. the microscopic colloidal system along the interface. First numerical results will be presented. Carlos Mora-Corral Basque Center for Applied Mathematics Axel Voigt, Sebastian Aland Bilbao, Spain TU Dresden [email protected] [email protected], [email protected]

MS63 MS64 Structured Flow and Fracture of Solids: A General Compositional Patterning on Surfaces via the Regularized Variational Model Phase-Field Crystal Approach

The regularized formulation àlaAmbrosio-Tortorelli of the In this work, we study compositional domain formation variational approach to fracture mechanics by Francfort- in binary alloys when deposited on a substrate, using the Marigo (1998) is here generalized through Structured- phase-field crystal (PFC) method. These alloys normally Deformation theory, to consider that the inelastic (struc- do not mix in the bulk, whereas they do mix when de- tured) deformations associated with flow and fracture may posited on a substrate due to the reduction of elastic en- be different according to the characteristic loosening of ergy. We derive a set of amplitude equations, starting from the underlying material microstructure. Changing the a PFC based energy functional that models the presence class of functions for admissible structured deformations, of compositional variables. Using this approach, we model we show also through numerical experiments that differ- the formation of misfit dislocations to study the case of ent responses, such as cleavage-, shear- and masonry-like- compositional domain formation for asymmetric mixtures. fractures, can be obtained. Gianni Royer-Carfagni Mikko Haataja University of Parma MAE Department Department of Civil Environmental Engineering Princeton University [email protected] [email protected]

Francesco Freddi University of Parma, Italy MS64 [email protected] Phase Field Crystal Modeling with an Improved Correlation Function

MS63 We present an alternative fitting method for describing the On the Global Stability of Two-dimensional, In- direct correlation function used in the free energy func- compressible, Elastic Bars in Uniaxial Extension tional of the Phase Field Crystal model. This method can easily be expanded to capture details beyond the first A bar, when stretched, often deforms uniformly until a peak of the correlation function without increasing the stiff- neck or shear bands develop. This experiment is sometimes ness of the equations. The applicability of this new fit- modeled as the in-plane deformation of a two-dimensional, ting method is demonstrated by simulating the liquid-solid elastic material. We show that, for many commonly used transition of copper and iron. constitutive relations, the uniformly deformed state always minimizes the energy. Such stored-energy functions can- Nirand Pisutha-Arnond not therefore predict these phenomena. Thus, either these Department of Materials Science and Engineering stored energies are inappropriate, this phenomena is three University of Michigan dimensional, or else necks and shear bands are beyond the [email protected] scope of nonlinear elasticity. Victor Chan Scott Spector Department of Materials Science and Engineering Southern Illinois University University of Michigan [email protected] [email protected]

J. Sivaloganathan Mrinal Iyer, Vikram Gavini University of Bath Mechanical Engineering, University of Michigan [email protected] [email protected], [email protected]

Katsuyo Thornton MS64 Department of Materials Science and Engineering Stabilizing Fluid-ﬂuid Interfaces by Nanoparti- University of Michigan cles - A Navier-Stokes-Cahn-Hilliard-Phase-Field- [email protected] Crystal Approach

Bicontinuous interfacially jammed emulsion gels (’bijels’) MS64 were proposed in 2005 as a hypothetical new class of soft Phase Field Crystal Models for Cubic Crystals and materials in which interpenetrating, continuous domains of MS10 Abstracts 107

Grain Growth

We study grain growth at the nanoscale using the phase Alexander V. Kildishev field crystal model. Our results show that grains can both Birck Nanotechnology Center School of ECE translate and rotate during grain growth. Consistent with Purdue University recent theory, we find that low angle grain boundaries [email protected] have a misorientation-dependent mobility. For intermediate misorientations, we observe a pronounced tangential Ludmila Prokopeva motion of grain boundary dislocations that changes the Institute of Computational Technologies, Novosibirsk, morphology of the grains. We will also discuss phase field Russia crystal models for cubic crystals. [email protected] Peter Voorhees Northwestern University Evgenii Narimanov Dept. of Material Science and Engineering School of ECE, Purdue University [email protected] [email protected]

Kuo-An Wu MS65 Dept. of Materials Science and Engineering Non-Euclidean Cloaking and Perfect Imaging Northwestern University [email protected] Optical materials act on light as if they change the geometry of space. In this lecture I show how implementations of certain curved geometries are useful for making broad- MS65 band invisibility devices and for perfect imaging without Cloaking Bending Waves in Structured Thin Plates negative refraction. We introduce a cylindrical cloak to control the bending Ulf Leonhardt waves propagating in thin-plates. This is achieved through University of St Andrews radially dependent isotropic mass density and radially de- [email protected] pendent and orthotropic flexural rigidity deduced from a coordinate transformation for the biharmonic propagation equation. A homogenization approach allows to obtain MS65 such parameters. We note that the studied bending waves Mathematical Analysis of the Active Exterior are of different physical and mathematical nature than Cloak their electromagnetic and acoustic counterparts. The mathematical ideas behind the active exterior cloak Sebastien Guenneau will be presented. We will discuss in detail the quasistatic Institut Fresnel, UMR CNRS 6133 case and briefly highlight the ideas behind the fixed fre- [email protected] quency active exterior cloaking for Helmholtz equation. To support our analysis numerical result will be presented. Mohamed Farhat Institut Fresnel Daniel Onofrei Marseille Department of Mathematics [email protected] University of Utah [email protected] Stefan Enoch CNRS Graeme Milton, Fernando Guevara Vasquez Institut Fresnel University of Utah [email protected] [email protected], [email protected]

Alexander Movchan MS66 Department of Mathematical Sciences University of Liverpool, UK Gaussian Approximation Potentials: Quantum Me- [email protected] chanical Accuracy Without the Electrons In this talk, we address the problem of approximating the MS65 Born- Oppenheimer potential energy surface (PES), without recourse to representing the electronic problem explic- An Analysis and Performance Evaluation of the itly.This is essentially an interpolation problem, with the Optical Black Hole added requirements of maintaining the exact physical sym- The almost ideal absorption of the optical black hole metries of the PES. We introduce a transformation of the (OBH) makes this conceptual device the very promising atomic coordinates to describe the neighbourhood of atoms choice for designing broadband and omnidirectional light and use a Gaussian Process, which is a non-linear regres- absorbers for solar energy harvesting and infrared sensing. sion method, to solve the interpolation task. The accuracy Our study investigates the design of a realistic OBH utiliz- of the interpolated PES (which we call a Gaussian Ap- ing both the exact frequency domain solutions for TM and proximation Potential, GAP) is remarkable for the bulk TE waves, and time-domain results obtained from a ﬁnite- phases of a wide variety of systems, including semicon- volume time-domain numerical solver. The dynamic be- ductors, metals and polarizable crystals. The speedup ob- havior of the light pulse propagation in OBH is presented. tained for a force evaluation using the approximate PES in comparison with plane wave density functional theory can reach a factor of a million for metallic systems. In addition 108 MS10 Abstracts

to being a practical calculation method, this success sheds Mechanical Engineering, University of Michigan new light on the nonlocal nature of the solutions to the [email protected], [email protected] Kohn-Sham equations.

Gabor Csanyi MS66 University of Cambridge Non-periodic Real-space Formulation of Kohn- [email protected] Sham Density Functional Theory

The Kohn-Sham Density Functional Theory (KSDFT) is MS66 widely used for ”ab initio” studies of materials. We de- Orbital Minimization with Localization scribe a real-space formulation and ﬁnite-element implementation of KSDFT, and demonstrate it with selected Orbital minimization is among the most promising lin- examples. We then discuss approaches to coarse-grain KS- ear scaling algorithms for electronic structure calculation. DFT for application in crystalline solids with isolated de- However, to achieve linear scaling, one has to truncate the fects. support of the orbitals and this introduces many problems, the most important of which is the occurrence of numerous Phanish Suryanarayana local minima. In this talk, we introduce a simple modiﬁ- California Institute of Technology cation of the orbital minimization method, by adding a [email protected] localization step into the algorithm. This localization step selects the most localized representation of the subspace Vikram Gavini spanned by the orbitals obtained during the intermediate Mechanical Engineering, University of Michigan stages of the iteration process. We show that the addition [email protected] of the localization step substantially reduces the chances that the iterations get trapped at local minima. Numerical Thomas Blesgen experiments for alkane molecules are also presented. This Max Planck Institute for the Mathematics in the Sciences is a joint work with Weinan E, Carlos J. Garcia-Cervera [email protected] and Jianfeng Lu. Weiguo Gao Malena Espanol Fudan University, China California Institute of Technology [email protected] [email protected]

Kaushik Bhattacharya MS66 Professor of Mechanics and Materials Science Electronic Structure Calculations at Macroscopic California Institute of Technology Scales Using Orbital-free DFT [email protected]

Recently proposed Quasi-Continuum Orbital Free Density Michael Ortiz Functional Theory (QC-OFDFT) is a seamless multi-scale California Institute of Technology scheme that has enabled the computation of electronic [email protected] structure at macroscopic scales, and has paved the way for an accurate electronic structure study of defects in materials [V. Gavini, K. Bhattacharya, and M. Ortiz., 2007, MS67 Quasi-Continuum orbital-free density-functional theory: A A Discrete Model for Reversible Unzipping route to multi-million atom non-periodic DFT calculation, J. Mech. Phys. Solids 55, 669]. It combines a real-space The extraordinary material properties of several biological formulation of OFDFT with a finite-element discretization and bio-inspired materials derive from a judicious design, that is amenable to coarse-graining. The initial develop- at the microscale, of chain networks constituted by elastic ment of QC-OFDFT, for the purpose of demonstration, and breakable links. The energetic competition of these used Thomas-Fermi-Weizsacker family of kinetic energy two components regulates the resulting macroscopic con- functionals. However, more accurate kinetic energy func- stitutive properties. We present two new type of discrete tionals have been proposed in the form of kernel energies models, both characterized by elastic and breakable links, that are non-local in real-space [Y.A. Wang, N. Govind, for the description of reversible unzipping in biological ad- and E.A. Carter., 1999, Orbital-free kinetic-energy density hesion (with application to geckos adhesion) and of damage functionals with a density-dependent kernel, Phys. Rev. in amorphous solids (with application to spider silks and B 60, 16 350]. In the present study, we develop a local nanopolymers). [ De Tommasi, G. Puglisi, G. Saccomandi, variational formulation for these kernel energies through a Localized versus Diffuse Damage in Amorphous Materials, system of coupled Helmholtz equations. We incorporate Phys.Rev.Lett.100 (2008), article] these kernel energies into the quasi-continuum framework and investigate the convergence of the method with respect Guiseppe Puglisi to coarse-graining and cell-size through studies on mono- Dipartimento di Ingegneria Civile e Ambientale vacancy and di-vacancies in aluminum. Our results show Politecnico di Bari remarkable cell-size effects in the energetics of vacancies, [email protected] and suggest much larger computational domains than those considered previously are necessary in electronic structure studies on defects. We further discuss the behavior of va- MS67 cancies, in their dilute limit, from electronic structure cal- Title Not Available at Time of Publication culations. Abstract not available at time of publication. Vikram Gavini, Balachandran Radhakrishnan Phoebus Rosakis MS10 Abstracts 109

University of Crete (Greece) set technique how such strain dependence of microscopic [email protected] parameters affects the ordering during growth. In particular, we will discuss the effect of strain on the scaled island size distribution in the submonolayer growth regime. MS67 Shocks Versus Kinks in a Discrete Model of Dis- Christian Ratsch placive Phase Transitions UCLA Department of Mathematics We consider dynamics of phase boundaries in a bistable [email protected] one-dimensional lattice with harmonic long-range interactions. Using Fourier transform and Wiener-Hopf technique, we construct traveling wave solutions that represent MS68 both subsonic phase boundaries (kinks) and intersonic ones Simulation of Heteroepitaxy in 3 Dimensions Using (shocks). We derive the kinetic relation for kinks that pro- Kinetic Monte Carlo vides a needed closure for the continuum theory. We show that the different structure of the roots of the dispersion In this talk, the efficient simulation of strained heteroepi- relation in the case of shocks introduces an additional free taxial growth in three dimensions growth using kinetic parameter in these solutions, which thus do not require Monte Carlo is discussed. The presentation will outline a kinetic relation on the macroscopic level. The case of several different methods of varying fidelity and speed, the ferromagnetic second-neighbor interactions is analyzed in fastest of which is based on updating the elastic displace- detail. We show that the model parameters have a signif- ment field on a mesoscopic time scale. Examples of self icant effect on the existence, structure and stability of the assembled stacked quantum dots and growth of quantum traveling waves, as well as their behavior near the sonic dots on patterned substrates will be presented. limit. Peter Smereka Evgeni Trofimov Department of Mathematics Department of Mathematics University of Michigan University of Pittburgh [email protected] [email protected] Tim Schulze Anna Vainchtein University of Tennessee Department of Mathematics Department of Mathematics University of Pittsburgh [email protected] [email protected] MS68 MS67 Phase Field Crystal Simulations of Stress-Driven Effect of Nonlinearity on the Kinetics of Twinning Surface Evolution Dislocations The stress-induced morphological instability of an inter- We consider the steady motion of a twinning dislocation face is examined with the recently developed phase field in a Frenkel-Kontorova lattice with double-well substrate crystal approach. We find that the critical wavenumber potential that has a non-degenerate spinodal region. Semi- of the instability deviates from the prediction of the con- analytical traveling wave solutions are constructed for the tinuum theory when the length scale of the instability is piecewise quadratic potential, and their stability and fur- on the order of the interface width. In addition, we find ther effects of nonlinearity are investigated numerically. that large stresses induce nonlinear elastic effects that alter We show that the width of the spinodal region and the both the wavelength of the instability and the interfacial nonlinearity of the potential have a significant effect on morphology. the dislocation kinetics, resulting in stable steady motion in some low-velocity intervals and lower propagation stress. Peter Voorhees We also conjecture that a stable steady propagation must Northwestern University correspond to an increasing portion of the kinetic relation Dept. of Material Science and Engineering between the applied stress and dislocation velocity. [email protected]

Anna Vainchtein Kuo-An Wu Department of Mathematics Northwestern University University of Pittsburgh Dept. Materials Science and Engineering [email protected] [email protected]

MS68 MS68 Strain Dependence of Microscopic Parameters and Heteroepitaxy - Interplay of Dislocations and Sur- its Effect on Ordering during Epitaxial Growth face Instabilities In this talk, we will present density-functional theory cal- By using the phase-field-crystal (PFC) model, we investi- culations that examine the effect of strain on a number of gate heteroepitaxial growth of thin films on vicinal sub- microscopic growth parameters, such as diffusion, dissocia- strates with step and terrace structure reproduced by a tion of small islands, detachment of adatoms from islands, sharp film-liquid interface and substrate rigidity adjusted and diffusion of adatoms along island edges. We will use using an external pining potential. A phase diagram of growth of Ag on Ag(100) as our model system. We will the stress-induced morphology of the strained film near then illustrate in growth simulations that employ the level- equilibrium is constructed, which identifies diverse growth 110 MS10 Abstracts

regimes, such as equally-spaced step flow, step bunching, Curve/Surface Smoothing and hill-and-valley facet growth with or without dislocation appearing, according to the increasing mismatch strain and A novel weighted phase field model for feature-sensitive the vicinal angle of the substrate. The morphology of the variational curve and surface smoothing is proposed. Var- growing strained thin film follows the equilibrium morpho- ious numerical examples demonstrate the efficiency, effec- logical phase diagram, but indicating less critical mismatch tiveness and robustness of the proposed numerical algo- strain for the dislocation formation. The mismatch strain rithms. Furthermore, adpation based on 3D FEM super- dependence of the dislocation formation indicates the mor- convergence and CVT has been realized for efficient surface phological instability properties of the strained thin film smoothing. grown on the vicinal substrate, such as the step instability and the hill-and-valley growth. Our simulations demon- Desheng Wang strate the potential of the PFC model for understanding Nanyang Technological University, Singapore the thin film growth morphology with steps, islands and Division of Mathematical Sciences dislocations interconnected. [email protected] Axel Voigt TU Dresden MS69 [email protected] Phase Field Modeling of Dissolutive Wetting Accurately modeling a spreading drop on a reactive sub- Yan-Mei Yu strate is enormously complicated. A minimal model re- Chinese Academy of Science quires the inclusion of three phases (and associated phase [email protected] changes), two alloy components (and associated advection- diffusion), and hydrodynamics. We solve several such a MS69 models, obtaining crucial insights into the nature of the spreading process, and are able to compare our results with Phase Field Modeling as a Numerical Tool to Solve recent state-of-the-art experiments. Coupled Bulk/surface Problems James Warren Simulations for almost all applications of interest require to National Institute of Standards and Technology solve partial differential equations in complex geometries. Materials Science and Engineering Laboratory We have introduced a diffuse domain method which can [email protected] handle such problems for general equations with general boundary conditions. In the approach the complex geom- Daniel Wheeler etry Ω1 is embedded into a larger regular domain Ω and represented using a phase-field function, which is a smooth National Institute of Standards and Technology approximation of the characteristic function of the domain [email protected] Ω1 such that the sharp boundary of the domain Γ1 = ∂Ω1 is replaced by a narrow diffuse interface layer. The equation MS69 to solve is reformulated on the larger, regular domain Ω with additional source terms that approximate the bound- Phase Field Modeling of Nucleation in Solid State ary conditions. The resulting partial differential equation Phase Transformations in Ω converges to the original partial differential equation We investigate the critical nucleus and equilibrium mor- with the original boundary conditions if the width of the phologies during precipitation of a second-phase particle diffuse interface layer turns to zero. The diffuse domain ap- in a solid. We show that a combination of diffuse-interface proach does not require any modification of standard finite description and a constrained string method is able to pre- element or finite difference software and thus offers a simple dict both the critical nucleus and equilibrium precipitate way to implement general problems which have to be solved morphologies simultaneously without aprioriassumptions. on complex geometries. We demonstrate the applicability Using the cubic to cubic transformation as an example, it of the approach by solving two-phase flow problems in com- is demonstrated that the maximum composition within a plex geometries, e.g. sliding droplets over nanostructured critical nucleus can be either higher or lower than that of surface and chaotic mixing in droplets flowing through a equilibrium precipitate while the morphology of an equi- winding channel. librium precipitate may exhibit lower symmetry than the Axel Voigt critical nucleus resulted from elastic interactions. TU Dresden Lei Zhang [email protected] Department of Math University of California, Irvine, John Lowengrub [email protected] Department of Mathematics University of California at Irvine Long-qing Chen [email protected] Department of Materials Science and Engineering Pennsylvania State University Sebastian Aland [email protected] TU Dresden [email protected] Qiang Du Penn State University MS69 Department of Mathematics [email protected] Phase Field Method for Feature-Sensitive MS10 Abstracts 111

MS70 spectively. Macroscopic Instabilities in Fiber-reinforced Elas- tomers at Finite Strain Martin Idiart Universidad Nacional de La Plata We investigate “macroscopic” (i.e., long wavelength) in- [email protected] stabilities in fiber-reinforced elastomers at finite strain. We make use of recently developed homogenization esti- Oscar Lopez-Pamies mates, together with a result of Geymonat, Muller and S.U.N.Y. Stony Brook Triantafyllidis linking the development of these instabili- Stony Brook, USA ties to the loss of strong ellipticity of the homogenized es- [email protected] timates. For composites with very stiff fibers and random microstructures, we derive a closed-form formula for the critical macroscopic deformation, and compare the result MS70 with classical (2-D) estimates for laminates. Microscopic and Macroscopic Onset-of-Failure Curves in Finitely Strained, Porous Elastomers Mihalis Agoras Under Plane Strain Loading University of Pennsylvania [email protected] The present work investigates the connections between microstructural instabilities and their macroscopic man- Oscar Lopez-Pamies ifestations defined as the loss of rank-one convexity of S.U.N.Y. Stony Brook the effective properties in finitely strained porous elas- Stony Brook, USA tomers with a) random iso-disperse and b) periodic mi- [email protected] crostructures. The powerful second order homogenization (SOH) approximation technique, initially developed by P. Pedro Ponte Castañeda Ponte Castaneda for random media, is also used here to University of Pennsylvania study the onset of failure for periodic microstructures and [email protected] the results are compared to more accurate finite element method (FEM) calculations. The influence of microgeometry (random and periodic with square and hexagonally MS70 arranged pores), initial porosity, matrix constitutive law Non-uniqueness in Energy Minimization of Atom- (neo-Hookean and Gent) and macroscopic load orientation istic Problems: A Branch-following and Bifurca- on the microscopic instability (loss of uniqueness of the tion Investigation principal solution for the case of periodic microstructures) and the macroscopic instability (loss of rank-one convexity Static atomistic simulations aim to obtain local energy of the homogenized energy density for all microstructures) minimum (stable equilibrium) configurations of a body is investigated in detail. In addition to the above-described composed of discrete atoms subject to applied boundary stability-based onset of failure mechanisms, limitations to conditions. In general, many such minimum energy con- the elastomers response at finite strains (such as void sur- figurations are expected. This work performs a Branch- face instability, percolation, pore closure and strain lock- Following and Bifurcation (BFB) investigation to map out ing) are also addressed, thus giving a complete picture of a large number of stable equilibrium configurations. From the different possible failure mechanisms present in finitely this picture of the system’s potential behaviors it is possible strained porous elastomers. to draw conclusions about the most likely behavior of the system. J.-C. Michel Mechanics and Acoustics Laboratory, Marseille, FRANCE Tsvetanka Sendova . Institute for Mathematics and Its Applications University of MInnesota Oscar Lopez-Pamies [email protected] S.U.N.Y. Stony Brook Stony Brook, USA Ryan S. Elliott,ElladB.Tadmor [email protected] University of Minnesota [email protected], [email protected] Pedro Ponte Castaneda University of Pennsylvania [email protected] MS70 Failure Surfaces for Fiber-Reinforced Elastomers Nicolas Triantafyllidis Under General 3D Loading Conditions Ecole Polytechnique, Palaiseau, FRANCE [email protected] We present a thorough investigation of local instabilities — including matrix cavitation, fiber debonding, and fiber failure — and global instabilities — defined as the loss of MS71 strict rank-one convexity of the effective properties — in High-order Modeling of the Smectic-A Mesophase: fiber-reinforced nonlinearly elastic solids. The results are Defect Structure, Kinetics, and Dynamics generated by means of an innovative iterated homogenization method, which incorporates direct microstructural in- A modeling and simulation study of material transformation up to the two-point correlation functions and formations from the disordered state to the lamellar- requires the solution to a Hamilton-Jacobi equation with ordered/smectic-A liquid crystalline state is presented. the fiber concentration and the macroscopic deformation Two-dimensional smectic defect structure, kinetics, and gradient playing the role of time and spatial variables, re- dynamicsarepresentedandcomparedwithanexperimen- 112 MS10 Abstracts

tal system sharing phase-transition symmetries. The for- Aaron L. Fogelson mation, structure, and complex interactions of giant split- University of Utah core edge dislocations, composite structures are presented [email protected] and validated by experimental observations of this phenomena. MS72 Nasser M. Abukhdeir The Inertial Manifold and Dimension Reduction University of Delaware for Systems of ODEs [email protected] In our continuing investigation of methods to reduce the Alejandro D. Rey dimensionality of systems of ordinary differential equa- Department of Chemical Engineering tions we are exploring an approach inspired by the center- McGill University manifold technique of dynamical systems. In this talk [email protected] we will discuss the generl ideas, give some examples, and present results. (Joint work with Shouhong Wang, Indiana University.) MS71 Hydrodynamics and Rheology of Active Suspen- Hans G. Kaper sions of Rigid Ellipsoids Georgetown University [email protected] Active soft materials are a challenging class of systems driven out of equilibrium by an internal or an external energy source. Examples are self-propelled particles in bac- MS72 terial colonies, or the membrane and the cytoskeleton of AsymptoticAnalysis for the Generalized Langevin eukaryotic cells, etc. In this talk, I will present a hydrody- Equation namic theory of flowing active ellipsoidal suspensions and discuss the flow and rheological behaviors of these materi- I’llbe presenting various properties of the Generalized als. Langevin equation and its approximation in higer dimensions,such as ergodicproperties, homogenization theorems, Zhenlu Cui short timeasymptotics and hypoelliptic-type estimates. Department of Mathematics and Computer Science Fayetteville State University Michele Ottobre [email protected] Imperial College London [email protected]

MS71 MS72 Anomalous Diffusion of Tracer Particles in Vis- coelastic Fluids Mescoscopic Dynamics of Large ODE Systems Due to compelling experimental observations using pas- The main question addressed in the talk is how to obtain sive microrheology there is theoretical interest in anoma- continuum equations for mesoscale averages from the ODE lous sub-diffusion – stochastic processes whose long-term of classical particle dynamics. Balance equations for con- mean-squared displacement satisfies E[x2(t)] ∼ tν where tinuum mechanical averages (density, linear momentum, ν<1. Such behavior can be observed for the Generalized energy) were derived by Noll, Hardy, Murdoch and oth- Langevin Equation with a Prony series memory kernel for ers. The missing ingredient in these works was closure: the friction. We introduce a single parameter for the struc- the equations were exact but calculation of fluxes required ture of the Prony series which can be tuned to produce any solving the underlying ODE system. We present a new sub-diffusive exponent ν and discuss issues of simulation, closure method based on the use of regularized deconvo- inference and first passage times from an interval. lutions. The applications discussed in the talk include one-dimensional chains of non-linear oscillators, granular Scott McKinley acoustics and discretizations of solid-fluid flows. Some er- Department of Mathematics ror estimates for closure approximations will be presented Duke University as well. [email protected] Alexander Panchenko Washington State University MS71 [email protected] Numerical Study of Chemical Reaction in Blood Flow MS72 Activated platelets play very important role in blood clot- On the Continuum Limit for a Discrete Model of ting since they are at the central stage of the process of An Elastic Body aggregation and coagulation in blood flow. To study the effect of chemical reactions on platelet surface for clotting, Waves, internal energy and fracture energy in the discrete we use embedded boundary technique to numerically sim- and continuum models. Wave localization. Lattice spac- ulate the reaction. Our numerical methods in 2D and some ing and crack resistance: a zero resistance in the limit. results will be presented in detail. Crack-speed-dependent crack resistance and the cell-size- independent energy release ratio. Quasi-static limit. Dis- Lingxing Yao crete and continuous stress distribution in a hyper-singular Utah University mode of fracture. Generalized continuum limits and pre- [email protected] limiting states. Discrete-continuous structures. A sound- MS10 Abstracts 113

less crack. MS73 Theory of Tunneling Transport in Periodic Molec- Leonid Slepyan ular Chains Tel Aviv University, Israel [email protected] There exists now a large body of high quality experimental data for charge transport through single molecules. In particular, the data on insulating molecular chains reveals MS72 the expected tunneling behavior displayed in the exponen- Title Not Available at Time of Publication tial decay of the conductance with the length of the chains, but also intricate and sometime unexpected effects related Abstract not available at time of publication. to the contacts between the electrodes and the chains. In Alexandre Tartakovsky this talk I will discuss an analytic expression of the asymp- Pacific Northwest National Laboratory totic tunneling conductance, which pinpoints, with atom- [email protected] istic precision, the effects of the contacts on the tunneling conductance and gives a fresh insight into the tunneling properties of the molecular chains. The theoretical expo- MS73 sition will be complemented by first-principle calculations Numerical Analysis of a Basic Electronic Density for alkyl and benzene chains connected to gold electrodes Functional via amine linkers and for alkyl chains covalently bonded to (semiconducting) silicon nano-wires. A comparison with We study a mixed finite element discretization of a basic the experiments will also be given. density functional, in which the electrostatic potential is introduced as an additional variable (Gavini et al.). We Emil Prodan will outline the convergence analysis including effects of Yeshiva University, New York numerical integration. The analysis is based on a local [email protected] notion of stability and techniques from nonlinear analysis to deal with the nonconvexity of the problem. We will also MS74 comment on optimal convergence orders. Time permitting we will present a few recent developments regarding the Modeling the Microstructural Effects in Electro- coarse graining of the density functional. chemical Systems Bernhard Langwallner Electrochemical systems often undergo phase transforma- Mathematical Institute tion and morphological evolution. We perform simulations University of Oxford of electrochemical systems, including fuel cell and bat- [email protected] tery electrodes, using a phase-field model and a smoothed boundary method. We demonstrate the linkage between microstructures and their predicted performance, as well MS73 as the means to understand the electrochemical impedance Exact Embedding of Local Defects in Quantum spectra, which is often difficult to interpret due to the mi- Crystals crostructural effect.

In this talk I will present a new model for quantum crystals Hsun-Yi Chen, Hui-Chia Yu, Katsuyo Thornton with local defects. The main idea is to describe at the same Department of Materials Science and Engineering time the electrons bound by the defect and the (nonlinear) University of Michigan behavior of the infinite crystal. This leads to a (rather pe- [email protected], [email protected], [email protected] culiar) bounded-below nonlinear functional whose variable is an operator of infinite-rank. I will provide the correct MS74 Nanoscale Phenomena in Catalyst Layers of PEM functional setting for this functional and discuss the prop- Fuel Cells erties of bound states. I will in particular relate them to the dielectric properties of the crystal. Finally, I will dis- Structures at the nanoscale determine properties and op- cuss discretization issues and show preliminary numerical eration of cathode catalyst layers of polymer electrolyte results in 1D. This is a review of joint works with Eric fuel cells. We consider a cylindrical water-filled nanochan- nel, decorated with Pt nanoparticles. The model couples electrostatic effects in the pore, incorporated via Poisson- Cancs and Amlie Deleurence (Ecole des Ponts, Paris). Nernst-Planck theory, with kinetic effects at pore walls in order to rationalize the current conversion efficiency. Im- Mathieu Lewin plications of this coupling for materials selection and for CNRS and University of Cergy structural design of catalyst layers with reduced Pt load- [email protected] ing will be discussed.

Karen Chan MS73 Simon Fraser University A Priori Error Estimates for Nonlinear Eigenvalue [email protected] Problems and Applications in DFT Michael H. Eikerling Abstract not available at time of publication. Department of Chemistry Simon Fraser University Yvon Maday [email protected] Universit´e Pierre et Marie Curie [email protected] 114 MS10 Abstracts

MS74 of a magnetic field. Pore Network Formation in Polymer Electrolyte Membranes Dimitri Molodov Institute of Physical Metallurgy and Metal Physics Energy conversion, and in particular conversion of chemical University of Aachen and photonic energy to useful voltage, requires the selective [email protected] conduction of charged ions through membranes. Polymer electrolytes membranes are a common class of sensitized membranes for selective ion conduction. They are cre- MS75 ated by emerging polymer electrolytes in a solvent in which Level Set Modeling of Grain Growth the polymers spontaneously form nanoscale pore networks which serve as primitive ion channels. We present a novel Substantial progress has been made with the development model for the formation of the nanoscale pore network as of a level set method and code. We are now able to sim- the gradient flow of novel classes of competing interfacial ulate the following phenomena using a single code: grain and bending energies. We compare numerical solutions of boundary motion in a polycrystalline network with grain the model equations to experimental data and derive sharp- boundary energy depending on interface normal as well interface evolution laws for pores. We show that they are as misorientation; interaction between moving boundaries given by a high-order nonlinear curvature-driven flow. This and particles; interaction between moving boundaries and curvature-driven flow gives rise to various configurations of solute fields (i.e. solute drag); dissolution/growth of parti- pore networks, including meandering pore channels, circu- cles with diffusion of solute away from/to the particle. lar channels and straight channels. Seth Wilson Nir Gavish Carnegie Mellon University Mathematics [email protected] Michigan State University [email protected] Anthony Rollett Carnegie Mellon University Keith Promislow Materials Science and Engineering Michigan State University [email protected] [email protected] MS75 MS74 Grain Boundary Migration, Grain Growth and Stack Level Models of Fuel Cells Grain Growth Microstructures: Cause and Effect

A model of steady state operation of Polymer Electrolyte The mechanism of grain boundary migration and grain Membrane Fuel Cell (PEMFC) stacks with straight gas boundary structure are intimately linked. Similarly, channels is presented. The model is based on a decoupling polycrystalline microstructure and the dynamics of grain of transport in the down-channel direction from transport boundary migration are intimately linked. Both of these in the cross-channel plane. Further, cross-channel trans- linkages are extremely complicated in the general case. We port is approximated heuristically using one-dimensional therefore propose a series of limiting assumptions and track processes. The model takes into account all mass, heat and their implications from structure, to boundary migration, charge transport phenomena of interest and is a nonstan- to grain growth to the final grain growth microstructures. dard system of non-smooth boundary value Differential Al- Our approach is based upon dislocation dynamics methods gebraic Equations (DAEs) with strong, nonlocal coupling. to study the migration of low angle grain boundaries and A discretization of the system and a successful iterative use these results as input to grain growth simulations, end- strategy are described. Representative computational re- ing with an analysis of the corresponding steady state grain sults, validation against existing experimental data and a growth microstructure. These studies are performed in numerical convergence study are shown. both two and three dimensions. The final results show the causal link between boundary structure and steady state Brian R. Wetton grain growth microstructure. University of British Columbia Department of Mathematics David Srolovitz [email protected] The Institute for High Performance Computing in Singapore [email protected] MS75 Control of Crystallographic Texture and Grain Mi- MS75 crostructure in Non-ferromagnetic Metals Through Application of a Magnetic Field Recent Progress on Quantifying Intrinsic and Ex- trinsic Grain Boundary Mobility The current research on texture and grain structure evolution during recrystallization and grain growth in non- This talk addresses two main issues related to computa- magnetic metals in high magnetic fields will be reviewed. tional efforts aimed at quantifying interfacial mobilities in The magnetically induced changes can be caused by the polycrystalline materials: i) the largely atomistic efforts generation of an additional magnetic driving force which employ driving forces that are orders of magnitudes higher arises from a difference in magnetic free energy density than those in experiments, and ii), the role of solutes in between differently oriented grains. Furthermore, the mo- determining the mobilities remains unclear, in spite of the bility of grain boundaries can be enhanced in the presence existence of several theoretical frameworks. The first part of this talk will focus on the use of the fluctuation dissipation theorem to extract the mobility of grain boundaries MS10 Abstracts 115

in the zero-driving force limit. Molecular dynamics stud- MS76 ies on fluctuating high angle grain boundaries in Al will Large-scale Finite Element Micromagnetic Simula- be used as a benchmark to compare the results with past tions with Hierarchical Matrices studies, both computational and experimental. The second part of this talk will focus on the application of a Monte- In micromagnetic FEM simulations, solving Poisson’s Carlo approach based on classical interatomic potentials equation is an established approach to calculate the mag- for an Al-Mg alloy to extract the solute-boundary interac- netostatic interaction. The memory requirements can how- tion energies, a key chemical parameter that allows for the ever be large, since the computation involves a densely pop- first time to directly quantify the effect of solute concentra- ulated matrix. By implementing the H-matrix method in tion on grain boundary mobilities in alloy systems. I will our hybrid FEM-BEM code, we have achieved significant conclude by discussing the implications of the generated improvement concerning the memory requirements. In this atomistic datasets on annealing phenomena in crystalline talk, a brief outline of the method will be presented and materials. a few applications on the magnetization dynamics in microstructures will be discussed. Moneesh Upmanyu Northeastern University Riccardo Hertel, Attila Kakay [email protected] Institute of Solid State Research IFF-9 Forschungszentrum Jülich GmbH [email protected], [email protected] MS76 Computational Steering of Parallel Micromagnetic Steffen Börm Calculations Scientific Computing, Institute for Informatics Christian-Albrechts-Universit{ We describe the design of the micromagnetic Nmag simu- ”a}t Kiel, 24118 Kiel lation framework (http://nmag.soton.ac.uk) and its choice [email protected] of extending an existing general purpose programming language (Python) through a library module that provides the micromagnetic simulation capabilities. This approach MS76 allows great flexibility in how the micromagnetic simula- Finite Element Numerical Micromagnetics: Old tion can be steered as the simulation user can combine Problems and New Solutions the use of the Nmag Python module with the use of other (existing) scientific, numerical, data processing and visu- This talk will discuss some of the problems and limitations alization modules. We show how the interactive control in numerical micromagnetic models and review recent ad- of the simulation session at the Python prompt can be vances. We developed and implemented new methods and combined with parallel execution of the computationally algorithms for the calculation of the magnetostatic field in demanding operations. The research leading to these re- a finite element model, which are enabling micromagnetic sults has received funding from the European Community’s simulations of significantly larger systems while reducing Seventh Framework Programme (FP7/2007-2013) under the memory requirements. Simulations of magnetic record- Grant Agreement nr 233552 (DYNAMAG), and from EP- ing systems, which demonstrate the new capabilities, will SRC (EP/E040063/1). be presented. Hans Fangohr, Matteo Franchin, Thomas Fischbacher Werner Scholz University of Southampton Seagate Technology [email protected], [email protected], [email protected] t.fi[email protected]

MS77 MS76 Energy and Structures of Optimal Multimaterial Convergence of a Geometric Integrator for LLG Anisotropic Elastic Composites

In our talk, we consider a finite element scheme for the We consider an elastic composite from three isotropic elas- Landau-Lifshitz-Gilbert equation (LLG) which describes tic materials, assembled with fixed volume fractions and the dynamics of ferromagnetism. In contrast to previ- placed into an arbitrary homogeneous plane stress field. ous works, cf. [S. Bartels, A. Prohl, Convergence of an We are seeking a structure that minimizes the energy of implicit finite element method for the Landau-Lifshitz- this composite, or maximizes its stiffness. We find a lower Gilbert equation, SIAM J. Numer. Anal., vol. 44, no. 4, bound for the energy using Localized Polyconvexity tech- 1405–1419 (electronic), 2006], [F. Alouges, A new finite ele- nique, a modification of the Translation method by ac- ment scheme for Landau-Lifchitz equations, Discrete Con- counting of inequalities on the range of field in the materi- tin. Dyn. Syst. Ser. S, vol.1, no. 2, 187–196, 2008], als in an optimal structure. When one of the three mixed we examine the LLG including the total magnetic field in- materials is void, the lower bound of he energy is found duced by several physical phenomena described in terms of explicitly. Depending of volume fractions and the loading exchange energy, anisotropy, stray-field, and exterior field. type, the bound assumes one of six analytic expressions. Besides a strong non-linearity, a non-convex side-constraint For one of these regimes, it coincides with the Translation represents a challenging task for the numerical integrator. bound; the other bounds are new. The obtained bounds are Nevertheless, we aim at proving unconditional convergence exact in all but one regime. We show that special finite- for the approximation of a weak solution. rank laminates realize the bound in the five regimes. In the regime where the lower bound is nonexact, we suggest Petra Goldenits, Dirk Praetorius a laminate structure that provides an upper bound for the Vienna University of Technology optimal energy, and compute the gap between them. All [email protected], multimaterial optimal structures are found by the same [email protected] regular procedure, that also demonstrates nonuniqueness 116 MS10 Abstracts

of optimal geometries. microscopic buckling (for periodic microgeometries) and macroscopic loss of ellipticity (for all microgeometries) is Andrej V. Cherkaev, Yuan Zhang investigated in detail. In addition, constraints to the prin- Department of Mathematics cipal solution due to fiber/matrix interface decohesion, ma- University of Utah trix cavitation and fiber contact are also addressed, thus [email protected], [email protected] giving a complete picture of the different possible failure mechanisms present in this class of elastomeric composites. MS77 The Energy Density of Martensitic Thin-structures J.-C. Michel via Dimension Reduction Mechanics and Acoustics Laboratory, Marseille, FRANCE . Variational limits defined on the space of one- or two- dimensional Young measures are obtained from three- Oscar Lopez-Pamies dimensional elasticity via dimension reduction. The rate S.U.N.Y. Stony Brook at which the energy becomes infinite when the volume lo- Stony Brook, USA cally vanishes characterizes the domain of the limit energy. [email protected] The obtained limit problems uniquely determine the energy density of the thin-structures. Pedro Ponte Castaneda Roberto Paroni University of Pennsylvania Università degli Studi di Sassari [email protected] [email protected] Nicolas Triantafyllidis Lorenzo Freddi Ecole Polytechnique, Palaiseau, FRANCE Università di Udine [email protected] [email protected] MS79 MS77 Simulation of the Dielectric Response of Compo- Macroscopic Instabilities in Nematic Elastomers sitionally Graded Ferroelectric Films with Wedge Domains We consider elastomers that are reinforced by aligned stiff inclusions and investigate the possible development of Functional materials with non-linear dielectric response are ‘macroscopic’ instabilities in these systems by computing suited for frequency tuning devices. Developing the theory the loss of strong ellipticity (or strict rank-one convexity) of of wedge domains in graded ferroelectrics, we present a the homogenized constitutive relation. We show that these quantitative model of domain evolution and dielectric re- instabilities can lead to ‘soft’ deformation modes that are sponse of compositionally graded ferroelectric multilayers. similar to those observed in nematic liquid crystal elas- We show that the domain structure adapts itself to the tomers, and make comparisons with these systems. applied electric field. The domains are swept away layer- by-layer upon the application of the electric field; resulting Pedro Ponte-Castaneda in a non-linear field dependence of the dielectric constant Department of Mechanical Engineering and Applied and tunability. We demonstrate that by controlling rel- Mechanics ative thicknesses of the layers that make up the graded University of Pennsylvania heterostructure, one could further enhance the dielectric [email protected] response and tunability. Pamir Alpay MS77 Univ. Conn Microscopic and Macroscopic Instabilities in [email protected] Finitely Strained, Fiber-Reiforced Elastomers Un- der Plane Strain Loading MS79 The present work is a detailed study of the connections Phase-Field Model of Phase Transformations and between microstructural instabilities and their macroscopic Microstructure Evolution in Polycrystals manifestations as captured through the effective properties in finitely strained fiberreinforced elastomers, subjected to Most materials in applications are polycrystalline, contain- finite, planestrain deformations normal to the fiber direc- ing grains of different crystallographic orientations sep- tion. The work, which is a complement to a previous and arated by grain boundaries. To predict the kinetics of analogous investigation by the same authors (“Microscopic phase transformations such as precipitation reactions and and Macroscopic Instabilities in Finitely Strained Porous the accompanying microstructure evolution in the presence Elastomers,” by: J. C. Michel, O. Lopez-Pamies, P. Ponte of grain boundaries is significantly more challenging than Castaneda, and N. Triantafyllidis, J. Mech. Phys. Solids, those in a uniform single crystal. Precipitation reactions in 55, 2007, pp. 900-938) on porous elastomers, uses the pow- a polycrystalline material involve the complicated coupling erful secondorder homogenization (S.O.H.) technique, ini- among a number of different processes: solute segregation tially developed for random media, to study the onset of or depletion near grain boundaries, grain boundary migra- failure in periodic fiberreinforced elastomers and to com- tion, precipitate nucleation, growth and coarsening. Fur- pare the results to more accurate finite element method thermore, the elastic moduli for a polycrystal are always (F.E.M.) calculations. The influence of different fiber dis- spatially inhomogeneous: each grain has different elastic tributions (random and periodic), initial fiber volume frac- modulus and the elastic constants in the grain boundary tion, matrix constitutive law and fiber crosssection on the regions are generally different from those inside the grains. In this presentation, a phase-field model will be presented MS10 Abstracts 117

for modeling solute segregation and precipitation of second- mization. phase particles in a polycrystal in the presence of the elastic strain with inhomogeneous modulus. Examples to be Tim Healey discussed include segregation behavior at grain boundaries Cornell University in the presence of coherent precipitates inside grains, the Universidad de Los Andes morphological evolution during isostructural phase separa- [email protected] tion in the presence of grain boundaries, and precipitation of tetragonal particles in polycrystalline cubic materials. Sanjay Dharmavaram Cornell University Long-Qing Chen [email protected] Materials Science and Engineering Penn State University [email protected] MS80 Equilibrium and Non-equilibrium Mechanics of Saswata Bhattacharya Semiflexible Cytoskeletal Networks Penn State University Department of Materials Science and Engineering Elasticity of cytoskeletal networks in cells appears to rely [email protected] on a combination of passive equilibrium properties of filaments and active internal stresses generated by molecular Taewook Heo motors, with changes in crosslink density and motor ac- The Pennsylvania State University tivity each capable of producing hundred-fold differences [email protected] in network elastic moduli. We present theoretical and computational studies examining the effects of anisotropy and polydispersity in filament distributions, and activity MS79 of molecular motors on the nonlinear mechanics of semi- Austenite-Martensite Interfaces in Shape Memory flexible cytoskeletal networks. Alloys William S. Klug A two-scale phase field simulation is developed for Mechanical and Aerospace Engineering austenite-martensite interface to understand the effects of University of California, Los Angeles crystalline symmetry and geometric compatibilities on the [email protected] reversibility of structural phase transformations in shape memory alloys. It is observed that when the middle eigen- Andrew Missel value of martensite transformation strain is equal to 0, an Chemistry and Biochemistry exact austenite-martensite interface is formed with negli- University of California, Los Angeles gible elastic energy. On the other hand, when the middle [email protected] eigenvalue is different from 0, an inexact interface between austenite and martensitic twin is formed, and the corre- Mo Bai sponding elastic energy increases with the increased mag- Mechanical and Aerospace Engineering nitude of the middle eigenvalue, resulting in substantially University of California, Los Angeles higher energy barrier for austenite-martensite transforma- [email protected] tion, and thus higher thermal hysteresis in shape memory alloys. Alex Levine Chemistry and Biochemistry Jiangyu Li University of California, Los Angeles U. Washington [email protected] [email protected]

MS80 MS79 Micromechanical Modeling of Aﬃne-Nonaﬃne De- Title Not Available at Time of Publication formation in Cytoskeleton Mechanics

Abstract not available at time of publication. Semiflexible polymer network, such as cell-cytoskeleton, Quanshui Zheng differ significantly from their flexible counter-part in the Tsinghua deformation energy storage mechanism. As a result, the [email protected] network elasticity is governed by both enthalpic and entropic variations. In addition, the enthalpic effect shows two predominantly distinct regimes of energy storage mech- MS80 anism, affine regime and non-affine regime. Recently some Modeling and Analysis of Two-Phase Lipid Bi-layer computational models, based on finite element analysis of Vesicles theactualnetwork,suchasMikadoModel,wereusedto demonstrate the basic physics involved in the mechanical We present and analyze a new model for two-phase lipid deformation of semiflexible network. These models are bilayer vesicles. We study symmetry-breaking patterns, as computationally expensive and it is very difficult, if not observed in experiment, in the presence of two fluid phases: impossible to develop a macroscopic constitutive relation an ordered phase and a disordered phase. We propose a based on them. In the present paper, we are proposing a rational continuum model that engenders no intrinsic cur- constitutive model (stress-strain relation) for a 2D semi- vature in either phase. We study the problem from the flexible random network. We idealize a semiflexible net- point of view of both global bifurcation and energy mini- work through a unit-cell representation, consisting of four semiflexible main chains and four equivalent springs. The 118 MS10 Abstracts

unit cell representation captures the actual networks dis- ple to rederive the peridynamics equations of motion. It tinct elastic energy storage mechanisms under the exter- also shows peridynamics can utilize any material model of nally applied deformation field. The transition from non- the classical continuum mechanics provided that the Piola- affine (bending dominant) to affine (axial stretching dom- Kirchhoff stress can be obtained directly or by using incre- inant) is captured through the change of the relative po- mental procedures. sitions of joints of the four chain, which also correspond to the crosslinking density. The current model provides Ergodan Madenci, Erkan Oterkus, Atila Barut a model frame to develop efficient continuum constitutive The University of Arizona models of cytoskeleton in the future. The possibility of ap- Aerospace and Mechanical Engineering plying current model to large deformation is explored at [email protected], [email protected], the end. [email protected] H. Jerry Qi Department of Mechanical Engineering MS81 University of Colorado, Boulder. Exact Mappings from Newtonian Particle Mechan- [email protected] ics to Continuum Mechanics

Sitikantha Roy Newtonian particle mechanics of the kind used in molecular Departiment of Mechanical Engineering dynamics (MD) simulations is a well known technique for University of Colorado, Boulder. modeling a wide class of material behaviors in fluids and [email protected] solids. In this presentation we discuss the relationship between these discrete simulations and continuum mechanics where the basic variables are fields (density, mass velocity MS80 or momentum, stress, etc.) and we are able to show that Mechanics of Bacterial Shape Regulation and Di- there exists exact mappings from the discrete system to a vision continuum system that obeys the usual set of equations. This procedure allows us to define the continuum quanti- Bacterial cells utilize a ring-like organelle (the Z-ring) to ties as averages of microscopic observables. We have some accomplish cell division. The Z-ring actively generates a new results for general force-fields for construction of mi- contractile force and influences cell wall growth. We will croscopic stress as well as a construction of nonlocal force discuss a general model of bacterial morphogenesis where density (e.g. peridynamic force density). We will discuss mechanical forces are coupled to the growth dynamics of how this mapping can be implemented as a post-processing the cell wall. The model suggests a physical mechanism step for MD simulations. We also point out that the av- that determines the shape of bacterial cells. The role of eraging process is not unique and so the continuum sys- several bacterial cytoskeletal proteins and the Z-ring are tem is not unique either except in the limit of large length discussed. We will explore molecular mechanisms of force and time scales. This does lead to an interesting theorem generation by the Z-ring and how cells can generate me- about correct averaging procedures for continuum theories, chanical forces without molecular motors. and the discussion of the exact relationship between microscopic models such as MD and continuum models lends new Sean Sun insight into informed construction of the latter. Whitaker Biomedical Engineering Institute John Hopkins University Mark P. Sears [email protected] Sandia National Laboratories [email protected]

MS81 Peridynamics of Heterogeneous Media MS81 A Domain Decomposition Method for Multiscale analysis of peridynamics inside two-phase het- Local/nonlocal Coupling erogeneous media is discussed. A two-scale asymptotic method that captures the ﬂuctuations of the local deforma- We investigate the coupling of local and nonlocal mod- tion ﬁeld is introduced. The asymptotic method provides els through the nonlocal continuum peridynamic theory. a multiscale numerical method with a cost that is far less We extend the nonlocal domain decomposition results in than solving the full microscale peridynamic equation over [Burak Aksoylu and Michael L. Parks, “Towards domain the entire macroscopic domain. decomposition for nonlocal problems’, submitted, 2009] to the case of nonlocal models with variable interaction Bacim Alali ranges, of which local/nonlocal coupling is a special case. Mathematics Department We derive transmission conditions for local/nonlocal cou- University of Utah pling, and show their connection to the classical theory. [email protected] We explore, analytically and numerically, the suitability of these transmission conditions.

MS81 Pablo Seleson Peridynamic Theory Based on Variational Princi- Department of Scientific Computing ple Florida State University [email protected] Classical continuum mechanics presents obstacles for predicting crack initiation and growth in materials. Recently Max Gunzburger introduced non-local peridynamic theory removes these ob- Dept. of Scientific Computing stacles, and it is applicable at different length scales. This Florida State University study presents an approach based on variational princi- [email protected] MS10 Abstracts 119

Michael L. Parks Mathematics Department Sandia National Laboratories University of Tennessee [email protected] [email protected]

Richard B. Lehoucq Axel Voigt Applied Mathematics and Applications TU Dresden Sandia National Laboratories [email protected] [email protected]

MS82 MS82 Spiral and Mound Growth - A Phase Field Study Uses and Shortcomings of One-Dimensional Mod- els of Step-Flow Growth: Some Examples We use a phase field approach to solve the discrete- continuous Burton-Cabrera-Frank model for step dynam- Kinetic Monte Carlo on a 2D model shows that terrace- ics. We are thereby interested in the interplay of Ehrlich- width distributions (TWD) of steps on vicinal surfaces Schwoebel barriers and elastic effects. The phase-field narrow progressively with increasing flux until the model model requires a degenerate mobility in order to approx- breaks down. The narrowing corresponds to kinetic repul- imate the jumps in the adatom density across the steps. sion between moving steps, due to the intrinsic asymmetry We consider spiral and mound growth and propose an ap- of the adatom diffusion current on growing surfaces. To proach to grow regularly ordered trenches which can be make analytic progress, we consider a 1D model, from a used as templates to grow nanowires. Burton-Cabrera-Frank approach. This model leads to attachment asymmetry in essentially the same way as does Axel Voigt electromigration or Ehrlich-Schwoebel barriers. Work sup- TU Dresden ported by U. of Maryland NSF-MRSEC under Grant DMR [email protected] 05-20471, with ancillary support from CNAM. Yan-Mei Yu Theodore L. Einstein Chinese Academy of Science University of Maryland [email protected] [email protected]

MS83 MS82 Undulatory Swimming in Viscoelastic Fluids Instability and Growth on a Silicon Surface: From Homeoepitaxy to Heteroepitaxy We investigate the effects of fluid elasticity on the swimming behavior of a slender micro-organism (C. elegans, Abstract not available at time of publication. L 1mm) in experiments using particle image velocimetry, and by tracking the organism motion. Results show that Thomas Frisch the organism moves in highly periodic fashion and gener- Institut Matériaux Microéléctronique Nanosciences de ate traveling waves which decay from head to tail. The Provenc organism velocity (U) decreases as the fluid elasticity is Ecole Centrale de Marseille increased. However, the Strouhal number (St), defined as [email protected] St=(fA)/U, decreases as the fluid elasticity increases. Here, f and A is the organism swimming frequency and ampli- MS82 tude, respectively. This suggests that the fluid rheology may have a strong effect on the organism swimming gait. Phase-field Modeling of Epitaxial Growth: Appli- cations to Step Trains and Island Dynamics Paulo E. Arratia Mechanical Engineering and Applied Mechanics We present a new phase-field model including combined ef- University of Pennsylvania, Philadelphia. fects of edge diffusion, the Ehrlich-Schwoebel barrier, depo- [email protected] sition and desorption to simulate epitaxial growth. A new free energy function together with a correction to the initial phase variable profile is used to efficiently capture the MS83 morphological evolution. The phase-field model is solved Swimming Microorganisms in Viscoelastic Fluids by a fully-implicit finite difference scheme with adaptive and Gels block-structured Cartesian meshes. The model is then use to investigate the evolution of small islands and step trains. While the basic principles of swimming in Newtonian fluids are well understood, in many cases the natural environments which microorganisms navigate are non-Newtonian Zhengzheng Hu fluids or even gels, which result in different swimming be- Department of Mathematics havior. For example, mammalian sperm swim through mu- North carolina State University cus in the female reproductive tract. I discuss how vis- [email protected] coelastic response affects swimming shapes and speeds of flexible swimmers such as sperm. Next, I describe issues John Lowengrub that arise for swimmers moving through viscoelastic gels. Department of Mathematics First, swimming through solids such as gels requires altered University of California at Irvine boundary conditions on the swimmer, and unlike incom- [email protected] pressible fluids, a gel can have compressional modes with relative motion between polymer and solvent fractions. In Steven M. Wise addition, many biological gels are heterogeneous on the 120 MS10 Abstracts

lengthscale of swimming microorganisms. I discuss the ef- tions described above. We discuss the stability of the base fect of microstructure heterogeneity in both continuum and ﬂow to these perturbations above this critical pressure drop microscopic models of swimming. and contrast this with the behavior of other models.

Henry Fu Pamela Cook Brown University Dept of Mathematical Sciences henry [email protected] UofDelaware [email protected]

MS83 Michael Cromer Bio-locomotion Near Boundaries University of Delaware [email protected] We study the locomotive behavior of organisms in various fluidic environments to mimic complex natural habitat. To explore their behavior, we perform controlled experiments Gareth McKinley in the following scenarios: fluids with different viscosities, Dept of Mechanical Engineering capillary tubes, and wet granular media. We find that, Massachusetts Institute of Technology as organisms increase contact area with solid boundaries, [email protected] they swim a greater distance per undulation without a significant change of their body stroke. Such high efficiency is MS84 typically not expected for the locomotion of small organisms in viscous fluid, but as we show, it is possible under Mathematical Models for Particle Laden Thin the influence of boundaries. Films Sunghwan Jung We consider mathematical models for particle laden thin Engineering Science and Mechanics films and discuss various advances and challenges for this Virginia Tech problem. We present experimental data for flow on a slope [email protected] with particles and compare with the models. Relevant physics includes hindered settling, shear-induced migration, and surface tension. MS83 Andrea L. Bertozzi A Second Order Virtual Node Algorithm for Pois- UCLA Department of Mathematics son Interface Problems on Irregular Domains [email protected] I will present a second order accurate, symmetric positive definite, geometrically flexible and easy to implement Matthew Mata, Nebosja Murisic method for solving the variable coefficient Poisson equation UCLA with interfacial discontinuities. We discretize the equations [email protected], [email protected] using an embedded approach employing virtual nodes at interfaces and boundaries. A variational method is used to define numerical stencils near these special virtual nodes MS84 and a Lagrange multiplier approach is used to enforce jump Dewetting of Thin Liquid Polymer Films conditions and Dirichlet boundary conditions. Numerical experiments indicate second order accuracy in L-infinty. For films with a free surface, such as for the dewetting of a nano-scale thin polymer film on a hydrophobic sub- Joseph Teran strate, the boundary condition at the substrate has been UCLA found to have a crucial influence on the dynamics and mor- [email protected] phology of the film. Experimental studies of unstable thin films coating solids have shown significant differences in the dewetting rates and the patterns that develop after the for- MS84 mation of growing “dry regions’ on the solid. The thin film Shear Banding and Interfacial Stability in Pres- models we derive allow systematic description of the film sure Driven Flow of Wormlike Micellar Solutions dynamics and profiles in time as the slip length is varied in Straight Narrow Channels and used for direct comparison with experiments. We examine the linear stability of the steady, one- Barbara Wagner dimensional, pressure-driven channel flow of the VCM Weierstrass Institute model (Vasquez, Cook, and McKinley, JNNFM 2007). [email protected] The VCM model is a two-species, microstructural network model developed to describe flows of wormlike micellar solutions. The equations for each species are coupled and MS84 form a system of nonlinear partial differential equations. In Transient Stability Analysis for an Inertially-driven addition to Rousian and reptative relaxation mechanisms, Extensional Motion of a Planar Liquid Sheet the VCM model incorporates the breakage and reforming of two micellar species (a long species ‘A and a short species We derive a time-dependent exact solution of the free sur- ‘B). We consider effects of small perturbations of the base- face problem for the Navier-Stokes equations describing state in both the flow and vorticity directions. Below a the planar extensional motion of a fluid sheet driven by critical pressure drop the VCM model base solution is al- inertia. The linear stability with respect to one- and two- most homogeneous across the channel, like the upper con- dimensional symmetric perturbations is examined within vected Maxwell model, but above this critical pressure drop the framework of the slender body equations. Both tran- the flow becomes inhomogeneous and shear bands. For the sient growth and long-time asymptotic stability are consid- lower pressure the base solution is stable to the perturba- ered. Analysis begins with one-dimensional perturbations MS10 Abstracts 121

in the axial and transverse directions for viscous and invis- cident or probing field by designing wave emitting devices cid sheets. that simultaneously cancel out the incident field in a given region and radiate very little waves in the far-field. Thus Thomas P. Witelski the scattering from an object in this region is significantly Duke University reduced, rendering the object invisible. Our approach al- Department of Mathematics lows for cloaking over a broad range of frequencies, but it [email protected] assumes the incident field is known.

Linda Smolka Fernando Guevara Vasquez Bucknell University University of Utah [email protected] [email protected]

Graeme W. Milton MS85 University of Utah Transformation Media Using Negative Refractive Department of Mathematics Materials [email protected]

We will show that some transformation optics mappings Daniel Onofrei can lead to many interesting optical illusion and wave ma- Department of Mathematics nipulation effects. We will focus of those fold-geometry University of Utah mappings that give negative refractive index materials. [email protected] One interesting example is a conceptual device that can optically transform one object into another object[Y. Lai, J. Ng, H. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and MS85 C. T. Chan, Phys. Rev. Lett. 102, 253902 (2009)]. The Acoustic and Electromagnetic Cloaking of Obsta- device is itself invisible, and does not need to encircle the cles object. What we mean is that transformation optics can design a passive device that when placed near to (say) a In this talk, we shall consider virtually reshaping acous- spoon, will make look like (say) a cup for a far-field ob- tic and electromagnetic obstacles by cloaking. First, we server. The functionality is enabled by the fact that a show that the cloaking medium must be anisotropic. Then, negative index material can form part of a complementary by using transformation media, we derive the cloaking de- media and at the same time, serves as a lens. Using similar vices. Finally, by scattering estimates corresponding to ideas, we can achieve cloaking at a distance. Using negative small obstacles, we show that the limit of virtual minifi- index materials, we propose an invisibility cloak operating cation cloaking gives the invisibility cloaking. Our study at a finite frequency that can cloak an object with a pre- are conducted in both homogeneous and general inhomo- specified shape and size within a certain distance outside geneous background space. the cloaking shell [Y. Lai, H.Y. Chen, Z.Q. Zhang, C.T. Chan, Phys. Rev. Lett. 102, 093901 (2009)]. Hongyu Liu University of Washington C. T. Chan Department of Mathematics Dept. of Physics, HKUST, Clear Water Bay, Kowloon, [email protected] Hong Kong, China [email protected] MS86 Force- and Energy-mixing Methods for Atomistic MS85 Multiscale Simulations of Solids Plasmonics Invisibility In the concurrent multiscale approach a small region is Our work is at the frontier between the so-called plasmonics described with one method that is accurate but computa- and metamaterials topics. We will report recent results on tionally expensive, while the larger surrounding region is the use of transformation optics for surface plasmons waves described with a less accurate but much cheaper method. propagating on a metallic interface. We will show how Despite the successes of this approach, the essential prob- structuring the surface allows to control the propagation lem of how best to couple two different methods is still of light and, thus, from that propose structures to make not resolved. In this talk I discuss some general issues in an invisibility cloak for plasmons. coupling atomistic methods, focusing on the tradeoffs between energy-based and force-based coupling. While the Stefan Enoch, Sebastien Guenneau former allows a total energy to be defined, it necessarily CNRS gives rise to force errors at the boundary. The latter can Institut Fresnel produce accurate forces, but at the cost of having to give [email protected], [email protected] up defining a total energy. I present a comparison of various energy and force based methods for coupling quantum- Muamer Kadic mechanical and interatomic-potential descriptions of bond- Aix-Marseille Université ing for simple bulk crystalline systems. From this compar- Institut Fresnel ison we conclude that (at least for this system) force-based [email protected] mixing and an abrupt transition produce optimal trajectories. I present our results for fracture in silicon using the force-mixing approach, where we have discovered low-speed MS85 instabilities in our atomistic simulation that we relate to Broadband Exterior Cloaking with Active Devices experimentally observed micron-scale ridges. Finally, I discuss the prospects for a method that combines the best We show how to make an object invisible from a known in- 122 MS10 Abstracts

features of the two approaches. ing high-resolution electron backscatter diffraction imaging, we find a band-like microstructure consisting of con- Noam Bernstein fined areas in the sample with rotated lattice. Digital im- Naval Research Laboratory age correlation allows us to exactly determine the macro- [email protected] scopic state of deformation of the sample. This data can be used as a side condition to calculate the lamination param- Gabor Csanyi eters from the theory of kinematically compatible lamina- University of Cambridge tion of separate material regions, each deforming in single [email protected] slip. The parameters given by the theory agree with the measured properties, i.e., a lattice rotation of 3 degrees and a lamination normal rotated 7 degrees counterclock- MS86 wise from a ¡111¿ direction. Interface Conditions for Coupling Molecular Dy- namics to Continuum Models Patrick W. Dondl Univeristy of Bonn Simple coupling of molecular dynamics (MD) simulations [email protected] with continuum models result in spurious reflections at the MD-continuum interface. We develop a coupling procedure to reduce these spurious reflections by incorporating MS87 the recently developed Perfectly Matched Discrete Lay- Several Applications of the Level-set Approach to ers (PMDL) technique into a domain-decomposition based Dislocation Dynamics multiscale framework, and adapting PMDL for finite temperature heat baths. Through numerical examples, we In this talk, we will present results obtained in collabora- show that this method shows promise to be an efficient tion with Nicolas Forcadel and Regis Monneau about the and accurate alternative to existing coupling strategies. dynamics of dislocation lines in a slip plane. First we will explain how the motion of several dislocation lines can be Murthy N. Guddati, Senganal Thirunavukkarasu described at the microscopic scale by solving a non-local North Carolina State University eikonal equation. We will next present homogenization re- [email protected], [email protected] sults to derive elasto-visco-plastic law at the macroscopic level. To finish with, we will present results about the level-set approach in the case of singular interactions. MS86 Coupling Molecular Dynamics and Peridynamics Cyril Imbert Paris-Dauphine university Our presentation considers the coupling of molecular dyan- [email protected] mics and peridynamics via the fluxes in balances laws. The peridynamic momentum and energy balances laws are derived using the principles of statistical mechanics. In par- MS87 ticular, we show that the peridynamic force density integral Surface Effects in the Inelastic Response of Molec- operator is the phase space expected value of internal force ular Crystals density given by a general multibody interatomic potential. The derivations generalize the seminal work of Irving- Understanding the mechanisms of deformation of molecu- Kirkwood (1950), and build upon the elegant ideas due to lar crystals is critical in processing of pharmaceutical prod- Noll (1955) that generalized the former work. ucts as well as in tailoring key drug properties such as dissolution rate and stability. The inelastic response of these Richard B. Lehoucq,MarkP.Sears crystalline materials is mediated by dislocation motion and Sandia National Laboratories their interaction with defects, such as second phase parti- [email protected], [email protected] cles, dislocations, grain boundaries and stress free surfaces. This is particularly important when the scale of the volume of analysis approaches the microstructure scale as in MS86 micron and submicron size particles. Here we propose a Atomistic-based Boundary Element Method model to study the transition from a high dislocation density crystal to an amorphous material during the process We present a dimension reduction method to reduce the of milling of molecular crystals. In particular we analyze number of degrees of freedom associated with atomistic the effect of grain and particle size in this transition with models. The model retains atoms in critical areas, e.g. 3D phase field dislocation dynamics simulations. around crack tips, and a boundary element representation is used to remove the surrounding atoms. We will discuss Lei Lei the formulation in both 2D and 3D. Department of Mechanical Engineering Purdue University Xiantao Li [email protected] Department of Mathematics Pennsylvania State University Marisol Koslowski [email protected] Purdue University [email protected] MS87 Lamination Mirostructure in a Copper Single Crys- MS87 tal Shear Experiment A Stochastic Model for the Propagation of Cracks We investigate the formation of microscopic patterns in a copper single crystal deformed in a shear experiment. Us- MS10 Abstracts 123

in Heterogeneous Solids

Crack propagation is the fundamental process leading to the failure of brittle solids. However, if one goes beyond the failure of a continuum homogeneous medium and considers more realistic situations, i.e. solids with inhomogeneous failure properties, various aspects of its dynamics become unclear, in particular about the intermittent dynamics of cracks or the variations of its growth velocity with the external driving force. In this work, we show how one can extend the classical theory of Fracture Mechanics to inhomogeneous media, and propose a stochastic equation of motion to describe the propagation of a crack. Our analysis shows that the quasi-static failure of inhomogeneous solids corresponds to a dynamical critical transition also referred to as a depinning transition: critical failure occurs when the driving force is sufficiently large to depin the crack front from the material heterogeneities. An- other remarkable prediction of this crack growth model is a highly intermittent crack dynamics close to the failure threshold. We show that propagation occurs through sud- den jumps, with power law distributed sizes and durations. These predictions compare quantitatively well with the direct observations of the propagation of interfacial cracks in heterogeneous solids. These results show that the depinning transition of cracks in heterogeneous solids is revealed both by the average crack dynamics and by its velocity fluctuations. Such an interpretation of failure of brittle materials opens new perspectives in the design of stronger solids with increased lifetime that will be finally discussed.

Laurent Ponson California Institute of Technology [email protected]