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 polycrys- tals. 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 re- liable, 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 evo- lution*. 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 criti- cal 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 behav- ior 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 pat- terns 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