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Full Description
Articles in this volume are based on lectures presented at the Park City summer school on ``Mathematics and Materials'' in July 2014. The central theme is a description of material behavior that is rooted in statistical mechanics. While many presentations of mathematical problems in materials science begin with continuum mechanics, this volume takes an alternate approach. All the lectures present unique pedagogical introductions to the rich variety of material behavior that emerges from the interplay of geometry and statistical mechanics. The topics include the order-disorder transition in many geometric models of materials including nonlinear elasticity, sphere packings, granular materials, liquid crystals, and the emerging field of synthetic self-assembly. Several lectures touch on discrete geometry (especially packing) and statistical mechanics. The problems discussed in this book have an immediate mathematical appeal and are of increasing importance in applications, but are not as widely known as they should be to mathematicians interested in materials science. The volume will be of interest to graduate students and researchers in analysis and partial differential equations, continuum mechanics, condensed matter physics, discrete geometry, and mathematical physics.
Contents
V. Elser, Three lectures on statistical mechanics
H. Cohn, Packing, coding, and ground states
A. A. Lee and D. Frenkel, Entropy, probability and packing
M. P. Brenner, Ideas about self assembly
P. Palffy-Muhoray, M. V. Pevnyi, E. G. Virga, and X. Zheng, The effects of particle shape in orientationally ordered soft materials
R. Kotecky, Statistical mechanics and nonlinear elasticity
P. Bella, A. Giunti, and F. Otto, Quantitative stochastic homogenization: Local control of homogenization error through corrector
