**IAS/Park City Mathematics Series**

Volume: 23;
2017;
327 pp;
Hardcover

MSC: Primary 82; 35; 74; 51; 52;

**Print ISBN: 978-1-4704-2919-5
Product Code: PCMS/23**

List Price: $104.00

AMS Member Price: $83.20

MAA Member Price: $93.60

**Electronic ISBN: 978-1-4704-3749-7
Product Code: PCMS/23.E**

List Price: $104.00

AMS Member Price: $83.20

MAA Member Price: $93.60

# Mathematics and Materials

Share this page *Edited by *
*Mark J. Bowick; David Kinderlehrer; Govind Menon; Charles Radin*

A co-publication of the AMS, IAS/Park City Mathematics Institute, and Society for Industrial and Applied Mathematics

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.

Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute.

#### Readership

Graduate students and researchers interested in mathematical aspects of material sciences.

#### Reviews & Endorsements

This book is a collection of snapshots of active work in materials science from the point of view of statistical mechanics, often with geometric considerations. Some articles may be useful for graduate students interested in finding out what's out there; some may be useful for researchers interested in familiarizing themselves with this part of the frontier.

-- Greg McColm, MAA Reviews

# Table of Contents

## Mathematics and Materials

- Cover Cover11
- Title page iii4
- Contents v6
- Preface ix10
- Introduction xi12
- Three Lectures on Statistical Mechanics (Veit Elser) 114
- Packing, Coding, and Ground States (Henry Cohn) 4356
- Entropy, Probability and Packing (Alpha A Lee, Daan Frenkel) 103116
- Ideas about Self Assembly (Michael P. Brenner) 167180
- The Effects of Particle Shape in Orientationally Ordered Soft Materials (P. Palffy-Muhoray, M. Pevnyi, E. G. Virga, and X. Zheng) 201214
- Statistical Mechanics and Nonlinear Elasticity (Roman Kotecký) 255268
- Quantitative Stochastic Homogenization: Local Control of Homogenization Error through Corrector (Peter Bella, Arianna Giunti, Felix Otto) 299312
- Back Cover Back Cover1342