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Product Code:  PCMS/23 
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eBook ISBN:  9781470437497 
Product Code:  PCMS/23.E 
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AMS Member Price:  $89.60 
Hardcover ISBN:  9781470429195 
eBook: ISBN:  9781470437497 
Product Code:  PCMS/23.B 
List Price:  $237.00 $181.00 
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AMS Member Price:  $189.60 $144.80 
Hardcover ISBN:  9781470429195 
Product Code:  PCMS/23 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470437497 
Product Code:  PCMS/23.E 
List Price:  $112.00 
MAA Member Price:  $100.80 
AMS Member Price:  $89.60 
Hardcover ISBN:  9781470429195 
eBook ISBN:  9781470437497 
Product Code:  PCMS/23.B 
List Price:  $237.00 $181.00 
MAA Member Price:  $213.30 $162.90 
AMS Member Price:  $189.60 $144.80 

Book DetailsIAS/Park City Mathematics SeriesVolume: 23; 2017; 327 ppMSC: Primary 82; 35; 74; 51; 52
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 orderdisorder transition in many geometric models of materials including nonlinear elasticity, sphere packings, granular materials, liquid crystals, and the emerging field of synthetic selfassembly. 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.
This volume is a copublication of the AMS, IAS/Park City Mathematics Institute, and Society for Industrial and Applied Mathematics
Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute.
ReadershipGraduate students and researchers interested in mathematical aspects of material sciences.

Table of Contents

Articles

Veit Elser — Three lectures on statistical mechanics

Henry Cohn — Packing, coding, and ground states

Alpha Lee and Daan Frenkel — Entropy, probability and packing

Michael Brenner — Ideas about self assembly

P. PalffyMuhoray, M. Pevnyi, E. Virga and X. Zheng — The effects of particle shape in orientationally ordered soft materials

Roman Kotecký — Statistical mechanics and nonlinear elasticity

Peter Bella, Arianna Giunti and Felix Otto — Quantitative stochastic homogenization: Local control of homogenization error through corrector


Additional Material

Reviews

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


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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 orderdisorder transition in many geometric models of materials including nonlinear elasticity, sphere packings, granular materials, liquid crystals, and the emerging field of synthetic selfassembly. 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.
This volume is a copublication of the AMS, IAS/Park City Mathematics Institute, and Society for Industrial and Applied Mathematics
Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute.
Graduate students and researchers interested in mathematical aspects of material sciences.

Articles

Veit Elser — Three lectures on statistical mechanics

Henry Cohn — Packing, coding, and ground states

Alpha Lee and Daan Frenkel — Entropy, probability and packing

Michael Brenner — Ideas about self assembly

P. PalffyMuhoray, M. Pevnyi, E. Virga and X. Zheng — The effects of particle shape in orientationally ordered soft materials

Roman Kotecký — Statistical mechanics and nonlinear elasticity

Peter Bella, Arianna Giunti and Felix Otto — Quantitative stochastic homogenization: Local control of homogenization error through corrector

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