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This book comprises an introductory lecture outlining the basic concepts and challenges in the field. This is followed by a collection of reprinted articles which are important in understanding the subject. The book will focus mainly on mathematical and physical foundations of the subject rather than experimental progress. By concentrating on theoretical topics, this volume has long-lasting as well as immediate value to physicists, crystallographers, metallurgists and mathematicians. Request Inspection Copy
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The conference promotes the theoretical and methodological development of crystallographic investigations of aperiodic crystals including modulated structures, polytypes, incommensurate misfit or composite crystals and quasi crystals. It also promotes scientific interchange among groups working in the various fields of aperiodic materials. Special emphasis will be given to multidisciplinary aspects of aperiodicity.
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-disorde...
This volume covers all scientific aspects relating to quasicrystals, such as tilings, generalized crystallography, sample preparation, structure determination, the growth mechanism, phase transition, and physical and chemical properties (including electronic, dynamical and mechanical properties).
The year's finest mathematical writing from around the world This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2020 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday aspects of math, and take readers behind the scenes of today’s hottest mathematical debates. Here, Steven Strog...
This book gathers a collection of reprints on the Hubbard Model. The major contributions to the subject since its origin are included, with the aim of providing all scientists working on the model and its applications with easy access to the relevant literature.The book is divided into five parts. The introductory part is concerned with the physical origin and motivations of the model, and contains a collection of mainly historical papers. The remaining four sections are intended to present a coherent scenario of the different approaches to the model solution: exact and rigorous statistical mechanics results; variational methods; perturbative approaches; numerical Quantum Monte Carlo and exact diagonalization studies. Among the applications special emphasis is given to high-Tc superconductivity. Each section is preceded by commentary notes from the editor.
This publication represents the culmination of the National Academies Keck Futures Initiative (NAKFI), a program of the National Academy of Sciences, the National Academy of Engineering, and the National Academy of Medicine supported by a 15-year, $40 million grant from the W. M. Keck Foundation to advance the future of science through interdisciplinary research. From 2003 to 2017, more than 2,000 researchers and other professionals across disciplines and sectors attended an annual "think-tank" style conference to contemplate real-world challenges. Seed grants awarded to conference participants enabled further pursuit of bold, new research and ideas generated at the conference.
For many decades, Martin Gardner, the Grand Master of mathematical puzzles, has provided the tools and projects to furnish our all-too-sluggish minds with an athletic workout. Gardner's problems foster an agility of the mind as they entertain. This volume presents a new collection of problems and puzzles not previously published in book form. Marti
This book goes beyond the scope of other works in the field with its thorough treatment of applications in a wide variety of disciplines. The third edition features a new section on constants of motion and symmetry and a new appendix on the Lorentz-Legendre expansion.