Mathematical Theory of Elasticity of Quasicrystals and Its Applications
This inter-disciplinary work covering the continuum mechanics of novel materials, condensed matter physics and partial differential equations discusses the mathematical theory of elasticity of quasicrystals (a new condensed matter) and its applications by
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Mathematical Theory of Elasticity of Quasicrystals and Its Applications
Tianyou Fan
Mathematical Theory of Elasticity of Quasicrystals and Its Applications With 82 figures
Author Tianyou Fan Department of Physics, School of Science Beijing Institue of Technology Beijing 100081, China
ISBN 978-7-03-025669-0 Science Press Beijing ISBN 978-3-642-14642-8 e-ISBN 978-3-642-14643-5 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010931505 © Science Press Beijing and Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: Frido Steinen-Broo, EStudio Calamar, Spain Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface This monograph is devoted to the development of a mathematical theory of elasticity of quasicrystals and its applications. Some results on elastodynamics and plasticity of quasicrystals are also included to document preliminary advances in recent years. The first quasicrystal was observed in 1982 and reported in November 1984. At that time several physical and mathematical theories for quasicrystal study already existed. Soon after the discovery, the theory of elasticity of quasicrystals was put forward. Based on Landau-Anderson symmetry-breaking, a new elementary excitation - the phason - was introduced in addition to the well known phonon. The phason concept was suggested in the 1960’s in incommensurate phase theory. Group theory and discrete geometry e.g. the Penrose tiling provide further explanations to quasicrystals and their elasticity from the standpoint of algebra and geometry. The phonon and phason elementary excitations form the basis of the theory of elasticity of this new solid phase. Many theoretical (condensed matter) physicists have spent a great deal of effort on constructing the fundamental physical framework of the theory of elasticity of quasicrystals. Applications of group theory and group representation theory further enhance the physical basis of the description. On the basis of the physical framework and by extending the methodology of mathematical physics and classical elasticity, the mathematical theory of elasticity of quasicrystals has been developed. Recent
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