Overview
- First monograph published on this subject area
- Includes theoretical system and methodology of elasticity and a series of analytic solutions for dislocations and cracks in various quasicrystal systems
- Offers an in-depth, original and innovational presentation of mathematical derivations and solutions
- Includes many results in new area such as plasticity, elasto-/hydrodynamics and the fracture theory of quasicrystals
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Table of contents (16 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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 setting up new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions. The new theories developed here dramatically simplify the solving of complicated elasticity equation systems. Large numbers of complicated equations involving elasticity are reduced to a single or a few partial differential equations of higher order. Systematical and direct methods of mathematical physics and complex variable functions are developed to solve the equations under appropriate boundary value and initial value conditions, and many exact analytical solutions are constructed.
The dynamic and non-linear analysis of deformation and fracture of quasicrystals in this volume presents an innovative approach. It gives a clear-cut, strict and systematic mathematical overview of the field. Comprehensive and detailed mathematical derivations guide readers through the work. By combining mathematical calculations and experimental data, theoretical analysis and practical applications, and analytical and numerical studies, readers will gain systematic, comprehensive and in-depth knowledge on continuum mechanics, condensed matter physics and applied mathematics.
Reviews
From the reviews:
“This treatise is one of few pioneering monographs devoted to the development of a mathematical theory of elasticity of quasicrystals and its applications, including some preliminary results on plasticity. The book comprises 16 chapters, each of which has appropriate references, and two appendices. … This is a timely and pioneering book on quasicrystals by an author who made some contributions in quasicrystals, and it will certainly stimulate graduate students and engineers for further research in the area of quasicrystals.” (M. Cengiz Dökmeci, Zentralblatt MATH, Vol. 1222, 2011)Authors and Affiliations
Bibliographic Information
Book Title: Mathematical Theory of Elasticity of Quasicrystals and Its Applications
Authors: Tianyou Fan
DOI: https://doi.org/10.1007/978-3-642-14643-5
Publisher: Springer Berlin, Heidelberg
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2011
eBook ISBN: 978-3-642-14643-5Published: 25 May 2011
Edition Number: 1
Number of Pages: 350
Number of Illustrations: 32 b/w illustrations, 8 illustrations in colour
Additional Information: Jointly published with Science Press.
Topics: Solid Mechanics, Condensed Matter Physics, Applications of Mathematics