# Mathematical Theory of Elasticity of Quasicrystals and Its Applications

• Tianyou Fan
Book

1. Front Matter
Pages i-xii
2. Tianyou Fan
Pages 1-11
3. Tianyou Fan
Pages 13-24
4. Tianyou Fan
Pages 25-33
5. Tianyou Fan
Pages 35-52
6. Tianyou Fan
Pages 53-66
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Pages 127-157
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Pages 257-272
13. Tianyou Fan
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14. Tianyou Fan
Pages 289-316
15. Tianyou Fan
Pages 317-328
16. Tianyou Fan
Pages 329-331
17. Back Matter
Pages 333-363

### Introduction

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.

### Keywords

Defects Exact analytic solutions Mathematical elasticity Potential theory Quasicrystal SCIPRESS

#### Authors and affiliations

• Tianyou Fan
• 1
1. 1.Department of Physics, School of ScienceBeijing Institue of TechnologyBeijingChina

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-14643-5
• Copyright Information Springer-Verlag Berlin Heidelberg 2011
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages Engineering
• Print ISBN 978-3-642-14642-8
• Online ISBN 978-3-642-14643-5