MATH THEORY OF ELASTIC & GENERAL DYN QUASICRYSTALS & APPLN

This book gives a detailed description on mathematical theory of elasticity and generalized dynamics of solid quasicrystals and its applications.

The Chinese edition of the book Mathematical Theory of Elasticity of Quasicrystals and Its Applications was published by the Beijing Institute of Technology Press in 1999, written by Prof Tian-You Fan. In this English edition of the book, the phonon-phason dynamics, defect dynamics and hydrodynamics of solid quasicrystals are included, so the scope of the book is beyond elasticity. Hence, the title in this edition is changed to Mathematical Theory of Elasticity and Generalized Dynamics of Quasicrystals and Its Applications. This book is the first and only monograph in the scope of quasicrystals since first published in 1999 in China and worldwide. In this edition, the two-dimensional quasicrystals of second kind, soft-matter quasicrystals and photonic bade-gap and application of photonic quasicrystals are added.

This book combines the mechanical and physical behavior of quasicrystals and mathematical physics, which may help graduate students and researchers in the fields of new materials, condensed matter physics, applied mathematics and engineering science.

Contents:

• Crystals
• Framework of Crystal Elasticity
• Solid Quasicrystals and Their Properties
• The Physical Basis of Elasticity of Solid Quasicrystals
• Elasticity Theory of One-dimensional Quasicrystals and Simplification
• Elasticity Theory of Two-dimensional Solid Quasicrystals of First Kind and Simplification
• Application I — Some Dislocation and Interface Problems and Solutions in One-dimensional and First Kind of Two-dimensional Quasicrystals
• Application II — Solutions of Notch and Crack Problems of One- and Two-dimensional Quasicrystals
• Theory of Elasticity of Three-dimensional Quasicrystals and Their Applications
• Phonon–Phason Dynamics and Defect Dynamics of Solid Quasicrystals
• Complex Analysis Method for Elasticity of Quasicrystals
• Variational Principle of Elasticity of Quasicrystals, Numerical Analysis and Applications
• Some Mathematical Principles on Solutions of Elasticity of Quasicrystals
• Nonlinear Behaviour of Solid Quasicrystals
• Fracture Theory of Solid Quasicrystals
• Hydrodynamics of Solid Quasicrystals
• Two-dimensional Quasicrystals of the Second Kind
• Identification and Phase Transitions of Soft-matter Quasicrystals
• Photonic Band Gap and Application of Two-dimensional Photonic Quasicrystals
• Concluding Remarks and Perspectives
• Appendices

Readership: Graduate students and researchers in the field of new materials, condensed matter physics, applied mathematics and engineering science.

Key Features:

• Potential theory of generalized elasticity, mathematical physics, exact analytic solutions of complicated boundary value problems of quasicrystals