Download Mathematical Theory of Elasticity of Quasicrystals and Its by Tian-You Fan PDF

By Tian-You Fan

This inter-disciplinary paintings overlaying the continuum mechanics of novel fabrics, condensed subject physics and partial differential equations discusses the mathematical conception of elasticity of quasicrystals (a new condensed topic) and its functions by way of developing new partial differential equations of upper order and their ideas lower than complex boundary price and preliminary price stipulations. the recent theories built the following dramatically simplify the fixing of advanced elasticity equation structures. huge numbers of complex equations regarding elasticity are decreased to a unmarried or a couple of partial differential equations of upper order. Systematical and direct tools of mathematical physics and intricate variable features are constructed to resolve the equations lower than applicable boundary price and preliminary price stipulations, and lots of particular analytical recommendations are built.

The dynamic and non-linear research of deformation and fracture of quasicrystals during this quantity provides an leading edge technique. It supplies a simple, strict and systematic mathematical assessment of the sphere. entire and particular mathematical derivations consultant readers in the course of the paintings. through combining mathematical calculations and experimental information, theoretical research and sensible functions, and analytical and numerical reports, readers will achieve systematic, accomplished and in-depth wisdom on continuum mechanics, condensed subject physics and utilized mathematics.

Show description

Read or Download Mathematical Theory of Elasticity of Quasicrystals and Its Applications PDF

Similar solid-state physics books

Introductory Solid State Physics (Second Edition)

Assuming an hassle-free wisdom of quantum and statistical physics, this ebook presents a accomplished advisor to primary actual houses of condensed topic, in addition to the underlying thought invaluable for a formal knowing in their origins. the subject material covers the valuable good points of condensed topic physics, yet with specific accessory at the houses of steel alloys.

Theory of High Temperature Superconductivity: A Conventional Approach

Drawing from the wide spectrum of phenomena, defined in additional than 100,000 articles on high-Tc superconductivity, during this ebook, the authors study these simple houses for which figuring out might be accomplished in the framework of conventional tools of theoretical physics. this can be the case of the overdoped cuprates for which the "Bardeen application" has been discovered: we all know their digital spectrum, we will be able to calculate their simple thermodynamic and electrodynamic homes, and expect new phenomena.

Nanotubes and Nanosheets: Functionalization and Applications of Boron Nitride and Other Nanomaterials

Nanotubes and nanosheets are low-dimensional nanomaterials with special homes that may be exploited for various purposes. This publication deals a whole review in their constitution, homes, improvement, modeling techniques, and functional use. It focuses realization on boron nitride (BN) nanotubes, that have had significant curiosity given their unique high-temperature homes, in addition to graphene nanosheets, BN nanosheets, and steel oxide nanosheets.

Additional info for Mathematical Theory of Elasticity of Quasicrystals and Its Applications

Sample text

Phys Rev Lett, 1986, 56(25): 2740–2743 [44] Sutherland B. Simple system with quasiperiodic dynamics: a spin in a magnetic field. Phys Rev B, 1986, 34(8): 5208–5211 [45] Fujiwara T, Yokokawa T. Universal pseudogap at Fermi energy in quasicrystals. Phys Rev Lett, 1991, 66(3): 333–336 Chapter 4 The physical basis of elasticity of quasicrystals The physical background on elasticity of quasicrystals is quite different from that of the classical elasticity, the discussion about this provides a basis of the subsequent contents of the book.

The unit-cell description based on the Penrose tiling is adopted too, but the density-wave description based on the Laudau phenomenological theory on symmetry-breaking of condensed matter has played the central role and been widely acknowledged. This means there are two elementary excitations of low-energy, phonon u and phason w for quasicrystals, in which vector u is in the parallel space E 3 and vector w is in the perpendicular 3 , respectively. 1-1), where ⊕ represents the direct sum. 1-2). 8.

How to describe mathematically the behaviour of the quasicrystal deformation? To answer these questions, it is necessary to consider the physical background of elasticity of quasicrystals. The study in this regard was conducted soon after discovery of the new solid phase. Because the quasicrystal is a new structure of solid, theoretical physicists have proposed various descriptions of its elasticity. The majority agrees that the Landau density wave theory (Refs[1-25]) is the physical basis of elasticity of the quasicrystals.

Download PDF sample

Rated 4.24 of 5 – based on 34 votes