00000cmm a22000004a 4500 UP-99796217611211914 Buklod 20241004163427.0 m go j cr cn |||aaaaa 241004s2011 gw ||||go||j| ||||||engdd 9783642146435 (eBook) 3642146430 (eBook) (iLib)UPD-00214608047 CSt DMLR rda eng DMLUC QC 173.4 Q36 F36 2011eb Fan, Tianyou author Mathematical theory of elasticity of quasicrystals and its applications by Tianyou Fan. Berlin, Heidelberg Springer 2011 1 online resource (xii, 363 pages) illustrations (some color) text rdacontent computer rdamedia online resource rdacarrier Includes bibliographical references and index Preface -- Crystals -- Framework of the classical theory of elasticity -- Quasicrystals and their properties -- Physical basis of the elasticity of quasicrystals -- Elasticity theory of one-dimensional quasicrystals and simplification -- Elasticity theory of two-dimensional quaiscrystals and simplification -- Application I--Some dislocation problems and solutions of one- and two-dimensional quasicrystals -- Application II--Some notch and crack problems and solutions of one- and two-dimensional quasicrystals -- Elasticity of three-dimensional quasicrystals and applications -- Elastodynamics of quasicrystals -- Complex variable function method -- Variational principles, numerical method and solutions of two-dimensional quasicrystals -- Some mathematical principles on solutions of elasticity of quasicrystals -- Nonlinear elasticity and plasticity -- Fracture theory of quasicrystals -- Possible applications of elasticity to the study of specific heat of quasicrystals. IP-based subscription, access limited to within on campus computer network Access via Electronic Resources of the UPD University Library Website 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 Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink. Quasicrystals Elastic properties Mathematical models. Quasicrystals Mathematics. Elasticity Mathematics. SpringerLink (Online service). http://link.springer.com/book/10.1007/978-3-642-14643-5 Available for University of the Philippines Diliman via SpringerLink. Click here to access FO UPD DMLR Electronic Resource