Mathematical Theory of Elasticity of Quasicrystals and Its Applications - Rilegato

Fan, Tianyou

Rilegato

ISBN 10: 3642146422 ISBN 13: 9783642146428

Casa editrice: Springer Verlag, 2011

Riassunto

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.

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Recensione

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)

Contenuti

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.

Dettagli dell'edizione

• Editore: Springer Verlag
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 3642146422
• ISBN 13: 9783642146428
• Rilegatura: Copertina rigida
• Numero di pagine: 363
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania