Mathematical Theory of Elasticity of Quasicrystals and Its Applications - neues Buch

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ISBN/EAN: 9783642146435

ISBN - alternative Schreibweisen:
978-3-642-14643-5
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: tian, fan
Titel des Buches: quasicrystal, mathematical theory elasticity, applications mathematical

Daten vom Verlag:

Autor/in: Tianyou Fan
Titel: Mathematical Theory of Elasticity of Quasicrystals and Its Applications
Verlag: Springer; Springer Berlin; Science Press
350 Seiten
Erscheinungsjahr: 2011-05-25
Berlin; Heidelberg; DE
Sprache: Englisch
212,93 € (DE)
218,90 € (AT)
247,00 CHF (CH)
Available
350 p. 40 illus., 8 illus. in color.

EA; E107; eBook; Nonbooks, PBS / Technik/Maschinenbau, Fertigungstechnik; Maschinenbau: Festkörpermechanik; Verstehen; Defects; Exact analytic solutions; Mathematical elasticity; Potential theory; Quasicrystal; SCIPRESS; C; Solid Mechanics; Condensed Matter Physics; Applications of Mathematics; Engineering; Physik der kondensierten Materie (Flüssigkeits- und Festkörperphysik); Angewandte Mathematik; BB

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.

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.

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