Mathematical Theory of Elasticity of Quasicrystals and Its Applications

Crystals.- Framework of crystal elasticity.- 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 quasicrystals and simplification.- Application I-Some dislocation and interface problems and solutions of one- and two-dimensional quasicrystals.- Application II-Solutions of notch and crack problems of one- and two-dimensional quasicrystals.- Elasticity of three-dimensional quasicrystals and its applications.- Phonon-phason dynamics and defects dynamics of solid quasicrystals.- Complex analysis method.- Variational principles 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 quasicrystals.- Conclusion remarkable.

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• Mecânica dos sólidos
• Ensaio de materiais
• Física da Matéria Condensada (física do estado sólido e estado líquido)
• Física Matemática

Mathematical elasticity of quasicrystals;Mechanical behaviour of quasicrystalline materials;Phonon-phason dynamics;Plastic deformation of quasicrystals;Soft-matter quasicrystals;Solid quasicrystals;Displacement potential function formulation;Stress potential function formulation