This book highlights the mathematical models and solutions of the
generalized dynamics of soft-matter quasicrystals (SMQ) and
introduces possible applications of the theory and methods. Based
on the theory of quasiperiodic symmetry and symmetry breaking, the
book treats the dynamics of individual quasicrystal systems by
reducing them to nonlinear partial differential equations and then
provides methods for solving the initial-boundary value problems in
these equations. The solutions obtained demonstrate the
distribution, deformation and motion of SMQ and determine the
stress, velocity and displacement fields. The interactions between
phonons, phasons and fluid phonons are discussed in some
fundamental materials samples. The reader benefits from a detailed
comparison of the mathematical solutions for both solid and
soft-matter quasicrystals, gaining a deeper understanding of the
universal properties of SMQ. The second edition covers the latest
research progress on quasicrystals in topics such as thermodynamic
stability, three-dimensional problems and solutions, rupture
theory, and the photonic band-gap and its applications. These novel
chapters make the book an even more useful and comprehensive
reference guide for researchers in condensed matter physics,
chemistry and materials sciences.
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