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.