The book systematically introduces the mathematical models and solutions of generalized hydrodynamics of soft-matter quasicrystals (SMQ). It provides methods for solving the initial-boundary value problems in these systems. The solutions obtained demonstrate the distribution, deformation and motion of the soft-matter quasicrystals, and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. Mathematical solutions for solid and soft-matter quasicrystals are compared, to help readers to better understand the featured properties of SMQ.

Presents an overview of the discovery, basics and general properties of soft-matter quasicrystals Discusses the dynamics of soft-matter quasicrystals with different rotational symmetries Provides the theoretical derivations and mathematical solutions in an easy-to-follow style Includes supplementary material: sn.pub/extras

Autorentext

After studying at Peking University, Tianyou FAN has begun his academic career in Beijing Institute of Technology, as Assistant and Lecturer (1963-1979), Associate Professor (1980-1985) and Professor (1986-present). He was an Alexander von Humboldt Research Fellow several times at the Universities of Kaiserlautern and Stuttgart, and held Visiting Professorships at the Universities of Waterloo, Tokyo and South Carolina etc.

FAN is nominated as member of the 9 th and 10 th National Committee of the People's Political Consultative Conference (1998-2007), and working as member of the American Mathematical Society, and the Association of Applied Mathematics and Mechanics (Gesselschaft fuer Angewandte Mathematik und Mechanik, GAMM) of Germany. He is the Associate Editor of Applied Mechanics Reviews of American Society of Mechanical Engineers, Reviewer of Mathematical Reviews of American Mathematical Society. He has published several monographs, including: Foundation of Fracture Mechanics (1978, in Chinese), Introduction to the Theory of Fracture Dynamics (1990, in Chinese), Mathematical Theory of Elasticity of Quasicrystals and Its Applications 1 st edition (1999 in Chinese, 2010 in English with Springer), Foundation of Fracture Theory (2003 in Chinese), Fracture Dynamics: Principle and Applications (2006, in Chinese), Mathematical Theory of Elasticity and Relevant Topics of Solid and Soft-Matter Quasicrystals (2014, in Chinese), Foundation of Defect and Fracture Theory of Solid and Soft Matter (2014, in Chinese). Recipient: the first grade prize in Science and Technology Prize of the Defense Science, Technology and Industrial Committee of China in 1999, China Book Prize in 1991, 2012, Outstanding Scientific Monograph Prize of Educational Committee of China in 1992, Nature Science Prize of Educational Ministry of China in 2007.

Inhalt

A brief introduction to soft matter.- Soft-matter quasicrystals and their properties.- Elasticity and hydrodynamics of solid quasicrystals.- Generalized Langevin equation.- Equation of state of structured liquid.- Poisson bracket method and equations of motion of soft-matter quasicrystals.- Dynamics of soft-matter quasicrystals with 12-fold symmetry.- Dynamics of soft-matter quasicrystals with 18-fold symmetry.- Dynamics of possible 5- and 10-fold symmetrical soft-matter quasicrystals.- Dynamics of possible soft-matter quasicrystals 8-fold symmetry.- An application to smectic-A liquid crystals, dislocation and crack.- Conclusions and remarks.