Generalized Dynamics of Soft-Matter Quasicrystals

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.

Autorentext
Prof. Tian-You Fan

After studying at Peking University, Tianyou Fan began his academic career at the 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 Kaiserslautern and Stuttgart, and held visiting professorships at the Universities of Waterloo, Tokyo and South Carolina.
Fan was nominated as a member of the 9th and 10th National Committee of the People's Political Consultative Conference (1998-2007), and has worked as a member of the American Mathematical Society, and the Association of Applied Mathematics and Mechanics (Gesellschaft fuer Angewandte Mathematik und Mechanik, GAMM) of Germany. He is the associate editor of Applied Mechanics Reviews of American Society of Mechanical Engineers, and a reviewer of Mathematical Reviews of the American Mathematical Society. He has published several monographs, and is recipient of numerous awards, including the Science and Technology Prize of the Defense Science, Technology and Industrial Committee of China (1999), the China Book Prize (1991 and 2012), Outstanding Scientific Monograph Prize of Educational Committee of China (1992), and the Nature Science Prize of Educational Ministry of China (2007).
Dr. Wenge Yang
Wenge Yang works in the Shanghai Laboratory of the Center of High Pressure Science & Technology Advanced Research as Staff Scientist and Associate Director.
Prof. Xiao-Hong Sun
Xiao-Hong Sun works in Zhengzhou University as Professor, with research interests in photonic band gap of quasicrystals.
Dr. Hui Cheng
**Hui Cheng works in Hebei University of Engineering, with research interests in generalized dynamics of soft matter.

Inhalt
NotationsPreface to the first editionPreface to the second Edition Chapter 1 Introduction to soft matterChapter 2 Discovery of soft-matter quasicrystals and their properties2.1 Experimental observation of quasicrystalline phases in soft matter2.2 Characters of soft-matter quasicrystals2.3 Some concepts concerning possible generalized dynamics on soft-matter quasicrystals2.4 First and second kinds of two-dimensional quasicrystals2.5 Motivation of our discussion in the bookChapter 3 Brief review on elasticity and hydrodynamics of solid quasicrystals3.1 Introduction of the elasticity of quasicrystals, phonon and phason3.2 Deformation tensor: strain and stress tensors3.3 Equations of motion3.4 Free energy density and elastic constants3.5 Generalized Hooke's law3.6 Boundary conditions and initial conditions3.7 Solutions of elasticity 3.8 Hydrodynamics of solid quasicrystals3.9 Solution of hydrodynamics of solid quasicrystals 3.10 SummaryChapter 4 Case study of equation of state of several structured fluids4.1 Overview on equation of state in some structured fluids4.2 Possible equations of state4.3 Application to dynamics of soft-matter quasicrystals4.4 The incompressible model of soft matterChapter 5 Poisson bracket method and equations of motion of soft-matter quasicrystals5.1 Brownian motion and Langevin equation5.2 Extended version of Langevin equation 5.3 Multivariable Langevin equation, coarse graining5.4 Poisson brackets in condensed matter physics5.5 Poisson brackets application to quasicrystals5.6 Equations of motion of soft-matter quasicrystals5.7 Poisson brackets based on Lie algebra5.8 On solving governing equations
Chapter 6 Oseen theory and Oseen solution6.1 Navier-Stokes equations6.2 Stokes approximation6.3 Stokes paradox 6.4 Oseen modification 6.5 Oseen steady solution of flow of incompressible fluid past cylinder 6.6 The reference meaning of Oseen theory and Oseen solution to the study in soft matterChapter 7 Dynamics of soft-matter quasicrystals with 12-fold symmetry7.1 Two-dimensional governing equations of soft-matter quasicrystals of 12-fold symmetry7.2 Simplification of equations7.3 Dislocation and solution7.4 Oseen modification 7.5 Steady dynamic equations under Oseen modification in polar coordinate system7.6 Flow past a circular cylinder7.7 Three-dimensional equations of generalized dynamics of soft-matter quasicrystals with 12-fold symmetry7.8 Governing equations of generalized dynamics of incompressible soft-matter quasicrystals of 12-fold symmetry7.9 Conclusion and discussionChapter 8 Dynamics of 10-fold symmetrical soft-matter quasicrystals 8.1 Statement on soft-matter quasicrystals of 10-fold symmetry8.2 Two-dimensional basic equations of soft-matter quasicrystals of point groups 8.3Dislocation and elastic displacement field8.4 Probe on modification of dislocation solution by considering fluid effect 8.5 Transient dynamic analysis 8.6 Three-dimensional equations of soft-matter quasicrystals of point groups 8.7 Incompressible complex fluid model of soft-matter quasicrystals with 10-fold symmetry8.8 Conclusion and discussionChapter 9 Dynamics of possible soft-matter quasicrystals with 8-fold symmetry9.1 Dynamic equations of quasicrystals with 8-fold symmetry9.2 Dislocation and elastic displacement field9.3 Transient dynamic analysis9.4 Flow past a circular cylind...