Generalized Dynamics of Soft-Matter Quasicrystals: Mathematical Models, Solutions and Applications

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 discussion Chapter 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 s