Książki

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.

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 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 cylinder9.5 Three-dimensional equations 9.6 Incompressible model of soft-matter quasicrystals with 8-fold symmetry9.7 Solution example of incompressible model9.8 Conclusion and discussion Chapter 10 Dynamics of soft-matter quasicrystals with 18-fold symmetry10.1 Six-dimensional embedded space10.2 Elasticity of possible solid quasicrystals with 18-fold symmetry10.3 Dynamics of soft-matter quasicrystals of 18-fold symmetry with point group   10.4 Static case of first and second phason fields 10.5 Dislocation and elastic displacement field10.6 Discussion on transient dynamics analysis10.7 Three-dimensional equations of generalized dynamics of soft matter quasicrystals of 18-fold symmetry with point group   10.8 Incompressible complex fluid model of soft-matter quasicrystals of 18-fold symmetry10.9 Conclusion and discussion Chapter 11 Dynamics of possible soft-matter quasicrystals with 7-, 9- and 14-fold symmetries11.1 The possible 7- fold symmetry quasicrystals with point group   of soft matter and the dynamic theory 11.2 The possible 9- fold symmetrical quasicrystals with point group  of soft matter and their dynamics11.3 Dislocation solution of 9-fold symmetry quasicrystals11.4 The possible 14- fold symmetrical quasicrystals with point group  of soft matter and their dynamics11.5 The numerical solution of dynamics of 14-fold symmetrical quasicrystals of soft matter11.6 Incompressible complex fluid model 11.7 Conclusion and discussionChapter 12 Re-discussion on symmetry breaking and elementary excitations concerning quasicrystalsChapter 13 An application to thermodynamic stability of soft-matter quasicrystals13.1 Introduction13.2 Extended free energy of the quasicrystal system in soft matter13.3 The positive definite nature of the rigidity matrix and the stability of the soft-matter quasicrystals with 12-fold symmetry13.4 Comparison and examination13.5 The stability of 8-fold symmetry soft-matter quasicrystals13.6 The stability of 10-fold symmetry soft-matter quasicrystals13.7 The stability of the 18-fold symmetry soft-matter quasicrystals13.8 Conclusion

Chapter 14 Applications to device physics---photon band-gap of holographic photonic quasicrystals 14.1 Introduction14.2 The design and formation of holographic quasicrystals 14.3 Band-gap of 8-fold quasicrystals 14.4 Band-gap of multi-fold complex quasicrystals 14.5 Fabrication of 10-fold holographic quasicrystals 14.6 Band-gap of choleteric liquid crystals14.7 ConclusionsChapter 15 Possible applications to general soft matter15.1 A basis of dynamics of two-dimensional soft matter15.2 The outline on governing equations of dynamics of soft matter15.3 The modification and supplement to equations (15.2.1)15.4  Solving for the dynamics of soft matter15.5 Conclusion and discussionChapter 16 Applications to smectic-A liquid crystals, dislocation and crack 16.1 Basic equations16.2 The Kleman-Pershan solution of screw dislocation16.3 Common fundamentals of discussion16.4 The simplest and most direct solving method and additional boundary condition16.5 The mathematical mistakes in the classical solution16.6 The physical mistakes in the classical solution16.7 Properties of the present solution16.8 Solution on plastic crack
Chapter 17 Conclusion remarks