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.
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
Notations
Preface to the first edition
Preface to the second Edition
Chapter 1 Introduction to soft matter
Chapter 2 Discovery of soft-matter quasicrystals and their properties
2.1 Experimental observation of quasicrystalline phases in soft matter
2.2 Characters of soft-matter quasicrystals
2.3 Some concepts concerning possible generalized dynamics on soft-matter quasicrystals
2.4 First and second kinds of two-dimensional quasicrystals
2.5 Motivation of our discussion in the book
Chapter 3 Brief review on elasticity and hydrodynamics of solid quasicrystals
3.1 Introduction of the elasticity of quasicrystals, phonon and phason
3.2 Deformation tensor: strain and stress tensors
3.3 Equations of motion
3.4 Free energy density and elastic constants
3.5 Generalized Hooke's law
3.6 Boundary conditions and initial conditions
3.7 Solutions of elasticity
3.8 Hydrodynamics of solid quasicrystals
3.9 Solution of hydrodynamics of solid quasicrystals 3.10 Summary
Chapter 4 Case study of equation of state of several structured fluids
4.1 Overview on equation of state in some structured fluids
4.2 Possible equations of state
4.3 Application to dynamics of soft-matter quasicrystals
4.4 The incompressible model of soft matter
Chapter 5 Poisson bracket method and equations of motion of soft-matter quasicrystals
5.1 Brownian motion and Langevin equation
5.2 Extended version of Langevin equation
5.3 Multivariable Langevin equation, coarse graining
5.4 Poisson brackets in condensed matter physics
5.5 Poisson brackets application to quasicrystals
5.6 Equations of motion of soft-matter quasicrystals
5.7 Poisson brackets based on Lie algebra
5.8 On solving governing equations
Chapter 6 Oseen theory and Oseen solution
6.1 Navier-Stokes equations
6.2 Stokes approximation
6.3 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 matter
Chapter 7 Dynamics of soft-matter quasicrystals with 12-fold symmetry
7.1 Two-dimensional governing equations of soft-matter quasicrystals of 12-fold symmetry
7.2 Simplification of equations
7.3 Dislocation and solution
7.4 Oseen modification
7.5 Steady dynamic equations under Oseen modification in polar coordinate system
7.6 Flow past a circular cylinder
7.7 Three-dimensional equations of generalized dynamics of soft-matter quasicrystals with 12-fold symmetry
7.8 Governing equations of generalized dynamics of incompressible soft-matter quasicrystals of 12-fold symmetry
7.9 Conclusion and discussion
Chapter 8 Dynamics of 10-fold symmetrical soft-matter quasicrystals
8.1 Statement on soft-matter quasicrystals of 10-fold symmetry
8.2 Two-dimensional basic equations of soft-matter quasicrystals of point groups
8.3Dislocation and elastic displacement field
8.4 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 symmetry
8.8 Conclusion and discussion
Chapter 9 Dynamics of possible soft-matter quasicrystals with 8-fold symmetry9.1 Dynamic equations of quasicrystals with 8-fold symmetry
9.2 Dislocation and elastic displacement field
9.3 Transient dynamic analysis
9.4 Flow past a circular cylind...
Titel
Generalized Dynamics of Soft-Matter Quasicrystals
Untertitel
Mathematical Models, Solutions and Applications
EAN
9789811666285
Format
E-Book (pdf)
Hersteller
Genre
Veröffentlichung
17.01.2022
Digitaler Kopierschutz
Wasserzeichen
Dateigrösse
5.92 MB
Anzahl Seiten
235
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