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E-raamat: Generalized Dynamics of Soft-Matter Quasicrystals: Mathematical models and solutions

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Generalized Dynamics of Soft-Matter Quasicrystals: Mathematical models and solutionsSuurem pilt
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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.

Arvustused

The pioneering treatise presents a clear and lucid account of the generalized dynamics of soft-matter quasicrystals. The treatise may give vision and insight to fascinate a very new and growing area of research field. Certainly, it may appeal to researchers and engineers just interested or working on soft-matter quasicrystal. (M. Cengiz Dökmeci, zbMATH 1383.82002, 2018)

1 Introduction to Soft Matter in Brief
1(4)
References
4(1)
2 Discovery of Soft-Matter Quasicrystals and Their Properties
5(8)
2.1 Soft-Matter Quasicrystals with 12- and 18-Fold Symmetries
5(3)
2.2 Characters of Soft-Matter Quasicrystals
8(1)
2.3 Some Concepts Concerning Possible Hydrodynamics on Soft-Matter Quasicrystals
9(1)
2.4 First and Second Kinds of Two-Dimensional Quasicrystals
9(2)
2.5 Motivation of Our Discussion in the Book
11(2)
References
11(2)
3 Review in Brief on Elasticity and Hydrodynamics of Solid Quasicrystals
13(18)
3.1 Physical Basis of Elasticity of Quasicrystals, Phonons and Phasons
13(3)
3.2 Deformation Tensors
16(1)
3.3 Stress Tensors and Equations of Motion
17(2)
3.4 Free Energy Density and Elastic Constants
19(2)
3.5 Generalized Hooke's Law
21(1)
3.6 Boundary Conditions and Initial Conditions
22(1)
3.7 Solutions of Elasticity
23(1)
3.8 Generalized Hydrodynamics of Solid Quasicrystals
23(3)
3.8.1 Viscosity of Solid
24(1)
3.8.2 Generalized Hydrodynamics of Solid Quasicrystals
25(1)
3.9 Solution of Generalized Hydrodynamics of Solid Quasicrystals
26(1)
3.10 Conclusion and Discussion
27(4)
References
27(4)
4 Equation of State of Some Structured Fluids
31(4)
4.1 Overview on Equation of State in Some Fluids
31(2)
4.2 Possible Equations of State
33(1)
4.3 Applications to Hydrodynamics of Soft-Matter Quasicrystals
33(2)
References
34(1)
5 Poisson Brackets and Derivation of Equations of Motion of Soft-Matter Quasicrystals
35(16)
5.1 Brown Motion and Langevin Equation
35(1)
5.2 Extended Version of Langevin Equation
35(1)
5.3 Multivariate Langevin Equation, Coarse Graining
36(1)
5.4 Poisson Bracket Method in Condensed Matter Physics
37(2)
5.5 Application to Quasicrystals
39(1)
5.6 Equations of Motion of Soft-Matter Quasicrystals
39(5)
5.6.1 Generalized Langevin Equation
40(1)
5.6.2 Derivation of Hydrodynamic Equations of Soft-Matter Quasicrystals
40(4)
5.7 Poisson Brackets Based on Lie Algebra
44(7)
References
48(3)
6 Oseen Flow and Generalized Oseen Flow
51(18)
6.1 Navier--Stokes Equations
51(1)
6.2 Stokes Approximation
52(1)
6.3 Stokes Paradox
52(1)
6.4 Oseen Modification
52(1)
6.5 Oseen Steady Solution of Flow of Incompressible Fluid Past Cylinder
53(7)
6.6 Generalized Oseen Flow of Compressible Viscous Fluid Past a Circular Cylinder
60(9)
6.6.1 Introduction
60(1)
6.6.2 Basic Equations
60(1)
6.6.3 Flow Past a Circular Cylinder
61(1)
6.6.4 Quasi-Steady Analysis---Numerical Solution
62(4)
6.6.5 Conclusion and Discussion
66(1)
References
67(2)
7 Dynamics of Soft-Matter Quasicrystals with 12-Fold Symmetry
69(28)
7.1 Two-Dimensional Governing Equations of Soft-Matter Quasicrystals of 12-Fold Symmetry
69(4)
7.2 Simplification of Governing Equations
73(1)
7.2.1 Steady Dynamic Problem of Soft-Matter Quasicrystals with 12-Fold Symmetry
73(1)
7.2.2 Pure Fluid Dynamics
74(1)
7.3 Dislocation and Solution
74(2)
7.4 Generalized Oseen Approximation Under Condition of Lower Reynolds Number
76(1)
7.5 Steady Dynamic Equations Under Oseen Modification in Polar Coordinate System
77(2)
7.6 Flow Past a Circular Cylinder
79(9)
7.6.1 Two-Dimensional Flow Past Obstacle, Stokes Paradox
79(1)
7.6.2 Statement on the Problem
79(1)
7.6.3 A Flow Past a Cylinder
80(1)
7.6.4 Quasi-Steady Analysis---Numerical Solution by Finite Difference Method
80(1)
7.6.5 Numerical Results and Analysis
81(7)
7.7 Three-Dimensional Equations of Generalized Dynamics of Soft-Matter Quasicrystals with 12-Fold Symmetry
88(2)
7.8 Possible Crack Problem and Analysis
90(3)
7.9 Conclusion and Discussion
93(4)
References
94(3)
8 Dynamics of Possible Five and Tenfold Symmetrical Soft-Matter Quasicrystals
97(18)
8.1 Statement on Possible Soft-Matter Quasicrystals of Five and Tenfold Symmetries
97(1)
8.2 Two-Dimensional Basic Equations of Soft-Matter Quasicrystals of Point Groups 5, 5 and 10, 10
97(3)
8.3 Dislocations and Solutions
100(2)
8.4 Probe on Modification of Dislocation Solution by Considering Fluid Effect
102(2)
8.5 Transient Dynamic Analysis
104(6)
8.5.1 Specimen and Initial-Boundary Conditions
104(1)
8.5.2 Numerical Analysis and Results
105(5)
8.6 Three-Dimensional Equations of Point Group 10 mm Soft-Matter Quasicrystals
110(3)
8.7 Conclusion and Discussion
113(2)
References
114(1)
9 Dynamics of Possible Soft-Matter Quasicrystals of Eightfold Symmetry
115(20)
9.1 Basic Equations of Possible Soft-Matter Eightfold Symmetrical Quasicrystals
115(2)
9.2 Dislocation in Quasicrystals with Eightfold Symmetry
117(2)
9.2.1 Elastic Static Solution
117(2)
9.2.2 Modification Considering Fluid Effect
119(1)
9.3 Transient Dynamics Analysis
119(8)
9.3.1 Specimen
119(1)
9.3.2 Computational Results
120(1)
9.3.3 Analysis of Results
120(7)
9.3.4 Some Discussions
127(1)
9.4 Flow Past a Circular Cylinder
127(3)
9.5 Three-Dimensional Soft-Matter Quasicrystals with Eightfold Symmetry of Point Group 8 mm
130(2)
9.6 Conclusion and Discussion
132(3)
References
132(3)
10 Dynamics of Soft-Matter Quasicrystals with 18-Fold Symmetry
135(16)
10.1 Six-Dimensional Embedded Space
135(1)
10.2 Elasticity of Possible Solid Quasicrystals with 18-Fold Symmetry
136(2)
10.3 Dynamics of Quasicrystals of 18-Fold Symmetry with Point Group 18 mm
138(4)
10.4 The Steady Dynamic and Static Case of First and Second Phason Fields
142(2)
10.5 Dislocations and Solutions
144(3)
10.5.1 The Zero-Order Approximate Solution of Dislocations of Soft-Matter Quasicrystals with 18-Fold Symmetry
144(3)
10.5.2 Modification to the Solution (10.5.3)--(10.5.6) Considering Fluid Effect
147(1)
10.6 Discussion on Transient Dynamics Analysis
147(2)
10.7 Other Solutions
149(2)
References
149(2)
11 The Possible 7-, 9- and 14-Fold Symmetry Quasicrystals in Soft Matter
151(14)
11.1 The Possible Sevenfold Symmetry Quasicrystals with Point Group 7m of Soft Matter and the Dynamic Theory
151(3)
11.2 The Possible Ninefold Symmetrical Quasicrystals with Point Group 9m of Soft Matter and Their Dynamics
154(3)
11.3 Dislocation Solutions of the Possible Ninefold Symmetrical Quasicrystals of Soft Matter
157(4)
11.4 The Possible 14-Fold Symmetrical Quasicrystals with Point Group 14mm of Soft Matter and Their Dynamics
161(2)
11.5 The Solutions and Possible Solutions of Statics and Dynamics of 7- and 14-Fold Symmetrical Quasicrystals of Soft Matter
163(1)
11.6 Conclusion and Discussion
163(2)
References
164(1)
12 An Application of Analytic Methods to Smectic A Liquid Crystals, Dislocation and Crack
165(14)
12.1 Basic Equations
165(2)
12.2 The Kleman--Pershan Solution of Screw Dislocation
167(1)
12.3 Common Fundamentals of Discussion
168(1)
12.4 The Simplest and Most Direct Solving Way and Additional Boundary Condition
168(2)
12.5 Mathematical Mistakes of the Classical Solution
170(1)
12.6 The Physical Mistakes of the Classical Solution
171(1)
12.7 Meaning of the Present Solution
172(1)
12.8 Solution of Plastic Crack
173(6)
References
176(3)
13 Conclusion Remarks
179(2)
Index 181
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 9th and 10th National Committee of the Peoples 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 1st 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. 
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