Generalized Dynamics of Soft-Matter Quasicrystals

<div><div>Notations</div><div>Preface to the first edition</div><div>Preface to the second Edition&nbsp;</div><div>Chapter 1 Introduction to soft matter</div><div>Chapter 2 Discovery of soft-matter quasicrystals and their properties</div><div>2.1 Experimental observation of quasicrystalline phases in soft matter</div><div>2.2 Characters of soft-matter quasicrystals</div><div>2.3 Some concepts concerning possible generalized dynamics on soft-matter quasicrystals</div><div>2.4 First and second kinds of two-dimensional quasicrystals</div><div>2.5 Motivation of our discussion in the book</div><div>Chapter 3 Brief review on elasticity and hydrodynamics of solid quasicrystals</div><div>3.1 Introduction of the elasticity of quasicrystals, phonon and phason</div><div>3.2 Deformation tensor: strain and stress tensors</div><div>3.3 Equations of motion</div><div>3.4 Free energy density and elastic constants</div><div>3.5 Generalized Hooke’s law</div><div>3.6 Boundary conditions and initial conditions</div><div>3.7 Solutions of elasticity&nbsp;</div><div>3.8 Hydrodynamics of solid quasicrystals</div>3.9 Solution of hydrodynamics of solid quasicrystals&nbsp;</div><div>3.10 Summary</div><div>Chapter 4 Case study of equation of state of several structured fluids</div><div>4.1 Overview on equation of state in some structured fluids</div><div>4.2 Possible equations of state</div><div>4.3 Application to dynamics of soft-matter quasicrystals</div><div>4.4 The incompressible model of soft matter</div><div>Chapter 5 Poisson bracket method and equations of motion of soft-matter quasicrystals</div><div>5.1 Brownian motion and Langevin equation</div><div>5.2 Extended version of Langevin equation&nbsp;</div><div>5.3 Multivariable Langevin equation, coarse graining</div><div>5.4 Poisson brackets in condensed matter physics</div><div>5.5 Poisson brackets application to quasicrystals</div><div>5.6 Equations of motion of soft-matter quasicrystals</div><div>5.7 Poisson brackets based on Lie algebra</div><div>5.8 On solving governing equations</div><div><br></div><div>Chapter 6 Oseen theory and Oseen solution</div><div>6.1 Navier-Stokes equations</div><div>6.2 Stokes approximation</div><div>6.3 Stokes paradox&nbsp;</div><div>6.4 Oseen modification&nbsp;</div><div>6.5 Oseen steady solution of flow of incompressible fluid past cylinder&nbsp;</div><div>6.6 The reference meaning of Oseen theory and Oseen solution to the study in soft matter</div><div>Chapter 7 Dynamics of soft-matter quasicrystals with 12-fold symmetry</div><div>7.1 Two-dimensional governing equations of soft-matter quasicrystals of 12-fold symmetry</div><div>7.2 Simplification of equations</div><div>7.3 Dislocation and solution</div><div>7.4 Oseen modification&nbsp;</div><div>7.5 Steady dynamic equations under Oseen modification in polar coordinate system</div><div>7.6 Flow past a circular cylinder</div><div>7.7 Three-dimensional equations of generalized dynamics of soft-matter quasicrystals with 12-fold symmetry</div><div>7.8 Governing equations of generalized dynamics of incompressible soft-matter quasicrystals of 12-fold symmetry</div><div>7.9 Conclusion and discussion </div><div>Chapter 8 Dynamics of 10-fold symmetrical soft-matter quasicrystals&nbsp;</div><div>8.1 Statement on soft-matter quasicrystals of 10-fold symmetry</div><div>8.2 Two-dimensional basic equations of soft-matter quasicrystals of point groups&nbsp;&nbsp;</div><div>8.3Dislocation and elastic displacement field</div><div>8.4 Probe on modification of dislocation solution by considering fluid effect&nbsp;</div><div>8.5 Transient dynamic analysis&nbsp;</div><div>8.6 Three-dimensional equations of soft-matter quasicrystals of point groups&nbsp;&nbsp;</div><div>8.7 Incompressible complex fluid model of soft-matter quasicrystals with 10-fold symmetry</div><div>8.8 Conclusion and discussion</div>Chapter 9 Dynamics of possible soft-matter quasicrystals with 8-fold symmetry<div>9.1 Dynamic equations of quasicrystals with 8-fold symmetry</div><div>9.2 Dislocation and elastic displacement field</div><div>9.3 Transient dynamic analysis</div><div>9.4 Flow past a circular cylinder</div><div>9.5 Three-dimensional equations&nbsp;</div><div>9.6 Incompressible model of soft-matter quasicrystals with 8-fold symmetry</div><div>9.7 Solution example of incompressible model</div><div>9.8 Conclusion and discussion&nbsp;</div><div>Chapter 10 Dynamics of soft-matter quasicrystals with 18-fold symmetry</div><div>10.1 Six-dimensional embedded space</div><div>10.2 Elasticity of possible solid quasicrystals with 18-fold symmetry</div><div>10.3 Dynamics of soft-matter quasicrystals of 18-fold symmetry with point group&nbsp; &nbsp;</div><div>10.4 Static case of first and second phason fields&nbsp;</div><div>10.5 Dislocation and elastic displacement field</div><div>10.6 Discussion on transient dynamics analysis</div><div>10.7 Three-dimensional equations of generalized dynamics of soft matter quasicrystals of 18-fold symmetry with point group&nbsp; &nbsp;</div><div>10.8 Incompressible complex fluid model of soft-matter quasicrystals of 18-fold symmetry</div>10.9 Conclusion and discussion&nbsp;<div>Chapter 11 Dynamics of possible soft-matter quasicrystals with 7-, 9- and 14-fold symmetries</div><div>11.1 The possible 7- fold symmetry quasicrystals with point group&nbsp; &nbsp;of soft matter and the dynamic theory&nbsp;</div><div>11.2 The possible 9- fold symmetrical quasicrystals with point group&nbsp; of soft matter and their dynamics</div><div>11.3 Dislocation solution of 9-fold symmetry quasicrystals</div><div>11.4 The possible 14- fold symmetrical quasicrystals with point group&nbsp; of soft matter and their dynamics</div><div>11.5 The numerical solution of dynamics of 14-fold symmetrical quasicrystals of soft matter</div><div>11.6 Incompressible complex fluid model&nbsp;</div><div>11.7 Conclusion and discussion</div><div>Chapter 12 Re-discussion on symmetry breaking and elementary excitations concerning quasicrystals</div><div>Chapter 13 An application to thermodynamic stability of soft-matter quasicrystals</div><div>13.1 Introduction</div><div>13.2 Extended free energy of the quasicrystal system in soft matter</div><div>13.3 The positive definite nature of the rigidity matrix and the stability of the soft-matter quasicrystals with 12-fold symmetry</div><div>13.4 Comparison and examination</div><div>13.5 The stability of 8-fold symmetry soft-matter quasicrystals</div><div>13.6 The stability of 10-fold symmetry soft-matter quasicrystals</div><div>13.7 The stability of the 18-fold symmetry soft-matter quasicrystals</div><div>13.8 Conclusion</div><div><br></div><div><br></div><div>Chapter 14 Applications to device physics---photon band-gap of holographic photonic quasicrystals&nbsp;</div><div>14.1 Introduction</div><div>14.2 The design and formation of holographic quasicrystals&nbsp;</div><div>14.3 Band-gap of 8-fold quasicrystals&nbsp;</div><div>14.4 Band-gap of multi-fold complex quasicrystals&nbsp;</div><div>14.5 Fabrication of 10-fold holographic quasicrystals&nbsp;</div><div>14.6 Band-gap of choleteric liquid crystals</div><div>14.7 Conclusions</div><div>Chapter 15 Possible applications to general soft matter</div><div>15.1 A basis of dynamics of two-dimensional soft matter</div><div>15.2 The outline on governing equations of dynamics of soft matter</div><div>15.3 The modification and supplement to equations (15.2.1)</div><div>15.4&nbsp; Solving for the dynamics of soft matter</div><div>15.5 Conclusion and discussion</div><div>Chapter 16 Applications to smectic-A liquid crystals, dislocation and crack&nbsp;</div>16.1 Basic equations<div>16.2 The Kleman-Pershan solution of screw dislocation</div><div>16.3 Common fundamentals of discussion</div><div>16.4 The simplest and most direct solving method and additional boundary condition</div><div>16.5 The mathematical mistakes in the classical solution</div><div>16.6 The physical mistakes in the classical solution</div><div>16.7 Properties of the present solution</div><div>16.8 Solution on plastic crack</div><div><br></div><div>Chapter 17 Conclusion remarks</div>