Generalized Dynamics of Soft-Matter Quasicrystals (2^nd Ed., 2nd ed. 2022) Mathematical Models, Solutions and Applications Springer Series in Materials Science Series, Vol. 260

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.

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

9.1 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 cylinder

9.5 Three-dimensional equations 

9.6 Incompressible model of soft-matter quasicrystals with 8-fold symmetry

9.7 Solution example of incompressible model

9.8 Conclusion and discussion 

Chapter 10 Dynamics of soft-matter quasicrystals with 18-fold symmetry

10.1 Six-dimensional embedded space

10.2 Elasticity of possible solid quasicrystals with 18-fold symmetry

10.3 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 field

10.6 Discussion on transient dynamics analysis

10.7 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 symmetry

Chapter 11 Dynamics of possible soft-matter quasicrystals with 7-, 9- and 14-fold symmetries

11.1 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 dynamics

11.3 Dislocation solution of 9-fold symmetry quasicrystals

11.4 The possible 14- fold symmetrical quasicrystals with point group  of soft matter and their dynamics

11.5 The numerical solution of dynamics of 14-fold symmetrical quasicrystals of soft matter

11.6 Incompressible complex fluid model 

11.7 Conclusion and discussion

Chapter 12 Re-discussion on symmetry breaking and elementary excitations concerning quasicrystals

Chapter 13 An application to thermodynamic stability of soft-matter quasicrystals

13.1 Introduction

13.2 Extended free energy of the quasicrystal system in soft matter

13.3 The positive definite nature of the rigidity matrix and the stability of the soft-matter quasicrystals with 12-fold symmetry

13.4 Comparison and examination

13.5 The stability of 8-fold symmetry soft-matter quasicrystals

13.6 The stability of 10-fold symmetry soft-matter quasicrystals

13.7 The stability of the 18-fold symmetry soft-matter quasicrystals

13.8 Conclusion

Chapter 14 Applications to device physics---photon band-gap of holographic photonic quasicrystals 

14.1 Introduction

14.2 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 crystals

14.7 Conclusions

Chapter 15 Possible applications to general soft matter

15.1 A basis of dynamics of two-dimensional soft matter

15.2 The outline on governing equations of dynamics of soft matter

15.3 The modification and supplement to equations (15.2.1)

15.4  Solving for the dynamics of soft matter

15.5 Conclusion and discussion

Chapter 16 Applications to smectic-A liquid crystals, dislocation and crack 

16.2 The Kleman-Pershan solution of screw dislocation

16.3 Common fundamentals of discussion

16.4 The simplest and most direct solving method and additional boundary condition

16.5 The mathematical mistakes in the classical solution

16.6 The physical mistakes in the classical solution

16.7 Properties of the present solution

16.8 Solution on plastic crack

Chapter 17 Conclusion remarks

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.