Dynamics of Self Organized and Self Assembled Structures 1st Edition by Rashmi Desai, Raymond Kapral ISBN 052188361X 978-0521883610

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Product details: 

ISBN 10: 052188361X 

ISBN 13: 978-0521883610

Author: Rashmi C. Desai, Raymond Kapral 
Physical and biological systems driven out of equilibrium may spontaneously evolve to form spatial structures. In some systems molecular constituents may self-assemble to produce complex ordered structures. This book describes how such pattern formation processes occur and how they can be modeled. Experimental observations are used to introduce the diverse systems and phenomena leading to pattern formation. The physical origins of various spatial structures are discussed, and models for their formation are constructed. In contrast to many treatments, pattern-forming processes in nonequilibrium systems are treated in a coherent fashion. The book shows how near-equilibrium and far-from-equilibrium modeling concepts are often combined to describe physical systems. This inter-disciplinary book can form the basis of graduate courses in pattern formation and self-assembly. It is a useful reference for graduate students and researchers in a number of disciplines, including condensed matter science, nonequilibrium statistical mechanics, nonlinear dynamics, chemical biophysics, materials science, and engineering.

Table of contents: 

1. Self-organized and self-assembled structures

2. Order parameter, free energy, and phase transitions

2.1 Mean field theory
2.2 Order parameter
2.3 Order parameter and its spatial correlations
3. Free energy functional

3.1 Ginzburg–Landau–Wilson free energy functional
3.2 Interfacial tension and the coefficient κ
3.3 Landau expansion of the local free energy density
4. Phase separation kinetics

4.1 Kinetics of phase ordering and phase separation
4.2 Dynamical scaling
5. Langevin model for nonconserved order parameter systems

5.1 Langevin model A
5.2 Model A reaction–diffusion system
6. Langevin model for conserved order parameter systems

6.1 Langevin model B
6.2 Critical quench in a model B system
6.3 Off-critical quench in a model B system
6.4 Model B interfacial structure
7. Interface dynamics at late times

7.1 Model B interface
7.2 Model A interface
8. Domain growth and structure factor for model B

8.1 Domain growth law
8.2 Porod’s law and other consequences of sharp interfaces
8.3 Small-k behavior of S(k, τ)
9. Order parameter correlation function

9.1 Dynamic scaling and Ohta–Jasnow–Kawasaki theory
9.2 Other theories
9.3 Extension to model B
10. Vector order parameter and topological defects

11. Liquid crystals

11.1 Nematic liquid crystals
11.2 Smectic liquid crystals
12. Lifshitz–Sloyozov–Wagner theory

12.1 Gibbs–Thomson boundary condition
12.2 LSW analysis for evaporating and growing droplets
13. Systems with long-range repulsive interactions

13.1 Langmuir monolayers
13.2 Block copolymers
13.3 Langevin models A and B including LRRI
14. Kinetics of systems with competing interactions

14.1 Equilibrium phase diagram
14.2 Linear stability analysis
14.3 Evolution of ψ(x, τ) during phase separation
15. Competing interactions and defect dynamics

15.1 Polydisperse systems
15.2 Monodisperse coarsening and defect dynamics
16. Diffusive rough interfaces

16.1 KPZ equation
16.2 Interface width scaling
16.3 Connection between Langevin and KPZ equations
16.4 Dynamics of curved interfaces
17. Morphological instability in solid films

17.1 Lattice misfit
17.2 Elastic free energy functional
17.3 Evolution equations for the morphological instability
17.4 Solution of mechanical equilibrium equations
17.5 Linear stability analysis
18. Propagating chemical fronts

18.1 Propagation into a metastable state
18.2 Propagation into an unstable state
19. Transverse front instabilities

19.1 Planar traveling fronts
19.2 Kuramoto–Sivashinsky equation
19.3 Linear stability analysis and front dynamics
20. Cubic autocatalytic fronts

20.1 Analysis of front instability
20.2 Experimental observation of front instability
21. Competing interactions and front repulsion

21.1 Competing interactions in bistable media
21.2 Front repulsion
22. Labyrinthine patterns in chemical systems

22.1 Interface dynamics in two dimensions
22.2 Transverse instabilities of planar fronts
22.3 Three-dimensional patterns
23. Turing patterns

23.1 Turing bifurcation conditions
23.2 Pattern selection
23.3 Steady-state patterns
23.4 Stripe patterns
23.5 Time-dependent amplitude equation for stripe patterns
24. Excitable media

24.1 Traveling waves in excitable media
24.2 Eikonal equation
24.3 Spiral wave solution
24.4 Kinematic theory
24.5 Spiral wave meander
24.6 Scroll wave dynamics
25. Oscillatory media and complex Ginzburg–Landau equation

25.1 Hopf bifurcation
25.2 Complex Ginzburg–Landau equation
25.3 Stability analysis of CGL equation
25.4 Spatiotemporal chaos
26. Spiral waves and defect turbulence

26.1 Core instability
26.2 Defect-mediated turbulence
26.3 Other spatiotemporal states
26.4 Scroll wave solutions
26.5 Twisted filaments
27. Complex oscillatory and chaotic media

27.1 Spiral waves and line defects
27.2 Archimedean spiral splay field and line defects
27.3 Line defect dynamics and spiral core motion
27.4 Turbulence in chaotic systems
27.5 Defect-mediated turbulence
28. Resonantly forced oscillatory media

28.1 2:1 resonance
28.2 Other strong resonances
28.3 Complex front dynamics
29. Nonequilibrium patterns in laser-induced melting

29.1 Laser-induced melting
29.2 Static solutions
29.3 Linear stability analysis
29.4 Phase diffusion description and lamellar stability
30. Reaction dynamics and phase segregation

30.1 Phase segregation in reacting systems
30.2 Protein-induced pattern formation in biomembranes
31. Active materials

31.1 Active nematics
31.2 Active Langmuir monolayers

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Rashmi Desai,Raymond Kapral,Dynamics of Self,Assembled Structures