Dynamics of Self-Organized and Self-Assembled StructuresPhysical 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. |
Contents
1 Selforganized and selfassembled structures | 1 |
2 Order parameter free energy and phase transitions | 6 |
3 Free energy functional | 20 |
4 Phase separation kinetics | 25 |
5 Langevin model for nonconserved order parameter systems | 32 |
6 Langevin model for conserved order parameter systems | 38 |
7 Interface dynamics at late times | 50 |
8 Domain growth and structure factor for model B | 60 |
18 Propagating chemical fronts | 157 |
19 Transverse front instabilities | 164 |
20 Cubic autocatalytic fronts | 172 |
21 Competing interactions and front repulsion | 179 |
22 Labyrinthine patterns in chemical systems | 189 |
23 Turing patterns | 201 |
24 Excitable media | 212 |
25 Oscillatory media and complex GinzburgLandau equation | 232 |
9 Order parameter correlation function | 65 |
10 Vector order parameter and topological defects | 71 |
11 Liquid crystals | 75 |
12 LifshitzSlyozovWagner theory | 87 |
13 Systems with longrange repulsive interactions | 96 |
14 Kinetics of systems with competing interactions | 107 |
15 Competing interactions and defect dynamics | 120 |
16 Diffusively rough interfaces | 128 |
17 Morphological instability in solid films | 140 |
26 Spiral waves and defect turbulence | 242 |
27 Complex oscillatory and chaotic media | 253 |
28 Resonantly forced oscillatory media | 268 |
29 Nonequilibrium patterns in laserinduced melting | 278 |
30 Reaction dynamics and phase segregation | 290 |
31 Active materials | 299 |
| 307 | |
| 324 | |
Common terms and phrases
American Physical Society amplitude analysis autocatalysis Burgers vector CGL equation Chapter chemical coarsening complex concentration field coordinate Copyright core correlation function curvature curve defined diffusion coefficient dimensionless disclination domain droplet dynamics eigenvalue energy density equation of motion equilibrium evolution field figure filament film find first fixed point fluctuations free energy density free energy functional front velocity gradient growth homogeneous Hopf bifurcation instability interface Kapral kinetics Langevin equation leads line defect linear liquid crystal long-range repulsive interactions mean field mechanical equilibrium molecules monolayers morphology nematic nonequilibrium nonlinear nonzero obtain off-critical order parameter oscillatory perturbations phase diagram phase separation Phys planar front profile propagating reaction reaction—diffusion equation regime region Reprinted Figure result rotating satisfies scalar segregation shown in Fig simulations solution spatial spatiotemporal spinodal spinodal decomposition spiral wave stripe surface symmetry temperature tensor term thermodynamic topological topological defects transition variables vector velocity wavenumber zero