Dynamics of self-organized and self-assembled structures

Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 15
1 Self-organized and self-assembled structures......Page 17
2 Order parameter, free energy, and phase transitions......Page 22
2.1.1 Binary mixtures: alloys, fluids, and polymer blends......Page 24
2.1.2 Para-ferromagnetic transition......Page 27
2.1.3 Liquid–vapor transition......Page 28
2.2 Order parameter......Page 30
2.3 Order parameter and its spatial correlations......Page 32
3 Free energy functional......Page 36
3.1 Ginzburg–Landau–Wilson free energy functional......Page 37
3.2 Interfacial tension and the coefficient κ......Page 38
3.3 Landau expansion of the local free energy density......Page 39
4.1 Kinetics of phase ordering and phase separation......Page 41
4.2 Dynamical scaling......Page 45
5.1 Langevin model A......Page 48
5.2 Model A reaction–diffusion system......Page 50
6.1 Langevin model B......Page 54
6.2 Critical quench in a model B system......Page 55
6.3 Off-critical quench in a model B system......Page 57
6.4 Model B interfacial structure......Page 61
7.1 Model B interface......Page 66
7.2 Model A interface......Page 72
Appendix: Derivation of equation for interface velocity......Page 73
8.1 Domain growth law......Page 76
8.2 Porod’s law and other consequences of sharp interfaces......Page 78
8.3 Small-k behavior of S(k, τ)......Page 80
9 Order parameter correlation function......Page 81
9.1 Dynamic scaling and Ohta–Jasnow–Kawasaki theory......Page 82
9.2 Other theories......Page 84
9.3 Extension to model B......Page 85
10 Vector order parameter and topological defects......Page 87
11 Liquid crystals......Page 91
11.1 Nematic liquid crystals......Page 92
11.2 Smectic liquid crystals......Page 98
12 Lifshitz–Slyozov–Wagner theory......Page 103
12.1 Gibbs–Thomson boundary condition......Page 104
12.2 LSW analysis for evaporating and growing droplets......Page 106
13 Systems with long-range repulsive interactions......Page 112
13.1 Langmuir monolayers......Page 113
13.2 Block copolymers......Page 116
13.3 Langevin models A and B including LRRI......Page 118
14.1 Equilibrium phase diagram......Page 123
14.2 Linear stability analysis......Page 128
14.2.1 Analysis in the absence of LRRI......Page 129
14.3 Evolution of ψ (x,  τ) during phase separation......Page 132
15 Competing interactions and defect dynamics......Page 136
15.1 Polydisperse systems......Page 137
15.2 Monodisperse coarsening and defect dynamics......Page 138
16.1 KPZ equation......Page 144
16.2 Interface width scaling......Page 147
16.3 Connection between Langevin and KPZ equations......Page 149
16.4 Dynamics of curved interfaces......Page 153
17 Morphological instability in solid films......Page 156
17.1 Lattice misfit......Page 157
17.2 Elastic free energy functional......Page 161
17.3 Evolution equations for the morphological instability......Page 166
17.4 Solution of mechanical equilibrium equations......Page 168
17.5 Linear stability analysis......Page 170
18 Propagating chemical fronts......Page 173
18.1 Propagation into a metastable state......Page 174
18.2 Propagation into an unstable state......Page 176
19.1 Planar traveling fronts......Page 180
19.2 Kuramoto–Sivashinsky equation......Page 182
19.3 Linear stability analysis and front dynamics......Page 185
20 Cubic autocatalytic fronts......Page 188
20.1 Analysis of front instability......Page 190
20.2 Experimental observation of front instability......Page 192
21.1 Competing interactions in bistable media......Page 195
21.2 Front repulsion......Page 200
22.1 Interface dynamics in two dimensions......Page 205
22.2 Transverse instabilities of planar fronts......Page 210
22.3 Three-dimensional patterns......Page 213
23 Turing patterns......Page 217
23.1 Turing bifurcation conditions......Page 218
23.2 Pattern selection......Page 222
23.4 Stripe patterns......Page 224
23.5 Time-dependent amplitude equation for stripe patterns......Page 226
24 Excitable media......Page 228
24.1 Traveling waves in excitable media......Page 231
24.2 Eikonal equation......Page 233
24.3 Spiral wave solution......Page 234
24.4 Kinematic theory......Page 235
24.5 Spiral wave meander......Page 238
24.6 Scroll wave dynamics......Page 242
25 Oscillatory media and complex Ginzburg–Landau equation......Page 248
25.2 Complex Ginzburg–Landau equation......Page 249
25.3.1 Homogeneous limit cycle......Page 253
25.4 Spatiotemporal chaos......Page 255
26 Spiral waves and defect turbulence......Page 258
26.1 Core instability......Page 259
26.2 Defect-mediated turbulence......Page 260
26.3 Other spatiotemporal states......Page 263
26.4 Scroll wave solutions......Page 264
26.5 Twisted filaments......Page 265
27 Complex oscillatory and chaotic media......Page 269
27.1 Spiral waves and line defects......Page 270
27.2 Archimedean spiral splay field and line defects......Page 272
27.3 Line defect dynamics and spiral core motion......Page 277
27.4 Turbulence in chaotic systems......Page 278
27.5 Defect-mediated turbulence......Page 280
28 Resonantly forced oscillatory media......Page 284
28.1 2:1 resonance......Page 288
28.2 Other strong resonances......Page 291
28.3 Complex front dynamics......Page 292
29.1 Laser-induced melting......Page 294
29.2 Static solutions......Page 297
29.2.1 Strong segregation limit......Page 298
29.2.2 Weak segregation limit......Page 300
29.3 Linear stability analysis......Page 301
29.4 Phase diffusion description and lamellar stability......Page 302
30.1 Phase segregation in reacting systems......Page 306
30.2 Protein-induced pattern formation in biomembranes......Page 309
31 Active materials......Page 315
31.1 Active nematics......Page 316
31.2 Active Langmuir monolayers......Page 319
References......Page 323
Index......Page 340