Pattern formation and dynamics in nonequilibrium systems:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
|
| Edition: | 1. publ. |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017143551&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XVI, 535 S. Ill., graph. Darst. |
| ISBN: | 9780521770507 |
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| 100 | 1 | |a Cross, Michael |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Pattern formation and dynamics in nonequilibrium systems |c Michael Cross ; Henry Greenside |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2009 | |
| 300 | |a XVI, 535 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
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|---|---|
| DE-BY-TUM_katkey | 1734977 |
| DE-BY-TUM_location | 02 |
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| adam_text | Contents
Preface
page
xiii
Introduction
1
1.1
The big picture: why is the Universe not boring?
2
1.2
Convection: a first example of a nonequilibrium system
3
1.3
Examples of nonequilibrium patterns and dynamics
10
1.3.1
Natural patterns
10
1.3.2
Prepared patterns
20
1.3.3
What are the interesting questions?
35
1.4
New features of pattern-forming systems
38
1.4.1
Conceptual differences
38
1.4.2
New properties
43
1.5
A strategy for studying pattern-forming nonequilibrium
systems
44
1.6
Nonequilibrium systems not discussed in this book
48
1.7
Conclusion
49
1.8
Further reading
50
Linear instability: basics
56
2.1
Conceptual framework for a linear stability analysis
57
2.2
Linear stability analysis of a pattern-forming system
63
2.2.1
One-dimensional Swift-Hohenberg equation
63
2.2.2
Linear stability analysis
64
2.2.3
Growth rates and instability diagram
67
2.3
Key steps of a linear stability analysis
69
2.4
Experimental investigations of linear stability
70
2.4.1
General remarks
70
2.4.2
Taylor-Couette instability
74
VII
viii Contents
2.5
Classification for linear
instabilities of a uniform state
75
2.5.1
Туре
-I
instability
77
2.5.2
Type
-П
instability
79
2.5.3
Type-III instability
80
2.6
Role of symmetry in a linear stability analysis
81
2.6.1
Rotationally invariant systems
82
2.6.2
Uniaxial
systems
84
2.6.3 Anisotropie
systems
86
2.6.4
Formal discussion
86
2.7
Conclusions
88
2.8
Further reading
88
3
Linear instability: applications
96
3.1
Turing instability
96
3.1.1
Reaction-diffusion equations
97
3.1.2
Linear stability analysis
99
3.1.3
Oscillatory instability
108
3.2
Realistic chemical systems
109
3.2.1
Experimental apparatus
109
3.2.2
Evolution equations
110
3.2.3
Experimental results
116
3.3
Conclusions
119
3.4
Further reading
120
4
Nonlinear states
126
4.1
Nonlinear saturation
129
4.1.1
Complex amplitude
130
4.1.2
Bifurcation theory
134
4.1.3
Nonlinear stripe state of the Swift-Hohenberg equation
137
4.2
Stability balloons
139
4.2.1
General discussion
139
4.2.2 Busse
balloon for
Rayleigh-Bénard
convection
147
4.3
Two-dimensional lattice states
152
4.4
Non-ideal states
158
4.4.1
Realistic patterns
158
4.4.2
Topological defects
160
4.4.3
Dynamics of defects
164
4.5
Conclusions
165
4.6
Further reading
166
Contents ix
Models 173
5.1 Swift-Hohenberg
model
175
5.1.1
Heuristic derivation
176
5.1.2
Properties
179
5.1.3
Numerical simulations
183
5.1.4
Comparison with experimental systems
185
5.2
Generalized Swift-Hohenberg models
187
5.2.1
Non-
symmetric model
187
5.2.2
Nonpotential models
188
5.2.3
Models with mean flow
188
5.2.4
Model for rotating convection
190
5.2.5
Model for quasicrystalline patterns
192
5.3
Order-parameter equations
192
5.4
Complex Ginzburg-Landau equation
196
5.5
Kuramoto-Sivashinsky equation
197
5.6
Reaction-diffusion models
199
5.7
Models that are discrete in space, time, or value
201
5.8
Conclusions
201
5.9
Further reading
202
One-dimensional amplitude equation
208
6.1
Origin and meaning of the amplitude
211
6.2
Derivation of the amplitude equation
214
6.2.1
Phenomenological derivation
214
6.2.2
Deduction of the amplitude-equation parameters
217
6.2.3
Method of multiple scales
218
6.2.4
Boundary conditions for the amplitude equation
219
6.3
Properties of the amplitude equation
221
6.3.1
Universality and scales
221
6.3.2
Potential dynamics
224
6.4
Applications of the amplitude equation
226
6.4.1
Lateral boundaries
226
6.4.2 Eckhaus
instability
230
6.4.3
Phase dynamics
234
6.5
Limitations of the amplitude-equation formalism
237
6.6
Conclusions
238
6.7
Further reading
239
Amplitude equations for two-dimensional patterns
244
7.1
Stripes in rotationally invariant systems
246
7.1.1
Amplitude equation
246
7.1.2
Boundary conditions
248
Contents
7.1.3 Potential 249
7.1.4
Stability balloon
250
7.1.5 Phase
dynamics
252
7.2
Stripes in anisotropic systems
253
7.2.1
Amplitude equation
253
7.2.2
Stability balloon
254
7.2.3
Phase dynamics
255
7.3
Superimposed stripes
255
7.3.1
Amplitude equations
256
7.3.2
Competition between stripes and lattices
261
7.3.3
Hexagons in the absence of field-inversion symmetry
264
7.3.4
Spatial variations
269
7.3.5
Cross-stripe instability
270
7.4
Conclusions
272
7.5
Further reading
273
Defects and fronts
279
8.1
Dislocations
281
8.1.1
Stationary dislocation
283
8.1.2
Dislocation dynamics
285
8.1.3
Interaction of dislocations
289
8.2
Grain boundaries
290
8.3
Fronts
296
8.3.1
Existence of front solutions
296
8.3.2
Front selection
303
8.3.3
Wave-number selection
307
8.4
Conclusions
309
8.5
Further reading
309
Patterns far from threshold
315
9.1
Stripe and lattice states
317
9.1.1 Goldstone
modes and phase dynamics
318
9.1.2
Phase diffusion equation
320
9.1.3
Beyond the phase equation
327
9.1.4
Wave-number selection
331
9.2
Novel patterns
337
9.2.1
Pinning and disorder
338
9.2.2
Localized structures
340
9.2.3
Patterns based on front properties
342
9.2.4
Spatiotemporal
chaos
345
9.3
Conclusions
352
9.4
Further reading
353
Contents xi
10
Oscillatory patterns
358
10.1
Convective and absolute instability
360
10.2
States arising from a type-III-o instability
363
10.2.1
Phenomenology
363
10.2.2
Amplitude equation
365
10.2.3
Phase equation
368
10.2.4
Stability balloon
370
10.2.5
Defects: sources, sinks, shocks, and spirals
372
10.3
Unidirectional waves in a type-I-o system
379
10.3.1
Amplitude equation
380
10.3.2
Criterion for absolute instability
382
10.3.3
Absorbing boundaries
383
10.3.4
Noise-sustained structures
384
10.3.5
Local modes
386
10.4
Bidirectional waves in a type-I-o system
388
10.4.1
Traveling and standing waves
389
10.4.2
Onset in finite geometries
390
10.4.3
Nonlinear waves with reflecting boundaries
392
10.5
Waves in a two-dimensional type-I-o system
393
10.6
Conclusions
395
10.7
Further reading
396
11
Excitable media
401
11.1
Nerve fibers and heart muscle
404
11.1.1
Hodgkin-Huxley model of action potentials
404
11.1.2
Models of electrical signaling in the heart
411
11.1.3
FitzHugh-Nagumo model
413
11.2
Oscillatory or excitable
416
11.2.1
Relaxation oscillations
419
11.2.2
Excitable dynamics
420
421
424
426
430
430
436
437
439
439
441
11.3
Front propagation
11.4
Pulses
11.5
Waves
11.6
Spirals
11.6.1
Structure
11.6.2
Formation
11.6.3
Instabilities
11.6.4
Three dimensions
11.6.5
Application to heart arrhythmias
11.7
Further
reading
xii Contents
12
Numerical methods
445
12.1
Introduction
445
12.2
Discretization of fields and equations
447
12.2.1
Finitely many operations on a finite amount of data
447
12.2.2
The discretization of continuous fields
449
12.2.3
The discretization of equations
451
12.3
Time integration methods for pattern-forming systems
457
12.3.1
Overview
457
12.3.2
Explicit methods
460
12.3.3
Implicit methods
465
12.3.4
Operator splitting
470
12.3.5
How to choose the spatial and temporal resolutions
473
12.4
Stationary states of a pattern-forming system
475
12.4.1
Iterative methods
476
12.4.2
Newton s method
477
12.5
Conclusion
482
12.6
Further reading
485
Appendix
1
Elementary bifurcation theory
496
Appendix
2
Multiple-scales perturbation theory
503
Glossary
520
References
526
Index
531
|
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| id | DE-604.BV035339231 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:28:52Z |
| institution | BVB |
| isbn | 9780521770507 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017143551 |
| oclc_num | 268793786 |
| open_access_boolean | |
| owner | DE-703 DE-384 DE-19 DE-BY-UBM DE-29T DE-91G DE-BY-TUM DE-11 |
| owner_facet | DE-703 DE-384 DE-19 DE-BY-UBM DE-29T DE-91G DE-BY-TUM DE-11 |
| physical | XVI, 535 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spellingShingle | Cross, Michael Greenside, Henry Pattern formation and dynamics in nonequilibrium systems Pattern formation (Physical sciences) Nichtgleichgewicht (DE-588)4171730-2 gnd Selbstorganisation (DE-588)4126830-1 gnd Musterbildung (DE-588)4137934-2 gnd |
| subject_GND | (DE-588)4171730-2 (DE-588)4126830-1 (DE-588)4137934-2 |
| title | Pattern formation and dynamics in nonequilibrium systems |
| title_auth | Pattern formation and dynamics in nonequilibrium systems |
| title_exact_search | Pattern formation and dynamics in nonequilibrium systems |
| title_full | Pattern formation and dynamics in nonequilibrium systems Michael Cross ; Henry Greenside |
| title_fullStr | Pattern formation and dynamics in nonequilibrium systems Michael Cross ; Henry Greenside |
| title_full_unstemmed | Pattern formation and dynamics in nonequilibrium systems Michael Cross ; Henry Greenside |
| title_short | Pattern formation and dynamics in nonequilibrium systems |
| title_sort | pattern formation and dynamics in nonequilibrium systems |
| topic | Pattern formation (Physical sciences) Nichtgleichgewicht (DE-588)4171730-2 gnd Selbstorganisation (DE-588)4126830-1 gnd Musterbildung (DE-588)4137934-2 gnd |
| topic_facet | Pattern formation (Physical sciences) Nichtgleichgewicht Selbstorganisation Musterbildung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017143551&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT crossmichael patternformationanddynamicsinnonequilibriumsystems AT greensidehenry patternformationanddynamicsinnonequilibriumsystems |
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