Pattern formation: an introduction to methods
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2006
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | x, 422 Seiten Illustrationen, Diagramme |
| ISBN: | 0521817501 9780521817509 |
Internformat
MARC
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| 100 | 1 | |a Hoyle, Rebecca B. |e Verfasser |0 (DE-588)132328925 |4 aut | |
| 245 | 1 | 0 | |a Pattern formation |b an introduction to methods |c Rebecca B. Hoyle |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2006 | |
| 300 | |a x, 422 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-014621064 | ||
Datensatz im Suchindex
| _version_ | 1804135098131415040 |
|---|---|
| adam_text | Contents
juce
page
ix
What are natural patterns?
1
1.1
Convection
3
1.2
Reaction-diffusion systems
12
1.3
Faraday waves
20
1.4
Outline of the rest of the book
22
A bit of bifurcation theory
23
2.1
Flows, stationary points and periodic orbits
23
2.2
Local bifurcations from stationary points
30
2.3
Normal forms for bifurcations
38
2.4
Codimension-one bifurcations
38
A bit of group theory
52
3.1
Groups
52
3.2
Subgroups, quotient groups and conjugacy
57
3.3
Mappings of groups
61
3.4
Products of groups
64
3.5
Lie groups
67
3.6
Representations of groups
68
3.7
Characters
77
3.8
Isotypic decomposition
82
Bifurcations with symmetry
85
4.1
Ordinary differential equations with spatial symmetry
85
4.2
The equivariant branching lemma
93
4.3
Bifurcations in a box
97
4.4 Hopf
bifurcations with symmetry
116
4.5
Heteroclinic cycles
122
4.6
Appendix: Proofs
131
vi
Contents
5 Simple
lattice
patterns
134
5.1
Lattices and lattice patterns
134
5.2
Bifurcations on a lattice
136
5.3
Steady bifurcation on a square lattice
141
5.4
Steady bifurcation on a hexagonal lattice
147
5.5
Roll/stripe solutions
157
5.6
The Kiippers-Lortz instability
158
5.7 Hopf
bifurcation on a one-dimensional lattice
161
6
Superlattices, hidden symmetries and other complications
168
6.1 Superlattice
patterns
168
6.2
Mode interactions
174
6.3
Spatial-period-multiplying bifurcations
178
6.4
Quasipatterns
182
6.5
Pseudoscalar actions of E{
2) 187
6.6
Hidden symmetries
190
6.7
Hidden symmetries and reflecting boundary conditions
198
7
Spatial modulation and envelope equations
209
7.1
Envelope equations for specific models
209
7.2
Envelope equations and symmetries
216
7.3
Free energies or Lyapunov functionals
224
7.4
Conservation of angular momentum
227
7.5 Hopf
bifurcations and the complex Ginzburg—Landau equation
232
7.6
Travelling waves and the nonlinear
Schrödinger
equation
234
7.7
Modulated hexagons
238
8
Instabilities of stripes and travelling plane waves
243
8.1
Universal instabilities of stripes
243
8.2
The
Eckhaus
instability
247
8.3
The zigzag instability
260
8.4
A general theory of phase dynamics
266
8.5
The cross-roll instability
274
8.6
Prandtl-number-dependent instabilities of convection rolls
277
8.7
The Benjamin-Feir instability
286
9
More instabilities of patterns
292
9.1
Instabilities of two-dimensional steady patterns
292
9.2
Drift instabilities
306
9.3
Galilean
invariance
and flat modes
315
9.4
Conservative systems and flat modes
319
10
Spirals, defects and spiral defect chaos
325
10.1
Types of isolated defect
325
10.2
Dislocation of a roll pattern
327
Contents
vii
10.3 Amplitude
grain boundaries
337
10.4
Domain boundaries between different patterns in systems
with a free energy
342
10.5
Energetic considerations for rolls in finite domains
349
10.6
Spirals
353
10.7
Spirals in oscillatory and excitable systems
354
10.8
Drifting and meandering spirals
362
10.9
Spiral defect chaos
375
11
Large-aspect-ratio systems and the Cross-Newell equation
380
11.1
Fully nonlinear patterns in large-aspect-ratio boxes
381
11,2
Stationary solutions of the Cross-Newell equation
388
11.3
Defect solutions of the Cross-Newell equation
390
11.4
Models with variational structure
400
11.5
Systems with mean drift
404
References
408
Index
417
|
| adam_txt |
Contents
juce
page
ix
What are natural patterns?
1
1.1
Convection
3
1.2
Reaction-diffusion systems
12
1.3
Faraday waves
20
1.4
Outline of the rest of the book
22
A bit of bifurcation theory
23
2.1
Flows, stationary points and periodic orbits
23
2.2
Local bifurcations from stationary points
30
2.3
Normal forms for bifurcations
38
2.4
Codimension-one bifurcations
38
A bit of group theory
52
3.1
Groups
52
3.2
Subgroups, quotient groups and conjugacy
57
3.3
Mappings of groups
61
3.4
Products of groups
64
3.5
Lie groups
67
3.6
Representations of groups
68
3.7
Characters
77
3.8
Isotypic decomposition
82
Bifurcations with symmetry
85
4.1
Ordinary differential equations with spatial symmetry
85
4.2
The equivariant branching lemma
93
4.3
Bifurcations in a box
97
4.4 Hopf
bifurcations with symmetry
116
4.5
Heteroclinic cycles
122
4.6
Appendix: Proofs
131
vi
Contents
5 Simple
lattice
patterns
134
5.1
Lattices and lattice patterns
134
5.2
Bifurcations on a lattice
136
5.3
Steady bifurcation on a square lattice
141
5.4
Steady bifurcation on a hexagonal lattice
147
5.5
Roll/stripe solutions
157
5.6
The Kiippers-Lortz instability
158
5.7 Hopf
bifurcation on a one-dimensional lattice
161
6
Superlattices, hidden symmetries and other complications
168
6.1 Superlattice
patterns
168
6.2
Mode interactions
174
6.3
Spatial-period-multiplying bifurcations
178
6.4
Quasipatterns
182
6.5
Pseudoscalar actions of E{
2) 187
6.6
Hidden symmetries
190
6.7
Hidden symmetries and reflecting boundary conditions
198
7
Spatial modulation and envelope equations
209
7.1
Envelope equations for specific models
209
7.2
Envelope equations and symmetries
216
7.3
Free energies or Lyapunov functionals
224
7.4
Conservation of'angular momentum'
227
7.5 Hopf
bifurcations and the complex Ginzburg—Landau equation
232
7.6
Travelling waves and the nonlinear
Schrödinger
equation
234
7.7
Modulated hexagons
238
8
Instabilities of stripes and travelling plane waves
243
8.1
Universal instabilities of stripes
243
8.2
The
Eckhaus
instability
247
8.3
The zigzag instability
260
8.4
A general theory of phase dynamics
266
8.5
The cross-roll instability
274
8.6
Prandtl-number-dependent instabilities of convection rolls
277
8.7
The Benjamin-Feir instability
286
9
More instabilities of patterns
292
9.1
Instabilities of two-dimensional steady patterns
292
9.2
Drift instabilities
306
9.3
Galilean
invariance
and flat modes
315
9.4
Conservative systems and flat modes
319
10
Spirals, defects and spiral defect chaos
325
10.1
Types of isolated defect
325
10.2
Dislocation of a roll pattern
327
Contents
vii
10.3 Amplitude
grain boundaries
337
10.4
Domain boundaries between different patterns in systems
with a free energy
342
10.5
Energetic considerations for rolls in finite domains
349
10.6
Spirals
353
10.7
Spirals in oscillatory and excitable systems
354
10.8
Drifting and meandering spirals
362
10.9
Spiral defect chaos
375
11
Large-aspect-ratio systems and the Cross-Newell equation
380
11.1
Fully nonlinear patterns in large-aspect-ratio boxes
381
11,2
Stationary solutions of the Cross-Newell equation
388
11.3
Defect solutions of the Cross-Newell equation
390
11.4
Models with variational structure
400
11.5
Systems with mean drift
404
References
408
Index
417 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T13:52:24Z |
| indexdate | 2024-07-09T20:35:06Z |
| institution | BVB |
| isbn | 0521817501 9780521817509 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014621064 |
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| spelling | Hoyle, Rebecca B. Verfasser (DE-588)132328925 aut Pattern formation an introduction to methods Rebecca B. Hoyle Cambridge Cambridge University Press 2006 x, 422 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Musterbildung - Mathematische Methode Musterbildung (DE-588)4137934-2 gnd rswk-swf Musterbildung (DE-588)4137934-2 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014621064&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hoyle, Rebecca B. Pattern formation an introduction to methods Musterbildung - Mathematische Methode Musterbildung (DE-588)4137934-2 gnd |
| subject_GND | (DE-588)4137934-2 |
| title | Pattern formation an introduction to methods |
| title_auth | Pattern formation an introduction to methods |
| title_exact_search | Pattern formation an introduction to methods |
| title_exact_search_txtP | Pattern formation an introduction to methods |
| title_full | Pattern formation an introduction to methods Rebecca B. Hoyle |
| title_fullStr | Pattern formation an introduction to methods Rebecca B. Hoyle |
| title_full_unstemmed | Pattern formation an introduction to methods Rebecca B. Hoyle |
| title_short | Pattern formation |
| title_sort | pattern formation an introduction to methods |
| title_sub | an introduction to methods |
| topic | Musterbildung - Mathematische Methode Musterbildung (DE-588)4137934-2 gnd |
| topic_facet | Musterbildung - Mathematische Methode Musterbildung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014621064&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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