Noise in spatially extended systems:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
1999
|
| Series: | Institute for nonlinear science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 289 - 301 |
| Physical Description: | XIII, 307 S. Ill., graph. Darst. |
| ISBN: | 0387988556 |
Staff View
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Record in the Search Index
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| adam_text | / JORDI GARCIA-OJALVO JOSE M. SANCHO NOISE IN SPATIALLY EXTENDED SYSTEMS
WITH 120 ILLUSTRATIONS SPRINGER CONTENTS PREFACE VII ACKNOWLEDGMENTS IX
1 INTRODUCTION 1 1.1 FLUCTUATIONS IN A MACROSCOPIC WORLD 1 1.1.1
DESCRIBING STOCHASTIC DYNAMICS 3 1.1.2 STOCHASTIC PARTIAL DIFFERENTIAL
EQUATIONS 4 1.1.3 EXPERIMENTAL SETUPS 4 1.1.4 NUMERICAL EXPERIMENTS 10
1.1.5 NOISE-INDUCED PHENOMENA 10 1.2 TRANSITIONS IN ZERO-DIMENSIONAL
SYSTEMS 11 1.2.1 INTERNAL NOISE 12 1.2.2 EXTERNAL NOISE 15 1.3 PHASE
TRANSITIONS IN D-DIMENSIONAL SYSTEMS 23 1.3.1 EQUILIBRIUM PHASE
TRANSITIONS 23 1.3.2 NONEQUILIBRIUM PHASE TRANSITIONS 32 1.3.3 DYNAMICS
OF PHASE TRANSITIONS 37 1.4 PATTERN FORMATION 39 1.4.1 ORDER-PARAMETER
EQUATIONS 40 1.4.2 PATTERN-FORMING INSTABILITIES 42 1.4.3 AMPLITUDE
EQUATIONS AND BEYOND 43 1.4.4 REAL PATTERNS 44 1.5 OTHER EFFECTS OF
NOISE IN EXTENDED MEDIA 45 XII CONTENTS 1.5.1 NOISE-SUSTAINED CONVECTIVE
STRUCTURES 45 1.5.2 SPATIAL STOCHASTIC RESONANCE 48 2 FUNDAMENTALS AND
TOOLS 53 2.1 INTRODUCTION TO STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
53 2.1.1 GENERALITIES AND MODELING 54 2.1.2 STOCHASTIC CALCULUS IN SPDES
58 2.1.3 FOKKER-PLANCK EQUATION FOR SPATIALLY EXTENDED SYSTEMS 64 2.1.4
STATISTICAL MOMENTS AND CORRELATIONS 65 2.2 ANALYTICAL TECHNIQUES 66
2.2.1 MEAN-FIELD ANALYSIS AND BEYOND 66 2.2.2 SMALL NOISE EXPANSIONS 69
2.2.3 LINEAR STABILITY ANALYSIS 72 2.2.4 DYNAMIC RENORMALIZATION GROUP
ANALYSIS . . . . 76 2.3 NUMERICAL TECHNIQUES 85 2.3.1 ALGORITHMS FOR
SOLVING SPDES 85 2.3.2 GENERATION OF CORRELATED NOISES 92 3
NOISE-INDUCED PHASE TRANSITIONS 115 3.1 ADDITIVE NOISE 115 3.1.1
GINZBURG-LANDAU MODEL WITH COLORED NOISE ... 116 3.1.2 NOISE-INDUCED
SHIFT OF THE TRANSITION POINT ... 117 3.1.3 FOKKER-PLANCK ANALYSIS 124
3.1.4 DYNAMIC RENORMALIZATION GROUP ANALYSIS . . . . 127 3.2 ADDITIVE
AND MULTIPLICATIVE NOISE 130 3.2.1 GINZBURG-LANDAU MODEL WITH
MULTIPLICATIVE NOISE 131 3.2.2 PURE NOISE-INDUCED PHASE TRANSITIONS 137
3.2.3 NOISE-INDUCED FIRST-ORDER PHASE TRANSITIONS . . . 150 3.3
MULTIPLICATIVE NOISE 153 3.3.1 MULTIPLICATIVE NOISE UNIVERSALITY CLASS
153 3.3.2 DISORDERING TRANSITIONS INDUCED BY PURE MULTI- PLICATIVE NOISE
155 3.3.3 NUMERICAL SIMULATION RESULTS 157 4 DYNAMICS OF PHASE
TRANSITIONS WITH FLUCTUATIONS 159 4.1 INTERNAL MULTIPLICATIVE NOISE 159
4.1.1 MESOSCOPIC DERIVATION 160 4.1.2 APPLICATION TO PHASE SEPARATION
DYNAMICS . . . . 167 4.1.3 EXTENSION TO NONCONSERVED ORDER PARAMETER . .
. 172 4.2 NOISE-INDUCED PHASE SEPARATION 174 4.2.1 EXTERNAL FLUCTUATIONS
IN PHASE SEPARATION . . . . 175 4.2.2 STABILITY ANALYSIS 176 4.2.3 PHASE
DIAGRAM 177 / CONTENTS XIII 5 PATTERN FORMATION UNDER MULTIPLICATIVE
NOISE 185 5.1 MULTIPLICATIVE NOISE IN THE SWIFT-HOHENBERG MODEL ... 185
5.1.1 A MODEL EQUATION FOR RAYLEIGH-BENARD CONVECTION 186 5.1.2
FLUCTUATIONS IN THE CONTROL PARAMETER 188 5.1.3 EFFECT OF A SPATIALLY
CORRELATED NOISE 203 5.2 PURE NOISE-INDUCED PATTERNS 211 6 FRONT
DYNAMICS AND EXTERNAL FLUCTUATIONS 219 6.1 EXTERNAL FLUCTUATIONS IN
DETERMINISTIC FRONTS 219 6.1.1 FRONT PROPAGATION IN FLUCTUATING MEDIA
221 6.1.2 THEORETICAL APPROACH AND PREDICTIONS 227 6.1.3 NOISE EFFECTS
ON THE FRONT SELECTION PROBLEM ... 230 6.1.4 PROFILE SHAPE AND VELOCITY
SHIFT 234 6.1.5 FRONT DIFFUSIVE SPREADING 238 6.2 NOISE-INDUCED FRONTS
246 6.2.1 MODELING AND ANALYTICAL RESULTS 246 6.2.2 NUMERICAL RESULTS
247 6.3 REACTIVE FRONTS UNDER TURBULENT ADVECTION 252 6.3.1 MODELING 252
6.3.2 A GAUSSIAN TURBULENCE? 255 6.3.3 THEORETICAL ANALYSIS AND
NUMERICAL RESULTS . . . 255 6.3.4 THE ROLE OF DIFFERENT SPECTRA 260 7
CONCLUSIONS 263 7.1 WHAT HAS BEEN DONE 263 7.2 WHAT NEEDS TO BE DONE 265
A CONTINUUM AND DISCRETE SPACE DESCRIPTIONS 269 A.L COARSE GRAINING 269
A.2 CONTINUUM LIMIT AND FUNCTIONAL ANALYSIS 270 8 FOURIER TRANSFORMS 273
B.L CONTINUUM FOURIER TRANSFORMS 273 B.2 DISCRETE FOURIER TRANSFORMS 274
B.3 DISCRETE FOURIER TRANSFORM OF A REAL UNCORRELATED FIELD 275 *
FOKKER*PLANCK EQUATION FOR AN ADDITIVE COLORED NOISE 279 D COLORED NOISE
IN A LINEAR MODEL 283 E FOKKER-PLANCK EQUATION FOR A MULTIPLICATIVE
NOISE 285 REFERENCES 289 INDEX 303
|
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| author | García-Ojalvo, Jordi Sancho, José M. |
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| isbn | 0387988556 |
| language | English |
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| spelling | García-Ojalvo, Jordi Verfasser aut Noise in spatially extended systems Jordi García-Ojalvo ; José M. Sancho New York, NY [u.a.] Springer 1999 XIII, 307 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Institute for nonlinear science Literaturverz. S. 289 - 301 Processus stochastiques ram Transitions de phases ram Noise Phase transformations (Statistical physics) Stochastic processes Phasenumwandlung (DE-588)4132140-6 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Fluktuation Physik (DE-588)4130671-5 gnd rswk-swf Rauschen (DE-588)4048606-0 gnd rswk-swf Strukturbildung (DE-588)4541700-3 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 s Strukturbildung (DE-588)4541700-3 s Fluktuation Physik (DE-588)4130671-5 s Rauschen (DE-588)4048606-0 s Stochastische Differentialgleichung (DE-588)4057621-8 s DE-604 Sancho, José M. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008717514&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | García-Ojalvo, Jordi Sancho, José M. Noise in spatially extended systems Processus stochastiques ram Transitions de phases ram Noise Phase transformations (Statistical physics) Stochastic processes Phasenumwandlung (DE-588)4132140-6 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Fluktuation Physik (DE-588)4130671-5 gnd Rauschen (DE-588)4048606-0 gnd Strukturbildung (DE-588)4541700-3 gnd |
| subject_GND | (DE-588)4132140-6 (DE-588)4057621-8 (DE-588)4130671-5 (DE-588)4048606-0 (DE-588)4541700-3 |
| title | Noise in spatially extended systems |
| title_auth | Noise in spatially extended systems |
| title_exact_search | Noise in spatially extended systems |
| title_full | Noise in spatially extended systems Jordi García-Ojalvo ; José M. Sancho |
| title_fullStr | Noise in spatially extended systems Jordi García-Ojalvo ; José M. Sancho |
| title_full_unstemmed | Noise in spatially extended systems Jordi García-Ojalvo ; José M. Sancho |
| title_short | Noise in spatially extended systems |
| title_sort | noise in spatially extended systems |
| topic | Processus stochastiques ram Transitions de phases ram Noise Phase transformations (Statistical physics) Stochastic processes Phasenumwandlung (DE-588)4132140-6 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Fluktuation Physik (DE-588)4130671-5 gnd Rauschen (DE-588)4048606-0 gnd Strukturbildung (DE-588)4541700-3 gnd |
| topic_facet | Processus stochastiques Transitions de phases Noise Phase transformations (Statistical physics) Stochastic processes Phasenumwandlung Stochastische Differentialgleichung Fluktuation Physik Rauschen Strukturbildung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008717514&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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