The dynamics of patterns:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2000
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 324 S. Ill., graph. Darst. |
| ISBN: | 9810240554 9810240562 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804128348744450048 |
|---|---|
| adam_text | BTOAMICS M I RABINOVICH UNIVERSITY OF CALIFORNIA, SAN DIEGO A B EZERSKY
RUSSIAN ACADEMY OF SCIENCES P D WEIDMAN UNIVERSITY OF COLORADO WORLD
SCIENTIFIC SINGAPORE * NEW JERSEY * LONDON * HONG KONG CONTENTS PREFACE
VN CHAPTER 1 PATTERNS: PRELUDE TO A DYNAMICAL DESCRIPTION 1 CHAPTER 2
LINEAR STAGE OF PATTERN FORMATION 15 CHAPTER 3 MODEL EQUATIONS 27 3.1
SWIFT-HOHENBERG EQUATION 29 3.2 NEWELL-WHITEHEAD-SEGEL EQUATION 35 3.3
COUPLED AMPLITUDE EQUATIONS 38 3.4 PHASE EQUATIONS 42 CHAPTER 4 THE
GINZBURG-LANDAU EQUATION 45 4.1 THE DISSIPATIVE GINZBURG-LANDAU EQUATION
46 4.2 NERVE MEMBRANE EXCITATION AND THE CGL EQUATION 48 4.3 OPTICAL
DYNAMICS AND THE CGL EQUATION 50 4.4 SIMPLE PATTERNS IN THE CGL EQUATION
52 4.5 PHASE EQUATIONS REVISITED 55 4.6 GALLERY OF PHENOMENA 57 CHAPTER
5 CRYSTAL FORMATION 63 CHAPTER 6 QUASICRYSTALS 75 6.1 OCTAGONS,
DECAGONS, AND DODECAGONS 78 6.2 A GENERALIZED SWIFT-HOHENBERG MODEL 81
6.3 THE TURBULENT CRYSTAL . 82 IX X CONTENTS CHAPTER 7 BREAKING OF
ORDER 87 7.1 A SIMPLE MODEL FOR DOMAIN WALLS 89 7.2 TOPOLOGICAL DEFECTS
92 7.3 THE BIRTH OF PENTA-HEPTA DEFECTS 96 7.4 DISLOCATIONS AND DOMAIN
WALLS IN FARADAY RIPPLES 102 CHAPTER 8 LOCALIZED PATTERNS 107 8.1
BISTABLE MEDIA 107 8.2 DYNAMICAL DISORDER OF STRUCTURES 114 8.3 PARTICLE
INTERACTION 115 8.4 CHAOTIC SCATTERING 118 CHAPTER 9 SPIRALS 129 9.1
ACTIVE SPIRALS 133 9.1.1 SPIRALS IN THE COMPLEX GINZBURG-LANDAU EQUATION
. . . 133 9.1.2 SPIRALS IN THE FITZHUGH-NAGUMO MODEL 136 9.2 PASSIVE
SPIRALS 142 9.2.1 SPIRALS IN THE FARADAY EXPERIMENT 143 9.2.2 SPIRALS IN
RAYLEIGH-BENARD CONVECTION X . 145 CHAPTER 10 PATTERNS IN OSCILLATING
SOAP FILMS 151 10.1 INTRODUCTION 151 10.2 OBSERVATIONS 152 10.3 MODELS
FOR VORTICITY GENERATION 158 10.3.1 MARANGONI WAVE MODEL 160 10.3.2 THE
ROLE OF AIR 162 CHAPTER 11 PATTERNS IN COLONIES OF MICROORGANISMS 173
11.1 DICTYOSTELIUM DISCOIDEUM 174 11.2 ESHERICHIA COLI 178 11.3 BACILLUS
SUBTILIS 184 CHAPTER 12 SPATIAL DISORDER 189 12.1 INTRODUCTORY REMARKS
189 12.2 CHARACTERISTICS OF SPACE SERIES 193 12.3 THE
GRASSBERGER-PROCACCIA ALGORITHM 197 12.4 QUALITATIVE DESCRIPTION OF
DEVELOPING DISORDER 199 12.5 DYNAMICAL DIMENSION OF DEFECT-MEDIATED
TURBULENCE 202 CONTENTS XI CHAPTER 13 PATTERNS IN CHAOTIC MEDIA 205 13.1
INTRODUCTORY REMARKS 205 13.2 CHAOTIC-SYNCHRONIZATION 208 13.3
COEXISTENCE OF REGULAR PATTERNS AND CHAOS 211 13.4 COARSE GRAIN
SPATIO-TEMPORAL PATTERNS 214 13.5 COHERENT PATTERNS ON A CHAOTIC
CHECKERBOARD 220 CHAPTER 14 EPILOGUE: LIVING MATTER AND DYNAMIC FORMS
225 14.1 HALLUCINATIONS 227 14.2 SPATIO-TEMPORAL PATTERNS AND
INFORMATION PROCESSING 234 APPENDIX A A SHORT GUIDE TO NONLINEAR
DYNAMICS 239 A.I DYNAMICAL SYSTEMS 239 A.1.1 TYPES OF DYNAMICAL SYSTEMS
240 A.1.2 EQUILIBRIUM STATES 241 A.1.3 HOMOCLINIC AND HETEROCLINIC
TRAJECTORIES 245 A.1.4 LIMIT CYCLES 248 A.1.5 QUASIPERIODIC MOTION 249
A.2 BIFURCATIONS 250 A.2.1 BIFURCATIONS OF EQUILIBRIUM STATES 252 A.2.2
BIRTH OF PERIODIC MOTIONS 258 A.2.3 CHANGE OF STABILITY IN PERIODIC
MOTIONS 260 A.3 CHAOTIC OSCILLATIONS 261 A.3.1 CHARACTERISTICS OF CHAOS
AND THE STRANGE ATTRACTOR . . . 261 A.3.2 CHAOTIC HAMILTONIAN SYSTEMS
263 A.3.3 CHAOTIC SELF-EXCITED OSCILLATIONS 264 A.4 SYNCHRONIZATION OF
OSCILLATIONS 266 A.5 DYNAMICAL CHAOS AND TURBULENCE 271 APPENDIX B KEY
EXPERIMENTS IN PATTERN FORMATION 279 B.I PARAMETRICALLY EXCITED PATTERNS
279 B.I.I EXPERIMENTS WITH LIQUIDS 279 B.I.2 EXPERIMENTS WITH GRANULAR
MATERIAL , 287 B.2 THERMAL CONVECTION 292 B.2.1 RAYLEIGH-BENARD
CONVECTION 292 B.2.2 PATTERNS IN RAYLEIGH-BENARD CONVECTION 295 B.2.3
BENARD-MARANGONI CONVECTION 297 B.3 DIFFUSIVE CHEMICAL REACTIONS 302 XII
CONTENTS B.3.1 TURING PATTERNS 302 B.3.2 OSCILLATING CHEMICAL REACTIONS
306 BIBLIOGRAPHY - 309 INDEX 320
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| any_adam_object | 1 |
| author | Rabinovič, Michail I. Ezerskij, A. B. Weidman, P. D. |
| author_facet | Rabinovič, Michail I. Ezerskij, A. B. Weidman, P. D. |
| author_role | aut aut aut |
| author_sort | Rabinovič, Michail I. |
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| dewey-full | 511.33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.33 |
| dewey-search | 511.33 |
| dewey-sort | 3511.33 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| indexdate | 2024-07-09T18:47:49Z |
| institution | BVB |
| isbn | 9810240554 9810240562 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009253285 |
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| owner_facet | DE-703 DE-11 DE-188 DE-19 DE-BY-UBM |
| physical | XII, 324 S. Ill., graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | World Scientific |
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| spelling | Rabinovič, Michail I. Verfasser aut The dynamics of patterns M. I. Rabinovich ; A. B. Ezersky ; P. D. Weidman Singapore [u.a.] World Scientific 2000 XII, 324 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chaos (théorie des systèmes) ram Perception des structures - Modèles mathématiques ram Musterbildung (DE-588)4137934-2 gnd rswk-swf Musterbildung (DE-588)4137934-2 s DE-604 Ezerskij, A. B. Verfasser aut Weidman, P. D. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009253285&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rabinovič, Michail I. Ezerskij, A. B. Weidman, P. D. The dynamics of patterns Chaos (théorie des systèmes) ram Perception des structures - Modèles mathématiques ram Musterbildung (DE-588)4137934-2 gnd |
| subject_GND | (DE-588)4137934-2 |
| title | The dynamics of patterns |
| title_auth | The dynamics of patterns |
| title_exact_search | The dynamics of patterns |
| title_full | The dynamics of patterns M. I. Rabinovich ; A. B. Ezersky ; P. D. Weidman |
| title_fullStr | The dynamics of patterns M. I. Rabinovich ; A. B. Ezersky ; P. D. Weidman |
| title_full_unstemmed | The dynamics of patterns M. I. Rabinovich ; A. B. Ezersky ; P. D. Weidman |
| title_short | The dynamics of patterns |
| title_sort | the dynamics of patterns |
| topic | Chaos (théorie des systèmes) ram Perception des structures - Modèles mathématiques ram Musterbildung (DE-588)4137934-2 gnd |
| topic_facet | Chaos (théorie des systèmes) Perception des structures - Modèles mathématiques Musterbildung |
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