Spatio-temporal pattern formation: with examples from physics, chemistry, and materials science
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1997
|
| Schriftenreihe: | Partially ordered systems
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 306 S. Ill., graph. Darst. |
| ISBN: | 0387948570 |
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Datensatz im Suchindex
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|---|---|
| adam_text | DANIEL WALGRAEF SPATIO-TEMPORAL PATTERN FORMATION WITH EXAMPLES FROM
PHYSICS, CHEMISTRY, AND MATERIALS SCIENCE WITH 121 ILLUSTRATIONS
SPRINGER CONTENTS PREFACE V 1 INTRODUCTION 1 2 INSTABILITIES AND
PATTERNS IN HYDRODYNAMICAL SYSTEMS 15 2.1 RAYLEIGH-BENARD INSTABILITY 15
2.2 TAYLOR-COUETTE INSTABILITY 17 2.3 LIQUID CRYSTAL INSTABILITIES 20 3
INSTABILITIES AND PATTERNS IN REACTION-DIFFUSION SYSTEMS 25 3.1 CHEMICAL
INSTABILITIES 25 3.2 DEFECT MICROSTRUCTURES IN IRRADIATED MATERIALS 31
3.3 PLASTIC DEFORMATION AND DISLOCATION PATTERNS 32 4 GENERIC ASPECTS OF
PATTERN-FORMING INSTABILITIES 37 4.1 PHENOMENOLOGY 37 4.2
REACTION-DIFFUSION DYNAMICS AND STABILITY 39 4.3 REDUCED DYNAMICS AND
AMPLITUDE EQUATIONS 41 4.4 SPATIAL PATTERNS: SELECTION AND STABILITY 43
4.4.1 ISOTROPIC SYSTEMS 43 4.4.2 ANISOTROPIC SYSTEMS 49 4.5 PHASE
DYNAMICS OF PERIODIC PATTERNS 52 4.5.1 ISOTROPIC SYSTEMS 52 4.5.2
ANISOTROPIC SYSTEMS 59 CONTENTS THE HOPF BIFURCATION AND RELATED
SPATIO-TEMPORAL PATTERNS 65 5.1 THE GENERIC ASPECTS OF OSCILLATORY MEDIA
65 5.1.1 THE COMPLEX GINZBURG-LANDAU EQUATION 65 5.1.2 PHASE DYNAMICS
AND SPIRAL WAVES 67 5.2 REAL CHEMICAL SYSTEMS AND THE COMPLEX
GINZBURG-LANDAU EQUATION 72 5.2.1 DETERMINATION OF THE CGLE PARAMETERS
IN REAL SYSTEMS . 72 5.2.2 CGLE PARAMETERS OF THE BZ REACTION 75 5.3 THE
EFFECT OF NATURAL FORCINGS ON CHEMICAL OSCILLATORS 77 5.3.1 THE EFFECT
OF CONVECTION ON CHEMICAL WAVES 77 5.3.2 THE EFFECT OF VERTICAL
GRADIENTS ON CHEMICAL OSCILLATIONS . 79 5.4 CONCLUSIONS 82 THE TURING
INSTABILITY AND ASSOCIATED SPATIAL STRUCTURES 87 6.1 THE TURING
MECHANISM 87 6.2 THE SEARCH FOR TURING STRUCTURES 90 6.2.1 CONVECTIVELY
DRIVEN CHEMICAL PATTERNS 90 6.2.2 DOUBLE DIFFUSION AND CHEMICAL FINGERS
91 6.3 AT LAST, GENUINE TURING STRUCTURES? 93 6.4 THE INTERACTION
BETWEEN TURING AND HOPF INSTABILITIES 98 6.4.1 AMPLITUDE EQUATIONS FOR
TURING-HOPF MODES 98 6.4.2 PATTERN SELECTION FOR CODIMENSION-2
TURING-HOPF BIFURCATIONS 99 6.4.3 DEFECTS, DEFECT BIFURCATIONS AND
LOCALIZED STRUCTURES ... 102 DEFECTS AND DEFECT BIFURCATIONS 107 7.1
GENERIC EXISTENCE OF DEFECTS 108 7.2 EXAMPLES OF DEFECTS ILL 7.2.1
CODIMENSION-1 DEFECTS ILL 7.2.2 CODIMENSION-2 DEFECTS 112 7.3 DEFECTS
AND DISORDER * , 114 7.4 BIFURCATION OF DEFECTS 121 THE EFFECT OF
EXTERNAL FIELDS 127 8.1 SPATIAL FORCING OF STATIONARY PATTERNS 129 8.1.1
RESONANT FORCINGS 129 8.1.2 NEAR-RESONANT FORCINGS AND COMMENSURATE
INCOMMENSURATE TRANSITIONS 130 8.2 TEMPORAL FORCING OF A HOPF
BIFURCATION 133 8.3 TEMPORAL FORCING OF ONE-DIMENSIONAL WAVE PATTERNS
135 8.3.1 PATTERN SELECTION AND DEFECTS 135 8.3.2 EXPERIMENTAL
OBSERVATIONS 146 8.4 TEMPORAL FORCING OF TWO-DIMENSIONAL WAVE PATTERNS
147 8.4.1 ISOTROPIC SYSTEMS 147. 8.4.2 ANISOTROPIC SYSTEMS 148 CONTENTS
IX 8.5 SPATIAL FORCING OF WAVE PATTERNS 151 8.6 FLOW FIELD EFFECTS ON
PATTERN FORMING INSTABILITIES 155 8.7 THE EFFECT OF NOISE ON WAVE
PATTERNS 158 8.8 CONCLUSIONS 162 9 FRONTS 169 9.1 ONE-DIMENSIONAL
ASPECTS 171 9.1.1 THE LEADING-EDGE APPROACH 171 9.1.2 BREAKDOWN OF THE
LEADING-EDGE APPROACH 174 9.1.3 ENVELOPE FRONTS 174 9.1.4 MULTIPLE
FRONTS 177 9.2 TWO-DIMENSIONAL ASPECTS 179 9.2.1 PROPAGATION OF ROLL
PATTERNS 181 9.2.2 PROPAGATION OF HEXAGONAL PATTERNS 184 10 PATTERN
FORMATION: GENERIC VERSUS NONGENERIC ASPECTS 189 10.1 KINETIC
COEFFICIENTS 189 10.2 NONGRADIENT DYNAMICS 190 10.3 EXPERIMENTAL SET-UPS
192 11 MICROSTRUCTURES IN IRRADIATED MATERIALS 197 11.1 PARTICLE
IRRADIATION OF METALS AND ALLOYS 197 11.1.1 A RATE THEORY MODEL FOR
MICROSTRUCTURE EVOLUTION UNDER IRRADIATION 198 11.1.2 DISLOCATION LOOP
DYNAMICS 200 11.1.3 THE LINEAR STABILITY ANALYSIS 204 11.1.4 THE WEAKLY
NONLINEAR REGIME 205 11.1.5 NUMERICAL ANALYSIS 209 11.1.6 CONCLUSIONS
216 11.2 LASER INDUCED DEFORMATION OF SURFACES 217 11.2.1 THIN FILM
DYNAMICS UNDER LASER IRRADIATION 221 11.2.2 LINEAR STABILITY ANALYSIS
222 11.2.3 WEAKLY NONLINEAR ANALYSIS 224 11.2.4 FINITE SIZE EFFECTS 227
11.2.5 CONCLUSIONS 228 12 PLASTIC INSTABILITIES 231 12.1 DISLOCATION
DYNAMICS AND RATE EQUATIONS 232 12.2 STABILITY ANALYSIS AND BIFURCATIONS
234 12.3 NONLINEAR ANALYSIS 236 12.4 MULTIPLE SLIP 237 13 AFTERWORD 241
14 APPENDICES 245 14.1 BIFURCATIONS AND NORMAL FORMS 245 X CONTENTS
14.1.1 BIFURCATIONS 245 14.1.2 STABILITY OF EQUILIBRIA 248 14.1.3
LYAPOUNOV FUNCTIONS 250 14.1.4 TYPICAL BIFURCATION EXAMPLES 252 14.1.5
THE HOPF BIFURCATION THEOREM 255 14.1.6 THE CENTER MANIFOLD THEOREM 257
14.2 MORE ABOUT DYNAMICAL MODELS 258 14.2.1 PROCTOR-SIVASHINSKY 258
14.2.2 GINZBURG-LANDAU 269 14.3 THE BRUSSELATOR: A TOY MODEL FOR PATTERN
FORMATION IN RD SYSTEMS 275 14.3.1 THE TURING INSTABILITY 277 14.3.2 THE
HOPF INSTABILITY 289 14.3.3 AMPLITUDE EQUATIONS FOR TURING-HOPF MODES
292 14.4 RESONANT FORCINGS OF NONLINEAR OSCILLATORS 293 14.4.1
PARAMETRIC FORCING 293 14.4.2 STRONG RESONANCES IN SPATIALLY EXTENDED
SYSTEMS 295 14.4.3 STATIONARY SOLUTIONS AND RESONANCE HORNS 296 14.4.4
FROM OSCILLATIONS TO EXCITABILITY 298 INDEX 303
|
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| language | English |
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| physical | X, 306 S. Ill., graph. Darst. |
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| spelling | Walgraef, Daniel Verfasser aut Spatio-temporal pattern formation with examples from physics, chemistry, and materials science Daniel Walgraef New York [u.a.] Springer 1997 X, 306 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Partially ordered systems Chemistry, Physical and theoretical Hydrodynamics Nonlinear theories Pattern formation (Biology) Pattern formation (Physical sciences) Spatial analysis Musterbildung (DE-588)4137934-2 gnd rswk-swf Raum (DE-588)4048561-4 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Chemie (DE-588)4009816-3 gnd rswk-swf Zeit (DE-588)4067461-7 gnd rswk-swf Werkstoffkunde (DE-588)4079184-1 gnd rswk-swf Raum (DE-588)4048561-4 s Zeit (DE-588)4067461-7 s Musterbildung (DE-588)4137934-2 s DE-604 Physik (DE-588)4045956-1 s Chemie (DE-588)4009816-3 s Werkstoffkunde (DE-588)4079184-1 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007646096&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Walgraef, Daniel Spatio-temporal pattern formation with examples from physics, chemistry, and materials science Chemistry, Physical and theoretical Hydrodynamics Nonlinear theories Pattern formation (Biology) Pattern formation (Physical sciences) Spatial analysis Musterbildung (DE-588)4137934-2 gnd Raum (DE-588)4048561-4 gnd Physik (DE-588)4045956-1 gnd Chemie (DE-588)4009816-3 gnd Zeit (DE-588)4067461-7 gnd Werkstoffkunde (DE-588)4079184-1 gnd |
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| title | Spatio-temporal pattern formation with examples from physics, chemistry, and materials science |
| title_auth | Spatio-temporal pattern formation with examples from physics, chemistry, and materials science |
| title_exact_search | Spatio-temporal pattern formation with examples from physics, chemistry, and materials science |
| title_full | Spatio-temporal pattern formation with examples from physics, chemistry, and materials science Daniel Walgraef |
| title_fullStr | Spatio-temporal pattern formation with examples from physics, chemistry, and materials science Daniel Walgraef |
| title_full_unstemmed | Spatio-temporal pattern formation with examples from physics, chemistry, and materials science Daniel Walgraef |
| title_short | Spatio-temporal pattern formation |
| title_sort | spatio temporal pattern formation with examples from physics chemistry and materials science |
| title_sub | with examples from physics, chemistry, and materials science |
| topic | Chemistry, Physical and theoretical Hydrodynamics Nonlinear theories Pattern formation (Biology) Pattern formation (Physical sciences) Spatial analysis Musterbildung (DE-588)4137934-2 gnd Raum (DE-588)4048561-4 gnd Physik (DE-588)4045956-1 gnd Chemie (DE-588)4009816-3 gnd Zeit (DE-588)4067461-7 gnd Werkstoffkunde (DE-588)4079184-1 gnd |
| topic_facet | Chemistry, Physical and theoretical Hydrodynamics Nonlinear theories Pattern formation (Biology) Pattern formation (Physical sciences) Spatial analysis Musterbildung Raum Physik Chemie Zeit Werkstoffkunde |
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