Dissipative structures and chaos: with 5 tables
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1998
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Japan. übers. |
| Beschreibung: | XIX, 299 S. Ill., graph. Darst. |
| ISBN: | 3540627448 |
Internformat
MARC
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| 100 | 1 | |a Mori, Hazime |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Sanitsu kozo to kaosu |
| 245 | 1 | 0 | |a Dissipative structures and chaos |b with 5 tables |c Hazime Mori ; Yoshiki Kuramoto |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1998 | |
| 300 | |a XIX, 299 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Aus dem Japan. übers. | ||
| 650 | 0 | 7 | |a Dissipative Struktur |0 (DE-588)4130307-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Chaostheorie |0 (DE-588)4009754-7 |2 gnd |9 rswk-swf |
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| 689 | 1 | 0 | |a Chaostheorie |0 (DE-588)4009754-7 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Kuramoto, Yoshiki |d 1940- |e Verfasser |0 (DE-588)172214300 |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007960160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007960160 | |
Datensatz im Suchindex
| _version_ | 1818957156904337408 |
|---|---|
| adam_text |
Contents
Part I. Dissipative Structures
Introduction 3
1. A Representative Example of Dissipative Structure 5
1.1 Benard Convection 5
1.2 The Belousov Zhabotinskii Reaction 14
2. Amplitude Equations and Their Applications 21
2.1 The Newell Whitehead Equation
and the Stability of Periodic Solutions 21
2.2 Anisotropic Fluids and the Ginzburg Pitaevskii Equation . 26
2.3 Topological Defects and Their Motion 29
2.4 The Amplitude Equation of an Oscillating Field 34
2.5 The Properties of the Complex Ginzburg Landau Equation . 36
2.5.1 Propagating Planar Wave Solutions and Their Stability 36
2.5.2 Rotating Spiral Waves 38
2.5.3 Hole Solutions and Disordered Patterns 39
3. Reaction Diffusion Systems and Interface Dynamics 43
3.1 Interfaces in Single Component Bistable Systems 43
3.2 Solitary Wave Pulses and Periodic Wave Pulse Trains
in Excitable Systems 47
3.3 Spiral Waves in Excitable Systems 52
3.4 Multiple Spiral Waves and the Turing Pattern 58
3.4.1 Compound Spiral Rotation 58
3.4.2 The Turing Pattern 59
3.5 The Instability of Interfaces and Formation of Structure 62
4. Phase Dynamics 69
4.1 Weak Turbulence of Periodic Structures
and the Phase Equation 69
4.2 Phase Waves and Phase Turbulence of Oscillating Fields 76
4.2.1 The Phase Equation of an Oscillating Field
and Its Applications 76
XVI Contents
4.2.2 Phase Waves and the Target Pattern 78
4.2.3 Phase Turbulence 82
4.3 The Phase Dynamics of Interfaces 84
4.4 Multiple Field Dynamics 86
5. Foundations of Reduction Theory 93
5.1 Two Simple Examples 93
5.2 The Destabilization of Stationary Solutions 98
5.3 Foundations of the Amplitude Equation 100
5.4 The Introduction of Continuous Spatial Degrees of Freedom . 107
5.4.1 The Hopf Bifurcation 107
5.4.2 The Turing Instability 109
5.5 Fundamentals of Phase Dynamics 112
5.5.1 Phase Dynamics in a Uniform Oscillating Field 113
5.5.2 Phase Dynamics for a System with Periodic Structure. 114
5.5.3 Interface Dynamics in a Two Dimensional Medium . 115
Supplement I:
Dynamics of Coupled Oscillator Systems 119
51.1 The Phase Dynamics of a Collection of Oscillators 119
51.2 Synchronization Phenomena 121
Part II. The Structure and Physics of Chaos
Introduction 127
6. A Physical Approach to Chaos 129
6.1 The Phase Space Structure
of Dissipative Dynamical Systems 129
6.2 The Phase Space Structure
of Conservative Dynamical Systems 134
6.3 Orbital Instability and the Mixing Nature of Chaos 139
6.3.1 The Liapunov Number 139
6.3.2 The Expansion Rate of Nearby Orbits, Xi{Xt) 141
6.3.3 Mixing and Memory Loss 144
6.4 The Statistical Description of Chaos 145
6.4.1 The Statistical Stability of Chaos 145
6.4.2 Time Coarse Graining and the Spectrum ip(A) 146
6.4.3 The Statistical Structure of Chaos 148
7. Bifurcation Phenomena of Dissipative Dynamical Systems 151
7.1 Band Chaos of the Henon Map 151
7.2 The Derivation of Several Low Dimensional Maps 155
7.2.1 The Henon Map 157
Contents XVII
7.2.2 The Annulus Map 157
7.2.3 The Standard Map (J = 1) 159
7.2.4 One Dimensional Maps (J = 0) 160
7.3 Bifurcations of the One Dimensional Quadratic Map 161
7.3.1 2n Bifurcations and 2" Band Bifurcations 161
7.3.2 The Self Similarity
and Renormalization Transformation
of 2n Bifurcations 166
7.3.3 The Similarity of 2n Band Bifurcations 170
7.4 Bifurcations of the One Dimensional Circle Map 174
7.4.1 Phase Locked Band Chaos 174
7.4.2 Phase Unlocked Fully Extended Chaos 177
8. The Statistical Physics of Aperiodic Motion 183
8.1 The Statistical Structure Functions
of the Coarse Grained Orbital Expansion Rate 183
8.1.1 The Baker Transformation 185
8.1.2 Attractor Destruction in the Quadratic Map 187
8.1.3 Attractor Merging in the Circle Map 189
8.1.4 Bifurcations of the Henon Map 192
8.1.5 The Slopes sQ and s0 of ip(A) 193
8.2 The Singularity Spectrum /(a) 195
8.2.1 The Multifractal Dimension D(q) 198
8.2.2 Partial Local Dimensions ai(X) and a2{X) 198
8.2.3 f(a) Spectra of Critical Attractors 199
8.3 Theory Regarding the Slope of ip(A) 203
8.3.1 The Slope sa Due to the Folding of Wu
for Tangency Structure 203
8.3.2 The Slope s$ Resulting from Collision
with the Saddle S 205
8.4 The Relation Between f(a) and ¦tp(A) 209
8.4.1 The Linear Segment of f(a)
Resulting from the Folding
of Wu in the Presence of Tangency Structure 212
8.4.2 The Linear Segment of f(a)
Caused by Bifurcation 214
9. Chaotic Bifurcations and Critical Phenomena 217
9.1 Crisis and Energy Dissipation in the Forced Pendulum 217
9.1.1 The Slope s5 Induced by the Cantor Repellor 218
9.1.2 The Spectrum ip{W) of the Energy Dissipation Rate . . 222
9.1.3 The Formation of the Attractor Form in Figure 6.1 . 224
9.2 Fully Extended Chaos That Exists After Attractor Merging. . 224
9.2.1 Attractor Merging in the Annulus Map 225
9.2.2 Attractor Merging in the Forced Pendulum 227
XVIII Contents
9.3 Critical Phenomena and Dynamical Similarity of Chaos 230
9.3.1 The Self Similar Time Series of Critical Attractors 230
9.3.2 The Algebraic Structure Functions
of the Critical Attractor 233
9.3.3 The Internal Similarity of Bands
for the Spectrum ip(A) 235
9.3.4 The Form Characterizing the Disappearance
of Two Dimensional Fractality 238
10. Mixing and Diffusion in Chaos
of Conservative Systems 241
10.1 The Dynamical Self Similarity of the Last KAM Torus 241
10.1.1 The Self Similar Fm Time Series 242
10.1.2 The Symmetric Spectrum V/j(/3) 242
10.2 The Mixing of Widespread Chaos 243
10.2.1 The Form of ip(A)
and the Breaking of Time Reversal Symmetry 245
10.2.2 The Appearance of Anomalous Scaling Laws
for Mixing 247
10.3 Anomalous Diffusion Due to Islands
of Accelerator Mode Tori 250
10.3.1 Accelerator Mode Periodic Orbits 250
10.3.2 Long Time Velocity Correlation 251
10.3.3 The Anomalous Nature of the Statistical Structure
of the Coarse Grained Velocity 252
10.4 Diffusion and Mixing of Fluids as a Result
of Oscillation of Laminar Flow 254
10.4.1 Islands of Accelerator Mode Tori Existing
Within Turnstiles 254
10.4.2 Anomalous Mixing Due to Long Time Correlation . 257
Supplement II:
On the Structure of Chaos 261
SII.l On Off Intermittency 261
SII. 2 Anomalous Diffusion
Induced by an Externally Applied Force 262
SII.3 Transport Coefficients and the Liapunov Spectrum 263
Summary of Part II 265
Contents XIX
A. Appendix 269
A.I Periodic Points of Conservative Maps
and Their Neighborhoods 269
A.2 Variance and the Time Correlation Function 271
A.3 The Cantor Repellor of Intermittent Chaos 271
Bibliography 279
Index 295 |
| any_adam_object | 1 |
| author | Mori, Hazime Kuramoto, Yoshiki 1940- |
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| author_facet | Mori, Hazime Kuramoto, Yoshiki 1940- |
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| dewey-raw | 003.857 |
| dewey-search | 003.857 |
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| dewey-tens | 000 - Computer science, information, general works |
| discipline | Physik Informatik |
| format | Book |
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| id | DE-604.BV011791306 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T11:05:22Z |
| institution | BVB |
| isbn | 3540627448 |
| language | German English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007960160 |
| oclc_num | 247771589 |
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| owner_facet | DE-20 DE-703 DE-1050 DE-384 DE-706 DE-526 DE-634 DE-83 DE-11 DE-188 |
| physical | XIX, 299 S. Ill., graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| spelling | Mori, Hazime Verfasser aut Sanitsu kozo to kaosu Dissipative structures and chaos with 5 tables Hazime Mori ; Yoshiki Kuramoto Berlin [u.a.] Springer 1998 XIX, 299 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Aus dem Japan. übers. Dissipative Struktur (DE-588)4130307-6 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Dissipative Struktur (DE-588)4130307-6 s DE-604 Chaostheorie (DE-588)4009754-7 s Kuramoto, Yoshiki 1940- Verfasser (DE-588)172214300 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007960160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mori, Hazime Kuramoto, Yoshiki 1940- Dissipative structures and chaos with 5 tables Dissipative Struktur (DE-588)4130307-6 gnd Chaostheorie (DE-588)4009754-7 gnd |
| subject_GND | (DE-588)4130307-6 (DE-588)4009754-7 |
| title | Dissipative structures and chaos with 5 tables |
| title_alt | Sanitsu kozo to kaosu |
| title_auth | Dissipative structures and chaos with 5 tables |
| title_exact_search | Dissipative structures and chaos with 5 tables |
| title_full | Dissipative structures and chaos with 5 tables Hazime Mori ; Yoshiki Kuramoto |
| title_fullStr | Dissipative structures and chaos with 5 tables Hazime Mori ; Yoshiki Kuramoto |
| title_full_unstemmed | Dissipative structures and chaos with 5 tables Hazime Mori ; Yoshiki Kuramoto |
| title_short | Dissipative structures and chaos |
| title_sort | dissipative structures and chaos with 5 tables |
| title_sub | with 5 tables |
| topic | Dissipative Struktur (DE-588)4130307-6 gnd Chaostheorie (DE-588)4009754-7 gnd |
| topic_facet | Dissipative Struktur Chaostheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007960160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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