The N-vortex problem: analytical techniques
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2001
|
| Schriftenreihe: | Applied mathematical sciences
145 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 357 - 409 |
| Beschreibung: | XVII, 415 S. Ill., graph. Darst. |
| ISBN: | 0387952268 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | PAUL K. NEWTON THE N- VORTEX PROBLEM ANALYTICAL TECHNIQUES WITH 79
FIGURES SPRINGER CONTENTS PREFACE VII 1 INTRODUCTION 1 1.1 VORTICITY
DYNAMICS 1 1.1.1 BASICS 1 1.1.2 INVARIANTS OF THE EULER EQUATIONS 5
1.1.3 TWO DIMENSIONS 8 1.1.4 POINT VORTEX DECOMPOSITION 12 1.1.5
BIBLIOGRAPHIC NOTES 18 1.2 -HAMILTONIAN DYNAMICS 20 1.2.1 CANONICAL
FORMULATION 20 1.2.2 NONCANONICAL FORMULATION 27 1.2.3 GEOMETRIC FLUID
MECHANICS 32 1.2.4 INTEGRABLE SYSTEMS AND ACTION-ANGLE COORDINATES 34
1.2.5 NEAR-INTEGRABLE SYSTEMS: KAM THEORY AND THE POINCARE-MELNIKOV
METHOD 42 1.2.6 ADIABATIC INVARIANTS AND GEOMETRIC PHASES 50 1.3 SUMMARY
OF BASIC QUESTIONS 61 1.4 EXERCISES 62 2 N VORTICES IN THE PLANE 65 2.1
GENERAL FORMULATION 66 2.2 N = 3 73 XVI CONTENTS 2.2.1 EQUILIBRIA 77
2.2.2 TRILINEAR FORMULATION 81 2.2.3 COLLAPSE 84 2.3 N = 4 88 2.3.1
REDUCTION 92 2.3.2 APPLICATION OF KAM THEORY 95 2.3.3 NONINTEGRABLE
CASES 97 2.4 BIBLIOGRAPHIC NOTES 112 2.5 EXERCISES 114 3 DOMAINS WITH
BOUNDARIES 117 3.1 GREEN S FUNCTION OF THE FIRST KIND 118 3.2 METHOD OF
IMAGES 122 3.3 CONFORMAL MAPPING TECHNIQUES 128 3.4 BREAKING
INTEGRABILITY 133 3.5 BIBLIOGRAPHIC NOTES 135 3.6 EXERCISES 136 4 VORTEX
MOTION ON A SPHERE 139 4.1 GENERAL FORMULATION 140 4.2 DYNAMICS OF THREE
VORTICES 146 4.2.1 GEOMETRIC CLASSIFICATION SCHEME 148 4.2.2 EQUILIBRIA
149 4.3 PHASE PLANE DYNAMICS 160 4.4 3-VORTEX COLLAPSE 163 4.4.1
GEOMETRY OF PARTNER STATES 170 4.5 STEREOGRAPHIC PROJECTION 172 4.6
INTEGRABLE STREAMLINE TOPOLOGIES 175 4.6.1 TWO VORTICES 177 4.6.2 THREE
VORTICES 180 4.6.3 ROTATING FRAMES 190 4.7 BOUNDARIES 193 4.7.1 IMAGES
195 4.8 BIBLIOGRAPHIC NOTES 204 4.9 EXERCISES 206 5 GEOMETRIC PHASES 209
5.1 GEOMETRIC PHASES IN VARIOUS CONTEXTS 210 5.2 PHASE CALCULATIONS FOR
SLOWLY VARYING SYSTEMS 216 5.3 DEFINITION OF THE ADIABATIC HANNAY ANGLE
223 5.4 3-VORTEX PROBLEM 228 5.4.1 GEOMETRIC INTERPRETATION 232 5.4.2
OTHER CONFIGURATIONS 234 5.5 APPLICATIONS 240 5.5.1 SPIRAL STRUCTURES
240 CONTENTS XVII 5.5.2 PATTERN EVOCATION 243 5.6 EXERCISES 244
STATISTICAL POINT VORTEX THEORIES 247 6.1 BASICS OF STATISTICAL PHYSICS
249 6.1.1 PROBABILITY DISTRIBUTION FUNCTIONS 249 6.1.2 ELEMENTS OF
ERGODIC THEORY 255 6.1.3 NEGATIVE TEMPERATURE STATES 258 6.2 STATISTICAL
EQUILIBRIUM THEORIES 260 6.2.1 POINTIN-LUNDGREN THEORY IN THE UNBOUNDED
PLANE 260 6.2.2 POINTIN-LUNDGREN THEORY IN BOUNDED REGIONS . . . 268 6.3
MAXIMUM ENTROPY THEORIES 273 6.3.1 JOYCE*MONTGOMERY APPROACH 273 6.4
NONEQUILIBRIUM THEORIES 277 6.5 EXERCISES 283 VORTEX PATCH MODELS 285
7.1 INTRODUCTION TO VORTEX PATCHES 286 7.2 THE KIDA-NEU VORTEX 287 7.3
TIME-DEPENDENT STRAIN 290 7.4 MELANDER-ZABUSKY-STYCZEK MODEL 294 7.5
GEOMETRIC PHASE FOR COROTATING PATCHES 302 7.6 VISCOUS SHEAR LAYER MODEL
307 7.7 BIBLIOGRAPHIC NOTES 313 7.8 EXERCISES 315 VORTEX FILAMENT MODELS
317 8.1 INTRODUCTION TO VORTEX FILAMENTS AND THE LIE 318 8.2
DARIOS-BETCHOV INTRINSIC EQUATIONS 332 8.3 HASIMOTO S TRANSFORMATION 336
8.4 LIA INVARIANTS 342 8.5 VORTEX-STRETCHING MODELS 345 8.6 NEARLY
PARALLEL FILAMENTS 348 8.7 THE VORTON MODEL 353 8.8 EXERCISES 354
REFERENCES 357 INDEX 411
|
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| discipline | Physik Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:54:45Z |
| institution | BVB |
| isbn | 0387952268 |
| language | English |
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| physical | XVII, 415 S. Ill., graph. Darst. |
| publishDate | 2001 |
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| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Newton, Paul K. Verfasser aut The N-vortex problem analytical techniques Paul K. Newton New York [u.a.] Springer 2001 XVII, 415 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 145 Literaturverz. S. 357 - 409 Wirbel <Physik> - Vielkörperproblem - Hamilton-Formalismus Vortex-motion Hamilton-Formalismus (DE-588)4376155-0 gnd rswk-swf Vielkörperproblem (DE-588)4078900-7 gnd rswk-swf Wirbel Physik (DE-588)4128386-7 gnd rswk-swf Wirbel Physik (DE-588)4128386-7 s Vielkörperproblem (DE-588)4078900-7 s Hamilton-Formalismus (DE-588)4376155-0 s DE-604 Applied mathematical sciences 145 (DE-604)BV000005274 145 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009538527&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Newton, Paul K. The N-vortex problem analytical techniques Applied mathematical sciences Wirbel <Physik> - Vielkörperproblem - Hamilton-Formalismus Vortex-motion Hamilton-Formalismus (DE-588)4376155-0 gnd Vielkörperproblem (DE-588)4078900-7 gnd Wirbel Physik (DE-588)4128386-7 gnd |
| subject_GND | (DE-588)4376155-0 (DE-588)4078900-7 (DE-588)4128386-7 |
| title | The N-vortex problem analytical techniques |
| title_auth | The N-vortex problem analytical techniques |
| title_exact_search | The N-vortex problem analytical techniques |
| title_full | The N-vortex problem analytical techniques Paul K. Newton |
| title_fullStr | The N-vortex problem analytical techniques Paul K. Newton |
| title_full_unstemmed | The N-vortex problem analytical techniques Paul K. Newton |
| title_short | The N-vortex problem |
| title_sort | the n vortex problem analytical techniques |
| title_sub | analytical techniques |
| topic | Wirbel <Physik> - Vielkörperproblem - Hamilton-Formalismus Vortex-motion Hamilton-Formalismus (DE-588)4376155-0 gnd Vielkörperproblem (DE-588)4078900-7 gnd Wirbel Physik (DE-588)4128386-7 gnd |
| topic_facet | Wirbel <Physik> - Vielkörperproblem - Hamilton-Formalismus Vortex-motion Hamilton-Formalismus Vielkörperproblem Wirbel Physik |
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