Scale invariance: self-similarity of the physical world
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Weinheim
Wiley-VCH
2015
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XX, 278 S. Ill., graph. Darst. |
| ISBN: | 3527413359 9783527413355 9783527687343 |
Internformat
MARC
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| 300 | |a XX, 278 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
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| adam_text |
VII
CONTENTS
PREFACE
XI
ACKNOWLEDGMENTS
XIII
INTRODUCTION
XV
1 ARBITRARY MEASURES OF THE PHYSICAL WORLD 1
1.1 SIMILARITY 1
1.2 DIMENSIONAL SIMILARITY 3
1.3 PHYSICAL EQUATIONS AND THE 'PI' THEOREM 6
1.4 APPLICATIONS OF THE PI THEOREM 10
1.4.1 PLANE PENDULUM 11
1.4.2 PIPE FLOW OF A FLUID 16
1.4.3 STEADY MOTION OF A RIGID OBJECT IN VISCOUS 'FLUID' 18
1.4.4 DIFFUSION AND SELF-SIMILARITY 20
1.4.5 SHIP WAVE DRAG 26
1.4.6 ADIABATIC GAS FLOW 28
1.4.7 TIME-DEPENDENT ADIABATIC FLOW 30
1.4.8 POINT EXPLOSION IN A GASEOUS MEDIUM 33
1.4.9 APPLICATIONS IN FUNDAMENTAL PHYSICS 35
1.4.10 DRAG ON A FLEXIBLE OBJECT IN STEADY MOTION 41
1.4.11 DIMENSIONAL ANALYSIS OF MAMMALS 42
1.4.12 TREES 47
REFERENCES 51
2 LIE GROUPS
AND SCALING SYMMETRY 53
2.1 THE RESCALING GROUP 53
2.1.1 RESCALING PHYSICAL OBJECTS 55
2.1.2 RECONCILIATION WITH THE BUCKINGHAM PI THEOREM 59
2.1.3 RESCALING AND SELF-SIMILARITY AS A LIE ALGEBRA 60
2.1.4 PRACTICAL LIE SELF-SIMILARITY 63
2.2 FAMILIAR PHYSICAL EXAMPLES
68
2.2.1 LINE VORTEX DIFFUSION: REPRISE 69
2.2.2 BURGERS' EQUATION 71
2.3 LESS FAMILIAR EXAMPLES 77
HTTP://D-NB.INFO/1059940337
VIII CONTENTS
2.3.1 SELF-GRAVITATING COLLISIONLESS PARTICLES: THE BOLTZMANN-POISSON
PROBLEM 77
REFERENCES 84
3 POINCARE GROUP PLUS RESCALING GROUP 87
3.1 GALILEAN SPACE-TIME 87
3.2 MINKOWSKI SPACE-TIME 96
3.2.1 SELF-SIMILAR LORENTZ BOOST 96
3.2.2 SELF-SIMILAR BOOST/ROTATION 102
3.3 KINEMATIC GENERAL RELATIVITY 108
REFERENCES 119
4 INSTRUCTIVE CLASSIC PROBLEMS 121
4.1 INTRODUCTION 121
4.2 IDEAL FLUID FLOW PAST A WEDGE: SELF-SIMILARITY OF THE 'SECOND
KIND' 121
4.3 BOUNDARY LAYER ON A FLAT PLATE: THE BLASIUS PROBLEM 126
4.4 ADIABATIC SELF-SIMILARITY IN THE DIFFUSION EQUATION 133
4.5 WAVES IN A UNIFORMLY ROTATING FLUID 140
REFERENCES 146
5 VARIATIONS ON LIE SELF-SIMILARITY 147
5.1 VARIATIONS ON THE BOLTZMANN-POISSON SYSTEM 147
5.1.1 INFINITE SELF-GRAVITATING COLLISIONLESS SPHERES 147
5.1.2 FINITE SELF-GRAVITATING COLLISIONLESS SPHERES 155
5.1.3 OTHER APPROACHES TO FINITE SPHERES 159
5.2 HYDRODYNAMIC EXAMPLES 164
5.2.1 GENERAL NAVIER-STOKES THEORY 164
5.2.2 MODIFIED COUETTE FLOW 166
5.2.3 FLOW AT LARGE SCALE INSIDE A LAMINAR WAKE 170
5.3 AXI-SYMMETRIC IDEAL MAGNETOHYDRODYNAMICS 178
5.3.1 INCOMPLETE SELF-SIMILARITY AS SEPARABLE MULTI-VARIABLE
SELF-SIMILARITY 182
5.3.2 ISOTHERMAL COLLAPSE 185
REFERENCES 187
6 EXPLORATIONS 189
6.1 ANISOTROPIC SELF-SIMILARITY 189
6.1.1 ANISOTROPIC SIMILARITY 192
6.2 MATHEMATICAL VARIATIONS 193
6.3 PERIODICITY AND SIMILARITY 198
6.3.1 LOG PERIODICITY AND SELF-SIMILARITY: DIFFUSION
EQUATION 203
REFERENCES 207
7 RENORMALIZATION GROUP AND NOETHER INVARIANTS 209
7.1 HYBRID LIE SELF-SIMILARITY/RENORMALIZATION GROUP 209
7.1.1 RENORMALIZING MORE COMPLICATED EQUATIONS 216
7.1.2 SCHRODINGER: ADIABATIC AND FRACTAL 219
7.1.3 NOETHER INVARIANTS AND SELF-SIMILARITY 223
REFERENCES 229
8 SCALING IN HYDRODYNAMICAL TURBULENCE 231
8.1 GENERAL INTRODUCTION 231
8.2 HOMOGENEOUS, ISOTROPIC, DECAYING TURBULENCE 232
8.2.1 THIRD-ORDER CORRELATION NEGLIGIBLE 236
8.2.2 RENORMALIZATION AND HOMOGENEOUS, ISOTROPIC, TURBULENCE 240
8.3 DIMENSIONAL PHENOMENOLOGY OF STATIONARY TURBULENCE 242
8.4 STRUCTURE IN 2D TURBULENCE 246
8.4.1 SIMILARITY OF TIME-DEPENDENT 2D VORTICAL FLUID FLOW 248
8.4.2 SIMILARITY IN PHYSICALLY STEADY, INVISCID VORTICAL FLUID FLOW 258
REFERENCES 264
EPILOGUE 267
APPENDIX: EXAMPLES FROM THE LITERATURE 269
CONTENTS IX
INDEX 273 |
| any_adam_object | 1 |
| author | Henriksen, Richard N. 1940- |
| author_GND | (DE-588)142721786 |
| author_facet | Henriksen, Richard N. 1940- |
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| author_sort | Henriksen, Richard N. 1940- |
| author_variant | r n h rn rnh |
| building | Verbundindex |
| bvnumber | BV042549887 |
| classification_rvk | SK 950 UG 3900 |
| ctrlnum | (OCoLC)894135758 (DE-599)DNB1059940337 |
| dewey-full | 530 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530 |
| dewey-search | 530 |
| dewey-sort | 3530 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV042549887 |
| illustrated | Illustrated |
| indexdate | 2024-08-03T02:22:13Z |
| institution | BVB |
| isbn | 3527413359 9783527413355 9783527687343 |
| language | English |
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| physical | XX, 278 S. Ill., graph. Darst. |
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| publishDateSearch | 2015 |
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| publisher | Wiley-VCH |
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| spelling | Henriksen, Richard N. 1940- Verfasser (DE-588)142721786 aut Scale invariance self-similarity of the physical world Richard N. Henriksen Weinheim Wiley-VCH 2015 XX, 278 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Selbstähnlichkeit (DE-588)4286650-9 gnd rswk-swf Fraktale Dimension (DE-588)4796905-2 gnd rswk-swf Dimensionsanalyse (DE-588)4133116-3 gnd rswk-swf Dimensionsanalyse (DE-588)4133116-3 s Selbstähnlichkeit (DE-588)4286650-9 s Fraktale Dimension (DE-588)4796905-2 s DE-604 Erscheint auch als Online-Ausgabe, EPUB 978-3-527-68735-0 Erscheint auch als Online-Ausgabe, MOBI 978-3-527-68736-7 Erscheint auch als Online-Ausgabe, PDF 978-3-527-68733-6 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4809113&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027983793&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Henriksen, Richard N. 1940- Scale invariance self-similarity of the physical world Selbstähnlichkeit (DE-588)4286650-9 gnd Fraktale Dimension (DE-588)4796905-2 gnd Dimensionsanalyse (DE-588)4133116-3 gnd |
| subject_GND | (DE-588)4286650-9 (DE-588)4796905-2 (DE-588)4133116-3 |
| title | Scale invariance self-similarity of the physical world |
| title_auth | Scale invariance self-similarity of the physical world |
| title_exact_search | Scale invariance self-similarity of the physical world |
| title_full | Scale invariance self-similarity of the physical world Richard N. Henriksen |
| title_fullStr | Scale invariance self-similarity of the physical world Richard N. Henriksen |
| title_full_unstemmed | Scale invariance self-similarity of the physical world Richard N. Henriksen |
| title_short | Scale invariance |
| title_sort | scale invariance self similarity of the physical world |
| title_sub | self-similarity of the physical world |
| topic | Selbstähnlichkeit (DE-588)4286650-9 gnd Fraktale Dimension (DE-588)4796905-2 gnd Dimensionsanalyse (DE-588)4133116-3 gnd |
| topic_facet | Selbstähnlichkeit Fraktale Dimension Dimensionsanalyse |
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