Scale invariance: from phase transitions to turbulence
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English French |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2012
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| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XV, 397 S. Ill., graph. Darst. |
| ISBN: | 9783642151224 9783642151231 |
Internformat
MARC
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| 245 | 1 | 0 | |a Scale invariance |b from phase transitions to turbulence |c Annick Lesne ; Michel Laguës |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2012 | |
| 300 | |a XV, 397 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1805145725710893056 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
1 CHANGES OF STATES OF MATTER 1
1.1 INTRODUCTION 1
1.2 SYMMETRY-BREAKING CHANGES OF STATE 4
1.3 OBSERVATIONS 6
1.3.1 BIFURCATIONS AND DIVERGENCES AT THE LIQUID -VAPOUR CRITICAL POINT
6
1.3.2 CRITICAL EXPONENTS 8
1.3.3 SUPERFLUID HELIUM 15
1.4 MODELS 16
1.4.1 THE IDEAL GAS MODEL 16
1.4.2 MAGNETISM AND THE ISING MODEL 18
1.4.3 A MINIMAL PHASE TRANSITION MODEL 22
1.4.4 VAN DER WAALS FLUID 23
1.4.5 WEISS MAGNET 24
1.4.6 UNIVERSALITY OF THE "MEAN FIELD" APPROACH 27
1.4.7 2D ISING MODEL 28
1.5 UNIVERSALITY OF CRITICAL BEHAVIOUR 28
1.5.1 EXTREMELY PRECISE MEASUREMENTS 28
1.5.2 INADEQUACY OF MODELS AND UNIVERSALITY OF EXPONENTS. 30 1.6
LIMITS OF THE MEAN FIELD APPROXIMATION 31
1.6.1 LANDAU-GINZBURG THEORY 31
1.6.2 SPATIAL VARIATION OF THE ORDER PARAMETER 35
REFERENCES 41
2 FRACTAL GEOMETRY 43
2.1 FRACTAL DIMENSIONS 43
2.1.1 FRACTAL STRUCTURES 43
2.1.2 FRACTAL DIMENSIONS 45
2.1.3 SELF-SIMILARITY (OR SCALE INVARIANCE) OF FRACTAL STRUCTURES 46
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1004409354
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
2.2 FRACTAL STRUCTURES IN THE NATURAL WORLD 48
2.2.1 STATISTICAL AND LIMITING PROPERTIES OF FRACTALS 48 2.2.2 THE
ORIGIN OF FRACTAL STRUCTURES 51
2.3 CONCLUSION 51
REFERENCES 53
UNIVERSALITY AS A CONSEQUENCE OF SCALE INVARIANCE 55
3.1 INTRODUCTION 56
3.1.1 ZOOM OUT AND DECIMATION 58
3.2 SCALING RELATIONS, INVARIANCE AND THE SCALING HYPOTHESIS 62 3.2.1 A
UNIFYING CONCEPT 63
3.2.2 WIDOMSCALING 64
3.2.3 DIVERGENCE OF F AND THE SCALING HYPOTHESIS 66
3.2.4 SCALING RELATIONS REVISITED WITH DECIMATION 67 3.3 TRANSITIONS AND
MODEL HAMILTONIANS 70
3.3.1 NUMBER OF COMPONENTS OF THE ORDER PARAMETER 70 3.3.2 THE
INTERACTIONS 70
3.3.3 THE ISING MODEL 71
3.4 ID AND 2D SOLUTIONS OF THE ISING MODEL 71
3.4.1 TRANSFER MATRICES 72
3.4.2 PROPERTIES OF THE ID ISING MODEL 73
3.4.3 PROPERTIES OF THE 2D ISING MODEL 75
3.5 RENORMALISATION 76
3.5.1 BRIEF HISTORY OF THE CONCEPT 76
3.5.2 RENORMALISATION STEPS 78
3.5.3 RENORMALISATION FLOW IN A SPACE OF MODELS 80
3.5.4 REMARKS 85
3.6 PHASE TRANSITIONS DESCRIBED BY RENORMALISATION 86
3.6.1 EXAMPLES OF RENORMALISATION 86
3.6.2 DEVELOPMENT IN = 4 - D 90
3.6.3 IN A ID SPACE 92
3.6.4 AND IN A 2D SPACE? 94
3.6.5 XY MODEL IN 2D: THE KOSTERLITZ-THOULESS TRANSITION . 95 3.7 AND
IN REAL SITUATIONS 99
3.7.1 CROSSOVER FROM ONE UNIVERSALITY CLASS TO ANOTHER 99 3.7.2
ESTABLISHMENT OF EQUILIBRIUM AND DYNAMIC CRITICAL EXPONENTS 100
3.7.3 SPINODAL DECOMPOSITION 100
3.7.4 TRANSITIONS AND SCALE INVARIANCE IN A FINITE SIZE SYSTEM 103
3.8 CONCLUSION: THE CORRECT USAGE OF A MODEL 105
REFERENCES 106
DIFFUSION 109
4.1 DIFFUSION: WHAT WE OBSERVE 109
4.1.1 THERMAL ENERGY 109
4.1.2 BROWNIAN MOTION 110
IMAGE 3
CONTENTS XI
4.1.3 SELF-SIMILARITY OF THE TRAJECTORIES 112
4.1.4 DIFFUSION FRONTS 114
4.1.5 DIFFUSION: EXCEPTIONAL MOTION 117
4.2 THE DIFFUSION EQUATION AND ITS VARIANTS 119
4.2.1 FICK'S LAW AND DIFFUSION EQUATION 119
4.2.2 SCALE INVARIANCE OF THE DIFFUSION EQUATION 121
4.2.3 DIFFUSION IN A POROUS MEDIUM 124
4.3 STOCHASTIC DESCRIPTIONS OF DIFFUSION 128
4.3.1 IDEAL RANDOM WALK AND NORMAL DIFFUSION 128
4.3.2 MATHEMATICAL MODELLING: THE WIENER PROCESS 131 4.4 FROM ONE SCALE
TO THE NEXT 134
4.4.1 HOW THE DIFFERENT DESCRIPTIONS ARE RELATED 134 4.4.2 EINSTEIN
FORMULA AND THE FLUCTUATION- DISSIPATION THEOREM 139
4.4.3 IRREVERSIBILITY OF DIFFUSION 145
4.5 ANOMALOUS DIFFUSION 147
4.5.1 POSSIBLE ORIGINS OF ANOMALIES 147
4.5.2 LEVY FLIGHTS 148
4.5.3 FRACTAL BROWNIAN MOTIONS 152
4.5.4 EXAMPLES 152
4.5.5 SPECTRAL DIMENSION 155
4.6 DRIVEN DIFFUSION AND PROCESSES FAR FROM EQUILIBRIUM 157 4.6.1 A
TYPICAL ONE DIMENSIONAL MODEL 157
4.6.2 DENSITY PROFILE AND PHASE DIAGRAM 158
4.6.3 LARGE DEVIATIONS 161
4.6.4 CRUCIAL DIFFERENCE FROM EQUILIBRIUM SYSTEMS 161 4.7 CONCLUSION 162
REFERENCES 163
5 THE PERCOLATION TRANSITION 167
5.1 INTRODUCTION 167
5.1.1 AN INITIAL MEAN FIELD APPROACH 168
5.1.2 A PATH THROUGH THE NETWORK: THE INFINITE CLUSTER, ITS MASS AND
BRANCHES 169
5.1.3 LIFETIME OF A FOREST FIRE AS A MEASURE OF THE PERCOLATION
THRESHOLD 171
5.1.4 SITE PERCOLATION AND BOND PERCOLATION 173
5.1.5 CORRELATED, DRIVEN AND STIRRED PERCOLATIONS 173 5.2 STATISTICS OF
CLUSTERS AND THE FERROMAGNETIC- PARAMAGNETIC TRANSITION 174
5.2.1 CORRELATIONS, CHARACTERISTIC LENGTHS AND COHERENCE LENGTH 175
5.2.2 ANALOGY WITH PHASE TRANSITIONS 175
5.2.3 HYPOTHESIS OF THE DOMINANT CLUSTER AND SCALING RELATIONS 176
5.2.4 BETHE'S MEAN FIELD CALCULATION ON CAYLEY'S TREE 177
IMAGE 4
CONTENTS
5.3 RENORMALISATION OF PERCOLATION MODELS 179
5.3.1 EXAMPLES OF RENORMALISATION IN TWO DIMENSIONAL SPACE 180
5.3.2 SCALING APPROACH ON A SYSTEM OF FINITE SIZE 182 5.3.3 FINITE SIZE
EXPONENTS 184
5.4 STRUCTURE OF THE INFINITE CLUSTER AT THE PERCOLATION THRESHOLD 185
5.4.1 FRACTAL DIMENSION OF THE INFINITE CLUSTER 186
5.5 DYNAMIC PROPERTIES NEAR A PERCOLATION TRANSITION 187 5.5.1
CONDUCTIVITY, DIFFUSION AND WALKING ANTS 188 5.5.2 DIFFUSION AND
CONDUCTION IN PERCOLATING CLUSTERS 189 5.6 CONCLUSION 193
REFERENCES 194
SPATIAL CONFORMATION OF POLYMERS 197
6.1 INTRODUCTION 197
6.1.1 REMARKABLE SCALING PROPERTIES 197
6.1.2 PERSISTENCE LENGTH 199
6.2 CONFORMATIONS OF AN ISOLATED FLEXIBLE POLYMER 202
6.2.1 POLYMERS AND RANDOM WALKS 202
6.2.2 SELF-AVOIDING RANDOM WALKS 203
6.2.3 THE ROLE OF SOLVENT: THE POINT 206
6.2.4 SCALING LAWS FOR A POLYELECTROLYTE 208
6.3 THEORETICAL TOOLS 211
6.3.1 FLORY THEORY 211
6.3.2 GOOD AND BAD SOLVENTS, 0 POINT AND FLORY-HUGGINS THEORY 213
6.3.3 RENORMALISATION APPROACHES 220
6.4 POLYMER SOLUTIONS 226
6.4.1 POLYMERMELTS 227
6.4.2 SEMIDILUTE SOLUTIONS 227
6.5 CONCLUSION 229
REFERENCES 230
HIGH TEMPERATURE SUPERCONDUCTORS 231
7.1 SUPERCONDUCTIVITY AND SUPERCONDUCTORS 231
7.1.1 MECHANISMS AND PROPERTIES 232
7.1.2 FAMILIES OF SUPERCONDUCTING COMPOUNDS 237
7.1.3 APPLICATIONS: FROM TELECOMMUNICATIONS TO MAGNETOENCEPHALOGRAPHY
238
7.2 THE PHASE DIAGRAM 238
7.2.1 DOPING 239
7.2.2 THE THERMAL TRANSITION 242
7.3 QUANTUM TRANSITIONS IN SUPERCONDUCTORS 249
7.3.1 SUPERCONDUCTOR-INSULATOR TRANSITION WITH RESPECT TO FILM THICKNESS
251
7.3.2 DOPING TRANSITIONS 253
IMAGE 5
CONTENTS XIII
7.4 AN OPEN DOMAIN 256
REFERENCES 256
8 GROWTH AND ROUGHNESS OF INTERFACES 259
8.1 INTRODUCTION 259
8.1.1 DISCRETE MODELS, CONTINUOUS EQUATIONS 261
8.1.2 CHARACTERISTIC EXPONENTS OF GROWTH 262
8.1.3 CORRELATIONS 264
8.1.4 MODEL OF RANDOM GROWTH 265
8.2 LINEAR APPROACH INCLUDING RELAXATION 266
8.2.1 SYMMETRY STUDY 267
8.2.2 THE EDWARDS-WILKINSON EQUATION 268
8.3 THE KARDAR-PARISI-ZHANG EQUATION 271
8.3.1 CONSTRUCTION OF THE KPZ EQUATION BY PHYSICAL ARGUMENTS 271
8.3.2 KPZ EXPONENTS FROM SCALING ARGUMENTS 272
8.4 DYNAMIC RENORMALISATION 273
8.4.1 RENORMALISATION FLOW EQUATIONS 274
8.4.2 KPZ REGIMES 276
8.5 MOLECULAR BEAM EPITAXY (MBE) 278
8.5.1 LINEAR MBE EQUATION 278
8.5.2 NONLINEAR MBE EQUATION 282
8.6 ROUGHENING TRANSITION 283
8.6.1 CONTINUOUS MODEL 284
8.6.2 RENORMALISATION 285
8.6.3 NONEQUILIBRIUM ROUGHENING TRANSITION 287
8.7 UNIVERSALITY CLASSES OF GROWTH 288
REFERENCES 290
9 DYNAMICAL SYSTEMS, CHAOS AND TURBULENCE 293
9.1 A DIFFERENT VIEW OF THE DYNAMICS OF A SYSTEM 294
9.1.1 A "GEOMETRY" OF DYNAMICS 294
9.1.2 BIFURCATIONS 298
9.1.3 ANALOGY WITH PHASE TRANSITIONS 302
9.1.4 NORMAL FORMS AND STRUCTURAL STABILITY 304
9.2 DETERMINISTIC CHAOS 307
9.2.1 A FEW REMARKABLE EXAMPLES 308
9.2.2 STATISTICAL DESCRIPTION AND ERGODICITY 311
9.2.3 THE BASIC INGREDIENTS 312
9.2.4 TRANSITION TO CHAOS 318
9.2.5 RANGE AND LIMITS OF THE CONCEPT OF CHAOS 323
9.3 CHAOS AS THE FOUNDATION OF STATISTICAL MECHANICS 325
9.3.1 BOLTZMANN'S ERGODIC HYPOTHESIS 325
9.3.2 CHAOTIC HYPOTHESIS AND NONEQUILIBRIUM STATISTICAL MECHANICS 326
9.3.3 CHAOS AND TRANSPORT PHENOMENA 328
IMAGE 6
X IV CONTENTS
9.4 INTERMITTENCY 328
9.4.1 INTERMITTENCY AFTER A SADDLE-NODE BIFURCATION 329 9.4.2 ON-OFF
INTERMITTENCY 330
9.5 FULLY DEVELOPED TURBULENCE 334
9.5.1 SCALE INVARIANCE OF HYDRODYNAMIC EQUATIONS 334 9.5.2 TURBULENCE
THRESHOLD 335
9.5.3 A QUALITATIVE PICTURE: RICHARDSON'S CASCADE 336 9.5.4 EMPIRICAL
SCALING LAWS 337
9.5.5 KOLMOGOROV'S THEORY (1941) 338
9.5.6 MULTIFRACTAL ANALYSIS 339
9.5.7 AN OPEN FIELD TODAY 341
REFERENCES 342
10 SELF-ORGANISED CRITICALITY 345
10.1 A NEW CONCEPT: SELF-ORGANISED CRITICALITY 345
10.1.1 SANDPILE 345
10.1.2 FOREST FIRES 349
10.1.3 THE BASIC INGREDIENTS 350
10.1.4 IN PRACTICE 352
10.2 EXAMPLES 352
10.2.1 DIFFUSION FRONTS 352
10.2.2 TRAFFIC FLOW AND TRAFFIC JAMS 353
10.2.3 EARTHQUAKES 354
10.2.4 INFLATION OF THE LUNGS 355
10.2.5 ECOSYSTEMS AND EVOLUTION 356
10.2.6 OTHER EXAMPLES 357
10.3 CONCLUSION 357
10.3.1 TOWARDS AN EXPLANATORY PICTURE: FEEDBACK LOOPS AND MARGINAL
STABILITY 357
10.3.2 SUCCESS AND RESERVATIONS 358
REFERENCES 359
11 SCALE INVARIANCE IN BIOLOGY 361
11.1 INTRODUCTION 361
11.2 UNIVERSALITY IN THE METABOLISM OF LIVING SYSTEMS 362 11.2.1
OBSERVATION OF ALLOMETRIC SCALING LAWS 362
11.2.2 PROPOSED EXPLANATIONS 364
11.2.3 OBJECTIONS TO THE RELIABILITY OF THE SCALING LAW 368 11.2.4 OTHER
EXAMPLES 369
11.3 LONG RANGE CORRELATIONS 370
11.3.1 CODING AND NON CODING DNA SEQUENCES 370
11.3.2 HEART RATE 374
11.3.3 ELECTROENCEPHALOGRAPHY (EEG) 375
11.4 BIOLOGICAL NETWORKS: COMPLEX NETWORKS 376
11.4.1 A NEW STATISTICAL MECHANICS 376
11.4.2 REAL NETWORKS: RANDOM GRAPHS? 377
IMAGE 7
CONTENTS XV
11.4.3 SCALE-FREE NETWORKS 379
11.4.4 IN PRACTICE: RECONSTRUCTION OF A COMPLEX NETWORK 380 11.4.5
AVENUES TO EXPLORE THE MULTISCALE STRUCTURE OF NETWORKS 380
11.5 CONCLUSION: A MULTISCALE APPROACH FOR LIVING SYSTEMS 381 REFERENCES
382
12 POWER AND LIMITS OF SCALING APPROACHES 385
12.1 CRITICALITY AND SCALING LAWS 385
12.2 EXPERIMENTAL DETERMINATION OF SCALING LAWS 386
12.3 RENORMALISATION AND STATUS OF MODELS 388
12.4 OPEN PERSPECTIVES 389
INDEX 391 |
| any_adam_object | 1 |
| author | Lesne, Annick Laguës, Michel 1946- |
| author_GND | (DE-588)1142242021 |
| author_facet | Lesne, Annick Laguës, Michel 1946- |
| author_role | aut aut |
| author_sort | Lesne, Annick |
| author_variant | a l al m l ml |
| building | Verbundindex |
| bvnumber | BV039757506 |
| classification_rvk | UG 3800 |
| classification_tum | PHY 065f |
| ctrlnum | (OCoLC)690089537 (DE-599)DNB1004409354 |
| dewey-full | 530.474 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.474 |
| dewey-search | 530.474 |
| dewey-sort | 3530.474 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV039757506 |
| illustrated | Illustrated |
| indexdate | 2024-07-21T00:18:35Z |
| institution | BVB |
| isbn | 9783642151224 9783642151231 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024618770 |
| oclc_num | 690089537 |
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| owner_facet | DE-11 DE-19 DE-BY-UBM DE-703 DE-355 DE-BY-UBR DE-91G DE-BY-TUM |
| physical | XV, 397 S. Ill., graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer |
| record_format | marc |
| spelling | Lesne, Annick Verfasser aut Invariances d'échelle Scale invariance from phase transitions to turbulence Annick Lesne ; Michel Laguës Berlin [u.a.] Springer 2012 XV, 397 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Kritisches Phänomen (DE-588)4165788-3 gnd rswk-swf Selbstähnlichkeit (DE-588)4286650-9 gnd rswk-swf Kritisches Phänomen (DE-588)4165788-3 s Selbstähnlichkeit (DE-588)4286650-9 s DE-604 Laguës, Michel 1946- Verfasser (DE-588)1142242021 aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3513880&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=024618770&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lesne, Annick Laguës, Michel 1946- Scale invariance from phase transitions to turbulence Kritisches Phänomen (DE-588)4165788-3 gnd Selbstähnlichkeit (DE-588)4286650-9 gnd |
| subject_GND | (DE-588)4165788-3 (DE-588)4286650-9 |
| title | Scale invariance from phase transitions to turbulence |
| title_alt | Invariances d'échelle |
| title_auth | Scale invariance from phase transitions to turbulence |
| title_exact_search | Scale invariance from phase transitions to turbulence |
| title_full | Scale invariance from phase transitions to turbulence Annick Lesne ; Michel Laguës |
| title_fullStr | Scale invariance from phase transitions to turbulence Annick Lesne ; Michel Laguës |
| title_full_unstemmed | Scale invariance from phase transitions to turbulence Annick Lesne ; Michel Laguës |
| title_short | Scale invariance |
| title_sort | scale invariance from phase transitions to turbulence |
| title_sub | from phase transitions to turbulence |
| topic | Kritisches Phänomen (DE-588)4165788-3 gnd Selbstähnlichkeit (DE-588)4286650-9 gnd |
| topic_facet | Kritisches Phänomen Selbstähnlichkeit |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3513880&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024618770&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lesneannick invariancesdechelle AT laguesmichel invariancesdechelle AT lesneannick scaleinvariancefromphasetransitionstoturbulence AT laguesmichel scaleinvariancefromphasetransitionstoturbulence |