Fractals, scaling and growth far from equilibrium:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1998
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge nonlinear science series
5 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 674 S. Ill., graph. Darst. |
| ISBN: | 0521452538 |
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| 650 | 7 | |a Mathematische fysica |2 gtt | |
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| 650 | 4 | |a Scaling laws (Statistical physics) | |
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| adam_text | FRACTALS, SCALING AND GROWTH FAR FROM EQUILIBRIUM PAUL MEAKIN DEPARTMENT
OF PHYSICS, UNIVERSITY OF OSLO CAMBRIDGE UNIVERSITY PRESS PREFACE XIII
CHAPTER I PATTERN FORMATION FAR FROM EQUILIBRIUM 1.1 POWER LAWS AND
SCALING 4 1.2 THE LOGISTIC MAP 16 1.3 THE VARIETY OF PATTERNS IN NATURE
22 1.3.1 EUCLIDEAN PATTERNS 24 1.3.2 CELLULAR PATTERNS 2J 1.3.3 SPIRAL
AND HELIX PATTERNS 31 1.3.4 LABYRINTHINE PATTERNS 32 * 1.3.5 FLUID
CONVECTION PATTERNS 34 1.4 MOVING-BOUNDARY PROCESSES 36 1.4.1
SOLIDIFICATION 37 1.4.2 GROWTH FROM SOLUTION 39 1.4.3 SOLIDIFICATION OF
IMPURE MATERIALS 42 1.4.4 VISCOUS FINGERING 44 1.4.5 PATTERN SELECTION
45 1.4.6 ANISOTROPY AND GROWTH VELOCITY 46 1.4.7 LAPLACIAN GROWTH 49
1.4.8 INSTABILITIES 49 1.4.9 CHARACTERISTIC LENGTHS 50 1.4.10 BEYOND
LINEAR-STABILITY ANALYSIS 5/ 1.5 SOLUTION OF INTERFACE EQUATIONS OF
MOTION VN VLLL 1.5.1 1.5.2 1.6 1.6.1 1.6.2 I-7 1.8 I-9 1.10 CONTENTS
NUMERICAL SOLUTION OF THE LOCAL MODELS 53 COMPLEX AND DISORDERLY
AGGREGATES 59 POLYMERS 60 SCALING SYMMETRY 61 NOTATION 62 MONTE CARLO
METHODS ADDITIONAL INFORMATION NON-LOCAL EQUATIONS PATTERNS 57 62 64
CHAPTER 2 FRACTALS AND SCALING 65 2.1 SELF-SIMILAR FRACTALS 65 2.1.1
STATISTICAL SELF-SIMILARITY 69 2.1.2 LACUNARITY JO 2.1.3 DETERMINATION
OF THE FRACTAL DIMENSIONALITY J4 2.1.4 THE DEVIL S STAIRCASE 81 2.2
SIMPLE RULES 83 2.3 FINITE-SIZE EFFECTS AND CROSSOVERS 85 2.4 POWER LAW
DISTRIBUTIONS 100 2.5 SCALING 104 2.5.1 CORRECTIONS TO SCALING IN 2.5.2
MULTISCALING 112 2.6 FRACTAL TREES AND INHOMOGENEOUS FRACTALS 113 2.7
SELF-AFFINE FRACTALS 119 2.7.1 GENERATION OF SELF-AFFINE SURFACES 124
2.7.2 THE GEOMETRY AND GROWTH OF ROUGH SURFACES 130 2.7.3
CHARACTERIZATION OF SELF-AFFINE ROUGH SURFACES 135 2.7.4 FINITE-SIZE
EFFECTS AND CROSSOVERS 152 2.7.5 STATUS 153 2.7.6 LONG RANGE PERSISTENCE
755 2.8 MULTIFRACTALS 160 2.9 UNIVERSALITY 765 2.10 ADDITIONAL
INFORMATION 766 CHAPTER 3 GROWTH MODELS 168 3.1 CLUSTER GROWTH AND
CLUSTER SURFACES 769 3.2 LATTICE ANIMALS 772 3.3 RANDOM WALKS 773
CONTENTS IX 3.3.1 SELF-AVOIDING RANDOM WALKS 174 3.3.2 INDEFINITELY
GROWING WALKS IJ6 3.3.3 THE DIFFUSION-LIMITED GROWTH WALK IJJ 3.3.4
RANDOM WALKS ON RANDOM SUBSTRATES 181 3.3.5 ACTIVE RANDOM WALK MODELS
182 3.4 CLUSTER GROWTH MODELS 7 S3 3.4.1 THE EDEN MODEL 184 3.4.2
BALLISTIC AGGREGATION 187 3.4.3 THE DIFFUSION-LIMITED AGGREGATION MODEL
189 3.4.4 THE DIELECTRIC BREAKDOWN MODEL 193 3.4.5 THE SCALING STRUCTURE
OF DLA 198 3.4.6 OTHER ASPECTS OF DLA 210 3.4.7 DIFFUSION-LIMITED
ANNIHILATION 211 3.5 PERCOLATION AND INVASION PERCOLATION 214 3.5.1
GROWTH MODELS FOR PERCOLATION 229 3.5.2 INVASION PERCOLATION 231 3.5.3
DIFFUSION FRONTS AND THE EFFECT OF GRADIENTS 234 3.5.4 DIRECTED
PERCOLATION 239 3.5.5 THE SCREENED GROWTH MODEL 242 3.5.6 FACETED GROWTH
MODELS 243 3.6 PACKING MODELS 246 3.7 GROWTH MODELS RELATED TO DLA 250
3.7.1 HOMOGENEOUS PERTURBATIONS 253 3.7.2 INHOMOGENEOUS PERTURBATIONS
25,6 3.7.3 ATTRACTIVE INTERACTION MODEL 269 3.7.4 GROWTH ON FIBERS AND
SURFACES 272 3.7.5 SIMPLIFIED DLA MODELS 279 3.8 NOISE REDUCTION AND
DETERMINISTIC MODELS 285 3.8.1 LATTICE STRUCTURE EFFECTS 291 3.9 MODELS
WITH QUENCHED DISORDER 295 3.9.1 GROWTH IN HIGH-DIMENSIONALITY SPACES
297 3.10 THEORETICAL METHODS 299 3.10.1 MEAN FIELD THEORIES 302 3.10.2
WEDGE GROWTH THEORIES 306 3.10.3 REAL-SPACE RENORMALIZATION THEORIES 316
3.10.4 OTHER APPROACHES 319 3.11 ADDITIONAL INFORMATION 325 CONTENTS
CHAPTER 4 EXPERIMENTAL STUDIES 326 4.1 DLA PROCESSES 327 4.1.1
ELECTROCHEMICAL DEPOSITION 328 4.1.2 FLUID-FLUID DISPLACEMENT
EXPERIMENTS 342 4.1.3 THIN FILMS AND INTERFACES 348 4.1.4 DISSOLUTION,
MELTING AND EROSION OF POROUS MEDIA 356 4.1.5 SOLIDIFICATION AND
CRYSTALLIZATION 360 4.1.6 DIELECTRIC BREAKDOWN 363 4.1.7 GROWTH
PROBABILITY DISTRIBUTIONS 364 4.2 DENSE BRANCHING MORPHOLOGY 366 4.2.1
ELECTROCHEMICAL DEPOSITION 369 4.2.2 THIN FILMS 375 4.2.3 FLUID-FLUID
DISPLACEMENT 377 4.2.4 SPHERULITES 380 4.3 PERCOLATION 381 4.4 INVASION
PERCOLATION 384 4.5 DISPLACEMENT IN COMPLEX FLUIDS 388 4.5.1 POLYMER
SOLUTIONS 389 4.5.2 COLLOIDAL SYSTEMS 389 4.5.3 FOAMS 393 4.5.4 FRACTAL
SYSTEMS 394 4.6 OTHER 2-DIMENSIONAL PATTERNS 397 4.7 ADDITIONAL
INFORMATION 400 CHAPTER 5 THE GROWTH OF SURFACES AND INTERFACES 401 5.1
THE STRUCTURE AND GROWTH OF ROUGH SURFACES 404 5.1.1 BASIC SURFACE
GROWTH EQUATIONS 405 5.1.2 SURFACE DIFFUSION 408 5.1.3 UNIVERSALITY
CLASSES 411 5.1.4 EXPONENT SCALING RELATIONSHIPS 415 5.1.5 THE
KURAMOTO-SIVASHINSKY EQUATION 417 5.2 SIMPLE MODELS 418 5.2.1 EDEN
GROWTH MODELS 419 5.2.2 BALLISTIC DEPOSITION MODELS 420 5.2.3
SOLID-ON-SOLID MODELS 425 5.2.4 THE POLYNUCLEAR GROWTH MODEL 428 5.2.5
DIRECTED POLYMERS 429 5.2.6 LANGEVIN DYNAMICS SIMULATIONS 432 CONTENTS
XI 5.2.7 DIRECTED PERCOLATION 433 5.3 THEORETICALLY MOTIVATED MODELS 434
5.3.1 SURFACE GROWTH WITH WEAK NON-LINEARITY 434 5.3.2 CORRELATED NOISE
439 5.3.3 NON-GAUSSIAN NOISE 445 5.3.4 GROWTH ON ROUGH SUBSTRATES 449
5.4 MODELS WITH QUENCHED DISORDER 450 5.4.1 MODELS AND SIMULATION
RESULTS 452 5.4.2 UNIVERSALITY CLASSES 465 5.4.3 EXPONENT SCALING
RELATIONSHIPS 469 5.5 EXPERIMENTS 475 5.5.1 FLUID-FLUID DISPLACEMENT
EXPERIMENTS 476 5.5.2 THE GROWTH OF CELL COLONIES 483 5.5.3 PHASE
BOUNDARIES AND GRAIN BOUNDARIES 484 5.5.4 DEPOSITION EXPERIMENTS 486
5.5.5 EROSION EXPERIMENTS 510 5.5.6 ELECTROCHEMICAL DEPOSITION 5.5.7
CORROSION AND OXIDATION 5.5.8 SOME GENERAL COMMENTS 5.6 THIN FILM GROWTH
MODELS 520 5.6.1 THE EFFECTS OF SURFACE DIFFUSION 521 5.6.2 STEP EDGE
DYNAMICS 546 5.6.3 ANOMALOUS SCALING 547 5.6.4 POROUS AND AMORPHOUS
FILMS 549 5.6.5 ANISOTROPIC SURFACES 557 5.6.6 THE HUYGENS PRINCIPLE
MODEL 552 5.7 OBLIQUE INCIDENCE AND SHADOWING MODELS 553 5.7.1 OBLIQUE
INCIDENCE BALLISTIC DEPOSITION MODELS 553 5.7.2 BALLISTIC FANS 561 5.7.3
SHADOWING MODELS 562 5.8 CLUSTER SHAPES AND FACETED GROWTH 569 5.9
ADDITIONAL INFORMATION 573 APPENDIX A INSTABILITIES 574 A. 1 THE
MULLINS-SEKERKA INSTABILITY 574 A.2 THE SAFFMAN-TAYLOR PROBLEM 580 XLL
CONTENTS APPENDIX B MULTIFRACTALS 5S5 B.I GENERATION OF SIMPLE
MULTIFRACTAL SETS 586 B.2 CHARACTERIZATION OF MULTIFRACTAL SETS 597 B.3
APPLICATIONS TO NON-EQUILIBRIUM GROWTH 597 B.3.1 QUENCHED AND ANNEALED
AVERAGES 605 B.3.2 MASS MULTIFRACTALS 606 REFERENCES 608 INDEX 663 COLOR
PLATES ARE BETWEEN PP. 242 AND 243.
|
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| id | DE-604.BV011738703 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:14:56Z |
| institution | BVB |
| isbn | 0521452538 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007918841 |
| oclc_num | 833100235 |
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| owner_facet | DE-703 DE-20 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 DE-188 |
| physical | XIV, 674 S. Ill., graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge nonlinear science series |
| series2 | Cambridge nonlinear science series |
| spelling | Meakin, Paul 1944- Verfasser (DE-588)1011675951 aut Fractals, scaling and growth far from equilibrium Paul Meakin 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1998 XIV, 674 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge nonlinear science series 5 Fractals gtt Groeimodellen gtt Mathematische fysica gtt Schaalmethoden gtt Mathematische Physik Fractals Mathematical physics Scaling laws (Statistical physics) Musterbildung (DE-588)4137934-2 gnd rswk-swf Skalierung (DE-588)4055202-0 gnd rswk-swf Fraktal (DE-588)4123220-3 gnd rswk-swf Nichtgleichgewicht (DE-588)4171730-2 gnd rswk-swf Fraktal (DE-588)4123220-3 s Musterbildung (DE-588)4137934-2 s Nichtgleichgewicht (DE-588)4171730-2 s DE-604 Skalierung (DE-588)4055202-0 s Cambridge nonlinear science series 5 (DE-604)BV004573757 5 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007918841&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Meakin, Paul 1944- Fractals, scaling and growth far from equilibrium Cambridge nonlinear science series Fractals gtt Groeimodellen gtt Mathematische fysica gtt Schaalmethoden gtt Mathematische Physik Fractals Mathematical physics Scaling laws (Statistical physics) Musterbildung (DE-588)4137934-2 gnd Skalierung (DE-588)4055202-0 gnd Fraktal (DE-588)4123220-3 gnd Nichtgleichgewicht (DE-588)4171730-2 gnd |
| subject_GND | (DE-588)4137934-2 (DE-588)4055202-0 (DE-588)4123220-3 (DE-588)4171730-2 |
| title | Fractals, scaling and growth far from equilibrium |
| title_auth | Fractals, scaling and growth far from equilibrium |
| title_exact_search | Fractals, scaling and growth far from equilibrium |
| title_full | Fractals, scaling and growth far from equilibrium Paul Meakin |
| title_fullStr | Fractals, scaling and growth far from equilibrium Paul Meakin |
| title_full_unstemmed | Fractals, scaling and growth far from equilibrium Paul Meakin |
| title_short | Fractals, scaling and growth far from equilibrium |
| title_sort | fractals scaling and growth far from equilibrium |
| topic | Fractals gtt Groeimodellen gtt Mathematische fysica gtt Schaalmethoden gtt Mathematische Physik Fractals Mathematical physics Scaling laws (Statistical physics) Musterbildung (DE-588)4137934-2 gnd Skalierung (DE-588)4055202-0 gnd Fraktal (DE-588)4123220-3 gnd Nichtgleichgewicht (DE-588)4171730-2 gnd |
| topic_facet | Fractals Groeimodellen Mathematische fysica Schaalmethoden Mathematische Physik Mathematical physics Scaling laws (Statistical physics) Musterbildung Skalierung Fraktal Nichtgleichgewicht |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007918841&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004573757 |
| work_keys_str_mv | AT meakinpaul fractalsscalingandgrowthfarfromequilibrium |