Fractal growth phenomena:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u. a.]
World Scientific
1992
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| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 488 S. Ill. |
| ISBN: | 9810206682 9810206690 |
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Record in the Search Index
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| adam_text | FRACTAL GROWTH PHENOMENA (SECOND EDITION) TAMAES VICSEK DEPARTMENT
OFATOMIC PHYSICS EOETVOES UNIVERSIIY BUDAPEST, PUSKIN U.5-7 H-1088 HUNGARY
UFE WORLD SCIENTIFIC SINGAPORE * NEW JERSEY * L SINGAPORE * NEW JERSEY *
LONDON * HONG KONG XV I CONTENTS FOREWORD VII PREFACE IX PREFACE TO THE
FIRST EDITION XI 1. INTRODUCTION 1 PART I. FRACTALS 2. FRACTAL GEOMETRY
2.1. FRACTALS AS MATHEMATICAL AND PHYSICAL OBJECTS 9 2.2. DEFINITIONS 13
2.3. TYPES OF FRACTALS 19 2.3.1. DETERMINISTIC AND RANDOM 19 2.3.2.
SELF-AFFINE 33 2.3.3. FAT 44 3. FRACTAL MEASURES 3.1. MULTIFRACTALITY 48
3.2. RELATIONS AMONG THE EXPONENTS . 52 3.3. FRACTAL MEASURES
CONSTRUCTED BY RECURSION 56 3.4. GEOMETRICAL MULTIFRACTALITY 65 XVI
CONTENTS 4. METHODS FOR DETERMINING FRACTAL DIMENSIONS 4.1. MEASURING
FRACTAL DIMENSIONS IN EXPERIMENTS 74 4.2. EVALUATION OF NUMERICAL DATA
81 4.3. RENORMALIZATION GROUP 89 REFERENCES 97 PART II. CLUSTER GROWTH
MODELS 5. LOCAL GROWTH MODELS 5.1. SPREADING PERCOLATION 105 5.2.
INVASION PERCOLATION 111 5.3. KINETIC GELATION 114 5.4. RANDOM WALKS 119
5.4.1. SELF-INTERSECTING 120 5.4.2. SELF-AVOIDING 125 5.4.3. WALKS ON
FRACTALS 132 6. DIFFUSION-LIMITED GROWTH 6.1. DIFFUSION-LIMITED
AGGREGATION (DLA) 137 6.1.1. FRACTAL DIMENSION 139 6.1.2. ANISOTROPY 146
6.1.3. THEORETICAL APPROACHES 153 6.1.4. MULTIFRACTAL SCALING . 158 6.2.
DIFFUSION-LIMITED DEPOSITION 167 6.3. DIELECTRIC BREAKDOWN MODEL 174
6.4. OTHER NON-LOCAL PARTICLE-CLUSTER GROWTH MODEIS 178 7. GROWING
SELF-AFFINE SURFACES 7.1. EDEN MODEL 186 7.2. BALLISTIC AGGREGATION 194
7.3. BALLISTIC DEPOSITION 197 7.4. THEORETICAL RESULTS 203 8.
CLUSTER-CLUSTER AGGREGATION (CCA) 8.1. STRUCTURE 215 CONTENTS XVII
8.1.1. FRACTAL DIMENSION FROM SIMULATIONS 215 8.1.2. THEORETICAL
APPROACHES 224 8.2. DYNAMIC SCALING FOR THE CLUSTER SIZE DISTRIBUTION
226 8.2.1. DIFFUSION-LIMITED CCA 227 8.2.2. REACTION-LIMITED CCA 235
8.2.3. STEADY-STATE AND REVERSIBLE CCA 237 8.2.4. MEAN-FIELD THEORIES
242 8.3. EXPERIMENTS 249 8.3.1. STRUCTURE 250 8.3.2. DYNAMICS 257
REFERENCES 261 PART III. FRACTAL PATTERN FORMATION 9. COMPUTER
SIMULATIONS 9.1. EQUATIONS 272 9.2. MODELS RELATED TO DIFFUSION-LIMITED
AGGREGATION 278 9.2.1. EFFECTS OF SURFACE TENSION 280 9.2.2.
NOISE-REDUCTION IN DLA 285 9.3. GENERALIZATIONS OF THE DIELECTRIC
BREAKDOWN MODEL . . . . 288 9.4. BOUNDARY INTEGRAL METHODS 294 10.
EXPERIMENTS ON LAPLACIAN GROWTH 10.1. VISCOUS FMGERING 302 10.1.1. THE
HELE-SHAW CELL 303 10.1.2. FRACTAL VISCOUS FMGERING 307 10.1.3. VISCOUS
FMGERING WITH ANISOTROPY 313 10.2. CRYSTALLIZATION 318 10.3.
ELECTROCHEMICAL DEPOSITION 326 10.4. OTHER RELATED EXPERIMENTS 330
REFERENCES 336 XVIII CONTENTS PART IV. RECENT DEVELOPMENTS 11. CLUSTER
MODELS OF SELF-SIMILAR GROWTH 11.1. DIFFUSION-LIMITED AGGREGATION 344
11.1.1. GLOBAL STRUCTURE 345 11.1.2. GROWTH PROBABILITY DISTRIBUTION 350
11.1.3. MULTIFRACTAL GEOMETRY 355 11.1.4. PATTERN FORMATION 360 11.2.
FRACTURE 364 11.2.1. EQUATIONS 365 11.2.2. LATTICE MODEIS OF SINGLE
CRACKS 368 11.2.3. SYSTEMS OF CRACKS 372 11.3. OTHER MODEIS 375 11.4.
THEORETICAL APPROACHES 380 12. DYNAMICS OF SELF-AFFINE SURFACES 12.1.
DYNAMIC SCALING 387 12.2. AGGREGATION MODEIS 390 12.3. CONTINUUM
EQUATION APPROACH 396 12.4. PHASE TRANSITION 401 12.5. RARE EVENTS
DOMINATED KINETIC ROUGHENING 405 12.6. MULTIAFFINITY 413 13. EXPERIMENTS
13.1. SELF-SIMILAR GROWTH 422 13.1.1. DIFFUSION-LIMITED GROWTH 422
13.1.2. FRACTURE 428 13.1.3. BIOLOGICAL GROWTH 433 13.2. SELF-AFFINE
GROWTH 438 13.2.1. TWO-PHASE VISCOUS FIOWS 439 13.2.2. DEPOSITION 445
13.2.3. BIOLOGICAL GROWTH 447 13.2.4. FRACTURE 452 REFERENCES 454
CONTENTS XIX APPENDICES A. ALGORITHM FOR GENERATING DIFFUSION-LIMITED
AGGREGATES . . . . 465 B. CONSTRUCTION OF A SIMPLE HELE-SHAW CELL 469 C.
BASIC CONCEPTS UNDERLYING MULTIFRACTAL MEASURES 471 AUTHOR INDEX 475
SUBJECT INDEX 483
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| any_adam_object | 1 |
| author | Vicsek, Tamás |
| author_facet | Vicsek, Tamás |
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| author_sort | Vicsek, Tamás |
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| bvnumber | BV025860412 |
| classification_rvk | UG 3900 |
| ctrlnum | (OCoLC)263574160 (DE-599)BVBBV025860412 |
| discipline | Physik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:13:53Z |
| institution | BVB |
| isbn | 9810206682 9810206690 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-019108133 |
| oclc_num | 263574160 |
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| physical | XIX, 488 S. Ill. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | World Scientific |
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| spelling | Vicsek, Tamás Verfasser aut Fractal growth phenomena Tamás Vicsek 2. ed. Singapore [u. a.] World Scientific 1992 XIX, 488 S. Ill. txt rdacontent n rdamedia nc rdacarrier Wachstumsmodell (DE-588)4127141-5 gnd rswk-swf Wachstum (DE-588)4064115-6 gnd rswk-swf Fraktal (DE-588)4123220-3 gnd rswk-swf Fraktal (DE-588)4123220-3 s Wachstum (DE-588)4064115-6 s DE-604 Wachstumsmodell (DE-588)4127141-5 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019108133&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vicsek, Tamás Fractal growth phenomena Wachstumsmodell (DE-588)4127141-5 gnd Wachstum (DE-588)4064115-6 gnd Fraktal (DE-588)4123220-3 gnd |
| subject_GND | (DE-588)4127141-5 (DE-588)4064115-6 (DE-588)4123220-3 |
| title | Fractal growth phenomena |
| title_auth | Fractal growth phenomena |
| title_exact_search | Fractal growth phenomena |
| title_full | Fractal growth phenomena Tamás Vicsek |
| title_fullStr | Fractal growth phenomena Tamás Vicsek |
| title_full_unstemmed | Fractal growth phenomena Tamás Vicsek |
| title_short | Fractal growth phenomena |
| title_sort | fractal growth phenomena |
| topic | Wachstumsmodell (DE-588)4127141-5 gnd Wachstum (DE-588)4064115-6 gnd Fraktal (DE-588)4123220-3 gnd |
| topic_facet | Wachstumsmodell Wachstum Fraktal |
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