Fractal Growth Phenomena (2nd Edition) / Edition 2

Fractal Growth Phenomena (2nd Edition) / Edition 2

by TamGas Vicsek
     
 

Product Details

ISBN-13:
9789810206680
Publisher:
World Scientific Publishing Company, Incorporated
Publication date:
06/28/1992
Edition description:
Second Edition
Pages:
488

Table of Contents

Foreword
Preface
Preface to the First Edition
1Introduction1
Pt. IFractals
2Fractal Geometry
2.1Fractals as mathematical and physical objects9
2.2Definitions13
2.3Types of fractals19
3Fractal Measures
3.1Multifractality48
3.2Relations among the exponents52
3.3Fractal measures constructed by recursion56
3.4Geometrical multifractality65
4Methods for Determining Fractal Dimensions
4.1Measuring fractal dimensions in experiments74
4.2Evaluation of numerical data81
4.3Renormalization group89
References97
Pt. IICluster Growth Models
5Local Growth Models
5.1Spreading percolation105
5.2Invasion percolation111
5.3Kinetic gelation114
5.4Random walks119
6Diffusion-limited Growth
6.1Diffusion-limited aggregation (DLA)137
6.2Diffusion-limited deposition167
6.3Dielectric breakdown model174
6.4Other non-local particle-cluster growth models178
7Growing Self-affine Surfaces
7.1Eden model186
7.2Ballistic aggregation194
7.3Ballistic deposition197
7.4Theoretical results203
8Cluster-cluster Aggregation (CCA)
8.1Structure215
8.2Dynamic scaling for the cluster size distribution226
8.3Experiments249
References261
IIIFractal Pattern Formation
9Computer Simulations
9.1Equations272
9.2Models related to diffusion-limited aggregation278
9.3Generalizations of the dielectric breakdown model288
9.4Boundary integral methods294
10Experiments on Laplacian Growth
10.1Viscous fingering302
10.2Crystallization318
10.3Electrochemical deposition326
10.4Other related experiments330
References336
IVRecent Developments
11Cluster Models of Self-similar Growth
11.1Diffusion-limited aggregation344
11.2Fracture364
11.3Other models375
11.4Theoretical approaches380
12Dynamics of Self-affine Surfaces
12.1Dynamic scaling387
12.2Aggregation models390
12.3Continuum equation approach396
12.4Phase transition401
12.5Rare events dominated kinetic roughening405
12.6Multiaffinity413
13Experiments
13.1Self-similar growth422
13.2Self-affine growth438
References454
App. A. Algorithm for generating diffusion-limited aggregates465
App. B. Construction of a simple Hele-Shaw cell469
App. C. Basic concepts underlying multifractal measures471
Author Index475
Subject Index483

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