Fractal Growth Phenomena

1st Edition

By: Tamas Vicsek

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Paperback | 1 January 1989

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368 Pages

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"... provided a much-needed new resource, a nice vehicle for gaining entry into the gradually developing hard science of fractals ... I think the book is excellent and likely to be interesting and informative to a wide class of readers." Robert Cawley Science, 1989 "... the first comprehensive book devoted entirely to the subject of fractal growth ... Vicsek has succeeded in producing a classic book on growth phenomena. It is an extremely readable and useful book and I recommend it highly to anyone looking for a good place to start learning about fractals and growth phenomena in particular." Fereydoon Family Journal of Statistical Physics, 1992

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You Can Find This Book In

Non-Fiction Mathematics Geometry Fractal Geometry Applied Mathematics Chaos Theory Booktopia Publisher Services World Scientific Publishing Science Physics Materials & States of Matter Condensed Matter Physics including Liquid State & Solid State Physics

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Foreword
Preface
Preface to the First Edition
Introduction	p. 1
Fractals
Fractal Geometry
Fractals as mathematical and physical objects	p. 9
Definitions	p. 13
Types of fractals	p. 19
Fractal Measures
Multifractality	p. 48
Relations among the exponents	p. 52
Fractal measures constructed by recursion	p. 56
Geometrical multifractality	p. 65
Methods for Determining Fractal Dimensions
Measuring fractal dimensions in experiments	p. 74
Evaluation of numerical data	p. 81
Renormalization group	p. 89
References	p. 97
Cluster Growth Models
Local Growth Models
Spreading percolation	p. 105
Invasion percolation	p. 111
Kinetic gelation	p. 114
Random walks	p. 119
Diffusion-limited Growth
Diffusion-limited aggregation (DLA)	p. 137
Diffusion-limited deposition	p. 167
Dielectric breakdown model	p. 174
Other non-local particle-cluster growth models	p. 178
Growing Self-affine Surfaces
Eden model	p. 186
Ballistic aggregation	p. 194
Ballistic deposition	p. 197
Theoretical results	p. 203
Cluster-cluster Aggregation (CCA)
Structure	p. 215
Dynamic scaling for the cluster size distribution	p. 226
Experiments	p. 249
References	p. 261
Fractal Pattern Formation
Computer Simulations
Equations	p. 272
Models related to diffusion-limited aggregation	p. 278
Generalizations of the dielectric breakdown model	p. 288
Boundary integral methods	p. 294
Experiments on Laplacian Growth
Viscous fingering	p. 302
Crystallization	p. 318
Electrochemical deposition	p. 326
Other related experiments	p. 330
References	p. 336
Recent Developments
Cluster Models of Self-similar Growth
Diffusion-limited aggregation	p. 344
Fracture	p. 364
Other models	p. 375
Theoretical approaches	p. 380
Dynamics of Self-affine Surfaces
Dynamic scaling	p. 387
Aggregation models	p. 390
Continuum equation approach	p. 396
Phase transition	p. 401
Rare events dominated kinetic roughening	p. 405
Multiaffinity	p. 413
Experiments
Self-similar growth	p. 422
Self-affine growth	p. 438
References	p. 454
App. A. Algorithm for generating diffusion-limited aggregates	p. 465
App. B. Construction of a simple Hele-Shaw cell	p. 469
App. C. Basic concepts underlying multifractal measures	p. 471
Author Index	p. 475
Subject Index	p. 483
Table of Contents provided by Blackwell. All Rights Reserved.

Fractal Growth Phenomena

1st Edition

At a Glance

Paperback

Shipping

How to return your order

Defective items

You Can Find This Book In

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