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Fractal Growth Phenomena - Tamas Vicsek

Fractal Growth Phenomena

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The investigation of phenomena involving fractals has gone through a spectacular development in the last decade. Many physical, technological and biological processes have been shown to be related to and described by objects with non-integer dimensions. The physics of far-from-equilibrium growth phenomena represents one of the most important fields in which fractal geometry is widely applied. During the past couple of years considerable experimental, numerical and theoretical information has accumulated concerning such processes. This book, written by a well known expert in the field, summarizes the basic concepts born in the studies of fractal growth and also presents some of the most important new results for more specialized readers. It also contains 15 colour plates demonstrating the richness of the geometry of fractal patterns. Accordingly, it may serve as a textbook on the geometrical aspects of fractal growth and treats this area in sufficient depth to make it useful as a reference book. No specific mathematical knowledge is required for reading this book which is intended to give a balanced account of the field. "Fractal Growth Software" (ISBN 981-02-0617-8) is available as a supplementary text to "Fractal Growth Phenomena", price US$19 or at the special price of $79.00/#46.00 for the set.

"The book 'Fractal Growth Phenomena' by T Vicsek is a complete up-to-date introduction, documentation and reference guide to this field. The book is written in a precise and fascinating manner. The clear style allows a fast understanding of the material also for those who did not study mathematics or physics." Martin Obert Justus-Liebig-Universitat Giessen "In summary the book offers an excellent introduction to and overview of a rapidly expanding field. It will serve as both a standard reference work for those already working in the area and as a comprehensive introduction for those wishing to learn more." Murray T Batchelor Australian & New Zealand Physicist, 1995

Preface to the First Edition
Introductionp. 1
Fractal Geometry
Fractals as mathematical and physical objectsp. 9
Definitionsp. 13
Types of fractalsp. 19
Fractal Measures
Multifractalityp. 48
Relations among the exponentsp. 52
Fractal measures constructed by recursionp. 56
Geometrical multifractalityp. 65
Methods for Determining Fractal Dimensions
Measuring fractal dimensions in experimentsp. 74
Evaluation of numerical datap. 81
Renormalization groupp. 89
Referencesp. 97
Cluster Growth Models
Local Growth Models
Spreading percolationp. 105
Invasion percolationp. 111
Kinetic gelationp. 114
Random walksp. 119
Diffusion-limited Growth
Diffusion-limited aggregation (DLA)p. 137
Diffusion-limited depositionp. 167
Dielectric breakdown modelp. 174
Other non-local particle-cluster growth modelsp. 178
Growing Self-affine Surfaces
Eden modelp. 186
Ballistic aggregationp. 194
Ballistic depositionp. 197
Theoretical resultsp. 203
Cluster-cluster Aggregation (CCA)
Structurep. 215
Dynamic scaling for the cluster size distributionp. 226
Experimentsp. 249
Referencesp. 261
Fractal Pattern Formation
Computer Simulations
Equationsp. 272
Models related to diffusion-limited aggregationp. 278
Generalizations of the dielectric breakdown modelp. 288
Boundary integral methodsp. 294
Experiments on Laplacian Growth
Viscous fingeringp. 302
Crystallizationp. 318
Electrochemical depositionp. 326
Other related experimentsp. 330
Referencesp. 336
Recent Developments
Cluster Models of Self-similar Growth
Diffusion-limited aggregationp. 344
Fracturep. 364
Other modelsp. 375
Theoretical approachesp. 380
Dynamics of Self-affine Surfaces
Dynamic scalingp. 387
Aggregation modelsp. 390
Continuum equation approachp. 396
Phase transitionp. 401
Rare events dominated kinetic rougheningp. 405
Multiaffinityp. 413
Self-similar growthp. 422
Self-affine growthp. 438
Referencesp. 454
App. A. Algorithm for generating diffusion-limited aggregatesp. 465
App. B. Construction of a simple Hele-Shaw cellp. 469
App. C. Basic concepts underlying multifractal measuresp. 471
Author Indexp. 475
Subject Indexp. 483
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9789810206680
ISBN-10: 9810206682
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 528
Published: 1993
Country of Publication: SG
Dimensions (cm): 26.04 x 17.15  x 3.81
Weight (kg): 1.27
Edition Number: 2
Edition Type: Revised

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