Fractal Growth Phenomena

By: Tamas Vicsek

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Hardcover | 1 December 1992 | Edition Number 2

At a Glance

Hardcover
510 Pages

Edition Type
Revised

Dimensions(cm)
24.41 x 16.99 x 2.87

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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.

Industry Reviews

"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

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You Can Find This Book In

Non-Fiction Mathematics Geometry Fractal Geometry Science Physics Chemistry Topology Booktopia Publisher Services World Scientific Publishing

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Paperback

Published: 1st December 1990

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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

At a Glance

Hardcover

Industry Reviews

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How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

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