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Fractal growth phenomena /
Vicsek, Tamás.
Fractal growth phenomena / Tamás Vicsek. - 2nd ed. - xix, 488 pages, 18 pages of plates : illustrations (some color) ; 26 cm.
Includes bibliographical references and indexes.
Foreword Preface Preface to the First Edition 1 Introduction Pt. I Fractals 2 Fractal Geometry 2.1 Fractals as mathematical and physical objects 2.2 Definitions 2.3 Types of fractals 3 Fractal Measures 3.1 Multifractality 3.2 Relations among the exponents 3.3 Fractal measures constructed by recursion 3.4 Geometrical multifractality 4 Methods for Determining Fractal Dimensions 4.1 Measuring fractal dimensions in experiments 4.2 Evaluation of numerical data 4.3 Renormalization group References Pt. II Cluster Growth Models 5 Local Growth Models 5.1 Spreading percolation 5.2 Invasion percolation 5.3 Kinetic gelation 5.4 Random walks 6 Diffusion-limited Growth 6.1 Diffusion-limited aggregation (DLA) 6.2 Diffusion-limited deposition 6.3 Dielectric breakdown model 6.4 Other non-local particle-cluster growth models 7 Growing Self-affine Surfaces 7.1 Eden model 7.2 Ballistic aggregation 7.3 Ballistic deposition 7.4 Theoretical results 8 Cluster-cluster Aggregation (CCA) 8.1 Structure 8.2 Dynamic scaling for the cluster size distribution 8.3 Experiments References III Fractal Pattern Formation 9 Computer Simulations 9.1 Equations 9.2 Models related to diffusion-limited aggregation 9.3 Generalizations of the dielectric breakdown model 9.4 Boundary integral methods 10 Experiments on Laplacian Growth 10.1 Viscous fingering 10.2 Crystallization 10.3 Electrochemical deposition 10.4 Other related experiments References IV Recent Developments 11 Cluster Models of Self-similar Growth 11.1 Diffusion-limited aggregation 11.2 Fracture 11.3 Other models 11.4 Theoretical approaches 12 Dynamics of Self-affine Surfaces 12.1 Dynamic scaling 12.2 Aggregation models 12.3 Continuum equation approach 12.4 Phase transition 12.5 Rare events dominated kinetic roughening 12.6 Multiaffinity 13 Experiments 13.1 Self-similar growth 13.2 Self-affine growth References App. A. Algorithm for generating diffusion-limited aggregates App. B. Construction of a simple Hele-Shaw cell App. C. Basic concepts underlying multifractal measures Author Index Subject Index
9810206682
92011311
Fractals.
QA614.86 / .V53 1999
Fractal growth phenomena / Tamás Vicsek. - 2nd ed. - xix, 488 pages, 18 pages of plates : illustrations (some color) ; 26 cm.
Includes bibliographical references and indexes.
Foreword Preface Preface to the First Edition 1 Introduction Pt. I Fractals 2 Fractal Geometry 2.1 Fractals as mathematical and physical objects 2.2 Definitions 2.3 Types of fractals 3 Fractal Measures 3.1 Multifractality 3.2 Relations among the exponents 3.3 Fractal measures constructed by recursion 3.4 Geometrical multifractality 4 Methods for Determining Fractal Dimensions 4.1 Measuring fractal dimensions in experiments 4.2 Evaluation of numerical data 4.3 Renormalization group References Pt. II Cluster Growth Models 5 Local Growth Models 5.1 Spreading percolation 5.2 Invasion percolation 5.3 Kinetic gelation 5.4 Random walks 6 Diffusion-limited Growth 6.1 Diffusion-limited aggregation (DLA) 6.2 Diffusion-limited deposition 6.3 Dielectric breakdown model 6.4 Other non-local particle-cluster growth models 7 Growing Self-affine Surfaces 7.1 Eden model 7.2 Ballistic aggregation 7.3 Ballistic deposition 7.4 Theoretical results 8 Cluster-cluster Aggregation (CCA) 8.1 Structure 8.2 Dynamic scaling for the cluster size distribution 8.3 Experiments References III Fractal Pattern Formation 9 Computer Simulations 9.1 Equations 9.2 Models related to diffusion-limited aggregation 9.3 Generalizations of the dielectric breakdown model 9.4 Boundary integral methods 10 Experiments on Laplacian Growth 10.1 Viscous fingering 10.2 Crystallization 10.3 Electrochemical deposition 10.4 Other related experiments References IV Recent Developments 11 Cluster Models of Self-similar Growth 11.1 Diffusion-limited aggregation 11.2 Fracture 11.3 Other models 11.4 Theoretical approaches 12 Dynamics of Self-affine Surfaces 12.1 Dynamic scaling 12.2 Aggregation models 12.3 Continuum equation approach 12.4 Phase transition 12.5 Rare events dominated kinetic roughening 12.6 Multiaffinity 13 Experiments 13.1 Self-similar growth 13.2 Self-affine growth References App. A. Algorithm for generating diffusion-limited aggregates App. B. Construction of a simple Hele-Shaw cell App. C. Basic concepts underlying multifractal measures Author Index Subject Index
9810206682
92011311
Fractals.
QA614.86 / .V53 1999
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