Fractals, Scaling and Growth Far from Equilibrium

Fractals, Scaling and Growth Far from Equilibrium

by Paul Meakin
     
 

ISBN-10: 0521189810

ISBN-13: 9780521189811

Pub. Date: 03/03/2011

Publisher: Cambridge University Press

This book is concerned with the formation of complex, disorderly patterns under far from equilibrium conditions. The application of fractal geomentry and scaling concepts to a broad range of phenomena is presented with emphasis on practical problems and pitfalls. The author illustrates how simple concepts and theoretical methods can be used to obtain answers to…  See more details below

Overview

This book is concerned with the formation of complex, disorderly patterns under far from equilibrium conditions. The application of fractal geomentry and scaling concepts to a broad range of phenomena is presented with emphasis on practical problems and pitfalls. The author illustrates how simple concepts and theoretical methods can be used to obtain answers to problems that would be difficult to address using other approaches. The techniques and topics discussed in this book are relevant to many areas of science and technology.

Product Details

ISBN-13:
9780521189811
Publisher:
Cambridge University Press
Publication date:
03/03/2011
Series:
Cambridge Nonlinear Science Series, #5
Edition description:
Reissue
Pages:
694
Product dimensions:
6.70(w) x 9.60(h) x 1.60(d)

Table of Contents

Preface
Ch. 1Pattern Formation Far From Equilibrium1
1.1Power Laws and Scaling4
1.2The Logistic Map16
1.3The Variety of Patterns in Nature22
1.4Moving-Boundary Processes36
1.5Solution of Interface Equations of Motion52
1.6Complex and Disorderly Patterns57
1.7Scaling Symmetry61
1.8Notation62
1.9Monte Carlo Methods62
Ch. 2Fractals and Scaling65
2.1Self-Similar Fractals65
2.2Simple Rules83
2.3Finite-Size Effects and Crossovers85
2.4Power Law Distributions100
2.5Scaling104
2.6Fractal Trees and Inhomogeneous Fractals113
2.7Self-Affine Fractals119
2.8Multifractals160
2.9Universality165
Ch. 3Growth Models168
3.1Cluster Growth and Cluster Surfaces169
3.2Lattice Animals172
3.3Random Walks173
3.4Cluster Growth Models183
3.5Percolation and Invasion Percolation214
3.6Packing Models246
3.7Growth Models Related to DLA250
3.8Noise Reduction and Deterministic Models285
3.9Models with Quenched Disorder295
3.10Theoretical Methods299
Ch. 4Experimental Studies326
4.1DLA Processes327
4.2Dense Branching Morphology366
4.3Percolation381
4.4Invasion Percolation384
4.5Displacement in Complex Fluids388
4.6Other 2-Dimensional Patterns397
Ch. 5The Growth of Surfaces and Interfaces401
5.1The Structure and Growth of Rough Surfaces404
5.2Simple Models418
5.3Theoretically Motivated Models434
5.4Models with Quenched Disorder450
5.5Experiments475
5.6Thin Film Growth Models520
5.7Oblique Incidence and Shadowing Models553
5.8Cluster Shapes and Faceted Growth569
App. AInstabilities574
App. BMultifractals585
References608
Index663

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