Fractals, Scaling and Growth Far from Equilibrium

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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.
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Editorial Reviews

From the Publisher
Review of the hardback: '… a true work of scholarship and a very helpful starting point into the appropriate research papers … The book is handsomely produced … A good investment for an institutional library in an important area of modern research.' Stephen K. Scott Chemistry in Britain

Review of the hardback: 'In Fractals, Scaling and Growth Far from Equilibrium Paul Meakin gives a masterly survey of the mathematical tools available for describing such surfaces, summarises models of growth and relevant experimental studies, and then applies the mathematics of fractals and scaling to the growth of surfaces and interfaces in materials. This book provides an authoritative account for graduate students and researcher studying the geometry of surfaces and interfaces. [It] provides a definitive account of the mathematical description of shapes of systems far from equilibrium, and richly deserves inclusion in the prestigious Cambridge Nonlinear Science series.' Andrew Briggs The Times Higher Education Supplement

Review of the hardback: 'This monograph provides and extensive exposition of the fundamental aspect of scaling, pattern formation far-from-equilibrium and fractals … The mathematical treatment of the book is carefully presented, emphasising the results, rather than intricate mathematical detail … the book provides [a] readable treatment of the basics of fractal geometry and scaling, to facilitate quantification of the structures grown under the non-equilibrium conditions … an extensive bibliography of over 1300 references makes this monograph a solid contribution in the field.' Miroslav M. Novak UK Nonlinear News

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Product Details

  • ISBN-13: 9780521189811
  • Publisher: Cambridge University Press
  • Publication date: 3/3/2011
  • 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. 1 Pattern Formation Far From Equilibrium 1
1.1 Power Laws and Scaling 4
1.2 The Logistic Map 16
1.3 The Variety of Patterns in Nature 22
1.4 Moving-Boundary Processes 36
1.5 Solution of Interface Equations of Motion 52
1.6 Complex and Disorderly Patterns 57
1.7 Scaling Symmetry 61
1.8 Notation 62
1.9 Monte Carlo Methods 62
Ch. 2 Fractals and Scaling 65
2.1 Self-Similar Fractals 65
2.2 Simple Rules 83
2.3 Finite-Size Effects and Crossovers 85
2.4 Power Law Distributions 100
2.5 Scaling 104
2.6 Fractal Trees and Inhomogeneous Fractals 113
2.7 Self-Affine Fractals 119
2.8 Multifractals 160
2.9 Universality 165
Ch. 3 Growth Models 168
3.1 Cluster Growth and Cluster Surfaces 169
3.2 Lattice Animals 172
3.3 Random Walks 173
3.4 Cluster Growth Models 183
3.5 Percolation and Invasion Percolation 214
3.6 Packing Models 246
3.7 Growth Models Related to DLA 250
3.8 Noise Reduction and Deterministic Models 285
3.9 Models with Quenched Disorder 295
3.10 Theoretical Methods 299
Ch. 4 Experimental Studies 326
4.1 DLA Processes 327
4.2 Dense Branching Morphology 366
4.3 Percolation 381
4.4 Invasion Percolation 384
4.5 Displacement in Complex Fluids 388
4.6 Other 2-Dimensional Patterns 397
Ch. 5 The Growth of Surfaces and Interfaces 401
5.1 The Structure and Growth of Rough Surfaces 404
5.2 Simple Models 418
5.3 Theoretically Motivated Models 434
5.4 Models with Quenched Disorder 450
5.5 Experiments 475
5.6 Thin Film Growth Models 520
5.7 Oblique Incidence and Shadowing Models 553
5.8 Cluster Shapes and Faceted Growth 569
App. A Instabilities 574
App. B Multifractals 585
References 608
Index 663
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