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" Fractals and Disordered Systems "
edited by Armin Bunde, Shlomo Havlin.
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BL
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| Record Number
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749623
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b569582
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| Main Entry
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edited by Armin Bunde, Shlomo Havlin.
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| Title & Author
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Fractals and Disordered Systems\ edited by Armin Bunde, Shlomo Havlin.
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| Publication Statement
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Berlin, Heidelberg : Springer Berlin Heidelberg, 1991
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| Page. NO
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(xiv, 350 pages 163 illustrations)
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| ISBN
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3540540709
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: 3642514359
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: 9783540540700
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: 9783642514357
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| Contents
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1. Fractals and Multifractals: The Interplay of Physics and Geometry --; 1.1 Introduction --; 1.2 Nonrandom Fractals --; 1.3 Random Fractals: The Unbiased Random Walk --; 1.4 The Concept of a Characteristic Length --; 1.5 Functional Equations and Fractal Dimension --; 1.6 An Archetype: Diffusion Limited Aggregation --; 1.7 DLA: Fractal Properties --; 1.8 DLA: Multifractal Properties --; 1.9 'Phase Transition' in DLA --; 1.10 The Void-Channel Model of DLA Growth --; 1.11 Applications of DLA to Fluid Mechanics --; 1.12 Applications of DLA to Dendritic Growth --; 1.13 Other Fractal Dimensions --; 1.14 Possible Origin of Fractality and Multifractality --; 1.A Appendix: Analogies with Thermodynamics and Multifractal Scaling --; References --; 2. Percolation I --; 2.1 Introduction --; 2.2 Percolation as a Critical Phenomenon --; 2.3 Structural Properties --; 2.4 Exact Results --; 2.5 Scaling Theory --; 2.6 Related Percolation Problems --; 2.7 Numerical Approaches --; 2.8 Theoretical Approaches --; References --; 3. Percolation II --; 3.1 Introduction --; 3.2 Anomalous Transport on Fractals --; 3.3 Transport on Percolation Clusters --; 3.4 Fractons --; 3.5 ac Transport --; 3.6 Dynamical Exponents --; 3.7 Multifractals --; 3.8 Transport in the Presence of Additional Physical Constraints --; References --; 4. Fractal Growth --; 4.1 Introduction --; 4.2 Fractals and Multifractals --; 4.3 Growth Models --; 4.4 Laplacian Growth Model --; 4.5 Aggregation in Percolating Systems --; 4.6 Crossover in Dielectric Breakdown with Cutoffs --; 4.7 Is Growth Multifractal? --; 4.8 Conclusion --; References --; 5. Fractures --; 5.1 Introduction --; 5.2 Some Basic Notions of Elasticity --; 5.3 Fracture as a Growth Model --; 5.4 Modelisation of Fracture on a Lattice --; 5.5 Deterministic Growth of a Fractal Crack --; 5.6 Scaling Laws of the Fracture of Heterogeneous Media --; 5.7 Conclusion --; References --; 6. Fractal Electrodes, Fractal Membranes, and Fractal Catalysts --; 6.1 Introduction --; 6.2 The Electrode Problem and the Constant Phase Angle Conjecture --; 6.3 The Diffusion Impedance and the Measurement of the Minkowski-Bouligand Exterior Dimension --; 6.4 The Generalized Modified Sierpinski Electrode --; 6.5 The Response of Ideally Polarizable Electrodes --; 6.6 Scaling Length in the Blocking Regime --; 6.7 Electrodes, Roots, Lungs --; 6.8 Fractal Catalysts --; 6.9 Summary --; References --; 7. Fractal Surfaces and Interfaces --; 7.1 Introduction --; 7.2 Rough Surfaces of Solids --; 7.3 Diffusion Fronts: Natural Fractal Interfaces in Solids --; 7.4 Fractal Fluid-Fluid Interfaces --; 7.5 Membranes and Tethered Surfaces --; 7.6 Conclusions --; References --; 8. Fractals and Experiments --; 8.1 Introduction --; 8.2 Growth Experiments: How to Make a Fractal --; 8.3 Structure Experiments: How to Determine the Fractal Dimension --; 8.4 Physical Properties --; 8.5 Outlook --; References --; 9. Cellular Automata --; 9.1 Introduction --; 9.2 A Simple Example --; 9.3 The Kauffman Model --; 9.4 Classification of Cellular Automata --; 9.A Appendix --; References --; 10. Exactly Self-Similar Left-Sided Multifractals --; 10.1 Introduction --; 10.2 Nonrandom Multifractals with an Infinite Base --; 10.3 Left-Sided Multifractality with Exponential Decay of Smallest Probability --; 10.4 A Gradual Crossover from Restricted to Left-Sided Multifractals --; 10.5 Pre-asymptotics --; 10.6 Miscellaneous Remarks --; 10.7 Summary --; 10.A Appendix --; References.
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| Abstract
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Fractals and disordered systems have recently become the focus of intense interest in research. This book discusses in great detail the effects of disorder on mesoscopic scales (fractures, aggregates, colloids, surfaces and interfaces, glasses, and polymers) and presents tools to describe them in mathematical language. A substantial part is devoted to the development of scaling theories based on fractal concepts. In 10 chapters written by leading experts in the field, including E. Stanley and B. Mandelbrot, the reader is introduced to basic concepts and techniques in disordered systems and is lead to the forefront of current research. In each chapter the connection between theory and experiment is emphasized, and a special chapter entitled "Fractals and Experiments" presents experimental studies of fractal systems in the laboratory. The book is written pedagogically. It can be used as a textbook for graduate students, by university teachers to prepare courses and seminars, and by active scientists who want to become familiar with a fascinating new field.
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| Subject
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Chemistry.
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Computer graphics.
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Physics.
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| LC Classification
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QA614.86E358 1991
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| Added Entry
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Armin Bunde
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Shlomo Havlin
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