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Fractals and Disordered Systems

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 mat...

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Bibliographic Details
Other Authors: Bunde, Armin (Editor), Havlin, Shlomo (Editor)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1996, 1996
Edition:2nd ed. 1996
Subjects:
Complex Systems
Chemistry, Physical And Theoretical
Physical Chemistry
Engineering
Engineering Mathematics
Theoretical Chemistry
Polymers
System Theory
Engineering / Data Processing
Technology And Engineering
Mathematical And Computational Engineering Applications
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 10.C The Minkowski Measure and Its Left-sided f(?), by B.B. Mandelbrot
  • References
  • 5.7 Hydraulic Fracture
  • 5.8 Conclusion
  • References
  • 6 Transport Across Irregular Interfaces: Fractal Electrodes, Membranes and Catalysts (With 8 Figures)
  • 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 A General Formulation of Laplacian Transfer Across Irregular Surfaces
  • 6.6 Electrodes, Roots, Lungs,
  • 6.7 Fractal Catalysts
  • 6.8 Summary
  • References
  • 7 Fractal Surfaces and Interfaces (With 27 Figures)
  • 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 (With 18 Figures)
  • 8.1 Introduction
  • 8.2 Growth Experiments: How to Make a Fractal
  • 2.7 Numerical Approaches
  • 2.8 Theoretical Approaches
  • 2.A Appendix: The Generating Function Method
  • References
  • 3 Percolation II (With 20 Figures)
  • 3.1 Introduction
  • 3.2 Anomalous Transport in Fractals
  • 3.3 Transport in Percolation Clusters
  • 3.4 Fractons
  • 3.5 ac Transport
  • 3.6 Dynamical Exponents
  • 3.7 Multifractals
  • 3.8 Related Transport Problems
  • References
  • 4 Fractal Growth (With 4 Figures)
  • 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 (With 18 Figures)
  • 5.1 Introduction
  • 5.2 Some Basic Notions of Elasticity and Fracture
  • 5.3 Fracture as a Growth Model
  • 5.4 Modelisation of Fracture on aLattice
  • 5.5 Deterministic Growth of a Fractal Crack
  • 5.6 Scaling Laws of the Fracture of Heterogeneous Media
  • 1 Fractals and Multifractals: The Interplay of Physics and Geometry (With 30 Figures)
  • 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 Scaling Properties of the Perimeter of 2d DLA: The “Glove” Algorithm
  • 1.10 Multiscaling
  • 1.11 The DLA Skeleton
  • 1.12 Applications of DLA to Fluid Mechanics
  • 1.13 Applications of DLA to Dendritic Growth
  • 1.14 Other Fractal Dimensions
  • 1.15 Surfaces and Interfaces
  • 1.A Appendix: Analogies Between Thermodynamics and Multifractal Scaling
  • References
  • 2 Percolation I (With 24 Figures)
  • 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
  • 8.3 Structure Experiments: How to Determine the Fractal Dimension
  • 8.4 Physical Properties
  • 8.5 Outlook
  • References
  • 9 Cellular Automata (With 6 Figures)
  • 9.1 Introduction
  • 9.2 A Simple Example
  • 9.3 The Kauffman Model
  • 9.4 Classification of Cellular Automata
  • 9.5 Recent Biologically Motivated Developments
  • 9.A Appendix
  • References
  • 10 Exactly Self-similar Left-sided Multifractals with new Appendices B and C by Rudolf H. Riedi and Benoit B. Mandelbrot (With 10 Figures)
  • 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 Details of Calculations and Further Discussions
  • 10.B Multifractal Formalism for Infinite Multinomial Measures, by R.H. Riedi and B.B. Mandelbrot

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