Book:Brian H. Kaye/A Random Walk through Fractal Dimensions

Brian H. Kaye: A Random Walk through Fractal Dimensions

Published $\text {1989}$, VCH Publishers

ISBN 0-89573-888-0

Subject Matter

• Chaos Theory

Contents

Preface (Sudbury, January 1989)

Acknowledgments

Word Finder

Coloured Plates

1 A Starting Point for the Randomwalk

References

2 Fractal Description of Fineparticle Boundaries

2.1 The Fractal Dimensions of a Famous Carbonblack Profile

2.2 The Dangerous Art of Extrapolation for Predicting Physical Phenomena

2.3 Discovering Texture Fractals

2.4 Experimental Methods for Characterising Fineparticle Boundaries

References

3 What Use are Fractals?

3.1 Elegance and Utility of Fractal Dimensions

3.2 Fractal Description of Powder Metal Grains and Special Metal Crystals

3.3 Fractals and the Flow of Dry Powders

3.4 Fractals in the Mining Industry

3.5 Fractal Structure of Cosmic Fineparticles

3.6 Fractal Structure of Some Types of Sand Grains

3.7 Fractal Structure of Some Respirable Dusts

3.7.1 What is the Technical Meaning of Respirable Dust?

3.7.2 Is Fumed Silica a Respirable Hazard?

3.7.3 Dust from Nuclear Reactor Systems

3.7.4 Fuse Fumes and Welding Dust

3.7.5 Characteristics of Dust Generated by Explosions

3.7.6 Diesel Soot and Fumed Pigments

3.7.7 Fractal Specimens of Flyash

3.8 Polymer Grains and Rubber Crumbs

3.9 Fineparticle Look-Alike:

References

4. Delinquent Coins and Staggering Drunks

4.1 A Capricious Selection of Terms that Describe Random Events

4.2 Chance, Probability and Error

4.3 Monte Carlo Technique for Studying Stochastic Processes

4.4 Randomwalks in One-Dimensional Space

4.5 Delinquent Coins and Cantorian Dusts

4.6 The Devil's Staircase and Crystal Structure

4.7 Pin-ball Machines and Some Random Thoughts on the Philosophical Significance of Fractal Dimensions

4.8 Plumes with Fractal Boundaries

4.9 Gaussian Graph Paper, Fractal Distributions and Elephants in the Face Powder

References

5 Fractal Systems Generated by Randomwalks in Two-Dimensional Space

5.1 Randomwalks on a Rectangular Lattice in Two-Dimensional Space

5.2 The Use of Polar Cc-ordinates to Describe Random Progress in Two-Dimensional Space

5.3 Randomwalk Modelling of Fractal Deposits in Two-Dimensional Space

5.4 Pigmented Coatings and Percolating Systems

5.5 Mathematical Description of Fractal Clusters

5.6 Percolating Pathways and Scaling Properties

5.7 The Fractal Structure of Clusters Generated by Diffusion-Limited Aggregation (DLA)

References

6 Vanishing Carpets, Fractal Felts and Dendritic Capture Trees

6.1 Sierpinski Carpets and Swiss Cheese

6.2 A Fractal Description of the Deposition Efficiency of Simulated Pesticide Spray Systems

6.3 Sierpinski Fractal Description of Real Dispersed Systems

6.4 Exploring the Fractal Structures of Filters

6.5 Dendritic Capture Trees in Filter Systems

6.6 Cantor on the Rocks

References

7 An Exploration of the Physical Significance of Fractal Structures in Three-Dimensional Space

7.1 Randomwalk Theory of Powder Mixing in Three- and Four-Dimensional Space

7.2 Fractal Geometry and Aerosol Physics

7.3 Assessing the Fractal Structure of a Rough Surface from Adsorption Studies

7.4 Interpreting Intrusion Porosimetry Data from a Fractal Geometry Perspective

References

8 Fractal Fingers and Floods

8.1 Fractal Fingers

8.2 Fractal Floods and Fronts in Porous Media

References

9 Fracture, Fragments and Fractals

9.1 The Fractal Structure of Fractured Surfaces

9.2 Describing Progress of a Fracture Process From a Fractal Perspective

9.3 The Fragmentation Fractal. A New Fractal Dimension for Characterising a Fragmented System

9.4 Fractal Geometry and New Perspectives in the Mineral Processing Industry

9.4.1 Dust Explosions

9.4.2 Energy Efficiency in a Pulverization Process

9.5 Brainstorming About Fractal Geometry and the Fracture Resistance of Composite Materials

References

10 Signposts to More Rambling Explorations of Fractal Space

Signpost 1 General Ramblings

References

Signpost 2 Fractal Scenery and Artistic Vision

References

Signpost 4 Lakes, Islands and other Geofractals

References

Signpost 5 Trees, Crabs, Cauliflowers and Camouflage

References

Signpost 6 Fractal Geometry and the Structure of Catalysts

References

Signpost 7 Solid-state Physics

References

Signpost 8 Butterflies, Ants and Caterpillars in the Garden of Eden

References

Signpost 9 Turbulence and Chaos

References

Signpost 10 The Philosophical Impact of Fractal Geometry

Signpost 11 Fun with Fractal Logic

References

Author Index

Subject Index