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

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Brian H. Kaye: A Random Walk through Fractal Dimensions

Published $1989$, VCH Publishers

ISBN 0-89573-888-0.


Subject Matter


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