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

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