Fractals in Engineering From Theory to Industrial Applications

Fractal analysis research is expanding into a variety of engineering domains. The strong potential of this work is now beginning to be seen in important applications in real industrial situations. Recent research progress has already led to new developments in domains such as signal processing and chemical engineering, and the major advances in fractal theory that underlie such developments are detailed here. New domains of applications are also presented, among them environmental science and rough surface analysis. Sections include multifractal analysis, iterated function systems, random processes, network traffic analysis, fractals and waves, image compression, and applications in physics. Fractals in Engineering emphasizes the connection between fractal analysis research and applications to industry. It is an important volume that illustrates the scientific and industrial value of this exciting field.

Mutifractal Analysis.- Some open problems about multifractal functions.- Integral Transforms of Multifractal Measures.- Texture characterization of ERS-1 images by Regional Multifractal analysis.- Multifractal Analysis of Dipmeter Well Logs for Description of Geological Lithofacies.- IFS Theory.- Correspondence Between Fractal-Wavelet Transforms and Iterated Function Systems With Grey Level Maps.- Modeling fractal shapes using generalisations of IFS techniques.- A Wavelet-based Solution to the Inverse Problem for Fractal Interpolation Functions.- Schémas continus de subdivision.- Random Processes.- Fractal percolation with neighbour interaction.- Identification of Elliptic Gaussian Random Processes.- Modeling and Estimation of Fractional Brownian Motion using Multiresolution Stochastic Processes.- 2D Self-Similar Processes with Stationary Fractional Increments.- Network Traffic Analysis.- Four approaches to the fractional Brownian storage.- Multi-dimensional Fractional Brownian Motion and some Applications to Queueing Theory.- Fractional Brownian motion and data traffic modeling: The other end of the spectrum.- Fractals and Waves.- Fractal Electrodynamics: From Super Antennas to Superlattices.- Multiband Fractal Antennas and Arrays.- Fractal-Surface-Enhanced Optical Responses.- Fractional Fourier analysis of objects with scaling symmetry.- Potential Scattering on Fractals in One Dimension.- Image Compression.- Wavelet and Fractal Transforms for Image Compression.- How to improve pixel-based fractal image coding with adaptive partitions.- Chemical Engineering.- Transport Phenomena on Fractals and Green-Function Renormalization.- Self-Similar Spatio-Temporal Structure of Material Filaments in Chaotic Flows.- Accessibility of a Catalyst’s Fractal Surface to Diffusingand Reacting Molecules.- Lévy Distribution of Collisions for Knudsen Diffusion in Fractal Pores.- New Topics.- ?-Stochastic Differential Equations and Option Pricing Model.- Modelling Contaminant Spread on the Ocean Surface and within Soils using fBm’s: Two Civil Engineering Applications.- The Retinal Vasculature: Towards an Understanding of the Formation Process.- Color Plates.