Fractals And Beyond Complexities In The Sciences

One of the ways to understand the complexity in scientific disciplines is through the use of fractal geometry. Tremendous progress has been made in this field since its inception some two decades ago. This book collects the papers at the cutting-edge, reflecting the current status of fractals. With its special emphasis on the multidisciplinary research, the book represents a unique contribution to the understanding of the complex phenomena in nature.

Every reader will find something of interest in this book — from superdiffusion of the ocean surface to fetal heartbeats, from solar wind to the wearing-out of tools, from radioactive contamination to texture analysis, from image rendering to neural developments. The all-pervading link connecting these disparate disciplines is the realization that a linear approach to the majority of natural processes is at best only an approximation that can frequently be downright misleading. Consequently, the rise of what is broadly called the theory of complexity has gained tremendous momentum in the last decade or two. This modern approach aims at, and frequently succeeds in, correctly explaining many natural processes.The papers in this volume are based on presentations of the sixth international conference exploring the above-mentioned issues. These conferences are now regular and well established among the nonlinear series of conferences. This conference series is organized in different geographical regions, to encourage international collaboration. Among the distinguishing features of the series is its multidisciplinary nature, which has been growing steadily.

Owing to the rapid emergence and growth of techniques in the engineering application of fractals, it has become necessary to gather the most recent advances on a regular basis. This book is a continuation of the first volume - published in 1997 - but contains interesting developments. A major point is that mathematics has become more and more involved in the definition and use of fractal models. It seems that the time of the qualitative observation of fractal phenomena has gone. Now the main models are strongly based upon theoretical arguments. Fractals: Theory and Applications in Engineering is a multidisciplinary book which should interest every scientist working in areas connected to fractals.

This book presents the state-of-the-art after fifteen years of exponentially growing applications of fractal geometry in soil science. It demonstrates the wide-ranging applicability of fractal models in soil science and indicates new opportunities to integrate processes in soils within or across scales using fractals. Contributed by some of the pioneers in the field, chapters represent a broad spectrum of applications from geochemistry to microbiology and from scales of micrometers to the landscape, and serve as an introduction to the subject. Topics include fractal aspects of soil structure, porosity and texture, scaling in preferential and hydraulic conductivity, anoxic volumes and adsorption in fractal models of soil, characterization of the pore surface irregularity, fractal properties of soil organic matter, fractal concepts in studies of soil fauna and mycelium in soils, and fractal analysis of spatial and temporal variability in soil properties and crop yields. A wide spectrum of methods for identifying and measuring fractal properties is introduced and critically discussed. Although the book focussed on solving problems in soil science, the applications and the fractal approach used share much in common with many other fields within and outside of the earth sciences. A unique bibliography on fractals in soils science is included.

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Scaling is a mathematical transformation that enlarges or diminishes objects. The technique is used in a variety of areas, including finance and image processing. This book is organized around the notions of scaling phenomena and scale invariance. The various stochastic models commonly used to describe scaling — self-similarity, long-range dependence and multi-fractals — are introduced. These models are compared and related to one another. Next, fractional integration, a mathematical tool closely related to the notion of scale invariance, is discussed, and stochastic processes with prescribed scaling properties (self-similar processes, locally self-similar processes, fractionally filtered processes, iterated function systems) are defined. A number of applications where the scaling paradigm proved fruitful are detailed: image processing, financial and stock market fluctuations, geophysics, scale relativity, and fractal time-space.

The application of fractals in the engineering sciences is evolving swiftly and the editors have turned to Springer for the third time to bring you the latest research emerging from the rapid growth in techniques available for the employment of the ideas of fractals and complexity to a variety of disciplines in and associated with the engineering field. The strong potential of this research can be seen in real industrial situations with recent progress being made in areas such as chemical engineering, internet traffic, physics and finance. Image processing continues to be a major field of application for fractal analysis and is well-represented here. It is important to note that the applications models are presented with a firm basis in theoretical argument, the qualitative observation of fractal phenomena no longer being sufficient. Consisting of papers written by a world-wide pool of experts, the multidisciplinary approach of this third volume will be of particular interest to industrial researchers and practitioners as well as to academics from many backgrounds. Fractals in Engineering: New Trends in Theory and Applications continues the publication of engineering-related research in fractal techniques begun in Fractals in Engineering and Fractals: Theory and Applications in Engineering (Springer London 1997 and 1999).