This conference focused on the current research and future perspectives on the application of disordered systems theory, fractals and chaotic dynamical systems to chemical engineering problems. The contributions published here are organised around 4 main themes: Chaos (Analysis and Control) in Reactors and Reacting Systems; Transport in Disordered Media; Time-Series Analysis; and Multiphase Flow Characterization.
"This volume is a collection of the papers presented at the International Conference on Fractal Concepts and the Application of Chaos in Chemical Engineering Problems. The book provides a detailed description of the current research on the application of fractal concepts, nonlinear dynamics and disordered systems in chemical engineering, with emphasis on interdisciplinary connections with related fields, such as control theory of nonlinear systems, dynamic theory of fractals, transport theory and physical chemistry of heterogeneous materials."--Publisher's website.
This book is written for all engineers, graduate students and beginners working in the application fields, and for experimental scientists in general. It is not presented as a purely theoretical treatise but shows mathematics at a workshop, so to speak, through important applications originating in a deep pure mathematical theory. Widely spread subjects which the author has encountered hitherto are briefly addressed in the book, as chaos and fractal science is a frontier of new research fields nowadays.
For almost ten years chaos and fractals have been enveloping many areas of mathematics and the natural sciences in their power, creativity and expanse. Reaching far beyond the traditional bounds of mathematics and science to the realms of popular culture, they have captured the attention and enthusiasm of a worldwide audience. The fourteen chapters of the book cover the central ideas and concepts, as well as many related topics including, the Mandelbrot Set, Julia Sets, Cellular Automata, L-Systems, Percolation and Strange Attractors, and each closes with the computer code for a central experiment. In the two appendices, Yuval Fisher discusses the details and ideas of fractal image compression, while Carl J.G. Evertsz and Benoit Mandelbrot introduce the foundations and implications of multifractals.
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
For students with a background in elementary algebra, this book provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia Sets and the Mandelbrot Set, power laws, and cellular automata. The book includes over 200 end-of-chapter exercises.
A deeply detailed discussion of fractals in biology, heterogeneous chemistry, polymers, and the earth sciences. Beginning with a general introduction to fractal geometry it continues with eight chapters on self-organized criticality, rough surfaces and interfaces, random walks, chemical reactions, and fractals in chemisty, biology, and medicine. A special chapter entitled "Computer Exploration of Fractals, Chaos, and Cooperativity" presents computer demonstrations of fractal models: 14 programs are included on a 3 1/2" MS-DOS diskette which run on any PC with at least 1 MB RAM and a EGA or VGA graphics card, 16 colors.
These days computer-generated fractal patterns are everywhere, from squiggly designs on computer art posters to illustrations in the most serious of physics journals. Interest continues to grow among scientists and, rather surprisingly, artists and designers. This book provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules. It also presents papers on seemingly paradoxical combinations of randomness and structure in systems of mathematical, physical, biological, electrical, chemical, and artistic interest. Topics include: iteration, cellular automata, bifurcation maps, fractals, dynamical systems, patterns of nature created through simple rules, and aesthetic graphics drawn from the universe of mathematics and art.Chaos and Fractals is divided into six parts: Geometry and Nature; Attractors; Cellular Automata, Gaskets, and Koch Curves; Mandelbrot, Julia and Other Complex Maps; Iterated Function Systems; and Computer Art.Additionally, information on the latest practical applications of fractals and on the use of fractals in commercial products such as the antennas and reaction vessels is presented. In short, fractals are increasingly finding application in practical products where computer graphics and simulations are integral to the design process. Each of the six sections has an introduction by the editor including the latest research, references, and updates in the field. This book is enhanced with numerous color illustrations, a comprehensive index, and the many computer program examples encourage reader involvement.
True deterministic chaos is characterized by unpredictable, apparently random motion in a dynamical system completely described by a deterministic dynamic law, usually a nonlinear differential equation, with no stochastic component. The inability to predict future behavior of a chaotic system occurs because trajectories evolving from arbitrarily close initial conditions diverge. Chaos is universal as it may arise in any system governed by one of a class of quite common, suitable nonlinear dynamic laws. This book discusses both the experimental observation and theoretical interpretation of chaos in chemical and biochemical systems. Examples are drawn from the Belousov-Zhabotinsky reaction, surface reactions, electrochemical reactions, enzyme reactions, and periodically perturbed oscillating systems.
Translates new mathematical ideas in nonlinear dynamics and chaos into a language that engineers and scientists can understand, and gives specific examples and applications of chaotic dynamics in the physical world. Also describes how to perform both computer and physical experiments in chaotic dynamics. Topics cover Poincare maps, fractal dimensions and Lyapunov exponents, illustrating their use in specific physical examples. Includes an extensive guide to the literature, especially that relating to more mathematically oriented works; a glossary of chaotic dynamics terms; a list of computer experiments; and details for a demonstration experiment on chaotic vibrations.
