Fractals in Chemistry


Book Description

A practical guide to solving problems in chemistry with fractal geometry. It has been two decades since Mandelbrot formulated his revolutionary theories of fractal geometry. Yet, in that brief time, fractals -those strangely beautiful infinite geometric patterns -and the computational processes that give rise to them have become a valued research tool in a broad array of scientific, social-scientific, and commercial fields. While inroads also have been made in applying fractals to theoretical and applied chemistry, there continues to be a dearth of texts and references on the subject. This book helps fill that gap in the literature. Fractals in Chemistry provides chemists with a concise, practical introduction to fractal theory and its applications to a wide range of "bread and butter" issues in chemistry. Drawing upon his considerable experience as a researcher who helped pioneer some of the methods he describes, Walter Rothschild critically appraises the power and limitations of the fractal approach and shows how it can provide more predictive classification schemes and explain phenomena difficult to handle by classical means. Then, with the help of nearly 100 illustrations, he demonstrates how to apply fractals to model chemical phenomena such as adsorption, aggregation, catalysis, chemical reactivity, degradation, and turbulent flames, and how to understand dynamics on fractals in terms of fractons in diffusion-limited reactions, dispersive spectroscopies, and energy transfer. Fractals in Chemistry is both a valuable working resource for professionals in physical chemistry, chemical physics, and computer modeling and an excellent graduate-level text for courses covering the use of fractals in chemistry.




Fractals in Science


Book Description

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.




Fractals, Quasicrystals, Chaos, Knots and Algebraic Quantum Mechanics


Book Description

At the end of the workshop on "New Theoretical Concepts in Physical Chemistry", one of the participants made an attempt to present a first impression of its achievements from his own personal standpoint. Appar ently his views reflected a general feeling, so that the organizers thought they would be suitable as a presentation of the proceedings for future readers. That is the background from which this foreword was born. The scope of the workshop is a very broad one. There are contribu tions from mathematics, physics, crystallography, chemistry and biology; the problems are approached either by means of axiomatic and rigorous methods, or at an empirical phenomenological level. This same diversifi cation can be found in the new basic concepts presented. Some arise from pure theoretical investigation in C*-algebra or in quantum probability theory; others from an analysis of very complex experimental data like nuclear energy levels, or processes on the frontier between classical and quantum physics; others again have their origin in the discovery of new ordered structures like the icosahedral crystal phases, or the knots of DNA molecules; others follow from the application of ideas like frac tals or chaos to new fields like spectral theory or chemical reactions. It is to be expected that readers will have to face the same sort of difficulties as did the participants in understanding such diverse languages, in applying themselves to subjects possibly far from their own experience, and in grasping highly sophisticated new concepts.




Diffusion and Reactions in Fractals and Disordered Systems


Book Description

This book describes diffusion and transport in disordered media such as fractals and random resistor networks.




Fractals, Scaling and Growth Far from Equilibrium


Book Description

A comprehensive, 1998 account of the practical aspects and pitfalls of the applications of fractal modelling in the physical sciences.




Fractals and Disordered Systems


Book Description

Fractals and disordered systems have recently become the focus of intense interest in research. This book discusses in great detail the effects of disorder on mesoscopic scales (fractures, aggregates, colloids, surfaces and interfaces, glasses and polymers) and presents tools to describe them in mathematical language. A substantial part is devoted to the development of scaling theories based on fractal concepts. In ten chapters written by leading experts in the field, the reader is introduced to basic concepts and techniques in disordered systems and is led to the forefront of current research. This second edition has been substantially revised and updates the literature in this important field.




Fractals in Chemistry, Geochemistry, and Biophysics


Book Description

In this introductory text, Dr. Birdi demonstrates experimental methods and analyses of fractal dimensions in natural processes. In addition to a general overview, he discusses in detail problems in the fields of chemistry, geochemistry, and biophysics. Both students and professionals with a minimum of mathematics or physical science training will learn to find and model shapes and patterns from their own everyday observations.




Fractals: A Very Short Introduction


Book Description

Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics. This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.




Physics and Fractal Structures


Book Description




Fractal Concepts in Surface Growth


Book Description

This book brings together two of the most exciting and widely studied subjects in modern physics: namely fractals and surfaces. To the community interested in the study of surfaces and interfaces, it brings the concept of fractals. To the community interested in the exciting field of fractals and their application, it demonstrates how these concepts may be used in the study of surfaces. The authors cover, in simple terms, the various methods and theories developed over the past ten years to study surface growth. They describe how one can use fractal concepts successfully to describe and predict the morphology resulting from various growth processes. Consequently, this book will appeal to physicists working in condensed matter physics and statistical mechanics, with an interest in fractals and their application. The first chapter of this important new text is available on the Cambridge Worldwide Web server: http://www.cup.cam.ac.uk/onlinepubs/Textbooks/textbookstop.html