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.

Hard Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications is a basic treatise on real-time computing, with particular emphasis on predictable scheduling algorithms. It introduces the fundamental concepts of real-time computing, illustrates the most significant results in the field, and provides the essential methodologies for designing predictable computing systems which can be used to support critical control applications. This volume serves as a textbook for advanced level courses on the topic. Each chapter provides basic concepts, which are followed by algorithms that are illustrated with concrete examples, figures and tables. Exercises are included with each chapter and solutions are given at the end of the book. The book also provides an excellent reference for those interested in real-time computing for designing and/or developing predictable control applications.

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.

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

The fern-like patterns of frost on a cold window, eroded landscapes, and particles grown in an aerosol all have forms that are conventionally regarded as irregular, with little or no symmetry. In this book the reader is introduced to the fractal dimension, a concept that unifies the description of such diverse and irregular objects and implies that they all possess a new form of symmetry. The growth of these different objects is controlled by similar simple processes; descriptions of simple experiments that will bring the principles involved to life in a modestly equipped laboratory are also provided. The relevance of fractal concepts to the structure and chemistry of porous solids, and to the growth of polymers and colloids in liquid and gaseous phases, is emphasized within this concise text.

This book provides an important structural analysis of polymer solutions and melts, using fractal analysis. The book covers the theoretical fundamentals of macromolecules fractal analysis. It then goes on to discuss the fractal physics of polymer solutions and the fractal physics of melts. The intended audience of the book includes specialists in c

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 10 chapters written by leading experts in the field, including E. Stanley and B. Mandelbrot, the reader is introduced to basic concepts and techniques in disordered systems and is lead to the forefront of current research. In each chapter the connection between theory and experiment is emphasized, and a special chapter entitled "Fractals and Experiments" presents experimental studies of fractal systems in the laboratory. The book is written pedagogically. It can be used as a textbook for graduate students, by university teachers to prepare courses and seminars, and by active scientists who want to become familiar with a fascinating new field.