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.
This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author -- hailed by Publishers Weekly as a modern Lewis Carroll -- conveys memorable insights in the form of puns and puzzles. 1992 edition.
A modern up-to-date introduction for readers outside statistical physics. It puts emphasis on a clear understanding of concepts and methods and provides the tools that can be of immediate use in applications.
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.
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.
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.
Historically, science has sought to reduce complex problems to their simplest components, but more recently it has recognized the merit of studying complex phenomena in situ. Fractal geometry is one such appealing approach, and this book discusses its application to complex problems in molecular biophysics. The book provides a detailed, unified treatment of fractal aspects of protein and structure dynamics, fractal reaction kinetics in biochemical systems, sequence correlations in DNA and proteins, and descriptors of chaos in enzymatic systems. In an area that has been slow to acknowledge the use of fractals, this is an important addition to the literature, offering a glimpse of the wealth of possible applications to complex problems.
The book is characterized by the illustration of cases of fractal, self-similar and multi-scale structures taken from the mechanics of solid and porous materials, which have a technical interest. In addition, an accessible and self-consistent treatment of the mathematical technique of fractional calculus is provided, avoiding useless complications.
This book primarily focuses on the study of various neurological disorders, including Parkinson’s (PD), Huntington (HD), Epilepsy, Alzheimer’s and Motor Neuron Diseases (MND) from a new perspective by analyzing the physiological signals associated with them using non-linear dynamics. The development of nonlinear methods has significantly helped to study complex nonlinear systems in detail by providing accurate and reliable information. The book provides a brief introduction to the central nervous system and its various disorders, their effects on health and quality of life, and their respective courses of treatment, followed by different bioelectrical signals like those detected by Electroencephalography (EEG), Electrocardiography (ECG), and Electromyography (EMG). In turn, the book discusses a range of nonlinear techniques, fractals, multifractals, and Higuchi’s Fractal Dimension (HFD), with mathematical examples and procedures. A review of studies conducted to date on neurological disorders like epilepsy, dementia, Parkinson’s, Huntington, Alzheimer’s, and Motor Neuron Diseases, which incorporate linear and nonlinear techniques, is also provided. The book subsequently presents new findings on neurological disorders of the central nervous system, namely Parkinson’s disease and Huntington’s disease, by analyzing their gait characteristics using a nonlinear fractal based technique: Multifractal Detrended Fluctuation Analysis (MFDFA). In closing, the book elaborates on several parameters that can be obtained from cross-correlation studies of ECG and blood pressure, and can be used as markers for neurological disorders.
