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Fractals’ Physical Origin and Properties
This volume contains the Proceedings of the Special Seminar on: FRAGTALS held from October 9-15, 1988 at the Ettore Majorana Centre for Scientific Culture, Erice (Trapani), Italy. The concepts of self-similarity and scale invariance have arisen independently in several areas. One is the study of critical properites of phase transitions; another is fractal geometry, which involves the concept of (non-integer) fractal dimension. These two areas have now come together, and their methods have extended to various fields of physics. The purpose of this Seminar was to provide an overview of the recent developments in the field. Most of the contributions are theoretical, but some experimental work i...
A Random Walk Through Fractal Dimensions
Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science. From reviews of the first edition: "...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems." MRS Bulletin
Cellular Automata and Modeling of Complex Physical Systems
Cellular automata are fully discrete dynamical systems with dynamical variables defined at the nodes of a lattice and taking values in a finite set. Application of a local transition rule at each lattice site generates the dynamics. The interpretation of systems with a large number of degrees of freedom in terms of lattice gases has received considerable attention recently due to the many applications of this approach, e.g. for simulating fluid flows under nearly realistic conditions, for modeling complex microscopic natural phenomena such as diffusion-reaction or catalysis, and for analysis of pattern-forming systems. The discussion in this book covers aspects of cellular automata theory related to general problems of information theory and statistical physics, lattice gas theory, direct applications, problems arising in the modeling of microscopic physical processes, complex macroscopic behavior (mostly in connection with turbulence), and the design of special-purpose computers.
Fractals and Disordered Systems
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.
Spin Eigenfunctions
The aim of this book is to give a comprehensive treatment of the different methods for the construction of spin eigenfunctions and to show their interrelations. The ultimate goal is the construction of an antisymmetric many-electron wave function that has both spatial and spin parts and the calculation of the matrix elements of the Hamiltonian over the total wave function. The representations of the symmetric group playa central role both in the construction of spin functions and in the calculation of the matrix elements of the Hamiltonian, so this subject will be treated in detail. We shall restrict the treatment to spin-independent Hamiltonians; in this case the spin does not have a direct...
Fractals, Scaling and Growth Far from Equilibrium
A comprehensive, 1998 account of the practical aspects and pitfalls of the applications of fractal modelling in the physical sciences.
Diffusion in Materials
This volume is the proceedings of the NATO Advanced Study Institute, "Diffusion in Materials", held at "Centre Paul Langevin", Aussois, during March 12-25, 1989. There were 105 participants of whom 24 were lecturers and members of the international advisory committee. In addition to the participants from NATO countries, a small number of participants came from Australia, Hungary, Poland and Tunisia. The principal aim of the organizing committee was to bring together scientists of wide interest and expertise in the field of diffusion and to familiarize the young workers in material science with the wide range of theoretical models and methods and of experimental techniques . The Institute was...
Universalities in Condensed Matter
Universality is the property that systems of radically different composition and structure exhibit similar behavior. The appearance of universal laws in simple critical systems is now well established experimentally, but the search for universality has not slackened. This book aims to define the current status of research in this field and to identify the most promising directions for further investigations. On the theoretical side, numerical simulations and analytical arguments have led to expectations of universal behavior in several nonequilibrium systems, e.g. aggregation, electric discharges, and viscous flows. Experimental work is being done on "geometric" phase transitions, e.g. aggregation and gelation, in real systems. The contributions to this volume allow a better understanding of chaotic systems, turbulent flows, aggregation phenomena, fractal structures, and quasicrystals. They demonstrate how the concepts of renormalization group transformations, scale invariance, and multifractality are useful for describing inhomogeneous materials and irreversible phenomena.
The Fractal Approach to Heterogeneous Chemistry
Discusses applications of fractal geometry to chemical systems involving complex and highly irregular structures. These new mathematical techniques have particular applications in chromatographic adsorbents, colloidal systems, irregular surfaces, branched polymers, and many other areas of polymer, colloidal, and surface chemistry.
