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Distributions in the Physical and Engineering Sciences, Volume 1
Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems which is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important to practitioners and researchers. The goal of the book is to give the reader, specialist and non-specialist usable and modern mathematical tools in their research and analysis. This new text is intended for graduate students and researchers in applied mathematics, physical sciences and engineering. The careful explanations, accessible writing style, and many illustrations/examples also make it suitable for use as a self-study reference by anyone seeking greater understanding and proficiency in the problem solving methods presented. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. The present, softcover reprint is designed to make this classic textbook available to a wider audience.
Distributions in the Physical and Engineering Sciences, Volume 2
Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems. It is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important for practitioners and researchers. The goal of the books is to give the reader, specialist and non-specialist, useable and modern mathematical tools in their research and analysis. Volume 2: Linear and Nonlinear Dynamics of Continuous Media continues the multivolume project which endeavors to show how the theory of distributions, also called the theory of generalized functions, can be used by graduate students and researche...
Theory of Zipf's Law and Beyond
Zipf’s law is one of the few quantitative reproducible regularities found in e- nomics. It states that, for most countries, the size distributions of cities and of rms (with additional examples found in many other scienti c elds) are power laws with a speci c exponent: the number of cities and rms with a size greater thanS is inversely proportional toS. Most explanations start with Gibrat’s law of proportional growth but need to incorporate additional constraints and ingredients introducing deviations from it. Here, we present a general theoretical derivation of Zipf’s law, providing a synthesis and extension of previous approaches. First, we show that combining Gibrat’s law at all r...
The Theory of Quantum Torus Knots
A detailed mathematical derivation of space curves is presented that links the diverse fields of superfluids, quantum mechanics, and hydrodynamics by a common foundation. The basic mathematical building block is called the theory of quantum torus knots (QTK).
Stochastic Modelling in Physical Oceanography
The study of the ocean is almost as old as the history of mankind itself. When the first seafarers set out in their primitive ships they had to understand, as best they could, tides and currents, eddies and vortices, for lack of understanding often led to loss of live. These primitive oceanographers were, of course, primarily statisticians. They collected what empirical data they could, and passed it down, ini tially by word of mouth, to their descendants. Data collection continued throughout the millenia, and although data bases became larger, more re liable, and better codified, it was not really until surprisingly recently that mankind began to try to understand the physics behind these data, and, shortly afterwards, to attempt to model it. The basic modelling tool of physical oceanography is, today, the partial differential equation. Somehow, we all 'know" that if only we could find the right set of equations, with the right initial and boundary conditions, then we could solve the mysteries of ocean dynamics once and for all.
Waves and Structures in Nonlinear Nondispersive Media
"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonli...
Proceedings of the Second International Symposium of Trans Black Sea Region on Applied Electromagnetism
This volume constitutes the proceedings of the Trans Black Sea Region Symposium on Applied Electromagnetism, held in 2000.
Quantum Chaos Y2K
Quantum chaos is becoming a very wide field that ranges from experiments to theoretical physics and purely mathematical issues. In view of this grand span, Nobel Symposium 116 focused on experiments and theory, and attempted to encourage interplay between them. There was emphasis on the interdisciplinary character of the subject, involving a broad range of subjects in physics, including condensed matter physics, nuclear physics, atomic physics and elementary particle physics. The physics involved in quantum chaos has much in common with acoustics, microwaves, optics, etc., and therefore the symposium also covered aspects of wave chaos in this broader sense. The program was structured according to the following areas: manifestations of classical chaos in quantum systems; transport phenomena; quantal spectra in terms of periodic orbits; semiclassical and random matrix approaches; quantum chaos in interacting systems; chaos and tunneling; wave-dynamic chaos. This important book constitutes the proceedings of the symposium.
Distributions in the Physical and Engineering Sciences, Volume 3
Continuing the authors’ multivolume project, this text considers the theory of distributions from an applied perspective, demonstrating how effective a combination of analytic and probabilistic methods can be for solving problems in the physical and engineering sciences. Volume 1 covered foundational topics such as distributional and fractional calculus, the integral transform, and wavelets, and Volume 2 explored linear and nonlinear dynamics in continuous media. With this volume, the scope is extended to the use of distributional tools in the theory of generalized stochastic processes and fields, and in anomalous fractional random dynamics. Chapters cover topics such as probability distri...
