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An Unbounded Experience In Random Walks With Applications
This volume comprises the author's account of the development of novel results in random walk theory and its applications during the fractal and chaos revolutions. The early history of probability is presented in an engaging manner, and peppered with pitfalls and paradoxes. Readers will find the introduction of Paul Lévy's work via Mandelbrot's Lévy flights which are featured uniquely as Weierstrass and Riemann random walks.Generalizations to coupled memories, internal states and fractal time are introduced at the level for graduate students. Mathematical developments are explained including Green's functions, inverse Mellin transforms, Jacobians, and matrix methods. Applications are made ...
Lévy Flights and Related Topics in Physics
P. Lévy's work on random walks with infinite moments, developed more than half a century ago, has now been fully appreciated as a foundation of probabilistic aspects of fractals and chaos as well as scale-invariant processes. This is the first book for physicists devoted to Lévy processes. It includes thorough review articles on applications in fluid and gas dynamics, in dynamical systems including anomalous diffusion and in statistical mechanics. Various articles approach mathematical problems and finally the volume addresses problems in theoretical biology. The book is introduced by a personal recollection of P. Lévy written by B. Mandelbrot.
Unsolved Problems Of Noise In Physics, Biology, Electronic Technology And Information Technology, Proc
Much has been learned about the subject of noise and random fluctuations over the last 170 years (some old milestones: Brownian motion, 1826; Einstein's diffusion theory, 1905; Johnson-Nyquist thermal noise, 1926), but much remains to be known. This volume will be interesting reading for physicists, engineers, mathematicians, biologists and PhD students. The invited papers in the volume survey classical unsolved problems while the regular papers present new problems and paradoxes.
Fractals In Natural Science
During the last couple of years, fractals have been shown to represent the common aspects of many complex processes occurring in an unusually diverse range of fields including biology, chemistry, earth sciences, physics and technology. Using fractal geometry as a language, it has become possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iteractive functions, colloidal aggregation, biological pattern formation and inhomogenous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality.This volume contains a selection of high quality papers that discuss the latest developments in the research of fractals. It is divided into 5 sections and contains altogether 64 papers. Each paper is written by a well known author or authors in the field. Beginning each section is a short introduction, written by a prominent author, which gives a brief overview of the topics discussed in the respective sections.
Lévy Flights and Related Topics in Physics
P. Lévy's work on random walks with infinite moments, developed more than half a century ago, has now been fully appreciated as a foundation of probabilistic aspects of fractals and chaos as well as scale-invariant processes. This is the first book for physicists devoted to Lévy processes. It includes thorough review articles on applications in fluid and gas dynamics, in dynamical systems including anomalous diffusion and in statistical mechanics. Various articles approach mathematical problems and finally the volume addresses problems in theoretical biology. The book is introduced by a personal recollection of P. Lévy written by B. Mandelbrot.
Nonlinear Dynamics Of Ocean Waves - Proceedings Of The Symposium
The Standard Model of elementary particles, although very successful, contains various elements that are put in by hand. Understanding their origin requires going beyond the model and searching for “new physics”. The present book elaborates on one particular proposal concerning such physics. While the original conception is 50 years old, it has not lost its appeal over time. Its basic idea is that space — an arena of events treated in the Standard Model as a classical background — is a concept which emerges from a strictly discrete quantum layer in the limit of large quantum numbers. This book discusses an extension of this view by replacing space with phase space. It combines the results of the author's research papers and places them in much broader philosophical and phenomenological contexts, thus providing further arguments in favor of the proposed alternative. The book should be of interest to the philosophically-minded readers who are willing to contemplate unorthodox ideas on the very nature of the world.
Stochastically Excited Nonlinear Ocean Structures
Ocean structures, including ships, boats, piers, docks, rigs and platforms, are subject to fair weather wind and waves, as well as violent storms. A scientific analysis of these structures, under varying conditions, requires a mix of civil engineering, physics and applied mathematics. Chapters by experts in these fields are presented which explore the nonlinear responses of ocean structures to stochastic forcing. Theoretical methods calculate aspects of time, frequency and phase space responses. Probabilities governed by stochastic differential equations are investigated directly or through moment correlations, such as power spectra. Calculations can also involve level crossing statistics and first passage times. This book will help scientists study stochastic nonlinear equations and help engineers design for short term survivability of structures in storms and long life in the face of everyday fatigue.
Fractals in Natural Sciences
During the last couple of years, fractals have been shown to represent the common aspects of many complex processes occurring in an unusually diverse range of fields including biology, chemistry, earth sciences, physics and technology. Using fractal geometry as a language, it has become possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iteractive functions, colloidal aggregation, biological pattern formation and inhomogenous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality.This volume contains a selection of high quality papers that discuss the latest developments in the research of fractals. It is divided into 5 sections and contains altogether 64 papers. Each paper is written by a well known author or authors in the field. Beginning each section is a short introduction, written by a prominent author, which gives a brief overview of the topics discussed in the respective sections.
The Wonderful World of Stochastics
Elliott W. Montroll. Dielectric relaxation via the Montroll-Weiss random walk of defects. The fascination of old texts. Some statistical and dynamical problems in quantum electronics. Theory of diffusion via an interstitial and vacancy mechanism. Mathieu difference equations. Mayer-Montroll equations (and some variants) through history for fun and profit. Illumination in a random medium. Random walks in crystallography. On the quantum Langevin equation: the linear oscillator. Some inequalities for anisotropic rotators. Some notes and applications of the characteristic value theory of integral equations: abstract of a doctor's dissertation. Statistical mechanics of imperfect gases. On the theory of Markoff Chains. Frequency spectrum of crystalline solids. Effect of defects on lattice vibrations: interaction of defects and an analogy with Meson Pair theory. Poincare cycles, ergodicity, and irreversibility in assemblies coupled harmonic oscillators. Studies in nonequilibrium rate processes. I: the relaxation of a system of harmonic oscillators. Randot of a fi19991222.
