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Chaos and Dynamics of Rays in Waveguide Media

Author : Sadrilla S. Abdullaev

Publisher : Routledge

Page : 336 pages

File Size : 38,88 MB

Release : 1993

Category : Mathematics

ISBN :

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Book Description

This unique and timely work is devoted to the problems of ray theory of long-range wave propagation in regularly inhomogeneous media using the modern theory of dynamic systems. The author, updating an old field with modern methods, uses the general concepts of ray dynamics and some fairly simple notions of nonlinear dynamics to define the subject, making the rading easy for even non-specialists. The essential ideas are initially formulated with waveguides and resonators, after which the more complicated problems of nonlinear ray dynamics in mobile and heterogeneous media are discussed. This original material encompasses such concepts as nonlinear resonance, chaos, the devil's ladder, and kinetics. S.S. Abdullaev is at the Institute for Biocybernetics, Uzbekistan Academy of Sciences, Tashkent. He has been specialising in the theory of wave propagation since 1975.



Ray and Wave Chaos in Ocean Acoustics

Author : Denis Makarov

Publisher : World Scientific

Page : 412 pages

File Size : 42,32 MB

Release : 2010

Category : Science

ISBN : 9814273171

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Book Description

A systematic study of chaotic ray dynamics in underwater acoustic waveguides began in the mid-1990s when it was realized that this factor plays a crucial role in long-range sound propagation in the ocean. The phenomenon of ray chaos and its manifestation at a finite wavelength ? wave chaos ? have been investigated by combining methods from the theory of wave propagation and the theory of dynamical and quantum chaos. This book is the first monograph summarizing results obtained in this field. Emphasis is made on the exploration of ray and modal structures of the wave field in an idealized environmental model with periodic range dependence and in a more realistic model with sound speed fluctuations induced by random internal waves. The book is intended for acousticians investigating the long-range sound transmission through the fluctuating ocean and also for researchers studying waveguide propagation in other media. It will be of major interest to scientists working in the field of dynamical and quantum chaos.



Hamiltonian Chaos Beyond the KAM Theory

Author : Albert C. J. Luo

Publisher : Springer Science & Business Media

Page : 312 pages

File Size : 14,44 MB

Release : 2011-01-04

Category : Science

ISBN : 3642127185

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Book Description

“Hamiltonian Chaos Beyond the KAM Theory: Dedicated to George M. Zaslavsky (1935—2008)” covers the recent developments and advances in the theory and application of Hamiltonian chaos in nonlinear Hamiltonian systems. The book is dedicated to Dr. George Zaslavsky, who was one of three founders of the theory of Hamiltonian chaos. Each chapter in this book was written by well-established scientists in the field of nonlinear Hamiltonian systems. The development presented in this book goes beyond the KAM theory, and the onset and disappearance of chaos in the stochastic and resonant layers of nonlinear Hamiltonian systems are predicted analytically, instead of qualitatively. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering. Dr. Albert C.J. Luo is a Professor at Southern Illinois University Edwardsville, USA. Dr. Valentin Afraimovich is a Professor at San Luis Potosi University, Mexico.



Proceedings of the 5th Experimental Chaos Conference

Author : Mingzhou Ding

Publisher : World Scientific

Page : 459 pages

File Size : 31,87 MB

Release : 2001

Category : Science

ISBN : 9810245610

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Book Description

The 5th Experimental Chaos Conference was a gathering of scientists and engineers who work on real-world systems that behave in a nonlinear and, often, chaotic fashion. The proceedings present discoveries of chaotic behavior, explanation of nonlinear phenomena in the laboratory, and applications of nonlinear and chaotic effects to devices and techniques for improving performance and surmounting technical obstacles. Experimental work is presented on chaos in semiconductor superlattices, spatiotemporal chaos in magnetic materials, instabilities in magnetic fluids, bifurcations of hexagonal patterns in lasers, and discrete rotating waves. New phenomena are exhibited on amplitude death in coupled oscillators, vortex crystals, wakes in soap films, chaotic dynamics of ocean waves, and microscopic chaos. Applications of chaotic dynamics are offered in the areas of chaotic pulse trains in digital communications, detection of changes in EEGs, detection of unstable periodic orbits in noisy data, cellular automata and warfare, detection of n: m phase synchronization, methods in acoustic chaos, chaos in the machine tool-cutting process, and a nonlinear airfoil. The broad range of topics and fields touches on a wide variety of systems whose behavior is now better understood and applied through the use of chaotic dynamics



Treatise on Geophysics

Author :

Publisher : Elsevier

Page : 5604 pages

File Size : 27,74 MB

Release : 2015-04-17

Category : Science

ISBN : 0444538038

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Book Description

Treatise on Geophysics, Second Edition, is a comprehensive and in-depth study of the physics of the Earth beyond what any geophysics text has provided previously. Thoroughly revised and updated, it provides fundamental and state-of-the-art discussion of all aspects of geophysics. A highlight of the second edition is a new volume on Near Surface Geophysics that discusses the role of geophysics in the exploitation and conservation of natural resources and the assessment of degradation of natural systems by pollution. Additional features include new material in the Planets and Moon, Mantle Dynamics, Core Dynamics, Crustal and Lithosphere Dynamics, Evolution of the Earth, and Geodesy volumes. New material is also presented on the uses of Earth gravity measurements. This title is essential for professionals, researchers, professors, and advanced undergraduate and graduate students in the fields of Geophysics and Earth system science. Comprehensive and detailed coverage of all aspects of geophysics Fundamental and state-of-the-art discussions of all research topics Integration of topics into a coherent whole



Construction of Mappings for Hamiltonian Systems and Their Applications

Author : Sadrilla S. Abdullaev

Publisher : Springer

Page : 384 pages

File Size : 11,47 MB

Release : 2006-08-02

Category : Science

ISBN : 3540334173

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Book Description

Based on the method of canonical transformation of variables and the classical perturbation theory, this innovative book treats the systematic theory of symplectic mappings for Hamiltonian systems and its application to the study of the dynamics and chaos of various physical problems described by Hamiltonian systems. It develops a new, mathematically-rigorous method to construct symplectic mappings which replaces the dynamics of continuous Hamiltonian systems by the discrete ones. Applications of the mapping methods encompass the chaos theory in non-twist and non-smooth dynamical systems, the structure and chaotic transport in the stochastic layer, the magnetic field lines in magnetically confinement devices of plasmas, ray dynamics in waveguides, etc. The book is intended for postgraduate students and researches, physicists and astronomers working in the areas of plasma physics, hydrodynamics, celestial mechanics, dynamical astronomy, and accelerator physics. It should also be useful for applied mathematicians involved in analytical and numerical studies of dynamical systems.



The 5th Experimental Chaos Conference

Author : Mingzhou Ding

Publisher : World Scientific

Page : 459 pages

File Size : 22,79 MB

Release : 2001-04-02

Category : Science

ISBN : 9814491500

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Book Description

The 5th Experimental Chaos Conference was a gathering of scientists and engineers who work on real-world systems that behave in a nonlinear and, often, chaotic fashion. The proceedings present discoveries of chaotic behavior, explanation of nonlinear phenomena in the laboratory, and applications of nonlinear and chaotic effects to devices and techniques for improving performance and surmounting technical obstacles. Experimental work is presented on chaos in semiconductor superlattices, spatiotemporal chaos in magnetic materials, instabilities in magnetic fluids, bifurcations of hexagonal patterns in lasers, and discrete rotating waves. New phenomena are exhibited on amplitude death in coupled oscillators, vortex crystals, wakes in soap films, chaotic dynamics of ocean waves, and microscopic chaos. Applications of chaotic dynamics are offered in the areas of chaotic pulse trains in digital communications, detection of changes in EEGs, detection of unstable periodic orbits in noisy data, cellular automata and warfare, detection of n:m phase synchronization, methods in acoustic chaos, chaos in the machine tool-cutting process, and a nonlinear airfoil. The broad range of topics and fields touches on a wide variety of systems whose behavior is now better understood and applied through the use of chaotic dynamics.



Physical Review

Author :

Publisher :

Page : 1250 pages

File Size : 41,79 MB

Release : 1999-02

Category : Fluids

ISBN :

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Book Description

Publishes papers that report results of research in statistical physics, plasmas, fluids, and related interdisciplinary topics. There are sections on (1) methods of statistical physics, (2) classical fluids, (3) liquid crystals, (4) diffusion-limited aggregation, and dendritic growth, (5) biological physics, (6) plasma physics, (7) physics of beams, (8) classical physics, including nonlinear media, and (9) computational physics.





Acoustics of Layered Media II

Author : Leonid M. Brekhovskikh

Publisher : Springer Science & Business Media

Page : 550 pages

File Size : 15,44 MB

Release : 1999-03-25

Category : Science

ISBN : 9783540655923

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Book Description

Acoustics of Layered Media II presents the theory of sound propagation and reflection of spherical waves and bounded beams in layered media. It is mathematically rigorous but at the same time care is taken that the physical usefulness in applications and the logic of the theory are not hidden. Both moving and stationary media, discretely and continuously layered, including a range-dependent environment, are treated for various types of acoustic wave sources. Detailed appendices provide further background on the mathematical methods. This second edition reflects the notable recent progress in the field of acoustic wave propagation in inhomogeneous media.