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Author: Sadrilla S. Abdullaev
Publisher: Routledge
ISBN:
Category : Mathematics
Languages : en
Pages : 336
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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.
Author: Sadrilla S. Abdullaev
Publisher: Routledge
ISBN:
Category : Mathematics
Languages : en
Pages : 336
Get Book Here
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.
Author: Denis Makarov
Publisher: World Scientific
ISBN: 981427318X
Category : Science
Languages : en
Pages : 412
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Book Description
1. Ray and wave propagation. 1.1. Underwater sound channel. 1.2. Basic equations. 1.3. Geometrical optics approximations and optical-mechanical analogy. The Hamiltonian formalism. 1.4. Ray travel times. 1.5. Range-dependent environments. 1.6. Acoustic ocean tomography. 1.7. Experiments on long-range sound propagation. 1.8. Summary -- 2. Ray chaos. 2.1. Hamiltonian chaos. 2.2. Lyapunov instability. 2.3. Ray-medium resonance. 2.4. Overlapping of resonances. 2.5. Vertical resonance. 2.6. Manifestation of regular and chaotic ray motion in distributions of ray travel times. 2.7. Summary -- 3. Wave chaos. 3.1. The problem of wave chaos. 3.2. Normal modes. 3.3. Mode coupling under chaotic conditions. 3.4. Influence of fine-scale inhomogeneities on wave dynamics. 3.5. Summary -- 4. Chaotic phenomena in random environment. 4.1. Ray chaos in a random medium. 4.2. Travel times of chaotic rays. 4.3. Modal structure of the sound field in a waveguide with random inhomogeneities. 4.4. Wave beam in an ocean acoustic waveguide. 4.5. Arrival times of sound pulses in the presence of internal waves and a mesoscale inhomogeneity. 4.6. Summary -- 5. Glossary of some concepts and notations in Hamiltonian chaos theory
Author: Albert C. J. Luo
Publisher: Springer Science & Business Media
ISBN: 3642127185
Category : Science
Languages : en
Pages : 312
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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.
Author: Mingzhou Ding
Publisher: World Scientific
ISBN: 9812811516
Category : Science
Languages : en
Pages : 459
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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. Contents: Condensed Matter: Self-Organized Quasiparticles and Other Patterns in Planar Gas-Discharge Systems (H-G Purwins et al.); Controllable Bifurcation Processes in Undoped, Photoexcited GaAs/A1As Superlattices (K J Luo et al.); Control: Analyzing Time-Delay Feedback Systems (R Hegger et al.); Chaos Control in Fast Systems Using Occasional Feedback (N J Corron et al.); Electronics: Characteristic Relations of Type-III Intermittency in an Electronic Circuit (C-M Kim et al.); Chaotic Pulse Trains in Digital Communications (M Sushchik et al.); Spatiotemporal: Continuum Coupled Maps: A Model for Patterns in Vibrated Sand (E Ott & S C Venkataramani); Pattern Control with Spatial Perturbations in a Wide Aperture Laser (R Meucci et al.); Biology: Robust Detection of Dynamical Change in Scalp Egg (P C Gailey et al.); Detection of Unstable Periodic Orbits in Noisy Data, and Choosing the Right Surrogates (K Dolan et al.); Synchronization: Experimental Manifestations of Phase and Lag Synchronizations in Coupled Chaotic Systems (Y-C Lai et al.); Amplitude Death in Coupled Opto-Thermal Oscillators (R Herrero et al.); Banquet Talk: Case Study in OC Experimental ComplexityOCO OCo An Artificial-Life Approach to Modeling Warfare (A Ilachinski); Optics: Adaptive Control of Strong Chaos (F T Arecchi); Optical Implementation of Chaotic Maps with Mach-Zehnder Interferometers (K Umeno et al.); Quantum Chaos: Methods in Acoustic Chaos (C Ellegaard & K Schaadt); Mechanics: Stability Transitions in a Nonlinear Airfoil (L Virgin et al.); Ray Chaos in Quadratic Index Media: A Non-Mechanical Application of Mechanics (R Tagg & M Asadi-Zeydabadi); Hydrodynamics: Dynamics, Statistics and Vortex Crystals in the Relaxation of 2D Turbulence (C F Driscoll et al.); Growth of Disordered Features in a Two-Dimensional Cylinder Wake (P Vorobieff & R E Ecke); General: Experimental Evidence for Microscopic Chaos (M E Briggs et al.); Magnetic Resonance Imaging of Structure and Coarsening in Three-Dimensional Foams (B A Prause & J A Glazier); and other papers. Readership: Nonlinear and computer scientists, physicists, biomedical/chemical/mechanical engineers, as well as researchers and graduate students in the field of chaos."
Author:
Publisher: Elsevier
ISBN: 0444538038
Category : Science
Languages : en
Pages : 5604
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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
Author: Sadrilla S. Abdullaev
Publisher: Springer
ISBN: 3540334173
Category : Science
Languages : en
Pages : 384
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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.
Author: Mingzhou Ding
Publisher: World Scientific
ISBN: 9814491500
Category : Science
Languages : en
Pages : 459
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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.
Author:
Publisher:
ISBN:
Category : Fluids
Languages : en
Pages : 1250
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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.
Author: E. Boschi
Publisher: Compositori
ISBN:
Category : Science
Languages : en
Pages : 590
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Book Description
Author: Leonid M. Brekhovskikh
Publisher: Springer Science & Business Media
ISBN: 9783540655923
Category : Science
Languages : en
Pages : 550
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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.
