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Author: Denis Makarov
Publisher: World Scientific
ISBN: 9814273171
Category : Science
Languages : en
Pages : 412
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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.
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: Denis Makarov
Publisher: World Scientific
ISBN: 9814273171
Category : Science
Languages : en
Pages : 412
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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.
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: Paul C. Etter
Publisher: CRC Press
ISBN: 1351679724
Category : Technology & Engineering
Languages : en
Pages : 639
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Book Description
This newest edition adds new material to all chapters, especially in mathematical propagation models and special applications and inverse techniques. It has updated environmental-acoustic data in companion tables and core summary tables with the latest underwater acoustic propagation, noise, reverberation, and sonar performance models. Additionally
Author: Paul C. Etter
Publisher: CRC Press
ISBN: 1466564938
Category : Technology & Engineering
Languages : en
Pages : 557
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Book Description
Underwater Acoustic Modeling and Simulation, Fourth Edition continues to provide the most authoritative overview of currently available propagation, noise, reverberation, and sonar-performance models. This fourth edition of a bestseller discusses the fundamental processes involved in simulating the performance of underwater acoustic systems and emphasizes the importance of applying the proper modeling resources to simulate the behavior of sound in virtual ocean environments. New to the Fourth Edition Extensive new material that addresses recent advances in inverse techniques and marine-mammal protection Problem sets in each chapter Updated and expanded inventories of available models Designed for readers with an understanding of underwater acoustics but who are unfamiliar with the various aspects of modeling, the book includes sufficient mathematical derivations to demonstrate model formulations and provides guidelines for selecting and using the models. Examples of each type of model illustrate model formulations, model assumptions, and algorithm efficiency. Simulation case studies are also included to demonstrate practical applications. Providing a thorough source of information on modeling resources, this book examines the translation of our physical understanding of sound in the sea into mathematical models that simulate acoustic propagation, noise, and reverberation in the ocean. The text shows how these models are used to predict and diagnose the performance of complex sonar systems operating in the undersea environment.
Author: Paul C. Etter
Publisher: CRC Press
ISBN: 1351679716
Category : Technology & Engineering
Languages : en
Pages : 776
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Book Description
This newest edition adds new material to all chapters, especially in mathematical propagation models and special applications and inverse techniques. It has updated environmental-acoustic data in companion tables and core summary tables with the latest underwater acoustic propagation, noise, reverberation, and sonar performance models. Additionally, the text discusses new applications including underwater acoustic networks and channel models, marine-hydrokinetic energy devices, and simulation of anthropogenic sound sources. It further includes instructive case studies to demonstrate applications in sonar simulation.
Author: Albert C. J. Luo
Publisher: Springer Science & Business Media
ISBN: 3642123430
Category : Science
Languages : en
Pages : 327
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Book Description
In memory of Dr. George Zaslavsky, "Long-range Interactions, Stochasticity and Fractional Dynamics" covers the recent developments of long-range interaction, fractional dynamics, brain dynamics and stochastic theory of turbulence, each chapter was written by established scientists in the field. The book is dedicated to Dr. George Zaslavsky, who was one of three founders of the theory of Hamiltonian chaos. The book discusses self-similarity and stochasticity and fractionality for discrete and continuous dynamical systems, as well as long-range interactions and diluted networks. A comprehensive theory for brain dynamics is also presented. In addition, the complexity and stochasticity for soliton chains and turbulence are addressed. 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: Sergey V. Prants
Publisher: Springer
ISBN: 3319530224
Category : Science
Languages : en
Pages : 285
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Book Description
This book uses the Lagrangian approach, especially useful and convenient for studying large-scale transport and mixing in the ocean, to present a detailed view of ocean circulation. This approach focuses on simulations and on monitoring the trajectories of fluid particles, which are governed by advection equations. The first chapter of the book is devoted to dynamical systems theory methods, which provide the framework, methodology and key concepts for the Lagrangian approach. The book then moves on to an analysis of chaotic mixing and cross-stream transport in idealized models of oceanic meandering currents like the Gulfstream in the Atlantic, the Kuroshio in the Pacific, and Antarctic Circumpolar Current, after which the current state of physical oceanography is reviewed. The latter half of the book applies the techniques and methods already described in order to study eddies, currents, fronts and large-scale mixing and transport in the Far-Eastern seas and the north-western part of the Pacific Ocean. Finally, the book concludes with a discussion of Lagrangian simulation and monitoring of water contamination after the Fukushima disaster of 2011. The propagation of Fukushima-derived radionuclides, surface transport across the Kuroshio Extension current, and the role of mesoscale eddies in the transport of Fukushima-derived cesium isotopes in the ocean are examined, and a comparison of simulation results with actual measurements are presented.Written by some of the world leaders in the application of Lagrangian methods in oceanography, this title will be of benefit to the oceanographic community by presenting the necessary background of the Lagrangian approach in an accessible manner.
Author: Dumitru Baleanu
Publisher: World Scientific
ISBN: 9814458635
Category : Mathematics
Languages : en
Pages : 426
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Book Description
The subject of fractional calculus and its applications (that is, convolution-type pseudo-differential operators including integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, mainly due to its applications in diverse fields of science and engineering. These operators have been used to model problems with anomalous dynamics, however, they also are an effective tool as filters and controllers, and they can be applied to write complicated functions in terms of fractional integrals or derivatives of elementary functions, and so on.This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models.All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book was written with a trade-off in mind between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. Numerical code is also provided.
Author: Dumitru Baleanu
Publisher: World Scientific
ISBN: 9814641111
Category : Mathematics
Languages : en
Pages : 209
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Book Description
This volume presents several important and recent contributions to the emerging field of fractional differential equations in a self-contained manner. It deals with new results on existence, uniqueness and multiplicity, smoothness, asymptotic development, and stability of solutions. The new topics in the field of fractional calculus include also the Mittag-Leffler and Razumikhin stability, stability of a class of discrete fractional non-autonomous systems, asymptotic integration with a priori given coefficients, intervals of disconjugacy (non-oscillation), existence of Lp solutions for various linear, and nonlinear fractional differential equations.
