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Nonlinear Ocean Waves And The Inverse Scattering Transform

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Nonlinear Ocean Waves and the Inverse Scattering Transform

Nonlinear Ocean Waves and the Inverse Scattering Transform Book
Author : Alfred R. Osborne
Publisher : Unknown
Release : 2010
ISBN : 9780125286299
Language : En, Es, Fr & De

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Book Description :

For more than 200 years, the Fourier Transform has been one of the most important mathematical tools for understanding the dynamics of linear wave trains. Nonlinear Ocean Waves and the Inverse Scattering Transform presents the development of the nonlinear Fourier analysis of measured space and time series, which can be found in a wide variety of physical settings including surface water waves, internal waves, and equatorial Rossby waves. This revolutionary development will allow hyperfast numerical modelling of nonlinear waves, greatly advancing our understanding of oceanic surface and internal waves. Nonlinear Fourier analysis is based upon a generalization of linear Fourier analysis referred to as the inverse scattering transform, the fundamental building block of which is a generalized Fourier series called the Riemann theta function. Elucidating the art and science of implementing these functions in the context of physical and time series analysis is the goal of this book. presents techniques and methods of the inverse scattering transform for data analysis geared toward both the introductory and advanced reader venturing further into mathematical and numerical analysis suitable for classroom teaching as well as research

Nonlinear Ocean Waves and the Inverse Scattering Transform

Nonlinear Ocean Waves and the Inverse Scattering Transform Book
Author : Alfred Osborne
Publisher : Academic Press
Release : 2010-04-07
ISBN : 9780080925103
Language : En, Es, Fr & De

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Book Description :

For more than 200 years, the Fourier Transform has been one of the most important mathematical tools for understanding the dynamics of linear wave trains. Nonlinear Ocean Waves and the Inverse Scattering Transform presents the development of the nonlinear Fourier analysis of measured space and time series, which can be found in a wide variety of physical settings including surface water waves, internal waves, and equatorial Rossby waves. This revolutionary development will allow hyperfast numerical modelling of nonlinear waves, greatly advancing our understanding of oceanic surface and internal waves. Nonlinear Fourier analysis is based upon a generalization of linear Fourier analysis referred to as the inverse scattering transform, the fundamental building block of which is a generalized Fourier series called the Riemann theta function. Elucidating the art and science of implementing these functions in the context of physical and time series analysis is the goal of this book. Presents techniques and methods of the inverse scattering transform for data analysis Geared toward both the introductory and advanced reader venturing further into mathematical and numerical analysis Suitable for classroom teaching as well as research

Scattering Two Volume Set

Scattering  Two Volume Set Book
Author : E. R. Pike,Pierre C. Sabatier
Publisher : Academic Press
Release : 2002
ISBN : 0126137609
Language : En, Es, Fr & De

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Book Description :

Part 1: SCATTERING OF WAVES BY MACROSCOPIC TARGET -- Interdisciplinary aspects of wave scattering -- Acoustic scattering -- Acoustic scattering: approximate methods -- Electromagnetic wave scattering: theory -- Electromagnetic wave scattering: approximate and numerical methods -- Electromagnetic wave scattering: applications -- Elastodynamic wave scattering: theory -- Elastodynamic wave scattering: Applications -- Scattering in Oceans -- Part 2: SCATTERING IN MICROSCOPIC PHYSICS AND CHEMICAL PHYSICS -- Introduction to direct potential scattering -- Introduction to Inverse Potential Scattering -- Visible and Near-visible Light Scattering -- Practical Aspects of Visible and Near-visible Light Scattering -- Nonlinear Light Scattering -- Atomic and Molecular Scattering: Introduction to Scattering in Chemical -- X-ray Scattering -- Neutron Scattering -- Electron Diffraction and Scattering -- Part 3: SCATTERING IN NUCLEAR PHYSICS -- Nuclear Physics -- Part 4: PARTICLE SCATTERING -- State of ...

Rogue and Shock Waves in Nonlinear Dispersive Media

Rogue and Shock Waves in Nonlinear Dispersive Media Book
Author : Miguel Onorato,Stefania Resitori,Fabio Baronio
Publisher : Springer
Release : 2016-09-19
ISBN : 331939214X
Language : En, Es, Fr & De

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Book Description :

This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists working on rogue and shock wave phenomena across a broad range of fields in applied physics and geophysics.

Guided Wave Optics

Guided Wave Optics Book
Author : Boris Malomed
Publisher : MDPI
Release : 2018-03-23
ISBN : 3038426148
Language : En, Es, Fr & De

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Book Description :

This book is a printed edition of the Special Issue "Guided-Wave Optics" that was published in Applied Sciences

Nonlinear Ocean Dynamics

Nonlinear Ocean Dynamics Book
Author : Maged Marghany
Publisher : Elsevier
Release : 2021-02-09
ISBN : 0128209259
Language : En, Es, Fr & De

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Book Description :

Nonlinear Ocean Dynamics: Synthetic Aperture Radar delivers the critical tools needed to understand the latest technology surrounding the radar imaging of nonlinear waves, particularly microwave radar, as a main source to understand, analyze and apply concepts in the field of ocean dynamic surface. Filling the gap between modern physics quantum theory and applications of radar imaging of ocean dynamic surface, this reference is packed with technical details associated with the potentiality of synthetic aperture radar (SAR). The book also includes key methods needed to extract the value-added information necessary, such as wave spectra energy, current pattern velocity, internal waves, and more. This book also reveals novel speculation of a shallow coastal front: named as Quantized Marghany's Front. Rounding out with practical simulations of 4-D wave-current interaction patterns using using radar images, the book brings an effective new source of technology and applications for today’s coastal scientists and engineers. Solves specific problems surrounding the nonlinearity of ocean surface dynamics in synthetic aperture radar data Helps develop new algorithms for retrieving ocean wave spectra and ocean current movements from synthetic aperture radar Includes over 100 equations that illustrate how to follow examples in the book

Princeton Companion to Applied Mathematics

Princeton Companion to Applied Mathematics Book
Author : Nicholas J. Higham
Publisher : Princeton University Press
Release : 2015-09-09
ISBN : 0691150397
Language : En, Es, Fr & De

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Book Description :

This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index

Ocean Wave Dynamics

Ocean Wave Dynamics Book
Author : Ian Young,Alexander Babanin
Publisher : World Scientific
Release : 2020-03-20
ISBN : 9811208689
Language : En, Es, Fr & De

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Book Description :

Ocean Wave Dynamics is the most up-to-date book of its kind on the three main processes responsible for the generation and evolution of ocean waves: (i) atmospheric input from the wind, (ii) wave breaking and (iii) nonlinear interactions.Ocean waves are important for many reasons. They are the major environmental impact on in the design of coastal or offshore structures. Ocean waves are also fundamental to the processes of coastal flooding and beach erosion. They will play a major role in storm related coastal flooding which will rise in frequency as a result of sea level rise. Ocean waves are also an important part of the coupled ocean-atmosphere system. They determine the roughness of the ocean surface and hence have an impact on winds, fluxes of energy, gases and heat to the ocean and even the stability of ice sheets.Containing the latest research on ocean waves, it is a valuable resource for an overview of knowledge in this important field.Related Link(s)

Dynamics of the Equatorial Ocean

Dynamics of the Equatorial Ocean Book
Author : John P. Boyd
Publisher : Springer
Release : 2017-09-25
ISBN : 3662554763
Language : En, Es, Fr & De

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Book Description :

This book is the first comprehensive introduction to the theory of equatorially-confined waves and currents in the ocean. Among the topics treated are inertial and shear instabilities, wave generation by coastal reflection, semiannual and annual cycles in the tropic sea, transient equatorial waves, vertically-propagating beams, equatorial Ekman layers, the Yoshida jet model, generation of coastal Kelvin waves from equatorial waves by reflection, Rossby solitary waves, and Kelvin frontogenesis. A series of appendices on midlatitude theories for waves, jets and wave reflections add further material to assist the reader in understanding the differences between the same phenomenon in the equatorial zone versus higher latitudes.

Numerical Modeling of Sea Waves

Numerical Modeling of Sea Waves Book
Author : Dmitry V. Chalikov
Publisher : Springer
Release : 2016-06-25
ISBN : 3319329162
Language : En, Es, Fr & De

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Book Description :

Presenting a novel approach to wave theory, this book applies mathematical modeling to the investigation of sea waves. It presents problems, solutions and methods, and explores issues such as statistical properties of sea waves, generation of turbulence, Benjamin-Feir instability and the development of wave fields under the action of wind. Special attention is paid to the processes of dynamic wind-wave interaction, the formation of freak waves, as well as the role that sea waves play in the dynamic ocean/atmosphere system. It presents theoretical results which are followed by a description of the algorithms used in the development of wave forecasting models, and provides illustrations to assist understanding of the various models presented. This book provides an invaluable resource to oceanographers, specialists in fluid dynamics and advanced students interested in investigation of the widely known but poorly investigated phenomenon of sea waves.

Recent Development in Theories Numerics

Recent Development in Theories   Numerics Book
Author : Yiu-Chung Hon,Masahiro Yamamoto
Publisher : World Scientific
Release : 2003
ISBN : 9812383662
Language : En, Es, Fr & De

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Book Description :

Annotation. Proceedings from the First International Conference on Inverse Problems, Recent Theoretical Development and Numerical Approaches, held at the City University of Hong Kong from January 9-12, 2002.

Transformation Wave Physics

Transformation Wave Physics Book
Author : Mohamed Farhat,Pai-Yen Chen,Sebastien Guenneau,Stefan Enoch
Publisher : CRC Press
Release : 2016-11-18
ISBN : 1315341085
Language : En, Es, Fr & De

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Book Description :

Space–time transformations as a design tool for a new class of composite materials (metamaterials) have proved successful recently. The concept is based on the fact that metamaterials can mimic a transformed but empty space. Light rays follow trajectories according to Fermat’s principle in this transformed electromagnetic, acoustic, or elastic space instead of laboratory space. This allows one to manipulate wave behaviors with various exotic characteristics such as (but not limited to) invisibility cloaks. This book is a collection of works by leading international experts in the fields of electromagnetics, plasmonics, elastodynamics, and diffusion waves. The experimental and theoretical contributions will revolutionize ways to control the propagation of sound, light, and other waves in macroscopic and microscopic scales. The potential applications range from underwater camouflaging and electromagnetic invisibility to enhanced biosensors and protection from harmful physical waves (e.g., tsunamis and earthquakes). This is the first book that deals with transformation physics for all kinds of waves in one volume, covering the newest results from emerging topical subjects such as transformational plasmonics and thermodynamics.

The Numerical Inverse Scattering Transform Nonlinear Fourier Analysis and Nonlinear Filtering of Oceanic Surface Waves

The Numerical Inverse Scattering Transform  Nonlinear Fourier Analysis and Nonlinear Filtering of Oceanic Surface Waves Book
Author : A. R. Osborne,HAWAII UNIV HONOLULU DEPT OF OCEANOGRAPHY.
Publisher : Unknown
Release : 1993
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Nonlinear Fourier analysis is discussed as it arises from the exact spectral solution to large classes of nonlinear wave equations which are integrable by the inverse scattering transform (IST). The approach may be viewed as a generalization of the ordinary, linear Fourier transform or Fourier series. Numerical methods are discussed which allow for implementation of the approach as a tool for the time series analysis of oceanic wave data. I specifically consider the case for shallow water, where integrable nonlinear wave motion is governed by the Korteweg-de Vries equation with periodic/quasi-periodic boundary conditions. Numerical procedures given herein allow the computation of a nonlinear Fourier series for a measured time series. The nonlinear oscillation modes of KdV obey a linear superposition law, just as do the sine waves of a linear Fourier series. However, the KdV basis functions themselves are highly nonlinear, undergo nonlinear interactions with each other and are distinctly non sinusoidal. I analyze surface wave data from the Adriatic Sea and apply the concept of nonlinear filtering to enhance understanding of nonlinear interactions.

Peregrine Soliton and Breathers in Wave Physics Achievements and Perspectives

Peregrine Soliton and Breathers in Wave Physics  Achievements and Perspectives Book
Author : Bertrand Kibler,Amin Chabchoub,Heremba Bailung
Publisher : Frontiers Media SA
Release : 2022-08-16
ISBN : 2889741117
Language : En, Es, Fr & De

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Book Description :

Download Peregrine Soliton and Breathers in Wave Physics Achievements and Perspectives book written by Bertrand Kibler,Amin Chabchoub,Heremba Bailung, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Optical Remote Sensing of Ocean Hydrodynamics

Optical Remote Sensing of Ocean Hydrodynamics Book
Author : Victor Raizer
Publisher : CRC Press
Release : 2019-03-04
ISBN : 1351119168
Language : En, Es, Fr & De

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Book Description :

Optical Remote Sensing is one of the main technologies used in sea surface monitoring. Optical Remote Sensing of Ocean Hydrodynamics investigates and demonstrates capabilities of optical remote sensing technology for enhanced observations and detection of ocean environments. It provides extensive knowledge of physical principles and capabilities of optical observations of the oceans at high spatial resolution, 1-4m, and on the observations of surface wave hydrodynamic processes. It also describes the implementation of spectral-statistical and fusion algorithms for analyses of multispectral optical databases and establishes physics-based criteria for detection of complex wave phenomena and hydrodynamic disturbances including assessment and management of optical databases. This book explains the physical principles of high-resolution optical imagery of the ocean surface, discusses for the first time the capabilities of observing hydrodynamic processes and events, and emphasizes the integration of optical measurements and enhanced data analysis. It also covers both the assessment and the interpretation of dynamic multispectral optical databases and includes applications for advanced studies and nonacoustic detection. This book is an invaluable resource for researches, industry professionals, engineers, and students working on cross-disciplinary problems in ocean hydrodynamics, optical remote sensing of the ocean and sea surface remote sensing. Readers in the fields of geosciences and remote sensing, applied physics, oceanography, satellite observation technology, and optical engineering will learn the theory and practice of optical interactions with the ocean.

Solitons and the Inverse Scattering Transform

Solitons and the Inverse Scattering Transform Book
Author : Mark J. Ablowitz,Harvey Segur
Publisher : SIAM
Release : 2006-05-15
ISBN : 089871477X
Language : En, Es, Fr & De

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Book Description :

A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation.

Springer Handbook of Ocean Engineering

Springer Handbook of Ocean Engineering Book
Author : Manhar R. Dhanak,Nikolaos I. Xiros
Publisher : Springer
Release : 2016-07-23
ISBN : 3319166492
Language : En, Es, Fr & De

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Book Description :

This handbook is the definitive reference for the interdisciplinary field that is ocean engineering. It integrates the coverage of fundamental and applied material and encompasses a diverse spectrum of systems, concepts and operations in the maritime environment, as well as providing a comprehensive update on contemporary, leading-edge ocean technologies. Coverage includes an overview on the fundamentals of ocean science, ocean signals and instrumentation, coastal structures, developments in ocean energy technologies and ocean vehicles and automation. It aims at practitioners in a range of offshore industries and naval establishments as well as academic researchers and graduate students in ocean, coastal, offshore and marine engineering and naval architecture. The Springer Handbook of Ocean Engineering is organized in five parts: Part A: Fundamentals, Part B: Autonomous Ocean Vehicles, Subsystems and Control, Part C: Coastal Design, Part D: Offshore Technologies, Part E: Energy Conversion

Advances in Dynamics Patterns Cognition

Advances in Dynamics  Patterns  Cognition Book
Author : Igor S. Aranson,Arkady Pikovsky,Nikolai F. Rulkov,Lev S. Tsimring
Publisher : Springer
Release : 2017-05-02
ISBN : 3319536737
Language : En, Es, Fr & De

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Book Description :

This book focuses on recent progress in complexity research based on the fundamental nonlinear dynamical and statistical theory of oscillations, waves, chaos, and structures far from equilibrium. Celebrating seminal contributions to the field by Prof. M. I. Rabinovich of the University of California at San Diego, this volume brings together perspectives on both the fundamental aspects of complexity studies, as well as in applications in different fields ranging from granular patterns to understanding of the cognitive brain and mind dynamics. The slate of world-class authors review recent achievements that together present a broad and coherent coverage of modern research in complexity greater than the sum of its parts.

Waves in Complex Media

Waves in Complex Media Book
Author : Luca Dal Negro
Publisher : Unknown
Release : 2021-12-02
ISBN : 1009178180
Language : En, Es, Fr & De

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Book Description :

A clear and interdisciplinary introduction to the structural and scattering properties of complex photonic media, focusing on deterministic aperiodic structures and their conceptual roots in geometry and number theory. Integrates important results and recent developments into a coherent and physically consistent story, balanced between mathematical designs, scattering and optical theories, and engineering device applications. Includes discussions of emerging device applications in metamaterials and nano-optics technology. Will be of interest to both academia and industry as it develops the underlying physical and mathematical background in partnership with engineering applications, providing a perspective on both fundamental optical sciences and photonic device technology. Emphasizing the comprehension of physical concepts and their engineering implications over the more formal developments, this is an essential introduction to the stimulating and fast-growing field of aperiodic optics and complex photonics. The book is completed by 8 Appendices that can be downloaded from the companion website at www.cambridge.org/9781107037502

Handbook of Applications of Chaos Theory

Handbook of Applications of Chaos Theory Book
Author : Christos H. Skiadas,Charilaos Skiadas
Publisher : CRC Press
Release : 2017-12-19
ISBN : 1315356546
Language : En, Es, Fr & De

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Book Description :

In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors from around the world show how chaos theory is used to model unexplored cases and stimulate new applications. Accessible to scientists, engineers, and practitioners in a variety of fields, the book discusses the intermittency route to chaos, evolutionary dynamics and deterministic chaos, and the transition to phase synchronization chaos. It presents important contributions on strange attractors, self-exciting and hidden attractors, stability theory, Lyapunov exponents, and chaotic analysis. It explores the state of the art of chaos in plasma physics, plasma harmonics, and overtone coupling. It also describes flows and turbulence, chaotic interference versus decoherence, and an application of microwave networks to the simulation of quantum graphs. The book proceeds to give a detailed presentation of the chaotic, rogue, and noisy optical dissipative solitons; parhelic-like circle and chaotic light scattering; and interesting forms of the hyperbolic prism, the Poincaré disc, and foams. It also covers numerous application areas, from the analysis of blood pressure data and clinical digital pathology to chaotic pattern recognition to economics to musical arts and research.