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Author: Maurice Roseau
Publisher: Elsevier
ISBN: 0444601910
Category : Mathematics
Languages : en
Pages : 360
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Book Description
Asymptotic Wave Theory investigates the asymptotic behavior of wave representations and presents some typical results borrowed from hydrodynamics and elasticity theory. It describes techniques such as Fourier-Laplace transforms, operational calculus, special functions, and asymptotic methods. It also discusses applications to the wave equation, the elements of scattering matrix theory, problems related to the wave equation, and diffraction. Organized into eight chapters, this volume begins with an overview of the Fourier-Laplace integral, the Mellin transform, and special functions such as the gamma function and the Bessel functions. It then considers wave propagation, with emphasis on representations of plane, cylindrical or spherical waves. It methodically introduces the reader to the reflexion and refraction of a plane wave at the interface between two homogeneous media, the asymptotic expansion of Hankel's functions in the neighborhood of the point at infinity, and the asymptotic behavior of the Laplace transform. The book also examines the method of steepest descent, the asymptotic representation of Hankel's function of large order, and the scattering matrix theory. The remaining chapters focus on problems of flow in open channels, the propagation of elastic waves within a layered spherical body, and some problems in water wave theory. This book is a valuable resource for mechanics and students of applied mathematics and mechanics.
Author: Maurice Roseau
Publisher: Elsevier
ISBN: 0444601910
Category : Mathematics
Languages : en
Pages : 360
Get Book Here
Book Description
Asymptotic Wave Theory investigates the asymptotic behavior of wave representations and presents some typical results borrowed from hydrodynamics and elasticity theory. It describes techniques such as Fourier-Laplace transforms, operational calculus, special functions, and asymptotic methods. It also discusses applications to the wave equation, the elements of scattering matrix theory, problems related to the wave equation, and diffraction. Organized into eight chapters, this volume begins with an overview of the Fourier-Laplace integral, the Mellin transform, and special functions such as the gamma function and the Bessel functions. It then considers wave propagation, with emphasis on representations of plane, cylindrical or spherical waves. It methodically introduces the reader to the reflexion and refraction of a plane wave at the interface between two homogeneous media, the asymptotic expansion of Hankel's functions in the neighborhood of the point at infinity, and the asymptotic behavior of the Laplace transform. The book also examines the method of steepest descent, the asymptotic representation of Hankel's function of large order, and the scattering matrix theory. The remaining chapters focus on problems of flow in open channels, the propagation of elastic waves within a layered spherical body, and some problems in water wave theory. This book is a valuable resource for mechanics and students of applied mathematics and mechanics.
Author: Alan Jeffrey
Publisher: Pitman Advanced Publishing Program
ISBN:
Category : Science
Languages : en
Pages : 282
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Book Description
Author: A. Jeffrey
Publisher: Halsted Press
ISBN: 9780470205068
Category :
Languages : en
Pages : 272
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Book Description
Author: Marco Sammartino
Publisher: World Scientific
ISBN: 9814475076
Category : Mathematics
Languages : en
Pages : 228
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Book Description
This book brings together several contributions from leading experts in the field of nonlinear wave propagation. This field, which during the last three decades has seen important breakthroughs from the theoretical point of view, has recently acquired increased relevance due to advances in the technology of fluids e.g. at microscale or nanoscale and the recognition of crucial applications to the understanding of biological phenomena.Nonlinear wave theory requires the use of disparate approaches, including formal and rigorous asymptotic methods, Lie group theory, energy methods, numerical analysis, and bifurcation theory. This book presents a unique blend in which different aspects of the theory are enlightened and several real-life applications are investigated. The book will be a valuable resource for applied scientists interested in some of the most recent advances in the theory and in the applications of wave propagation, shock formation, nonequilibrium thermodynamics and energy methods.
Author: V. M. Babich
Publisher: Alpha Science International, Limited
ISBN: 9781842652329
Category : Asymptotic expansions
Languages : en
Pages : 0
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Book Description
Dedicated to modern approaches of a high-frequency technique in diffraction theory, Asymptotic Methods in Short-Wavelength Diffraction Theory outlines a variety of crucial topics. The book considers a multitude of matters, ranging from the ray method to the theory of high-frequency whispering-gallery waves alongside the reviewing and reflecting on recent results from the literature dealing with localized asymptotic solutions and uniform representation of a high-frequency wave-field. The book serves as an exclusive address to experts on electromagnetics, seismology and acoustics as well as to mathematicians interested in modern approaches of mathematical physics.
Author: P. A. Martin
Publisher: Cambridge University Press
ISBN: 9780521414142
Category : Mathematics
Languages : en
Pages : 262
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Book Description
This volume contains papers by distinguished researchers in fluid mechanics and asymptotics. The papers collected here outline the development of these topics.
Author: Lev Ostrovsky
Publisher: World Scientific
ISBN: 178326473X
Category : Juvenile Nonfiction
Languages : en
Pages : 227
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Book Description
This book is an introduction to the perturbation theory for linear and nonlinear waves in dispersive and dissipative media. The main focus is on the direct asymptotic method which is based on the asymptotic expansion of the solution in series of one or more small parameters and demanding finiteness of the perturbations; this results in slow variation of the main-order solution. The method, which does not depend on integrability of basic equations, is applied to quasi-harmonic and non-harmonic periodic waves, as well as to localized waves such as solitons, kinks, and autowaves. The basic theoretical ideas are illustrated by many physical examples throughout the book.
Author: John P. Boyd
Publisher: Springer
ISBN: 9781461558262
Category : Mathematics
Languages : en
Pages : 596
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Book Description
This is the first thorough examination of weakly nonlocal solitary waves, which are just as important in applications as their classical counterparts. The book describes a class of waves that radiate away from the core of the disturbance but are nevertheless very long-lived nonlinear disturbances.
Author: S.H. Patil
Publisher: Springer Science & Business Media
ISBN: 3642573177
Category : Science
Languages : en
Pages : 178
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Book Description
Quantum mechanics and the Schrodinger equation are the basis for the de scription of the properties of atoms, molecules, and nuclei. The development of reliable, meaningful solutions for the energy eigenfunctions of these many is a formidable problem. The usual approach for obtaining particle systems the eigenfunctions is based on their variational extremum property of the expectation values of the energy. However the complexity of these variational solutions does not allow a transparent, compact description of the physical structure. There are some properties of the wave functions in some specific, spatial domains, which depend on the general structure of the Schrodinger equation and the electromagnetic potential. These properties provide very useful guidelines in developing simple and accurate solutions for the wave functions of these systems, and provide significant insight into their physical structure. This point, though of considerable importance, has not received adequate attention. Here we present a description of the local properties of the wave functions of a collection of particles, in particular the asymptotic properties when one of the particles is far away from the others. The asymptotic behaviour of this wave function depends primarily on the separation energy of the outmost particle. The universal significance of the asymptotic behaviour of the wave functions should be appreciated at both research and pedagogic levels. This is the main aim of our presentation here.
Author: Vasili M. Babic
Publisher: Springer
ISBN: 9783642834615
Category : Science
Languages : en
Pages : 0
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Book Description
In the study of short-wave diffraction problems, asymptotic methods - the ray method, the parabolic equation method, and its further development as the "etalon" (model) problem method - play an important role. These are the meth ods to be treated in this book. The applications of asymptotic methods in the theory of wave phenomena are still far from being exhausted, and we hope that the techniques set forth here will help in solving a number of problems of interest in acoustics, geophysics, the physics of electromagnetic waves, and perhaps in quantum mechanics. In addition, the book may be of use to the mathematician interested in contemporary problems of mathematical physics. Each chapter has been annotated. These notes give a brief history of the problem and cite references dealing with the content of that particular chapter. The main text mentions only those pUblications that explain a given argument or a specific calculation. In an effort to save work for the reader who is interested in only some of the problems considered in this book, we have included a flow chart indicating the interdependence of chapters and sections.
