Wavefronts And Rays As Characteristics And Asymptotics

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Wavefronts And Rays As Characteristics And Asymptotics

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Author : Andrej B¢na
language : en
Publisher: World Scientific
Release Date : 2011

Wavefronts And Rays As Characteristics And Asymptotics written by Andrej B¢na and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.

This textbook ? incorporated with many illuminating examples and exercises ? is aimed at graduate students of physical sciences and engineering. The purpose is to provide a background of physics and underlying mathematics for the concept of rays, filling the gap between mathematics and physics textbooks for a coherent treatment of all topics. The authors' emphasis and extremely good presentation of the theory of characteristics, which defines the rays, accentuate the beauty and versatility of this theory. To this end, the rigour of the formulation ? by a pure mathematician's standards ? is downplayed to highlight the physical meaning and to make the subject accessible to a wider audience. The authors describe in detail the theory of characteristics for different types of differential equations, the applications to wave propagation in different types of media, and the phenomena such as caustics.

Wavefronts And Rays As Characteristics And Asymptotics Third Edition

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Author : Andrej Bona
language : en
Publisher: World Scientific
Release Date : 2020-09-24

Wavefronts And Rays As Characteristics And Asymptotics Third Edition written by Andrej Bona and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-24 with Science categories.

Characteristics and asymptotics of partial differential equations play an important role in mathematical physics since they lead to insightful solutions of complex problems that might not be solvable otherwise. They constitute, however, a difficult subject, and the purpose of this book, with its additions and refinements that led to its third edition, is to present this subject in an accessible manner, without decreasing the rigor. As any method, characteristics and asymptotics have their limitations. This important issue is addressed in the last chapter, where we discuss caustics, which must be understood in applications of the method, and which constitute a fertile ground for further mathematical research.The book is both a research reference and a textbook. Its careful and explanatory style, which includes numerous exercises with detailed solutions, makes it an excellent textbook for senior undergraduate and graduate courses, as well as for independent studies. Six appendices are provided, which form a self-contained course on applied mathematics and can be used as a textbook on its own.

Wavefronts And Rays As Characteristics And Asymptotics 2nd Edition

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Author : Michael A Slawinski
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-12-30

Wavefronts And Rays As Characteristics And Asymptotics 2nd Edition written by Michael A Slawinski and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-30 with Science categories.

This textbook — incorporated with many illuminating examples and exercises — is aimed at graduate students of physical sciences and engineering. The purpose is to provide a background of physics and underlying mathematics for the concept of rays, filling the gap between mathematics and physics textbooks for a coherent treatment of all topics. The authors' emphasis and extremely good presentation of the theory of characteristics, which defines the rays, accentuate the beauty and versatility of this theory. To this end, the rigour of the formulation — by a pure mathematician's standards — is downplayed to highlight the physical meaning and to make the subject accessible to a wider audience. The authors describe in detail the theory of characteristics for different types of differential equations, the applications to wave propagation in different types of media, and phenomena such as caustics.

Waves And Rays In Elastic Continua 3rd Edition

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Author : Michael A Slawinski
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-12-15

Waves And Rays In Elastic Continua 3rd Edition written by Michael A Slawinski and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-15 with Science categories.

The present book — which is the third, significantly revised edition of the textbook originally published by Elsevier Science — emphasizes the interdependence of mathematical formulation and physical meaning in the description of seismic phenomena. Herein, we use aspects of continuum mechanics, wave theory and ray theory to explain phenomena resulting from the propagation of seismic waves.The book is divided into three main sections: Elastic Continua, Waves and Rays and Variational Formulation of Rays. There is also a fourth part, which consists of appendices.In Elastic Continua, we use continuum mechanics to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such a material. In Waves and Rays, we use these equations to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, we invoke the concept of a ray. In Variational Formulation of Rays, we show that, in elastic continua, a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary traveltime. Consequently, many seismic problems in elastic continua can be conveniently formulated and solved using the calculus of variations. In the Appendices, we describe two mathematical concepts that are used in the book; namely, homogeneity of a function and Legendre's transformation. This section also contains a list of symbols.

Waves And Rays In Elastic Continua Fourth Edition

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Author : Michael A Slawinski
language : en
Publisher: World Scientific
Release Date : 2020-09-24

Waves And Rays In Elastic Continua Fourth Edition written by Michael A Slawinski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-24 with Science categories.

Seismology, as a branch of mathematical physics, is an active subject of both research and development. Its reliance on computational and technological advances continuously motivates the developments of its underlying theory. The fourth edition of Waves and Rays in Elastic Continua responds to these needs.The book is both a research reference and a textbook. Its careful and explanatory style, which includes numerous exercises with detailed solutions, makes it an excellent textbook for the senior undergraduate and graduate courses, as well as for an independent study. Used in its entirety, the book could serve as a sole textbook for a year-long course in quantitative seismology. Its parts, however, are designed to be used independently for shorter courses with different emphases. The book is not limited to quantitive seismology; it can serve as a textbook for courses in mathematical physics or applied mathematics.

Asymptotic And Hybrid Methods In Electromagnetics

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Author : I. Andronov
language : en
Publisher: IET
Release Date : 2005-07-18

Asymptotic And Hybrid Methods In Electromagnetics written by I. Andronov and has been published by IET this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-18 with Science categories.

Asymptotic methods provide considerable physical insight and understanding of diffraction mechanisms and are very useful in the design of electromagnetic devices such as radar targets and antennas. However, difficulties can arise when trying to solve problems using multipole and asymoptotic methods together, such as in radar crosssection objects. This new book offers a solution to this problem by combining these approaches into hybrid methods, therefore creating high demand for both understanding and learning how to apply asymptotic and hybrid methods to solve diffraction problems.

Quasilinear Hyperbolic Systems Compressible Flows And Waves

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Author : Vishnu D. Sharma
language : en
Publisher: CRC Press
Release Date : 2010-04-29

Quasilinear Hyperbolic Systems Compressible Flows And Waves written by Vishnu D. Sharma and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-29 with Mathematics categories.

Filled with practical examples, Quasilinear Hyperbolic Systems, Compressible Flows, and Waves presents a self-contained discussion of quasilinear hyperbolic equations and systems with applications. It emphasizes nonlinear theory and introduces some of the most active research in the field.After linking continuum mechanics and quasilinear partial di

Ray Methods For Nonlinear Waves In Fluids And Plasmas

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Author : Marcelo Anile
language : en
Publisher: CRC Press
Release Date : 2021-06-24

Ray Methods For Nonlinear Waves In Fluids And Plasmas written by Marcelo Anile and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-24 with Mathematics categories.

Presents in a systematic and unified manner the ray method, in its various forms, for studying nonlinear wave propagation in situations of physical interest, essentially fluid dynamics and plasma physics.

Asymptotic Perturbation Theory Of Waves

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Author : Lev Ostrovsky
language : en
Publisher: World Scientific
Release Date : 2014-09-23

Asymptotic Perturbation Theory Of Waves written by Lev Ostrovsky and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-23 with Juvenile Nonfiction categories.

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.

Rays Waves And Scattering

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Author : John Adam
language : en
Publisher: Princeton University Press
Release Date : 2017-05-30

Rays Waves And Scattering written by John Adam and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-30 with Mathematics categories.

This one-of-a-kind book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas. Rays, Waves, and Scattering is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technical material), and several informative appendixes. Provides a panoramic look at wave motion in many different contexts Features problems and exercises throughout Includes numerous appendixes, some on topics not often covered An ideal reference book for practitioners Can also serve as a supplemental text in classical applied mathematics, particularly wave theory and mathematical methods in physics and engineering Accessible to anyone with a strong background in ordinary differential equations, partial differential equations, and functions of a complex variable