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Mathematical Methods For Wave Propagation In Science And Engineering
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Book Synopsis Mathematical methods for wave propagation in science and engineering by : Mario Durán
Download or read book Mathematical methods for wave propagation in science and engineering written by Mario Durán and published by Ediciones UC. This book was released on 2017 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series of books deals with the mathematical modeling and computational simulation of complex wave propagation phenomena in science and engineering. This first volume of the series introduces the basic mathematical and physical fundamentals, and it is mainly intended as a reference guide and a general survey for scientists and engineers. It presents a broad and practical overview of the involved foundations, being useful as much in industrial research, development, and innovation activities, as in academic labors.
Book Synopsis Mathematics of Wave Propagation by : Julian L. Davis
Download or read book Mathematics of Wave Propagation written by Julian L. Davis and published by Princeton University Press. This book was released on 2021-01-12 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Earthquakes, a plucked string, ocean waves crashing on the beach, the sound waves that allow us to recognize known voices. Waves are everywhere, and the propagation and classical properties of these apparently disparate phenomena can be described by the same mathematical methods: variational calculus, characteristics theory, and caustics. Taking a medium-by-medium approach, Julian Davis explains the mathematics needed to understand wave propagation in inviscid and viscous fluids, elastic solids, viscoelastic solids, and thermoelastic media, including hyperbolic partial differential equations and characteristics theory, which makes possible geometric solutions to nonlinear wave problems. The result is a clear and unified treatment of wave propagation that makes a diverse body of mathematics accessible to engineers, physicists, and applied mathematicians engaged in research on elasticity, aerodynamics, and fluid mechanics. This book will particularly appeal to those working across specializations and those who seek the truly interdisciplinary understanding necessary to fully grasp waves and their behavior. By proceeding from concrete phenomena (e.g., the Doppler effect, the motion of sinusoidal waves, energy dissipation in viscous fluids, thermal stress) rather than abstract mathematical principles, Davis also creates a one-stop reference that will be prized by students of continuum mechanics and by mathematicians needing information on the physics of waves.
Book Synopsis Wave Propagation in Electromagnetic Media by : Julian L. Davis
Download or read book Wave Propagation in Electromagnetic Media written by Julian L. Davis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second work of a set of two volumes on the phenomena of wave propagation in nonreacting and reacting media. The first, entitled Wave Propagation in Solids and Fluids (published by Springer-Verlag in 1988), deals with wave phenomena in nonreacting media (solids and fluids). This book is concerned with wave propagation in reacting media-specifically, in electro magnetic materials. Since these volumes were designed to be relatively self contained, we have taken the liberty of adapting some of the pertinent material, especially in the theory of hyperbolic partial differential equations (concerned with electromagnetic wave propagation), variational methods, and Hamilton-Jacobi theory, to the phenomena of electromagnetic waves. The purpose of this volume is similar to that of the first, except that here we are dealing with electromagnetic waves. We attempt to present a clear and systematic account of the mathematical methods of wave phenomena in electromagnetic materials that will be readily accessible to physicists and engineers. The emphasis is on developing the necessary mathematical tech niques, and on showing how these methods of mathematical physics can be effective in unifying the physics of wave propagation in electromagnetic media. Chapter 1 presents the theory of time-varying electromagnetic fields, which involves a discussion of Faraday's laws, Maxwell's equations, and their appli cations to electromagnetic wave propagation under a variety of conditions.
Book Synopsis Mathematical Studies in Nonlinear Wave Propagation by : Dominic P. Clemence
Download or read book Mathematical Studies in Nonlinear Wave Propagation written by Dominic P. Clemence and published by American Mathematical Soc.. This book was released on 2005 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lively discussions and stimulating research were part of a five-day conference on Mathematical Methods in Nonlinear Wave Propagation sponsored by the NSF and CBMS. This volume is a collection of lectures and papers stemming from that event. Leading experts present dynamical systems and chaos, scattering and spectral theory, nonlinear wave equations, optimal control, optical waveguide design, and numerical simulation. The book is suitable for a diverse audience of mathematical specialists interested in fiber optic communications and other nonlinear phenomena. It is also suitable for engineers and other scientists interested in the mathematics of nonlinear wave propagation.
Book Synopsis Wave Propagation in Solids and Fluids by : Julian L. Davis
Download or read book Wave Propagation in Solids and Fluids written by Julian L. Davis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this volume is to present a clear and systematic account of the mathematical methods of wave phenomena in solids, gases, and water that will be readily accessible to physicists and engineers. The emphasis is on developing the necessary mathematical techniques, and on showing how these mathematical concepts can be effective in unifying the physics of wave propagation in a variety of physical settings: sound and shock waves in gases, water waves, and stress waves in solids. Nonlinear effects and asymptotic phenomena will be discussed. Wave propagation in continuous media (solid, liquid, or gas) has as its foundation the three basic conservation laws of physics: conservation of mass, momentum, and energy, which will be described in various sections of the book in their proper physical setting. These conservation laws are expressed either in the Lagrangian or the Eulerian representation depending on whether the boundaries are relatively fixed or moving. In any case, these laws of physics allow us to derive the "field equations" which are expressed as systems of partial differential equations. For wave propagation phenomena these equations are said to be "hyperbolic" and, in general, nonlinear in the sense of being "quasi linear" . We therefore attempt to determine the properties of a system of "quasi linear hyperbolic" partial differential equations which will allow us to calculate the displacement, velocity fields, etc.
Book Synopsis Wave Propagation and Diffraction by : Igor T. Selezov
Download or read book Wave Propagation and Diffraction written by Igor T. Selezov and published by Springer. This book was released on 2017-09-05 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents two distinct aspects of wave dynamics – wave propagation and diffraction – with a focus on wave diffraction. The authors apply different mathematical methods to the solution of typical problems in the theory of wave propagation and diffraction and analyze the obtained results. The rigorous diffraction theory distinguishes three approaches: the method of surface currents, where the diffracted field is represented as a superposition of secondary spherical waves emitted by each element (the Huygens–Fresnel principle); the Fourier method; and the separation of variables and Wiener–Hopf transformation method. Chapter 1 presents mathematical methods related to studying the problems of wave diffraction theory, while Chapter 2 deals with spectral methods in the theory of wave propagation, focusing mainly on the Fourier methods to study the Stokes (gravity) waves on the surface of inviscid fluid. Chapter 3 then presents some results of modeling the refraction of surf ace gravity waves on the basis of the ray method, which originates from geometrical optics. Chapter 4 is devoted to the diffraction of surface gravity waves and the final two chapters discuss the diffraction of waves by semi-infinite domains on the basis of method of images and present some results on the problem of propagation of tsunami waves. Lastly, it provides insights into directions for further developing the wave diffraction theory.
Book Synopsis Applied Wave Mathematics II by : Arkadi Berezovski
Download or read book Applied Wave Mathematics II written by Arkadi Berezovski and published by Springer Nature. This book was released on 2019-11-16 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers contributions on various aspects of the theory and applications of linear and nonlinear waves and associated phenomena, as well as approaches developed in a global partnership of researchers with the national Centre of Excellence in Nonlinear Studies (CENS) at the Department of Cybernetics of Tallinn University of Technology in Estonia. The papers chiefly focus on the role of mathematics in the analysis of wave phenomena. They highlight the complexity of related topics concerning wave generation, propagation, transformation and impact in solids, gases, fluids and human tissues, while also sharing insights into selected mathematical methods for the analytical and numerical treatment of complex phenomena. In addition, the contributions derive advanced mathematical models, share innovative ideas on computing, and present novel applications for a number of research fields where both linear and nonlinear wave problems play an important role. The papers are written in a tutorial style, intended for non-specialist researchers and students. The authors first describe the basics of a problem that is currently of interest in the scientific community, discuss the state of the art in related research, and then share their own experiences in tackling the problem. Each chapter highlights the importance of applied mathematics for central issues in the study of waves and associated complex phenomena in different media. The topics range from basic principles of wave mechanics up to the mathematics of Planet Earth in the broadest sense, including contemporary challenges in the mathematics of society. In turn, the areas of application range from classic ocean wave mathematics to material science, and to human nerves and tissues. All contributions describe the approaches in a straightforward manner, making them ideal material for educational purposes, e.g. for courses, master class lectures, or seminar presentations.
Book Synopsis Topics in Computational Wave Propagation by : Mark Ainsworth
Download or read book Topics in Computational Wave Propagation written by Mark Ainsworth and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: These ten detailed and authoritative survey articles on numerical methods for direct and inverse wave propagation problems are written by leading experts. Researchers and practitioners in computational wave propagation, from postgraduate level onwards, will find the breadth and depth of coverage of recent developments a valuable resource. The articles describe a wide range of topics on the application and analysis of methods for time and frequency domain PDE and boundary integral formulations of wave propagation problems. Electromagnetic, seismic and acoustic equations are considered. Recent developments in methods and analysis ranging from finite differences to hp-adaptive finite elements, including high-accuracy and fast methods are described with extensive references.
Book Synopsis Wave Propagation in Infinite Domains by : Lutz Lehmann
Download or read book Wave Propagation in Infinite Domains written by Lutz Lehmann and published by Springer Science & Business Media. This book was released on 2007-05-24 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents theoretical fundamentals and applications of a new numerical model that has the ability to simulate wave propagation. Coverage examines linear waves in ideal fluids and elastic domains. In addition, the book includes a numerical simulation of wave propagation based on scalar and vector wave equations, as well as fluid-structure interaction and soil-structure interaction.
Book Synopsis Mathematical Techniques for Wave Interaction with Flexible Structures by : Trilochan Sahoo
Download or read book Mathematical Techniques for Wave Interaction with Flexible Structures written by Trilochan Sahoo and published by CRC Press. This book was released on 2012-10-24 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Techniques for Wave Interaction with Flexible Structures is a thoughtful compilation of the various mathematical techniques used to deal with wave structure interaction problems. The book emphasizes unique determination of the solution for a class of physical problems associated with Laplace- or Helmholtz-type equations satisfying higher order boundary conditions with the applications of the theory of ordinary and partial differential equations, Fourier analysis, and more. Features: Provides a focused mathematical treatment for gravity wave interaction with floating and submerged flexible structures Highlights solution methods for a special class of boundary value problems in wave structure interaction Introduces and expands upon differential equations and the fundamentals of wave structure interaction problems This is an ideal handbook for naval architects, ocean engineers, and geophysicists dealing with the design of floating and/or flexible marine structures. The book’s underlying mathematical tools can be easily extended to deal with physical problems in the area of acoustics, electromagnetic waves, wave propagation in elastic media, and solid‐state physics. Designed for both the classroom and independent study, Mathematical Techniques for Wave Interaction with Flexible Structures enables readers to appreciate and apply the mathematical tools of wave structure interaction research to their own work.
Book Synopsis Mathematical Methods in Wave Propagation and Scattering Theory by : Calvin H. Wilcox
Download or read book Mathematical Methods in Wave Propagation and Scattering Theory written by Calvin H. Wilcox and published by . This book was released on 1983 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transient wave propagation phenomena are exploited in many branches of engineering and applied science. Examples include pulsed sonar and radar systems, pulsed laser beams and their applications; the use of seismic pulses in geophysical prospecting and ultrasonic pulses in medical imaging. The engineering literature provides an almost unlimited number of other examples. The continuing goal of the research performed under the contracts mentioned above was to develop mathematical methods which would provide both qualitative and quantitative understanding of transient wave propagation and scattering phenomena, with emphasis on acoustic and electromagnetic problems. (Author).
Book Synopsis Mathematical Methods for Optical Physics and Engineering by : Gregory J. Gbur
Download or read book Mathematical Methods for Optical Physics and Engineering written by Gregory J. Gbur and published by Cambridge University Press. This book was released on 2011-01-06 with total page 819 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first textbook on mathematical methods focusing on techniques for optical science and engineering, this text is ideal for upper division undergraduate and graduate students in optical physics. Containing detailed sections on the basic theory, the textbook places strong emphasis on connecting the abstract mathematical concepts to the optical systems to which they are applied. It covers many topics which usually only appear in more specialized books, such as Zernike polynomials, wavelet and fractional Fourier transforms, vector spherical harmonics, the z-transform, and the angular spectrum representation. Most chapters end by showing how the techniques covered can be used to solve an optical problem. Essay problems based on research publications and numerous exercises help to further strengthen the connection between the theory and its applications.
Book Synopsis Recent Mathematical Methods in Nonlinear Wave Propagation by : Guy Boillat
Download or read book Recent Mathematical Methods in Nonlinear Wave Propagation written by Guy Boillat and published by Springer. This book was released on 2006-11-14 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes of the courses presented at the first CIME session 1994 by leading scientists present the state of the art in recent mathematical methods in Nonlinear Wave Propagation.
Book Synopsis Linear And Nonlinear Wave Propagation by : Spencer P Kuo
Download or read book Linear And Nonlinear Wave Propagation written by Spencer P Kuo and published by World Scientific. This book was released on 2021-04-16 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Waves are essential phenomena in most scientific and engineering disciplines, such as electromagnetism and optics, and different mechanics including fluid, solid, structural, quantum, etc. They appear in linear and nonlinear systems. Some can be observed directly and others are not. The features of the waves are usually described by solutions to either linear or nonlinear partial differential equations, which are fundamental to the students and researchers.Generic equations, describing wave and pulse propagation in linear and nonlinear systems, are introduced and analyzed as initial/boundary value problems. These systems cover the general properties of non-dispersive and dispersive, uniform and non-uniform, with/without dissipations. Methods of analyses are introduced and illustrated with analytical solutions. Wave-wave and wave-particle interactions ascribed to the nonlinearity of media (such as plasma) are discussed in the final chapter.This interdisciplinary textbook is essential reading for anyone in above mentioned disciplines. It was prepared to provide students with an understanding of waves and methods of solving wave propagation problems. The presentation is self-contained and should be read without difficulty by those who have adequate preparation in classic mechanics. The selection of topics and the focus given to each provide essential materials for a lecturer to cover the bases in a linear/nonlinear wave course.
Book Synopsis Parabolic Equation Methods for Electromagnetic Wave Propagation by : Mireille Levy
Download or read book Parabolic Equation Methods for Electromagnetic Wave Propagation written by Mireille Levy and published by IET. This book was released on 2000 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides scientists and engineers with a tool for accurate assessment of diffraction and ducting on radio and radar systems. The author gives the mathematical background to parabolic equations modeling and describes simple parabolic equation algorithms before progressing to more advanced topics such as domain truncation, the treatment of impedance boundaries, and the implementation of very fast hybrid methods combining ray-tracing and parabolic equation techniques. The last three chapters are devoted to scattering problems, with application to propagation in urban environments and to radar-cross- section computation. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Mathematical Methods for Wave Phenomena by : Norman Bleistein
Download or read book Mathematical Methods for Wave Phenomena written by Norman Bleistein and published by Academic Press. This book was released on 2012-12-02 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer Science and Applied Mathematics: Mathematical Methods for Wave Phenomena focuses on the methods of applied mathematics, including equations, wave fronts, boundary value problems, and scattering problems. The publication initially ponders on first-order partial differential equations, Dirac delta function, Fourier transforms, asymptotics, and second-order partial differential equations. Discussions focus on prototype second-order equations, asymptotic expansions, asymptotic expansions of Fourier integrals with monotonic phase, method of stationary phase, propagation of wave fronts, and variable index of refraction. The text then examines wave equation in one space dimension, as well as initial boundary value problems, characteristics for the wave equation in one space dimension, and asymptotic solution of the Klein-Gordon equation. The manuscript offers information on wave equation in two and three dimensions and Helmholtz equation and other elliptic equations. Topics include energy integral, domain of dependence, and uniqueness, scattering problems, Green's functions, and problems in unbounded domains and the Sommerfeld radiation condition. The asymptotic techniques for direct scattering problems and the inverse methods for reflector imaging are also elaborated. The text is a dependable reference for computer science experts and mathematicians pursuing studies on the mathematical methods of wave phenomena.
Book Synopsis Mathematical and Numerical Aspects of Wave Propagation WAVES 2003 by : Gary Cohen
Download or read book Mathematical and Numerical Aspects of Wave Propagation WAVES 2003 written by Gary Cohen and published by Springer Science & Business Media. This book was released on 2003-06-17 with total page 896 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings include articles of the Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2003), held in Jyviiskylii, Finland, from June 30 to July 4, 2003. As in the previous five conferences in this series, its program covered a broad range of topics related to the mathematical modeling and numerical simulation of wave phenomena. Topics of specific interest included various areas of acoustics, electromagnetics, elasticity, and related optimization and inverse problems. In addition to the nine invited presentations, we selected for this confer ence 152 high-level papers from over 20 countries, especially from Europe. Most of them are contained in this book. They provide an extensive overview on the recent developments in the theoretical and applied wave propagation. The conference was organized by the University of Jyviiskylii and the Institut National de Recherche en Informatique et en Automatique (INRIA) in cooperation with Jyviiskylii Congresses. The editors would like to thank the organizing institutions and the in ternational scientific committee for their efforts in the preparation of this conference. We are also grateful to all the authors of the papers for their contributions to these proceedings. Special acknowledgment is due to Ms. Dominique Potherat, to Ms. Helene Chanut and to Ms. Marja-Leena Ranta lainen for their valuable assistance in the preparation of this proceedings volume. Jyviiskylii, Gary C. Cohen February 2003 Erkki H eikkola Patrick loly Pekka Neittaanmiiki Contents Part I Invited Presentations Dispersive Properties of High Order Finite Elements Mark Ainsworth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . ."
