Mathematical Methods For Wave Phenomena
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Mathematical Methods For Wave Phenomena
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Author : Norman Bleistein
language : en
Publisher: Academic Press
Release Date : 2012-12-02
Mathematical Methods For Wave Phenomena written by Norman Bleistein and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Mathematics categories.
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.
Mathematics Of Wave Phenomena
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Author : Willy Dörfler
language : en
Publisher: Springer Nature
Release Date : 2020-10-01
Mathematics Of Wave Phenomena written by Willy Dörfler and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-01 with Mathematics categories.
Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics. The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.
Hyperbolic Partial Differential Equations And Wave Phenomena
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Author : Mitsuru Ikawa
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Hyperbolic Partial Differential Equations And Wave Phenomena written by Mitsuru Ikawa and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Deals with initial boundary value problems for second order hyperbolic equations, concentrating on linear hyperbolic equations of second order with a scalar-valued unknown function and elucidating properties of phenomena governed by particular equations. Chapters cover wave phenomena and hyperbolic equations, the existence of a solution for a hyperbolic equation and its properties, construction of asymptotic solutions, and local energy of the wave equation. Includes exercises and solutions. Originally published in Japanese by Iwanami Shoten, Publishers, Tokyo, 1997. Annotation copyrighted by Book News, Inc., Portland, OR
Mathematics Of Wave Propagation
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Author : Julian L. Davis
language : en
Publisher: Princeton University Press
Release Date : 2021-01-12
Mathematics Of Wave Propagation written by Julian L. Davis 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 2021-01-12 with Mathematics categories.
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.
Wave Propagation In Electromagnetic Media
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Author : Julian L. Davis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Wave Propagation In Electromagnetic Media written by Julian L. Davis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
Analytical And Numerical Methods For Wave Propagation In Fluid Media
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Author : K. Murawski
language : en
Publisher: World Scientific
Release Date : 2002
Analytical And Numerical Methods For Wave Propagation In Fluid Media written by K. Murawski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Science categories.
This book surveys analytical and numerical techniques appropriate to the description of fluid motion with an emphasis on the most widely used techniques exhibiting the best performance.Analytical and numerical solutions to hyperbolic systems of wave equations are the primary focus of the book. In addition, many interesting wave phenomena in fluids are considered using examples such as acoustic waves, the emission of air pollutants, magnetohydrodynamic waves in the solar corona, solar wind interaction with the planet venus, and ion-acoustic solitons.
Effective Computational Methods For Wave Propagation
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Author : Nikolaos A. Kampanis
language : en
Publisher: CRC Press
Release Date : 2008-02-25
Effective Computational Methods For Wave Propagation written by Nikolaos A. Kampanis and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-25 with Mathematics categories.
Due to the increase in computational power and new discoveries in propagation phenomena for linear and nonlinear waves, the area of computational wave propagation has become more significant in recent years. Exploring the latest developments in the field, Effective Computational Methods for Wave Propagation presents several modern, valuable
Applied Wave Mathematics Ii
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Author : Arkadi Berezovski
language : en
Publisher: Springer Nature
Release Date : 2019-11-16
Applied Wave Mathematics Ii written by Arkadi Berezovski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-16 with Mathematics categories.
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.
Physics Of Oscillations And Waves
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Author : Arnt Inge Vistnes
language : en
Publisher: Springer
Release Date : 2018-08-21
Physics Of Oscillations And Waves written by Arnt Inge Vistnes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-21 with Science categories.
In this textbook a combination of standard mathematics and modern numerical methods is used to describe a wide range of natural wave phenomena, such as sound, light and water waves, particularly in specific popular contexts, e.g. colors or the acoustics of musical instruments. It introduces the reader to the basic physical principles that allow the description of the oscillatory motion of matter and classical fields, as well as resulting concepts including interference, diffraction, and coherence. Numerical methods offer new scientific insights and make it possible to handle interesting cases that can’t readily be addressed using analytical mathematics; this holds true not only for problem solving but also for the description of phenomena. Essential physical parameters are brought more into focus, rather than concentrating on the details of which mathematical trick should be used to obtain a certain solution. Readers will learn how time-resolved frequency analysis offers a deeper understanding of the interplay between frequency and time, which is relevant to many phenomena involving oscillations and waves. Attention is also drawn to common misconceptions resulting from uncritical use of the Fourier transform. The book offers an ideal guide for upper-level undergraduate physics students and will also benefit physics instructors. Program codes in Matlab and Python, together with interesting files for use in the problems, are provided as free supplementary material.