Mathematical Problems in Wave Propagation Theory PDF Download
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Author: V. M. Babich
Publisher: Springer Science & Business Media
ISBN: 1475703341
Category : Science
Languages : en
Pages : 109
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Book Description
The papers comprising this collection are directly or indirectly related to an important branch of mathematical physics - the mathematical theory of wave propagation and diffraction. The paper by V. M. Babich is concerned with the application of the parabolic-equation method (of Academician V. A. Fok and M. A, Leontovich) to the problem of the asymptotic behavior of eigenfunc tions concentrated in a neighborhood of a closed geodesie in a Riemannian space. The techniques used in this paper have been föund useful in solving certain problems in the theory of open resonators. The topic of G. P. Astrakhantsev's paper is similar to that of the paper by V. M. Babich. Here also the parabolic-equation method is used to find the asymptotic solution of the elasticity equations which describes Love waves concentrated in a neighborhood of some surface ray. The paper of T. F. Pankratova is concerned with finding the asymptotic behavior of th~ eigenfunc tions of the Laplace operator from the exact solution for the surface of a triaxial ellipsoid and the re gion exterior to it. The first three papers of B. G. Nikolaev are somewhat apart from the central theme of the col lection; they treat the integral transforms with respect to associated Legendre functions of first kind and their applications. Examples of such applications are the use of this transform for the solution of integral equations with symmetrie kernels and for the solution of certain problems in the theory of electrical prospecting.
Author: V. M. Babich
Publisher: Springer Science & Business Media
ISBN: 1475703341
Category : Science
Languages : en
Pages : 109
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Book Description
The papers comprising this collection are directly or indirectly related to an important branch of mathematical physics - the mathematical theory of wave propagation and diffraction. The paper by V. M. Babich is concerned with the application of the parabolic-equation method (of Academician V. A. Fok and M. A, Leontovich) to the problem of the asymptotic behavior of eigenfunc tions concentrated in a neighborhood of a closed geodesie in a Riemannian space. The techniques used in this paper have been föund useful in solving certain problems in the theory of open resonators. The topic of G. P. Astrakhantsev's paper is similar to that of the paper by V. M. Babich. Here also the parabolic-equation method is used to find the asymptotic solution of the elasticity equations which describes Love waves concentrated in a neighborhood of some surface ray. The paper of T. F. Pankratova is concerned with finding the asymptotic behavior of th~ eigenfunc tions of the Laplace operator from the exact solution for the surface of a triaxial ellipsoid and the re gion exterior to it. The first three papers of B. G. Nikolaev are somewhat apart from the central theme of the col lection; they treat the integral transforms with respect to associated Legendre functions of first kind and their applications. Examples of such applications are the use of this transform for the solution of integral equations with symmetrie kernels and for the solution of certain problems in the theory of electrical prospecting.
Author: Julian L. Davis
Publisher: Princeton University Press
ISBN: 0691223378
Category : Mathematics
Languages : en
Pages : 411
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Book Description
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.
Author: Guy Chavent
Publisher: Springer Science & Business Media
ISBN: 1461218780
Category : Mathematics
Languages : en
Pages : 502
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Book Description
Inverse problems in wave propagation occur in geophysics, ocean acoustics, civil and environmental engineering, ultrasonic non-destructive testing, biomedical ultrasonics, radar, astrophysics, as well as other areas of science and technology. The papers in this volume cover these scientific and technical topics, together with fundamental mathematical investigations of the relation between waves and scatterers.
Author: O. A. Ladyzhenskaya
Publisher: Springer Science & Business Media
ISBN: 1475746660
Category : Science
Languages : en
Pages : 86
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Book Description
Author: Igor T. Selezov
Publisher: Springer
ISBN: 9811049238
Category : Science
Languages : en
Pages : 251
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Book Description
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.
Author:
Publisher: Springer Nature
ISBN: 1461585880
Category :
Languages : en
Pages : 133
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Author: V. M. Kalinin
Publisher: Springer Science & Business Media
ISBN: 1468482114
Category : Science
Languages : en
Pages : 149
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Author: N.J. Vlaar
Publisher: Springer Science & Business Media
ISBN: 9400928572
Category : Science
Languages : en
Pages : 410
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Book Description
The contributions to this book follow a topical trend. In several geophysical fields evidence is accumulating concerning the deviation of the earth's structure from radial symmetry. Seismology provides the most adequate resolution for revealing the earth's lateral inhomogeneity on a global to local scale. Lateral structure in the density distribution is also manifest in the earth's gravity field and in the geoid. Asphericity in physical parameters, generally supposed only to vary with the vertical coordinate, has a profound influence on geodynamics. The effects of these deviations from spherical symmetry concern in particular convection theory, post-glacial rebound and the dynamics of the lithosphere and upper mantle in general. At the 16th International Conference on Mathematical Geophysics which was held in Oosterbeek, the Netherlands, in 1986, the need was felt to present the state of the art. Several prospective authors were found interested to contribute to the present book. This Oosterbeek conference was one in a long series of topical conferences starting with the Upper Mantle Project Symposia on Geophysical Theory and Computers in the 1960s, and thence their successors, the conferences on Mathematical Geophysics, until the present.
Author: Akira Ishimaru
Publisher: John Wiley & Sons
ISBN: 1119079535
Category : Science
Languages : en
Pages : 1045
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Book Description
One of the most methodical treatments of electromagnetic wave propagation, radiation, and scattering—including new applications and ideas Presented in two parts, this book takes an analytical approach on the subject and emphasizes new ideas and applications used today. Part one covers fundamentals of electromagnetic wave propagation, radiation, and scattering. It provides ample end-of-chapter problems and offers a 90-page solution manual to help readers check and comprehend their work. The second part of the book explores up-to-date applications of electromagnetic waves—including radiometry, geophysical remote sensing and imaging, and biomedical and signal processing applications. Written by a world renowned authority in the field of electromagnetic research, this new edition of Electromagnetic Wave Propagation, Radiation, and Scattering: From Fundamentals to Applications presents detailed applications with useful appendices, including mathematical formulas, Airy function, Abel’s equation, Hilbert transform, and Riemann surfaces. The book also features newly revised material that focuses on the following topics: Statistical wave theories—which have been extensively applied to topics such as geophysical remote sensing, bio-electromagnetics, bio-optics, and bio-ultrasound imaging Integration of several distinct yet related disciplines, such as statistical wave theories, communications, signal processing, and time reversal imaging New phenomena of multiple scattering, such as coherent scattering and memory effects Multiphysics applications that combine theories for different physical phenomena, such as seismic coda waves, stochastic wave theory, heat diffusion, and temperature rise in biological and other media Metamaterials and solitons in optical fibers, nonlinear phenomena, and porous media Primarily a textbook for graduate courses in electrical engineering, Electromagnetic Wave Propagation, Radiation, and Scattering is also ideal for graduate students in bioengineering, geophysics, ocean engineering, and geophysical remote sensing. The book is also a useful reference for engineers and scientists working in fields such as geophysical remote sensing, bio–medical engineering in optics and ultrasound, and new materials and integration with signal processing.
Author: Valeriĭ Pavlovich Ilʹin
Publisher: Springer
ISBN:
Category : Science
Languages : en
Pages : 168
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Book Description
