Equations Of Mathematical Diffraction Theory
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Equations Of Mathematical Diffraction Theory
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Author : Mezhlum A. Sumbatyan
language : en
Publisher: CRC Press
Release Date : 2004-09-29
Equations Of Mathematical Diffraction Theory written by Mezhlum A. Sumbatyan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-29 with Science categories.
Equations of Mathematical Diffraction Theory focuses on the comparative analysis and development of efficient analytical methods for solving equations of mathematical diffraction theory. Following an overview of some general properties of integral and differential operators in the context of the linear theory of diffraction processes, the authors provide estimates of the operator norms for various ranges of the wave number variation, and then examine the spectral properties of these operators. They also present a new analytical method for constructing asymptotic solutions of boundary integral equations in mathematical diffraction theory for the high-frequency case. Clearly demonstrating the close connection between heuristic and rigorous methods in mathematical diffraction theory, this valuable book provides you with the differential and integral equations that can easily be used in practical applications.
Equations Of Mathematical Diffraction Theory
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Author : Mezhlum A. Sumbatyan
language : en
Publisher:
Release Date : 2005
Equations Of Mathematical Diffraction Theory written by Mezhlum A. Sumbatyan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Diffraction categories.
Mathematical Theory Of Diffraction
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Author : Arnold Sommerfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Theory Of Diffraction written by Arnold Sommerfeld 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 Mathematics categories.
A. Sommerfeld's "Mathematische Theorie der Diffraction" marks a milestone in optical theory, full of insights that are still relevant today. In a stunning tour de force, Sommerfeld derives the first mathematically rigorous solution of an optical diffraction problem. Indeed, his diffraction analysis is a surprisingly rich and complex mix of pure and applied mathematics, and his often-cited diffraction solution is presented only as an application of a much more general set of mathematical results. This complete translation, reflecting substantial scholarship, is the first publication in English of Sommerfeld's original work. The extensive notes by the translators are rich in historical background and provide many technical details for the reader.
Diffraction Theory
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Author : V. M. Babich
language : en
Publisher: Alpha Science International, Limited
Release Date : 2008
Diffraction Theory written by V. M. Babich and has been published by Alpha Science International, Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
This title contains the detailed descriptions of the Sommerfeld-Malyuzhinets technique and the related mathematical aspects.
Mathematical Questions In The Theory Of Wave Diffraction
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Author : V. M. Babich
language : en
Publisher: American Mathematical Soc.
Release Date : 1974
Mathematical Questions In The Theory Of Wave Diffraction written by V. M. Babich 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 1974 with Mathematics categories.
Papers and articles about wave diffraction and its algebraic applications.
Mathematical Modeling In Diffraction Theory
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Author : Alexander G. Kyurkchan
language : en
Publisher: Elsevier
Release Date : 2015-09-19
Mathematical Modeling In Diffraction Theory written by Alexander G. Kyurkchan and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-19 with Science categories.
Mathematical Modeling in Diffraction Theory: Based on A Priori Information on the Analytical Properties of the Solution provides the fundamental physical concepts behind the theory of wave diffraction and scattered wave fields as well as its application in radio physics, acoustics, optics, radio astronomy, biophysics, geophysics, and astrophysics. This book provides a coherent discussion of several advanced topics that have the potential to push forward progress in this field. It begins with examples illustrating the importance of taking a priori information into account when developing algorithms for solving diffraction problems, with subsequent chapters discussing the basic analytical representations of wave fields, the auxiliary current and source methods for solving the problems of diffraction at compact scatterers, the null field and matrix methods that are widely used to solve problems in radio-physics, radio-astronomy, and biophysics, and the continued boundary condition and pattern equation method. Provides ideas and techniques for obtaining a priori information on analytical properties of wave fields and provides methods for solving diffraction problems Includes numerous concrete examples of localization of singularities of analytical continuation of wave fields Presents a qualitative explanation of the formation of visions of objects Formulates the concept of “invisible objects Supplies appropriate computer programs for all presented methods
The Mathematical Theory Of Huygens Principle
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Author : Bevan B. Baker
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
The Mathematical Theory Of Huygens Principle written by Bevan B. Baker 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 2003 with Mathematics categories.
Baker and Copson originally set themselves the task of writing a definitive text on partial differential equations in mathematical physics. However, at the time, the subject was changing rapidly and greatly, particularly via the developments coming from quantum mechanics. Instead, the authors chose to focus on a particular area of the broad theory, producing a monograph complete in itself. The resulting book deals with Huygens' principle in optics and its application to the theory of diffraction. Baker and Copson concern themselves with the general theory of the solution of the PDEs governing the propagation of light. Extensive use is made of Green's method. A chapter is dedicated to Sommerfeld's theory of diffraction, including diffraction of polarized light by a perfectly reflecting half-plane and by a black half-plane. New material was added for subsequent editions, notably Rayleigh's method of integral equations to the problem of diffraction by a planar screen. Some of the simpler diffraction problems are discussed as examples. Baker and Copson's book quickly became the standard reference on the subject of Huygens' principle. It remains so today.
Wave Propagation And Diffraction
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Author : Igor T. Selezov
language : en
Publisher: Springer
Release Date : 2017-09-05
Wave Propagation And Diffraction written by Igor T. Selezov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-05 with Science categories.
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.
Modern Mathematical Methods In Diffraction Theory And Its Applications In Engineering
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Author : Erhard Meister
language : en
Publisher: Peter Lang Publishing
Release Date : 1997
Modern Mathematical Methods In Diffraction Theory And Its Applications In Engineering written by Erhard Meister and has been published by Peter Lang Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Science categories.
In 1896 A Sommerfeld published his famous paper "Zur Theorie der Diffraktion" in vol. 47 of the "Mathematische Annalen". His investigations initiated the study of boundary value problems in scattering theory. A long series of research works on general mixed boundary value problems sprang up then. Boundary integral equations together with the Wiener-Hopf method have been generalized and are now a basis for analytical and numerical studies by many mathematicians and engineers working on wave diffraction problems. Commemorating the centenary of Sommerfeld's paper, the aim of this conference is to join the experts and young researchers to present surveys and new results.
Stationary Diffraction By Wedges
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Author : Alexander Komech
language : en
Publisher: Springer Nature
Release Date : 2019-09-16
Stationary Diffraction By Wedges written by Alexander Komech and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-16 with Mathematics categories.
This book presents a new and original method for the solution of boundary value problems in angles for second-order elliptic equations with constant coefficients and arbitrary boundary operators. This method turns out to be applicable to many different areas of mathematical physics, in particular to diffraction problems in angles and to the study of trapped modes on a sloping beach. Giving the reader the opportunity to master the techniques of the modern theory of diffraction, the book introduces methods of distributions, complex Fourier transforms, pseudo-differential operators, Riemann surfaces, automorphic functions, and the Riemann–Hilbert problem. The book will be useful for students, postgraduates and specialists interested in the application of modern mathematics to wave propagation and diffraction problems.