Asymptotic Methods In Short Wavelength Diffraction Theory

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Short Wavelength Diffraction Theory

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Author : Vasili M. Babic
language : en
Publisher: Springer
Release Date : 2011-12-08

Short Wavelength Diffraction Theory written by Vasili M. Babic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-08 with Science categories.

In the study of short-wave diffraction problems, asymptotic methods - the ray method, the parabolic equation method, and its further development as the "etalon" (model) problem method - play an important role. These are the meth ods to be treated in this book. The applications of asymptotic methods in the theory of wave phenomena are still far from being exhausted, and we hope that the techniques set forth here will help in solving a number of problems of interest in acoustics, geophysics, the physics of electromagnetic waves, and perhaps in quantum mechanics. In addition, the book may be of use to the mathematician interested in contemporary problems of mathematical physics. Each chapter has been annotated. These notes give a brief history of the problem and cite references dealing with the content of that particular chapter. The main text mentions only those pUblications that explain a given argument or a specific calculation. In an effort to save work for the reader who is interested in only some of the problems considered in this book, we have included a flow chart indicating the interdependence of chapters and sections.

Short Wavelength Diffraction Theory

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Author : Vasili M. Babic
language : en
Publisher: Springer
Release Date : 1991

Short Wavelength Diffraction Theory written by Vasili M. Babic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Science categories.

In the study of short-wave diffraction problems, asymptotic methods - the ray method, the parabolic equation method, and its further development as the "etalon" (model) problem method - play an important role. These are the meth ods to be treated in this book. The applications of asymptotic methods in the theory of wave phenomena are still far from being exhausted, and we hope that the techniques set forth here will help in solving a number of problems of interest in acoustics, geophysics, the physics of electromagnetic waves, and perhaps in quantum mechanics. In addition, the book may be of use to the mathematician interested in contemporary problems of mathematical physics. Each chapter has been annotated. These notes give a brief history of the problem and cite references dealing with the content of that particular chapter. The main text mentions only those pUblications that explain a given argument or a specific calculation. In an effort to save work for the reader who is interested in only some of the problems considered in this book, we have included a flow chart indicating the interdependence of chapters and sections.

Asymptotic Methods In Short Wavelength Diffraction Theory

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Author : V. M. Babich
language : en
Publisher: Alpha Science International, Limited
Release Date : 2009

Asymptotic Methods In Short Wavelength 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 2009 with Asymptotic expansions categories.

Dedicated to modern approaches of a high-frequency technique in diffraction theory, Asymptotic Methods in Short-Wavelength Diffraction Theory outlines a variety of crucial topics. The book considers a multitude of matters, ranging from the ray method to the theory of high-frequency whispering-gallery waves alongside the reviewing and reflecting on recent results from the literature dealing with localized asymptotic solutions and uniform representation of a high-frequency wave-field. The book serves as an exclusive address to experts on electromagnetics, seismology and acoustics as well as to mathematicians interested in modern approaches of mathematical physics.

Pseudodifferential Operators And Spectral Theory

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Author : M.A. Shubin
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-07-03

Pseudodifferential Operators And Spectral Theory written by M.A. Shubin 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 2001-07-03 with Mathematics categories.

This is the second edition of Shubin's classical book. It provides an introduction to the theory of pseudodifferential operators and Fourier integral operators from the very basics. The applications discussed include complex powers of elliptic operators, Hörmander asymptotics of the spectral function and eigenvalues, and methods of approximate spectral projection. Exercises and problems are included to help the reader master the essential techniques. The book is written for a wide audience of mathematicians, be they interested students or researchers.

Wave Dynamics Mechanics And Physics Of Microstructured Metamaterials

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Author : Mezhlum A. Sumbatyan
language : en
Publisher: Springer
Release Date : 2019-05-17

Wave Dynamics Mechanics And Physics Of Microstructured Metamaterials written by Mezhlum A. Sumbatyan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-17 with Technology & Engineering categories.

This book addresses theoretical and experimental methods for exploring microstructured metamaterials, with a special focus on wave dynamics, mechanics, and related physical properties. The authors use various mathematical and physical approaches to examine the mechanical properties inherent to particular types of metamaterials. These include: • Boundary value problems in reduced strain gradient elasticity for composite fiber-reinforced metamaterials • Self-organization of molecules in ferroelectric thin films • Combined models for surface layers of nanostructures • Computer simulation at the micro- and nanoscale • Surface effects with anisotropic properties and imperfect temperature contacts • Inhomogeneous anisotropic metamaterials with uncoupled and coupled surfaces or interfaces • Special interface finite elements and other numerical and analytical methods for composite structures

Problems Of High Frequency Diffraction By Elongated Bodies

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Author : Ivan Andronov
language : en
Publisher: Springer Nature
Release Date : 2023-04-14

Problems Of High Frequency Diffraction By Elongated Bodies written by Ivan Andronov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-14 with Science categories.

Classical asymptotic expansions, while producing a good approximation for the diffracted fields in general, appear hardly applicable in the case of extremely elongated bodies. Thus, there are problems that are on the one hand too difficult for numerical solvers due to large system size, and on the other hand make the description with classical asymptotic methods hard. The book explains why this happens and suggests the way out. By defining the characteristics of a strongly elongated body it introduces a special class of asymptotic approximations, which are in some sense uniform with respect to the rate of body elongation. Chapter 1 briefly describes the results of V. A. Fock and further developments of his approach towards the problems of diffraction by elongated obstacles. It formulates the cases of moderately and strongly elongated bodies. The rest of the book describes the approach of special parabolic equations, which lead to new asymptotic approximations for the diffracted fields. Chapters 2, 3 and 4 discuss diffraction by bodies of elliptical shape: The elliptic cylinder with a strongly elongated cross section and prolate spheroid with a high aspect ratio. Chapter 5 generalizes the approach to some other shapes such as narrow cones and narrow hyperboloids. Mathematical formulas for the Whittaker functions widely used in the book are collected in the Appendix. The concise derivations are supplied with numerous test examples that compare asymptotic approximations with numerically computed fields and clarify the specifics of high frequency diffraction by strongly elongated bodies. The reference solutions presented in the book enable one to validate the newly developed numerical solvers.

Electromagnetic Radiation Scattering And Diffraction

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Author : Prabhakar H. Pathak
language : en
Publisher: John Wiley & Sons
Release Date : 2021-12-07

Electromagnetic Radiation Scattering And Diffraction written by Prabhakar H. Pathak and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-07 with Science categories.

Electromagnetic Radiation, Scattering, and Diffraction Discover a graduate-level text for students specializing in electromagnetic wave radiation, scattering, and diffraction for engineering applications In Electromagnetic Radiation, Scattering and Diffraction, distinguished authors Drs. Prabhakar H. Pathak and Robert J. Burkholder deliver a thorough exploration of the behavior of electromagnetic fields in radiation, scattering, and guided wave environments. The book tackles its subject from first principles and includes coverage of low and high frequencies. It stresses physical interpretations of the electromagnetic wave phenomena along with their underlying mathematics. The authors emphasize fundamental principles and provide numerous examples to illustrate the concepts contained within. Students with a limited undergraduate electromagnetic background will rapidly and systematically advance their understanding of electromagnetic wave theory until they can complete useful and important graduate-level work on electromagnetic wave problems. Electromagnetic Radiation, Scattering and Diffraction also serves as a practical companion for students trying to simulate problems with commercial EM software and trying to better interpret their results. Readers will also benefit from the breadth and depth of topics, such as: Basic equations governing all electromagnetic (EM) phenomena at macroscopic scales are presented systematically. Stationary and relativistic moving boundary conditions are developed. Waves in planar multilayered isotropic and anisotropic media are analyzed. EM theorems are introduced and applied to a variety of useful antenna problems. Modal techniques are presented for analyzing guided wave and periodic structures. Potential theory and Green's function methods are developed to treat interior and exterior EM problems. Asymptotic High Frequency methods are developed for evaluating radiation Integrals to extract ray fields. Edge and surface diffracted ray fields, as well as surface, leaky and lateral wave fields are obtained. A collective ray analysis for finite conformal antenna phased arrays is developed. EM beams are introduced and provide useful basis functions. Integral equations and their numerical solutions via the method of moments are developed. The fast multipole method is presented. Low frequency breakdown is studied. Characteristic modes are discussed. Perfect for graduate students studying electromagnetic theory, Electromagnetic Radiation, Scattering, and Diffraction is an invaluable resource for professional electromagnetic engineers and researchers working in this area.

Wave Dynamics And Composite Mechanics For Microstructured Materials And Metamaterials

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Author : Mezhlum A. Sumbatyan
language : en
Publisher: Springer
Release Date : 2017-03-28

Wave Dynamics And Composite Mechanics For Microstructured Materials And Metamaterials written by Mezhlum A. Sumbatyan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-28 with Science categories.

This volume deals with topical problems concerning technology and design in construction of modern metamaterials. The authors construct the models of mechanical, electromechanical and acoustical behavior of the metamaterials, which are founded upon mechanisms existing on micro-level in interaction of elementary structures of the material. The empiric observations on the phenomenological level are used to test the created models. The book provides solutions, based on fundamental methods and models using the theory of wave propagation, nonlinear theories and composite mechanics for media with micro- and nanostructure. They include the models containing arrays of cracks, defects, with presence of micro- and nanosize piezoelectric elements and coupled physical-mechanical fields of different nature. The investigations show that the analytical, numerical and experimental methods permit evaluation of the qualitative and quantitative properties of the materials of this sort, with diagnosis of their effective characteristics, frequency intervals of effective energetic cutting and passing, as well as effective regimes of damage evaluation by the acoustic methods.

Modern Electromagnetic Scattering Theory With Applications

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Author : Andrey V. Osipov
language : en
Publisher: John Wiley & Sons
Release Date : 2017-04-17

Modern Electromagnetic Scattering Theory With Applications written by Andrey V. Osipov and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-17 with Technology & Engineering categories.

This self-contained book gives fundamental knowledge about scattering and diffraction of electromagnetic waves and fills the gap between general electromagnetic theory courses and collections of engineering formulas. The book is a tutorial for advanced students learning the mathematics and physics of electromagnetic scattering and curious to know how engineering concepts and techniques relate to the foundations of electromagnetics

Integral Methods In Science And Engineering

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Author : Christian Constanda
language : en
Publisher: Springer Nature
Release Date : 2022-10-13

Integral Methods In Science And Engineering written by Christian Constanda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-13 with Mathematics categories.

This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. Chapters in this book are based on talks given at the Symposium on the Theory and Applications of Integral Methods in Science and Engineering, held virtually in July 2021, and are written by internationally recognized researchers. This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.