Mathematical Modeling In Diffraction Theory
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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
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.
Mathematical Modeling In Optical Science
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Author : Gang Bao
language : en
Publisher: SIAM
Release Date : 2001-01-01
Mathematical Modeling In Optical Science written by Gang Bao and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Science categories.
This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of mathematical models and the design and analysis of new computational approaches. The book contains cutting-edge discourses on emerging technology in optics that provides significant challenges and opportunities for applied mathematicians, researchers, and engineers.
A Celebration Of Mathematical Modeling
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Author : Dan Givoli
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-04-30
A Celebration Of Mathematical Modeling written by Dan Givoli 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 2004-04-30 with Mathematics categories.
This volume celebrates the eightieth birthday of the famous applied mathematician Joseph B. Keller. The book contains 12 chapters, each on a specific area of mathematical modeling, written by established researchers who have collaborated with J.B. Keller during his long career. These chapters, all inspired by J.B. Keller, deal with a variety of application fields and together span the broad subject of mathematical modeling. The models discussed in the book describe the behavior of various systems such as those related to finance, waves, microorganisms, shocks, DNA, flames, contact, optics, fluids, bubbles and jets. The book also contains a preface written by the Editors, a full list of J.B. Keller's publications, and a comprehensive index. The book is intended for mathematicians, scientists and engineers, as well as graduate students in these fields, who are interested in mathematical models of physical phenomena.
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.
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.
Scattering Theory For Diffraction Gratings
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Author : Calvin H. Wilcox
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Scattering Theory For Diffraction Gratings written by Calvin H. Wilcox 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.
The scattering of acoustic and electromagnetic waves by periodic sur faces plays a role in many areas of applied physics and engineering. Opti cal diffraction gratings date from the nineteenth century and are still widely used by spectroscopists. More recently, diffraction gratings have been used as coupling devices for optical waveguides. Trains of surface waves on the oceans are natural diffraction gratings which influence the scattering of electromagnetic waves and underwater sound. Similarly, the surface of a crystal acts as a diffraction grating for the scattering of atomic beams. This list of natural and artificial diffraction gratings could easily be extended. The purpose of this monograph is to develop from first principles a theory of the scattering of acoustic and electromagnetic waves by periodic surfaces. In physical terms, the scattering of both time-harmonic and transient fields is analyzed. The corresponding mathematical model leads to the study of boundary value problems for the Helmholtz and d'Alembert wave equations in plane domains bounded by periodic curves. In the formal ism adopted here these problems are intimately related to the spectral analysis of the Laplace operator, acting in a Hilbert space of functions defined in the domain adjacent to the grating.
Laser Interaction With Biological Material
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Author : Kirill Kulikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-16
Laser Interaction With Biological Material written by Kirill Kulikov 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 2013-09-16 with Science categories.
This book covers the principles of laser interaction with biological cells and tissues of varying degrees of organization. The problems of biomedical diagnostics are considered. Scattering of laser irradiation of blood cells is modeled for biological structures (dermis, epidermis, vascular plexus). An analytic theory is provided which is based on solving the wave equation for the electromagnetic field. It allows the accurate analysis of interference effects arising from the partial superposition of scattered waves. Treated topics of mathematical modeling are: optical characterization of biological tissue with large-scale and small-scale inhomogeneities in the layers, heating blood vessel under laser irradiation incident on the outer surface of the skin and thermo-chemical denaturation of biological structures at the example of human skin.
Seismic Diffraction
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Author : Kamill Davydovich Klem-Musatov
language : en
Publisher:
Release Date : 2016
Seismic Diffraction written by Kamill Davydovich Klem-Musatov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Diffraction categories.
The use of diffraction imaging to complement the seismic reflection method is rapidly gaining momentum in the oil and gas industry. As the industry moves toward exploiting smaller and more complex conventional reservoirs and extensive new unconventional resource plays, the application of the seismic diffraction method to image sub-wavelength features such as small-scale faults, fractures and stratigraphic pinchouts is expected to increase dramatically over the next few years. "Seismic Diffraction" covers seismic diffraction theory, modeling, observation, and imaging. Papers and discussion include an overview of seismic diffractions, including classic papers which introduced the potential of diffraction phenomena in seismic processing; papers on the forward modeling of seismic diffractions, with an emphasis on the theoretical principles; papers which describe techniques for diffraction mathematical modeling as well as laboratory experiments for the physical modeling of diffractions; key papers dealing with the observation of seismic diffractions, in near-surface-, reservoir-, as well as crustal studies; and key papers on diffraction imaging.
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.