Mathematical Modeling in Diffraction Theory

Mathematical Modeling in Diffraction Theory
Author: Alexander G. Kyurkchan,Nadezhda I. Smirnova
Publsiher: Elsevier
Total Pages: 280
Release: 2015-09-19
Genre: Science
ISBN: 9780128037485

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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

Mathematical Modeling in Optical Science

Mathematical Modeling in Optical Science
Author: Gang Bao,Lawrence Cowsar,Wen Masters
Publsiher: SIAM
Total Pages: 349
Release: 2001-01-01
Genre: Science
ISBN: 0898717590

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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

A Celebration of Mathematical Modeling
Author: Dan Givoli,Marcus J. Grote,George Papanicolaou
Publsiher: Springer Science & Business Media
Total Pages: 292
Release: 2004-04-30
Genre: Mathematics
ISBN: 1402018428

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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.

Wave Propagation and Diffraction

Wave Propagation and Diffraction
Author: Igor T. Selezov,Yuriy G. Kryvonos,Ivan S. Gandzha
Publsiher: Springer
Total Pages: 241
Release: 2017-09-05
Genre: Science
ISBN: 9789811049231

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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 Models for Simple Harmonic Linear Water Waves

Mathematical Models for Simple Harmonic Linear Water Waves
Author: J. C. Berkhoff
Publsiher: Unknown
Total Pages: 103
Release: 1976
Genre: Electronic Book
ISBN: OCLC:246307757

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Mathematical Theory of Diffraction

Mathematical Theory of Diffraction
Author: Arnold Sommerfeld
Publsiher: Springer Science & Business Media
Total Pages: 157
Release: 2012-12-06
Genre: Mathematics
ISBN: 9780817681968

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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.

Stationary Diffraction by Wedges

Stationary Diffraction by Wedges
Author: Alexander Komech,Anatoli Merzon
Publsiher: Springer Nature
Total Pages: 167
Release: 2019-09-16
Genre: Mathematics
ISBN: 9783030266998

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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.

Numerical Simulation of Water Waves

Numerical Simulation of Water Waves
Author: Jianhua Tao
Publsiher: Springer Nature
Total Pages: 482
Release: 2020-03-30
Genre: Technology & Engineering
ISBN: 9789811528415

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This book discusses the numerical simulation of water waves, which combines mathematical theories and modern techniques of numerical simulation to solve the problems associated with waves in coastal, ocean, and environmental engineering. Bridging the gap between practical mathematics and engineering, the book describes wave mechanics, establishment of mathematical wave models, modern numerical simulation techniques, and applications of numerical models in engineering. It also explores environmental issues related to water waves in coastal regions, such as pollutant and sediment transport, and introduces numerical wave flumes and wave basins. The material is self-contained, with numerous illustrations and tables, and most of the mathematical and engineering concepts are presented or derived in the text. The book is intended for researchers, graduate students and engineers in the fields of hydraulic, coastal, ocean and environmental engineering with a background in fluid mechanics and numerical simulation methods.