Author: Erhard Meister Publisher: Peter Lang Publishing ISBN: Category : Science Languages : en Pages : 330
Book Description
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.
Author: Erhard Meister Publisher: Peter Lang Gmbh, Internationaler Verlag Der Wissenschaften ISBN: Category : Mathematics Languages : en Pages : 328
Book Description
Contains papers from a fall 1996 conference commemorating the centenary of A. Sommerfeld's landmark paper that initiated the study of boundary value problems in scattering theory. Topics include applications of ultrasonic diffraction theory to crack detection and characterization, scattering by an orthotropic medium, radiation conditions and uniqueness, recent analytical developments in diffraction theory, and long time asymptotic behavior of solutions to linear and nonlinear wave problems. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Igor T. Selezov Publisher: Springer ISBN: 9811049238 Category : Science Languages : en Pages : 251
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: Alexander Kyurkchan Publisher: Elsevier ISBN: 9780128037287 Category : Languages : en Pages : 280
Book Description
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
Author: Mezhlum A. Sumbatyan Publisher: CRC Press ISBN: 0203643488 Category : Science Languages : en Pages : 307
Book Description
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.
Author: Israel Gohberg Publisher: Birkhäuser ISBN: 3034879261 Category : Mathematics Languages : en Pages : 472
Book Description
This volume is devoted to the life and work of the applied mathematician Professor Erhard Meister (1930-2001). He was a member of the editorial boards of this book series Operator The ory: Advances and Applications as well as of the journal Integral Equations and Operator Theory, both published by Birkhauser (now part of Springer-Verlag). Moreover he played a decisive role in the foundation of these two series by helping to establish contacts between Birkhauser and the founder and present chief editor of this book series after his emigration from Moldavia in 1974. The volume is divided into two parts. Part A contains reminiscences about the life of E. Meister including a short biography and an exposition of his professional work. Part B displays the wide range of his scientific interests through eighteen original papers contributed by authors with close scientific and personal relations to E. Meister. We hope that a great part of the numerous features of his life and work can be re-discovered from this book.
Author: Michael Trott Publisher: Springer Science & Business Media ISBN: 0387288155 Category : Computers Languages : en Pages : 1490
Book Description
Provides reader with working knowledge of Mathematica and key aspects of Mathematica symbolic capabilities, the real heart of Mathematica and the ingredient of the Mathematica software system that makes it so unique and powerful Clear organization, complete topic coverage, and an accessible writing style for both novices and experts Website for book with additional materials: http://www/MathematicaGuideBooks.org Accompanying DVD containing all materials as an electronic book with complete, executable Mathematica 5.1 compatible code and programs, rendered color graphics, and animations
Author: Alexander Komech Publisher: Springer Nature ISBN: 3030266990 Category : Mathematics Languages : en Pages : 167
Book Description
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.
Author: Erhard Meister
Author: Erhard Meister
Author: Erhard Meister
Author: Igor T. Selezov
Author: Alexander Kyurkchan
Author: 
Author: Mezhlum A. Sumbatyan
Author: Israel Gohberg
Author: Michael Trott
Author: Alexander Komech