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Author: Alexander Komech Publisher: Springer Nature ISBN: 3030266990 Category : Mathematics Languages : en Pages : 157
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: Alexander Komech Publisher: Springer Nature ISBN: 3030266990 Category : Mathematics Languages : en Pages : 157
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: Pyotr Ya. Ufimtsev Publisher: John Wiley & Sons ISBN: 1118753666 Category : Science Languages : en Pages : 496
Book Description
The book is a complete, comprehensive description of the modern Physical Theory of Diffraction (PTD) based upon the concept of elementary edge waves. The theory is demonstrated with examples of the diffraction of acoustic and electromagnetic waves at perfectly reflecting objects. Readers develop the skills to apply PTD to solve various scattering problems. The derived analytic expressions clearly illustrate the physical structure of the scattered field. They additionally describe all of the reflected and diffracted rays and beams, as well as the fields in the vicinity of caustics and foci. Shadow radiation, a fundamental component of PTD, is introduced and proven to contain half the total scattered power. The equivalence relationships between acoustic and electromagnetic diffracted waves are established and emphasized. Throughout the book, the author enables readers to master both the theory and its practical applications. Plotted numeric results supplement the theory and facilitate the visualization of individual contributions of distinct parts of the scattering objects to the total diffracted field Detailed comments help readers understand and implement all the critical steps of the analytic and numeric calculations Problem sets in each chapter give readers an opportunity to analyse and investigate the diffraction phenomena
Author: J.M.L Bernard Publisher: ALPHA SCIENCE INTERNATIONAL LIMITED ISBN: 1783320281 Category : Mathematics Languages : en Pages : 169
Book Description
The mathematical problem concerning the diffraction by a semi-infinite cone with circular cross section for the Helmholtz equation, which has well-known solutions for Dirichlet and Neumann boundary conditions, is here considered for the more general boundary condition of constant impedance type. As previously stated by D.S. Jones, the problem then changes in complexity, beginning with the difficulty of obtaining the uniqueness of the solution. An exact analytical method is developed to reduce this problem to the determination of the solution of a well-posed non-oscillatory integral equation, of which the solution can be directly used to express the field in an integral form. Some generalization, in particular to the electromagnetic case, are also given.
Author: M. S. Agranovich Publisher: American Mathematical Soc. ISBN: 9780821833032 Category : Mathematics Languages : en Pages : 292
Book Description
Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplecticgeometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and general unbounded domains, linear elliptic problems with a parameter for mixed order systems, infinite-dimensional Schrodinger equations, Navier-Stokes equations, and nonlinear Maxwellequations. The book ends on a historical note with a paper about Vishik's seminar as a whole and a list of selected talks given from 1964 through 1989. The book is suitable for graduate students and researchers in pure and applied mathematics and mathematical physics.
Author: S. Flügge Publisher: Springer Science & Business Media ISBN: 3642825028 Category : Science Languages : en Pages : 759
Book Description
Das vielbändige Handbuch der Physik, herausgegeben von Siegfried Flügge, ist wesentlicher Bestand in jeder einschlägigen Bibliothek. Mit seinen herausragenden, teilweise epochemachenden Beiträgen, den umfassenden Überblicken und zahllosen Faktensammlungen stellt es weiterhin eine erstklassige Referenzquelle und ein unerschöpfliches Nachschlagewerk dar. Das nunmehr vorliegende, lange verlangte Generalregister vervollständigt das Handbuch und macht über gemeinsame Autoren- und Sachregister den Inhalt aller 54 Bände auf einfache Weise zugänglich. Damit gehört das Generalregister in die Bibliothek jedes Physikinstitutes als Orientierungshilfe und unentbehrliches Arbeitsmittel.
Author: Alexander Komech Publisher: Cambridge University Press ISBN: 100903605X Category : Mathematics Languages : en Pages :
Book Description
This monograph is the first to present the theory of global attractors of Hamiltonian partial differential equations. A particular focus is placed on the results obtained in the last three decades, with chapters on the global attraction to stationary states, to solitons, and to stationary orbits. The text includes many physically relevant examples and will be of interest to graduate students and researchers in both mathematics and physics. The proofs involve novel applications of methods of harmonic analysis, including Tauberian theorems, Titchmarsh's convolution theorem, and the theory of quasimeasures. As well as the underlying theory, the authors discuss the results of numerical simulations and formulate open problems to prompt further research.
Author: Frédéric Molinet Publisher: Momentum Press ISBN: 160650102X Category : Technology & Engineering Languages : en Pages : 702
Book Description
Covering analytical research in aerial and underwater acoustics, this new scholarly work treats the interaction of acoustic waves with obstacles which may be rigid, soft, elastic, or characterized by an impedance boundary condition. The approach is founded on asymptotic high frequency methods which are based on the concept of rays. For despite the progress in numerical methods for diffraction problems, ray methods still remain the most useful method of approximation for analyzing wave motions. They provide not only considerable physical insight and understanding of diffraction mechanisms but they are also able to treat objects which are still too large in terms of wavelength to fall in the realm of numerical analysis.
Author: Alexander Komech
Author: Alexander Komech
Author: Vladimir Andreevich Borovikov
Author: Pyotr Ya. Ufimtsev
Author: J.M.L Bernard
Author: M. S. Agranovich
Author: S. Flügge
Author: 
Author: R. C. Rudduck
Author: Alexander Komech
Author: Frédéric Molinet