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Iterative Methods For Calculating Static Fields And Wave Scattering By Small Bodies
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Book Synopsis Iterative Methods for Calculating Static Fields and Wave Scattering by Small Bodies by : Alexander G. Ramm
Download or read book Iterative Methods for Calculating Static Fields and Wave Scattering by Small Bodies written by Alexander G. Ramm and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative methods for calculating static fields are presented in this book. Static field boundary value problems are reduced to the boundary integral equations and these equations are solved by means of iterative processes. This is done for interior and exterior problems and for var ious boundary conditions. Most problems treated are three-dimensional, because for two-dimensional problems the specific and often powerful tool of conformal mapping is available. The iterative methods have some ad vantages over grid methods and, to a certain extent, variational methods: (1) they give analytic approximate formulas for the field and for some functionals of the field of practical importance (such as capacitance and polarizability tensor), (2) the formulas for the functionals can be used in a computer program for calculating these functionals for bodies of arbitrary shape, (3) iterative methods are convenient for computers. From a practical point of view the above methods reduce to the cal culation of multiple integrals. Of special interest is the case of inte grands with weak singularities. Some of the central results of the book are some analytic approximate formulas for scattering matrices for small bodies of arbitrary shape. These formulas answer many practical questions such as how does the scattering depend on the shape of the body or on the boundary conditions, how does one calculate the effective field in a medium consisting of many small particles, and many other questions.
Book Synopsis Wave Scattering by Small Bodies of Arbitrary Shapes by : Alexander G. Ramm
Download or read book Wave Scattering by Small Bodies of Arbitrary Shapes written by Alexander G. Ramm and published by World Scientific. This book was released on 2005 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents analytical formulas which allow one to calculate the S-matrix for the acoustic and electromagnetic wave scattering by small bodies or arbitrary shapes with arbitrary accuracy. Equations for the self-consistent field in media consisting of many small bodies are derived. Applications of these results to ultrasound mammography and electrical engineering are considered.The above formulas are not available in the works of other authors. Their derivation is based on a mathematical theory for solving integral equations of electrostatics, magnetostatics, and other static fields. These equations are at a simple characteristic value. Convergent iterative processes are constructed for stable solution of these equations. The theory completes the classical work of Rayleigh on scattering by small bodies by providing analytical formulas for polarizability tensors for bodies of arbitrary shapes.
Book Synopsis Wave Scattering By Small Bodies: Creating Materials With A Desired Refraction Coefficient And Other Applications by : Alexander G Ramm
Download or read book Wave Scattering By Small Bodies: Creating Materials With A Desired Refraction Coefficient And Other Applications written by Alexander G Ramm and published by World Scientific. This book was released on 2023-09-21 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a research monograph. An asymptotically exact solution of the many-body scattering problem is given under the assumption a ≪ d ≪ λ, where a is the characteristic size of a small particle, d is the smallest distance between particles and λ is the wavelength in the medium in which the particles are embedded. Scattering of scalar and electromagnetic waves is considered. Heat transfer theory in the medium in which many small bodies are embedded is developed. Quantum-mechanical theory of scattering by many potentials with small support is constructed.On the basis of these theoretical results, important applications are presented. First, a method for creating materials with a desired refraction coefficient is given. Secondly, a method for creating wave-focusing materials is developed. Technological problems to be solved for practical usage of these applied results are discussed.This book contains the contents of the author's earlier monograph, published in 2013. New appendices, based on the author's review papers published after 2013, are added.
Book Synopsis Low Frequency Scattering by : George Dassios
Download or read book Low Frequency Scattering written by George Dassios and published by Oxford University Press. This book was released on 2000 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering theory deals with the interactions of waves with obstacles in their path, and low frequency scattering occurs when the obstacles involved are very small. This book gives an overview of the subject for graduates and researchers, for the first time unifying the theories covering acoustic, electromagnetic and elastic waves.
Book Synopsis Operator Theory and Its Applications by : Alexander G. Ramm
Download or read book Operator Theory and Its Applications written by Alexander G. Ramm and published by American Mathematical Soc.. This book was released on 2000 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Together with the papers on the abstract operator theory are many papers on the theory of differential operators, boundary value problems, inverse scattering and other inverse problems, and on applications to biology, chemistry, wave propagation, and many other areas."--BOOK JACKET.
Book Synopsis Scattering by Obstacles by : Alexander G. Ramm
Download or read book Scattering by Obstacles written by Alexander G. Ramm and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Book Synopsis Numerical Integration III by : HÄMMERLIN
Download or read book Numerical Integration III written by HÄMMERLIN and published by Birkhäuser. This book was released on 2013-12-14 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Inverse Problems by : Alexander G. Ramm
Download or read book Inverse Problems written by Alexander G. Ramm and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.
Book Synopsis Continuous Optimization by : V. Jeyakumar
Download or read book Continuous Optimization written by V. Jeyakumar and published by Springer Science & Business Media. This book was released on 2006-03-09 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuous optimization is the study of problems in which we wish to opti mize (either maximize or minimize) a continuous function (usually of several variables) often subject to a collection of restrictions on these variables. It has its foundation in the development of calculus by Newton and Leibniz in the 17*^ century. Nowadys, continuous optimization problems are widespread in the mathematical modelling of real world systems for a very broad range of applications. Solution methods for large multivariable constrained continuous optimiza tion problems using computers began with the work of Dantzig in the late 1940s on the simplex method for linear programming problems. Recent re search in continuous optimization has produced a variety of theoretical devel opments, solution methods and new areas of applications. It is impossible to give a full account of the current trends and modern applications of contin uous optimization. It is our intention to present a number of topics in order to show the spectrum of current research activities and the development of numerical methods and applications.
Book Synopsis Operator Theory for Electromagnetics by : George W. Hanson
Download or read book Operator Theory for Electromagnetics written by George W. Hanson and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text discusses electromagnetics from the view of operator theory, in a manner more commonly seen in textbooks of quantum mechanics. It includes a self-contained introduction to operator theory, presenting definitions and theorems, plus proofs of the theorems when these are simple or enlightening.
Book Synopsis Reviews in Numerical Analysis, 1980-86 by :
Download or read book Reviews in Numerical Analysis, 1980-86 written by and published by . This book was released on 1987 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: These five volumes bring together a wealth of bibliographic information in the area of numerical analysis. Containing over 17,600 reviews of articles, books, and conference proceedings, these volumes represent all the numerical analysis entries that appeared in Mathematical Reviews between 1980 and 1986. Author and key indexes appear at the end of volume 5.
Book Synopsis Scattering, Two-Volume Set by : E. R. Pike
Download or read book Scattering, Two-Volume Set written by E. R. Pike and published by Academic Press. This book was released on 2002 with total page 985 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part 1: SCATTERING OF WAVES BY MACROSCOPIC TARGET -- Interdisciplinary aspects of wave scattering -- Acoustic scattering -- Acoustic scattering: approximate methods -- Electromagnetic wave scattering: theory -- Electromagnetic wave scattering: approximate and numerical methods -- Electromagnetic wave scattering: applications -- Elastodynamic wave scattering: theory -- Elastodynamic wave scattering: Applications -- Scattering in Oceans -- Part 2: SCATTERING IN MICROSCOPIC PHYSICS AND CHEMICAL PHYSICS -- Introduction to direct potential scattering -- Introduction to Inverse Potential Scattering -- Visible and Near-visible Light Scattering -- Practical Aspects of Visible and Near-visible Light Scattering -- Nonlinear Light Scattering -- Atomic and Molecular Scattering: Introduction to Scattering in Chemical -- X-ray Scattering -- Neutron Scattering -- Electron Diffraction and Scattering -- Part 3: SCATTERING IN NUCLEAR PHYSICS -- Nuclear Physics -- Part 4: PARTICLE SCATTERING -- State of the Art of Peturbative Methods -- Scattering Through Electro-weak Interactions (the Fermi Scale) -- Scattering Through Strong Interactions (the Hadronic or QCD Scale) -- Part 5: SCATTERING AT EXTREME PHYSICAL SCALES -- Scattering at Extreme Physical Scales -- Part 6: SCATTERING IN MATHEMATICS AND NON-PHYSICAL SCIENCES -- Relations with Other Mathematical Theories -- Inverse Scattering Transform and Non-linear Partial Differenttial Equations -- Scattering of Mathematical Objects.
Book Synopsis Scattering By Obstacles And Potentials by : Ramm Alexander G
Download or read book Scattering By Obstacles And Potentials written by Ramm Alexander G and published by World Scientific. This book was released on 2017-11-23 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is important as it contains results many of which are not available in the literature, except in the author's papers. Among other things, it gives uniqueness theorems for inverse scattering problems when the data are non-over-determined, numerical method for solving inverse scattering problems, a method (MRC) for solving direct scattering problem. Contents: Scattering by ObstaclesScattering by PotentialsModified Rayleigh Conjecture (MRC) Method Readership: Researchers and graduate students in mathematics, computational mathematics, physics, acoustics, mechanical engineering. Keywords: Wave Scattering;Scattering by Obstacles;Scattering by PotentialsReview: Key Features: It contains material part of which is not available in the literature (except in the author's papers)Most of the results belong to the authorNew material is added to the author's earlier monograph "Scattering by obstacles"
Book Synopsis Revue Roumaine de Mathématiques Pures Et Appliquées by :
Download or read book Revue Roumaine de Mathématiques Pures Et Appliquées written by and published by . This book was released on 1984 with total page 980 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory and Applications of Some New Classes of Integral Equations by : Alexander G. Ramm
Download or read book Theory and Applications of Some New Classes of Integral Equations written by Alexander G. Ramm and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for &tudents, research engineers, and mathematicians interested in applications or numerical analysis. Pure analysts will also find some new problems to tackle. Most of the material can be understood by a reader with a relatively modest knowledge of differential and inte gral equations and functional analysis. Readers interested in stochastic optimization will find a new theory of prac tical . importance. Readers interested in problems of static and quasi-static electrodynamics, wave scattering by small bodies of arbitrary shape, and corresponding applications in geophysics, optics, and radiophysics will find explicit analytical formulas for the scattering matrix, polarizability tensor, electrical capacitance of bodies of an arbitrary shape; numerical examples showing the practical utility of these formulas; two-sided variational estimates for the pol arizability tensor; and some open problems such as working out a standard program for calculating the capacitance and polarizability of bodies of arbitrary shape and numerical calculation of multiple integrals with weak singularities. Readers interested in nonlinear vibration theory will find a new method for qualitative study of stationary regimes in the general one-loop passive nonlinear network, including stabil ity in the large, convergence, and an iterative process for calculation the stationary regime. No assumptions concerning the smallness of the nonlinearity or the filter property of the linear one-port are made. New results in the theory of nonlinear operator equations form the basis for the study.
Download or read book Review of Radio Science written by and published by . This book was released on 1984 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 916 pages. Available in PDF, EPUB and Kindle. Book excerpt:
