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.
Download or read book Methods for calculating static fields and wave scattering small bodies written by and published by . This book was released on 1982 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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 2005-05-24 with total page 313 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.
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.
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:
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.
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.
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.
Download or read book Revue Roumaine de Math matiques Pures Et Appliqu es written by and published by . This book was released on 1984 with total page 980 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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 Inverse Methods in Electromagnetic Imaging written by Wolfgang M. Boerner and published by . This book was released on 1985 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
Download or read book Mathematical Sciences Research Hot line written by and published by . This book was released on 1997 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The American Mathematical Monthly written by and published by . This book was released on 1983 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt:
