Wave Scattering By Small Bodies Of Arbitrary Shapes

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Wave Scattering By Small Bodies Of Arbitrary Shapes

Author : Alexander G Ramm
Publisher : World Scientific
ISBN 13 : 981448086X
Total Pages : 313 pages
Book Rating : 4.8/5 (144 download)

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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 2005-05-24 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.

Wave Scattering By Small Bodies: Creating Materials With A Desired Refraction Coefficient And Other Applications

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Author : Alexander G Ramm
Publisher : World Scientific
ISBN 13 : 9811276501
Total Pages : 291 pages
Book Rating : 4.8/5 (112 download)

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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.

Iterative Methods for Calculating Static Fields and Wave Scattering by Small Bodies

Author : Alexander G. Ramm
Publisher : Springer Science & Business Media
ISBN 13 : 1461257158
Total Pages : 131 pages
Book Rating : 4.4/5 (612 download)

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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.

Mathematical Analysis and Applications

Author : Michael Ruzhansky
Publisher : John Wiley & Sons
ISBN 13 : 1119414334
Total Pages : 1021 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Mathematical Analysis and Applications by : Michael Ruzhansky

Download or read book Mathematical Analysis and Applications written by Michael Ruzhansky and published by John Wiley & Sons. This book was released on 2018-04-11 with total page 1021 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

Handbook of Applications of Chaos Theory

Author : Christos H. Skiadas
Publisher : CRC Press
ISBN 13 : 1466590440
Total Pages : 934 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Handbook of Applications of Chaos Theory by : Christos H. Skiadas

Download or read book Handbook of Applications of Chaos Theory written by Christos H. Skiadas and published by CRC Press. This book was released on 2017-12-19 with total page 934 pages. Available in PDF, EPUB and Kindle. Book excerpt: In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors from around the world show how chaos theory is used to model unexplored cases and stimulate new applications. Accessible to scientists, engineers, and practitioners in a variety of fields, the book discusses the intermittency route to chaos, evolutionary dynamics and deterministic chaos, and the transition to phase synchronization chaos. It presents important contributions on strange attractors, self-exciting and hidden attractors, stability theory, Lyapunov exponents, and chaotic analysis. It explores the state of the art of chaos in plasma physics, plasma harmonics, and overtone coupling. It also describes flows and turbulence, chaotic interference versus decoherence, and an application of microwave networks to the simulation of quantum graphs. The book proceeds to give a detailed presentation of the chaotic, rogue, and noisy optical dissipative solitons; parhelic-like circle and chaotic light scattering; and interesting forms of the hyperbolic prism, the Poincaré disc, and foams. It also covers numerous application areas, from the analysis of blood pressure data and clinical digital pathology to chaotic pattern recognition to economics to musical arts and research.

Inverse Problems

Author : Alexander G. Ramm
Publisher : Springer Science & Business Media
ISBN 13 : 0387232184
Total Pages : 453 pages
Book Rating : 4.3/5 (872 download)

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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.

Theory and Applications of Some New Classes of Integral Equations

Author : Alexander G. Ramm
Publisher : Springer Science & Business Media
ISBN 13 : 1461381126
Total Pages : 353 pages
Book Rating : 4.4/5 (613 download)

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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.

Scattering By Obstacles And Potentials

Author : Alexander G Ramm
Publisher : World Scientific
ISBN 13 : 9813220988
Total Pages : 621 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Scattering By Obstacles And Potentials by : Alexander G Ramm

Download or read book Scattering By Obstacles And Potentials written by Alexander G Ramm and published by World Scientific. This book was released on 2017-11-23 with total page 621 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.

Chaos Theory

Author : Christos H. Skiadas
Publisher : World Scientific
ISBN 13 : 9814350338
Total Pages : 467 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Chaos Theory by : Christos H. Skiadas

Download or read book Chaos Theory written by Christos H. Skiadas and published by World Scientific. This book was released on 2011 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: The work done in chaotic modeling and simulation during the last decades has changed our views of the world around us and has introduced new scientific tools, methods and techniques. Advanced topics of these achievements are included in this volume on Chaos Theory which focuses on Chaotic Modeling, Simulation and Applications of the nonlinear phenomena. This volume includes the best papers presented in the 3rd International Conference on CHAOS. This interdisciplinary conference attracted people from many scientific fields dealing with chaos, nonlinear dynamics, fractals and the works presented and the papers included here are of particular interest that could provide a broad understanding of chaos in its various forms. The chapters relate to many fields of chaos including Dynamical and Nonlinear Systems, Attractors and Fractals. Hydro-Fluid Dynamics and Mechanics, Chaos in Meteorology and Cosmology, Chaos in Biology and Genetics, Chaotic Control, Chaos in Economy and Markets, and Computer Composition and Chaotic Simulations, including related applications, are presented.

Imaging, Multi-scale and High Contrast Partial Differential Equations

Author : Habib Ammari
Publisher : American Mathematical Soc.
ISBN 13 : 1470419238
Total Pages : 160 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Imaging, Multi-scale and High Contrast Partial Differential Equations by : Habib Ammari

Download or read book Imaging, Multi-scale and High Contrast Partial Differential Equations written by Habib Ammari and published by American Mathematical Soc.. This book was released on 2016-03-23 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Seoul ICM 2014 Satellite Conference on Imaging, Multi-scale and High-Contrast PDEs, held from August 7-9, 2014, in Daejeon, Korea. The mathematical analysis of partial differential equations modelling materials, or tissues, presenting multiple scales has been a very active area of research. The study of the corresponding imaging or reconstruction problem is a more recent area. If the material parameters of the partial differential equation present high contrast ratio, then the solution to the PDE becomes particularly challenging to analyze and compute. On the other hand, imaging in highly heterogeneous media poses significant challenges to the mathematical community. The focus of this volume is on recent progress towards complete understanding of the direct problem with high contrast or high frequencies, and unified approaches to the inverse and imaging problems for both small and large contrast or frequencies. Of particular importance in imaging are shape representation techniques and regularization approaches. Special attention is devoted to new models and problems coming from physics leading to innovative imaging and signal processing methods.

Chaos Theory

Author : Mykhaylo Andriychuk
Publisher : BoD – Books on Demand
ISBN 13 : 1837681228
Total Pages : 92 pages
Book Rating : 4.8/5 (376 download)

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Book Synopsis Chaos Theory by : Mykhaylo Andriychuk

Download or read book Chaos Theory written by Mykhaylo Andriychuk and published by BoD – Books on Demand. This book was released on 2024-05-22 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos Theory – Recent Advances, New Perspectives and Applications provides a comprehensive overview of chaos theory. It includes five chapters that discuss the history and development of chaos theory, the effectiveness of a chaos auto-associated model based on the Chebyshev-type activation function, neurite morphology, chemical self-replication, and the use of chaotic small particles to create materials with specific refractive index and magnetic permeability.

Antenna Synthesis through the Characteristics of Desired Amplitude

Author : Mykhaylo I. Andriychuk
Publisher : Cambridge Scholars Publishing
ISBN 13 : 1527539822
Total Pages : 166 pages
Book Rating : 4.5/5 (275 download)

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Book Synopsis Antenna Synthesis through the Characteristics of Desired Amplitude by : Mykhaylo I. Andriychuk

Download or read book Antenna Synthesis through the Characteristics of Desired Amplitude written by Mykhaylo I. Andriychuk and published by Cambridge Scholars Publishing. This book was released on 2019-09-12 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the synthesis problems that arise in the theory and design of radiating systems (antennas). The characteristics of desired amplitude are data placed into a synthesis problem. A synthesis problem belongs to a class of inverse problems and its aim is to determine a distribution of current or fields in an antenna, which produces the amplitude radiation characteristic as close as possible to the desired one. Freedom of choice of phase distribution of the desired radiation pattern (RP) is used as an additional possibility of better approximation to such RPs. This book studies various different types of antennas and arrays as the radiation systems under consideration. A special class of problems related to acoustic and electromagnetic scattering on a set of bodies (particles) of small size is also discussed, while the constructive procedures of creating inhomogeneous materials with specific properties are proposed.

Numerical Simulations of Physical and Engineering Processes

Author : Jan Awrejcewicz
Publisher : BoD – Books on Demand
ISBN 13 : 9533076208
Total Pages : 616 pages
Book Rating : 4.5/5 (33 download)

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Book Synopsis Numerical Simulations of Physical and Engineering Processes by : Jan Awrejcewicz

Download or read book Numerical Simulations of Physical and Engineering Processes written by Jan Awrejcewicz and published by BoD – Books on Demand. This book was released on 2011-09-26 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Simulations of Physical and Engineering Process is an edited book divided into two parts. Part I devoted to Physical Processes contains 14 chapters, whereas Part II titled Engineering Processes has 13 contributions. The book handles the recent research devoted to numerical simulations of physical and engineering systems. It can be treated as a bridge linking various numerical approaches of two closely inter-related branches of science, i.e. physics and engineering. Since the numerical simulations play a key role in both theoretical and application oriented research, professional reference books are highly needed by pure research scientists, applied mathematicians, engineers as well post-graduate students. In other words, it is expected that the book will serve as an effective tool in training the mentioned groups of researchers and beyond.

Scattering by Obstacles

Author : Alexander G. Ramm
Publisher : Springer Science & Business Media
ISBN 13 : 9400945442
Total Pages : 439 pages
Book Rating : 4.4/5 (9 download)

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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.

Encyclopaedia of Mathematics, Supplement III

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 0306483734
Total Pages : 564 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Encyclopaedia of Mathematics, Supplement III by : Michiel Hazewinkel

Download or read book Encyclopaedia of Mathematics, Supplement III written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2007-11-23 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Creating Materials with a Desired Refraction Coefficient

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Author : Alexander G. Ramm
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1681747111
Total Pages : 86 pages
Book Rating : 4.6/5 (817 download)

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Book Synopsis Creating Materials with a Desired Refraction Coefficient by : Alexander G. Ramm

Download or read book Creating Materials with a Desired Refraction Coefficient written by Alexander G. Ramm and published by Morgan & Claypool Publishers. This book was released on 2017-12-20 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: Creating Materials with a Desired Refraction Coefficient' provides a recipe for creating materials with a desired refraction coefficient, and the many-body wave scattering problem for many small impedance bodies is solved. The physical assumptions make the multiple scattering effects essential. On the basis of this theory, a recipe for creating materials with a desired refraction coefficient is given. Technological problems are formulated which, when solved, make the theory practically applicable. The Importance of a problem of producing a small particle with a desired boundary impedance is emphasized, and inverse scattering with non-over-determined scattering data is considered.

Analysis of the Navier-Stokes Problem

Author : Alexander G. Ramm
Publisher : Springer Nature
ISBN 13 : 3031307232
Total Pages : 91 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Analysis of the Navier-Stokes Problem by : Alexander G. Ramm

Download or read book Analysis of the Navier-Stokes Problem written by Alexander G. Ramm and published by Springer Nature. This book was released on 2023-06-24 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book revises and expands upon the prior edition, The Navier-Stokes Problem. The focus of this book is to provide a mathematical analysis of the Navier-Stokes Problem (NSP) in R^3 without boundaries. Before delving into analysis, the author begins by explaining the background and history of the Navier-Stokes Problem. This edition includes new analysis and an a priori estimate of the solution. The estimate proves the contradictory nature of the Navier-Stokes Problem. The author reaches the conclusion that the solution to the NSP with smooth and rapidly decaying data cannot exist for all positive times. By proving the NSP paradox, this book provides a solution to the millennium problem concerning the Navier-Stokes Equations and shows that they are physically and mathematically contradictive.