• Science

Computational Methods for Electromagnetic Inverse Scattering


Author: Xudong Chen
Publisher: John Wiley & Sons
ISBN: 1119312019
Category: Science
Page: 328
View: 3539
A comprehensive and updated overview of the theory, algorithms and applications of for electromagnetic inverse scattering problems Offers the recent and most important advances in inverse scattering grounded in fundamental theory, algorithms and practical engineering applications Covers the latest, most relevant inverse scattering techniques like signal subspace methods, time reversal, linear sampling, qualitative methods, compressive sensing, and noniterative methods Emphasizes theory, mathematical derivation and physical insights of various inverse scattering problems Written by a leading expert in the field

    • Mathematics

Inverse Acoustic and Electromagnetic Scattering Theory


Author: David Colton,Rainer Kress
Publisher: Springer Science & Business Media
ISBN: 1461449413
Category: Mathematics
Page: 406
View: 4471
The inverse scattering problem is central to many areas of science and technology such as radar and sonar, medical imaging, geophysical exploration and nondestructive testing. This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. In this third edition, new sections have been added on the linear sampling and factorization methods for solving the inverse scattering problem as well as expanded treatments of iteration methods and uniqueness theorems for the inverse obstacle problem. These additions have in turn required an expanded presentation of both transmission eigenvalues and boundary integral equations in Sobolev spaces. As in the previous editions, emphasis has been given to simplicity over generality thus providing the reader with an accessible introduction to the field of inverse scattering theory. Review of earlier editions: “Colton and Kress have written a scholarly, state of the art account of their view of direct and inverse scattering. The book is a pleasure to read as a graduate text or to dip into at leisure. It suggests a number of open problems and will be a source of inspiration for many years to come.” SIAM Review, September 1994 “This book should be on the desk of any researcher, any student, any teacher interested in scattering theory.” Mathematical Intelligencer, June 1994

Scattering, Two-Volume Set

Scattering and Inverse Scattering in Pure and Applied Science
Author: E R Pike,Pierre Celestin Sabatier
Publisher: Academic Press
ISBN: 0126137609
Category:
Page: 1831
View: 2480
Scattering is the collision of two objects that results in a change of trajectory and energy. For example, in particle physics, such as electrons, photons, or neutrons are "scattered off" of a target specimen, resulting in a different energy and direction. In the field of electromagnetism, scattering is the random diffusion of electromagnetic radiation from air masses is an aid in the long-range sending of radio signals over geographic obstacles such as mountains. This type of scattering, applied to the field of acoustics, is the spreading of sound in many directions due to irregularities in the transmission medium. Volume I of Scattering will be devoted to basic theoretical ideas, approximation methods, numerical techniques and mathematical modeling. Volume II will be concerned with basic experimental techniques, technological practices, and comparisons with relevant theoretical work including seismology, medical applications, meteorological phenomena and astronomy. This reference will be used by researchers and graduate students in physics, applied physics, biophysics, chemical physics, medical physics, acoustics, geosciences, optics, mathematics, and engineering. This is the first encyclopedic-range work on the topic of scattering theory in quantum mechanics, elastodynamics, acoustics, and electromagnetics. It serves as a comprehensive interdisciplinary presentation of scattering and inverse scattering theory and applications in a wide range of scientific fields, with an emphasis, and details, up-to-date developments. Scattering also places an emphasis on the problems that are still in active current research. The first interdisciplinary reference source on scattering to gather all world expertise in this technique Covers the major aspects of scattering in a common language, helping to widening the knowledge of researchers across disciplines The list of editors, associate editors and contributors reads like an international Who's Who in the interdisciplinary field of scattering

    • Electromagnetic waves

The Linear Sampling Method in Inverse Electromagnetic Scattering


Author: Fioralba Cakoni,David Colton,Peter Monk
Publisher: SIAM
ISBN: 0898719402
Category: Electromagnetic waves
Page: 142
View: 5088
The linear sampling method is the oldest and most developed of the qualitative methods in inverse scattering theory. It is based on solving a linear integral equation and then using the equation's solution as an indicator function for the determination of the support of the scattering object. This book describes the linear sampling method for a variety of electromagnetic scattering problems. It presents uniqueness theorems and the derivation of various inequalities on the material properties of the scattering object from a knowledge of the far field pattern of the scattered wave.

    • Mathematics

Integral Equation Methods in Scattering Theory


Author: David Colton,Rainer Kress
Publisher: SIAM
ISBN: 1611973155
Category: Mathematics
Page: 271
View: 5439
This classic book provides a rigorous treatment of the Riesz?Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous and HÓlder continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. Readers will benefit from a full discussion of the mapping properties of scalar and vector potentials in spaces of continuous and HÓlder continuous functions, an in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves, and an introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.


    • Mathematics

Qualitative Methods in Inverse Scattering Theory

An Introduction
Author: Fioralba Cakoni,David Colton
Publisher: Springer Science & Business Media
ISBN: 3540312307
Category: Mathematics
Page: 227
View: 3717
Inverse scattering theory has been a particularly active and successful field in applied mathematics and engineering for the past twenty years. The increasing demands of imaging and target identification require new powerful and flexible techniques besides the existing weak scattering approximation or nonlinear optimization methods. One class of such methods comes under the general description of qualitative methods in inverse scattering theory. This textbook is an easily-accessible "class-tested" introduction to the field. It is accessible also to readers who are not professional mathematicians, thus making these new mathematical ideas in inverse scattering theory available to the wider scientific and engineering community.

    • Mathematics

A Qualitative Approach to Inverse Scattering Theory


Author: Fioralba Cakoni,David Colton
Publisher: Springer Science & Business Media
ISBN: 1461488273
Category: Mathematics
Page: 297
View: 842
Inverse scattering theory is an important area of applied mathematics due to its central role in such areas as medical imaging , nondestructive testing and geophysical exploration. Until recently all existing algorithms for solving inverse scattering problems were based on using either a weak scattering assumption or on the use of nonlinear optimization techniques. The limitations of these methods have led in recent years to an alternative approach to the inverse scattering problem which avoids the incorrect model assumptions inherent in the use of weak scattering approximations as well as the strong a priori information needed in order to implement nonlinear optimization techniques. These new methods come under the general title of qualitative methods in inverse scattering theory and seek to determine an approximation to the shape of the scattering object as well as estimates on its material properties without making any weak scattering assumption and using essentially no a priori information on the nature of the scattering object. This book is designed to be an introduction to this new approach in inverse scattering theory focusing on the use of sampling methods and transmission eigenvalues. In order to aid the reader coming from a discipline outside of mathematics we have included background material on functional analysis, Sobolev spaces, the theory of ill posed problems and certain topics in in the theory of entire functions of a complex variable. This book is an updated and expanded version of an earlier book by the authors published by Springer titled Qualitative Methods in Inverse Scattering Theory Review of Qualitative Methods in Inverse Scattering Theory All in all, the authors do exceptionally well in combining such a wide variety of mathematical material and in presenting it in a well-organized and easy-to-follow fashion. This text certainly complements the growing body of work in inverse scattering and should well suit both new researchers to the field as well as those who could benefit from such a nice codified collection of profitable results combined in one bound volume. SIAM Review, 2006

    • Mathematics

Finite Element Methods for Maxwell's Equations


Author: Peter Monk
Publisher: Oxford University Press
ISBN: 9780198508885
Category: Mathematics
Page: 450
View: 2033
The emphasis in on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell's equations is the main focus of the book.

    • Mathematics

Point Sources and Multipoles in Inverse Scattering Theory


Author: Roland Potthast
Publisher: CRC Press
ISBN: 1420035487
Category: Mathematics
Page: 302
View: 2582
Over the last twenty years, the growing availability of computing power has had an enormous impact on the classical fields of direct and inverse scattering. The study of inverse scattering, in particular, has developed rapidly with the ability to perform computational simulations of scattering processes and led to remarkable advances in a range of applications, from medical imaging and radar to remote sensing and seismic exploration. Point Sources and Multipoles in Inverse Scattering Theory provides a survey of recent developments in inverse acoustic and electromagnetic scattering theory. Focusing on methods developed over the last six years by Colton, Kirsch, and the author, this treatment uses point sources combined with several far-reaching techniques to obtain qualitative reconstruction methods. The author addresses questions of uniqueness, stability, and reconstructions for both two-and three-dimensional problems. With interest in extracting information about an object through scattered waves at an all-time high, Point Sources and Multipoles in Inverse Scattering Theory provides a valuable source of information from both the mathematical and applications perspectives. It offers insight into the general recovery of information from incomplete data and has direct, practical relevance to work on image reconstruction.

    • Inverse problems (Differential equations)

An Introduction to Inverse Scattering and Inverse Spectral Problems


Author: Khosrow Chadan,David Colton,William Rundell,Lassi Pãivãrinta
Publisher: SIAM
ISBN: 9780898719710
Category: Inverse problems (Differential equations)
Page: 198
View: 4879
Here is a clearly written introduction to three central areas of inverse problems: inverse problems in electromagnetic scattering theory, inverse spectral theory, and inverse problems in quantum scattering theory. Inverse problems, one of the most attractive parts of applied mathematics, attempt to obtain information about structures by nondestructive measurements. Based on a series of lectures presented by three of the authors, all experts in the field, the book provides a quick and easy way for readers to become familiar with the area through a survey of recent developments in inverse spectral and inverse scattering problems.

    • Technology & Engineering

Advanced Electromagnetics and Scattering Theory


Author: Kasra Barkeshli
Publisher: Springer
ISBN: 3319115472
Category: Technology & Engineering
Page: 359
View: 7259
This book present the lecture notes used in two courses that the late Professor Kasra Barkeshli had offered at Sharif University of Technology, namely, Advanced Electromagnetics and Scattering Theory. The prerequisite for the sequence is vector calculus and electromagnetic fields and waves. Some familiarity with Green's functions and integral equations is desirable but not necessary. The book provides a brief but concise introduction to classical topics in the field. It is divided into three parts including annexes. Part I covers principle of electromagnetic theory. The discussion starts with a review of the Maxwell's equations in differential and integral forms and basic boundary conditions. The solution of inhomogeneous wave equation and various field representations including Lorentz's potential functions and the Green's function method are discussed next. The solution of Helmholtz equation and wave harmonics follow. Next, the book presents plane wave propagation in dielectric and lossy media and various wave velocities. This part concludes with a general discussion of planar and circular waveguides. Part II presents basic concepts of electromagnetic scattering theory. After a brief discussion of radar equation and scattering cross section, the author reviews the canonical problems in scattering. These include the cylinder, the wedge and the sphere. The edge condition for the electromagnetic fields in the vicinity of geometric discontinuities are discussed. The author also presents the low frequency Rayleigh and Born approximations. The integral equation method for the formulation of scattering problems is presented next, followed by an introduction to scattering from periodic structures. Part III is devoted to numerical methods. It begins with finite-difference methods to solve elliptic equations, and introduces the finite-difference time-domain method for the solution of hyperbolic and parabolic equations. Next, the part turns to the method of moments for the solution of integral equations. This part ends with a short introduction to the finite-element method.

    • Science

A Dynamical Theory of the Electromagnetic Field


Author: James Clerk Maxwell
Publisher: Martino Fine Books
ISBN: 9781614275213
Category: Science
Page: 78
View: 9692
2013 Reprint of 1865 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. One of the unquestioned triumphs of nineteenth century physics was Maxwell's discovery of the equations for the electromagnetic field. "A Dynamical Theory of the Electromagnetic Field" is the third of James Clerk Maxwell's papers regarding electromagnetism, published in 1865. It is the paper in which the original set of four Maxwell's equations first appeared. The concept of displacement current, which he had introduced in his 1861 paper "On Physical Lines of Force," was utilized for the first time, to derive the electromagnetic wave equation.


    • Mathematics

Solitons and the Inverse Scattering Transform


Author: Mark J. Ablowitz,Harvey Segur
Publisher: SIAM
ISBN: 089871477X
Category: Mathematics
Page: 425
View: 3626
A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation.

    • Mathematics

Inside Out

Inverse Problems and Applications
Author: Gunther Uhlmann
Publisher: Cambridge University Press
ISBN: 9780521824699
Category: Mathematics
Page: 400
View: 9984
Inverse problems arise in practical situations such as medical imaging, geophysical exploration, and non-destructive evaluation where measurements made on the exterior of a body are used to determine properties of the inaccessible interior. There have been substantial developments in the mathematical theory of inverse problems, and applications have expanded greatly. In this volume, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics in modern inverse problems, such as microlocal analysis, reflection seismology, tomography, inverse scattering, and X-ray transforms. Each article covers a particular topic or topics with an emphasis on accessibility and integration with the whole volume. Thus the collection can be at the same time stimulating to researchers and accessible to graduate students.

    • Nuclear energy

INIS Atomindex

INIS Atomindeks
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Nuclear energy
Page: N.A
View: 3444

    • Science

Mathematical Foundations of Imaging, Tomography and Wavefield Inversion


Author: Anthony J. Devaney
Publisher: Cambridge University Press
ISBN: 1139510142
Category: Science
Page: N.A
View: 1848
Inverse problems are of interest and importance across many branches of physics, mathematics, engineering and medical imaging. In this text, the foundations of imaging and wavefield inversion are presented in a clear and systematic way. The necessary theory is gradually developed throughout the book, progressing from simple wave equation based models to vector wave models. By combining theory with numerous MATLAB based examples, the author promotes a complete understanding of the material and establishes a basis for real world applications. Key topics of discussion include the derivation of solutions to the inhomogeneous and homogeneous Helmholtz equations using Green function techniques; the propagation and scattering of waves in homogeneous and inhomogeneous backgrounds; and the concept of field time reversal. Bridging the gap between mathematics and physics, this multidisciplinary book will appeal to graduate students and researchers alike. Additional resources including MATLAB codes and solutions are available online at www.cambridge.org/9780521119740.

    • Mathematics

Analytical and Computational Methods in Scattering and Applied Mathematics


Author: Fadil Santosa,Ivar Stakgold
Publisher: CRC Press
ISBN: 9781420035971
Category: Mathematics
Page: 288
View: 6376
Professor Ralph Kleinman was director of the Center for the Mathematics of Waves and held the UNIDEL Professorship of the University of Delaware. Before his death in 1998, he made major scientific contributions in the areas of electromagnetic scattering, wave propagation, and inverse problems. He was instrumental in bringing together the mathematical and engineering communities working in these fields, and actively collaborated with a number of colleagues from both communities. It was in Professor Kleinman's memory that leading researchers in the fields of wave propagation, scattering, and applied mathematics gathered for an international conference at the University of Delaware in November 1998. This Research Note comprises papers on these topics presented at the conference along with other contributions by Ralph's colleagues. The papers consist of authoritative overviews by experts in their fields and new results from leading researchers. With many of the contributions multidisciplinary in nature and presentation of recent advances, Analytical and Computational Methods in Scattering and Applied Mathematics will prove of interest to engineers working in electromagnetics and wave propagation and to applied mathematicians working in partial differential equations and inverse problems