An Introduction to Linear and Nonlinear Scattering Theory PDF Download
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Author: G F Roach
Publisher: Routledge
ISBN: 135146714X
Category : Mathematics
Languages : en
Pages : 268
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Book Description
This monograph has two main purposes, first to act as a companion volume to more advanced texts by gathering together the principal mathematical topics commonly used in developing scattering theories and, in so doing, provide a reasonable, self-contained introduction to linear and nonlinear scattering theory for those who might wish to begin working in the area. Secondly, to indicate how these various aspects might be applied to problems in mathematical physics and the applied sciences. Of particular interest will be the influence of boundary conditions.
Author: G F Roach
Publisher: Routledge
ISBN: 135146714X
Category : Mathematics
Languages : en
Pages : 268
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Book Description
This monograph has two main purposes, first to act as a companion volume to more advanced texts by gathering together the principal mathematical topics commonly used in developing scattering theories and, in so doing, provide a reasonable, self-contained introduction to linear and nonlinear scattering theory for those who might wish to begin working in the area. Secondly, to indicate how these various aspects might be applied to problems in mathematical physics and the applied sciences. Of particular interest will be the influence of boundary conditions.
Author: Gary Roach
Publisher: Springer Science & Business Media
ISBN: 1846288525
Category : Science
Languages : en
Pages : 323
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Book Description
This is an introduction to scattering phenomena and a guide to the technical requirements for investigating wave scattering problems. It reviews the principal mathematical topics required for approaching wave propagation and scattering problems, and shows how to develop the required solutions. The emphasis is on concepts and results rather than on the fine detail of proof. Each chapter ends with a bibliography pointing to more detailed proofs.
Author: George Dassios
Publisher: World Scientific
ISBN: 9789810243913
Category : Science
Languages : en
Pages : 328
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Book Description
This book addresses issues of scattering theory and biomedical engineering, as well as methodological approaches and tools from related scientific areas such as applied mathematics, mechanics, numerical analysis, and signal and image processing.
Author: Hassan Emamirad
Publisher: Springer Nature
ISBN: 9811623732
Category : Science
Languages : en
Pages : 179
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Book Description
The scattering theory for transport phenomena was initiated by P. Lax and R. Phillips in 1967. Since then, great progress has been made in the field and the work has been ongoing for more than half a century. This book shows part of that progress. The book is divided into 7 chapters, the first of which deals with preliminaries of the theory of semigroups and C*-algebra, different types of semigroups, Schatten–von Neuman classes of operators, and facts about ultraweak operator topology, with examples using wavelet theory. Chapter 2 goes into abstract scattering theory in a general Banach space. The wave and scattering operators and their basic properties are defined. Some abstract methods such as smooth perturbation and the limiting absorption principle are also presented. Chapter 3 is devoted to the transport or linearized Boltzmann equation, and in Chapter 4 the Lax and Phillips formalism is introduced in scattering theory for the transport equation. In their seminal book, Lax and Phillips introduced the incoming and outgoing subspaces, which verify their representation theorem for a dissipative hyperbolic system initially and also matches for the transport problem. By means of these subspaces, the Lax and Phillips semigroup is defined and it is proved that this semigroup is eventually compact, hence hyperbolic. Balanced equations give rise to two transport equations, one of which can satisfy an advection equation and one of which will be nonautonomous. For generating, the Howland semigroup and Howland’s formalism must be used, as shown in Chapter 5. Chapter 6 is the highlight of the book, in which it is explained how the scattering operator for the transport problem by using the albedo operator can lead to recovery of the functionality of computerized tomography in medical science. The final chapter introduces the Wigner function, which connects the Schrödinger equation to statistical physics and the Husimi distribution function. Here, the relationship between the Wigner function and the quantum dynamical semigroup (QDS) can be seen.
Author: Govind P. Agrawal
Publisher: Academic Press
ISBN: 9780123695161
Category : Science
Languages : en
Pages : 560
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Book Description
Since the 3rd edition appeared, a fast evolution of the field has occurred. The fourth edition of this classic work provides an up-to-date account of the nonlinear phenomena occurring inside optical fibers. The contents include such important topics as self- and cross-phase modulation, stimulated Raman and Brillouin scattering, four-wave mixing, modulation instability, and optical solitons. Many new figures have been added to help illustrate the concepts discussed in the book. New to this edition are chapters on highly nonlinear fibers and and the novel nonlinear effects that have been observed in these fibers since 2000. Such a chapter should be of interest to people in the field of new wavelengths generation, which has potential application in medical diagnosis and treatments, spectroscopy, new wavelength lasers and light sources, etc. Continues to be industry bestseller providing unique source of comprehensive coverage on the subject of nonlinear fiber optics Fourth Edition is a completely up-to-date treatment of the nonlinear phenomena occurring inside optical fibers Includes 2 NEW CHAPTERS on the properties of highly nonlinear fibers and their novel nonlinear effects
Author: Michael Reed
Publisher: Elsevier
ISBN: 0080925383
Category : Science
Languages : en
Pages : 480
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Book Description
Scattering theory is the study of an interacting system on a scale of time and/or distance which is large compared to the scale of the interaction itself. As such, it is the most effective means, sometimes the only means, to study microscopic nature. To understand the importance of scattering theory, consider the variety of ways in which it arises. First, there are various phenomena in nature (like the blue of the sky) which are the result of scattering. In order to understand the phenomenon (and to identify it as the result of scattering) one must understand the underlying dynamics and its scattering theory. Second, one often wants to use the scattering of waves or particles whose dynamics on knows to determine the structure and position of small or inaccessible objects. For example, in x-ray crystallography (which led to the discovery of DNA), tomography, and the detection of underwater objects by sonar, the underlying dynamics is well understood. What one would like to construct are correspondences that link, via the dynamics, the position, shape, and internal structure of the object to the scattering data. Ideally, the correspondence should be an explicit formula which allows one to reconstruct, at least approximately, the object from the scattering data. The main test of any proposed particle dynamics is whether one can construct for the dynamics a scattering theory that predicts the observed experimental data. Scattering theory was not always so central the physics. Even thought the Coulomb cross section could have been computed by Newton, had he bothered to ask the right question, its calculation is generally attributed to Rutherford more than two hundred years later. Of course, Rutherford's calculation was in connection with the first experiment in nuclear physics.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 930
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Book Description
Author: G.T. Herman
Publisher: Springer Science & Business Media
ISBN: 364293157X
Category : Mathematics
Languages : en
Pages : 317
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Book Description
G.T. Herman F. Natterer Universitat des Saarlandes Medical Image Processing Group Department of Computer Science Angewandte Mathematik und State University of New York at Informatik 66 Saarbrucken Buffalo Germany 4226 Ridge Lea Road Amherst, N.Y. 14226 USA In August 1978 we have attended a working conference on Computer Aided Tomography and Ultrasonics in Medicine which was held in Haifa, Israel under the auspices of the International Federation for Information Pro cessing [1]. That meeting, in common with other meetings relating to computerized tomography, concentrated on the physical, engineering and clinical aspects of the topic, with little attention paid to the under lying mathematics, and no attention paid to recent developments in ma thematics inspired by computerized tomography (although not necessarily) useful for computerized tomography). We both felt that it would be worthwhile to organize a meeting of mathematicians which would concen trate on the mathematical aspects of computerized tomography. This vol ume (and the meeting on which it is based) is the outcome of our decision in August 1978 to attempt to bring together such a meeting. In the meantime much has been published on the topic of computerized to mography.
Author: David Colton
Publisher: SIAM
ISBN: 1611973155
Category : Mathematics
Languages : en
Pages : 286
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Book Description
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 H?lder 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 H?lder 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.
Author: Govind P. Agrawal
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 504
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Book Description
This book provides an up-to-date account of current trends in nonlinear optics. It is intended for researchers already engaged in the field of nonlinear optics. It may also be used by graduate students due to its comprehensive coverage and pedagogical presentation.
