Download or read book Recent development on the time dependent approach to the three dimensional inverse scattering problem written by Gustavo Perla Menzala and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse Scattering Theory and Transmission Eigenvalues written by Fioralba Cakoni and published by SIAM. This book was released on 2022-12-07 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers—a subset of transmission eigenvalues—using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles. This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.
Download or read book An Introduction to Inverse Scattering and Inverse Spectral Problems written by Khosrow Chadan and published by SIAM. This book was released on 1997-01-01 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book THREE DIMENSIONAL INVERSE SCATTERING PROBLEM written by IRVIN W. KAY and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Transmutation Scattering Theory and Special Functions written by R. Carroll and published by Elsevier. This book was released on 2011-08-18 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transmutation, Scattering Theory and Special Functions
Download or read book Inverse Scattering Theory and Transmission Eigenvalues written by Fioralba Cakoni and published by SIAM. This book was released on 2016-10-28 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse scattering theory is a major theme of applied mathematics, and it has applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting particular problems in the development of efficient inversion algorithms. Although linearized models continue to play an important role in many applications, an increased need to focus on problems in which multiple scattering effects cannot be ignored has led to a central role for nonlinearity, and the possibility of collecting large amounts of data over limited regions of space means that the ill-posed nature of the inverse scattering problem has become a problem of central importance. Initial efforts to address the nonlinear and the ill-posed nature of the inverse scattering problem focused on nonlinear optimization methods. While efficient in many situations, strong a priori information is necessary for their implementation. This problem led to a qualitative approach to inverse scattering theory in which the amount of a priori information is drastically reduced, although at the expense of only obtaining limited information about the values of the constitutive parameters. This qualitative approach (the linear sampling method, the factorization method, the theory of transmission eigenvalues, etc.) is the theme of Inverse Scattering Theory and Transmission Eigenvalues. The authors begin with a basic introduction to the theory, then proceed to more recent developments, including a detailed discussion of the transmission eigenvalue problem; present the new generalized linear sampling method in addition to the well-known linear sampling and factorization methods; and in order to achieve clarification of presentation, focus on the inverse scattering problem for scalar homogeneous media.
Download or read book The Three Dimensional Inverse Scattering Problem Classic Reprint written by Irvin W. Kay and published by Forgotten Books. This book was released on 2018-03-14 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Three-Dimensional Inverse Scattering Problem The purpose of this paper is to put together in a concrete form the mathematical theory of an inverse scattering problem which was originally formulated in quantum mechanical terms but which is related to the problem of determining the variation of electron density in an ionized gas such as the earth's ionosphere by means of radio sounding experiments. The theory described here was developed by H. E. Moses and the present writer and was originally presented. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book Inverse Problems in Scattering written by G.M.L. Gladwell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse Problems in Scattering exposes some of the mathematics which has been developed in attempts to solve the one-dimensional inverse scattering problem. Layered media are treated in Chapters 1--6 and quantum mechanical models in Chapters 7--10. Thus, Chapters 2 and 6 show the connections between matrix theory, Schur's lemma in complex analysis, the Levinson--Durbin algorithm, filter theory, moment problems and orthogonal polynomials. The chapters devoted to the simplest inverse scattering problems in quantum mechanics show how the Gel'fand--Levitan and Marchenko equations arose. The introduction to this problem is an excursion through the inverse problem related to a finite difference version of Schrödinger's equation. One of the basic problems in inverse quantum scattering is to determine what conditions must be imposed on the scattering data to ensure that they correspond to a regular potential, which involves Lebesque integrable functions, which are introduced in Chapter 9.
Download or read book One dimensional Inverse Scattering written by Panayiotis Vassilios Frangos and published by . This book was released on 1986 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Point Sources and Multipoles in Inverse Scattering Theory written by Roland Potthast and published by CRC Press. This book was released on 2001-05-30 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book The Three dimensional Inverse Scattering Problem written by Irvin W. Kay and published by . This book was released on 1962 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1976 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Japanese Science and Technology 1983 1984 written by United States. National Aeronautics and Space Administration. Scientific and Technical Information Branch and published by . This book was released on 1985 with total page 1080 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Energy Research Abstracts written by and published by . This book was released on 1992-10 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Direct Methods for Inverse Scattering with Time Dependent and Reduced Data written by Jacob D. Rezac and published by . This book was released on 2017 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is focused on the motion of acoustic waves through penetrable media, and the use of such waves to reconstruct material properties of the fluid through which the waves are moving. The reconstruction methods developed in this thesis fall under the category of qualitative inversion methods and, as such, are fast and mathematically justified. Unlike in typical qualitative methods, however, these new methods require only small amounts of scattered field data to be collected. In particular, we demonstrate that with both far field time harmonic data and near field time dependent data, the location of weakly scattering point obstacles can be reconstructed with reduced data collection requirements compared to typical qualitative schemes. We give full mathematical justification for the time harmonic method and partial justification for the time dependent method. We also analyze the transmission eigenvalue problem for weakly scattering media, proving that, under this assumption, transmission eigenvalues are discrete and can sometimes have complex part which grows without bound. Finally, we introduce a fast method for simulating time harmonic and time dependent acoustic wave scattering and apply this method to optimization schemes for reconstructing penetrable media based on scattered field data.
Download or read book Nonlinear Topics in Ocean Physics written by A.R. Osborne and published by Elsevier. This book was released on 1991-07-04 with total page 1032 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main fields presented at this school were mesoscale and large scale flows, and nonlinear wave dynamics. The resulting proceedings present the latest developments in these fields.
