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 Finite Element Methods for Eigenvalue Problems written by Jiguang Sun and published by CRC Press. This book was released on 2016-08-19 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers finite element methods for several typical eigenvalues that arise from science and engineering. Both theory and implementation are covered in depth at the graduate level. The background for typical eigenvalue problems is included along with functional analysis tools, finite element discretization methods, convergence analysis, techniques for matrix evaluation problems, and computer implementation. The book also presents new methods, such as the discontinuous Galerkin method, and new problems, such as the transmission eigenvalue problem.
Download or read book Integral Methods in Science and Engineering Volume 1 written by Christian Constanda and published by Birkhäuser. This book was released on 2017-09-08 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume contains a collection of articles on the most recent advances in integral methods. The first of two volumes, this work focuses on the construction of theoretical integral methods. Written by internationally recognized researchers, the chapters in this book are based on talks given at the Fourteenth International Conference on Integral Methods in Science and Engineering, held July 25-29, 2016, in Padova, Italy. A broad range of topics is addressed, such as:• Integral equations• Homogenization• Duality methods• Optimal design• Conformal techniques This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines, and to other professionals who use integration as an essential tool in their work.
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 The Linear Sampling Method in Inverse Electromagnetic Scattering written by Fioralba Cakoni and published by SIAM. This book was released on 2011-01-01 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advanced Topics In Scattering Theory And Biomedical Engineering Proceedings Of The 9th International Workshop On Mathematical Methods In Scattering Theory And Biomedical Engineering written by Dimitrios I Fotiadis and published by World Scientific. This book was released on 2010-08-26 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of proceedings consists of the papers presented during the 9th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Engineering, held in Patras, Greece, on 9-11 October 2009.The book contains papers on scattering theory and biomedical engineering — two rapidly evolving fields which have a considerable impact on today's research. All the papers are state-of-the-art, have been carefully reviewed before publication and the authors are well-known in the scientific community. In addition, some papers focus more on applied mathematics, which provides a solid ground for development and innovative research in scattering and biomedical engineering.
Download or read book Advanced Topics in Scattering and Biomedical Engineering written by A. Charalambopoulos and published by World Scientific. This book was released on 2008 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of proceedings consists of the papers presented during the 8th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Engineering, held in Lefkada, Greece, on 27-29 September 2007.The book contains papers on scattering theory and biomedical engineering ? two rapidly evolving fields which have a considerable impact on today's research. All the papers are state-of-the-art, have been carefully reviewed before publication and the authors are well-known in the scientific community. In addition, some papers focus more on applied mathematics, which is the solid ground for development and innovative research in scattering and biomedical engineering.
Download or read book Inverse Acoustic and Electromagnetic Scattering Theory written by David Colton and published by Springer Science & Business Media. This book was released on 2012-10-26 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Maxwell s Equations written by Ulrich Langer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-07-08 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects longer articles on the analysis and numerics of Maxwell’s equations. The topics include functional analytic and Hilbert space methods, compact embeddings, solution theories and asymptotics, electromagnetostatics, time-harmonic Maxwell’s equations, time-dependent Maxwell’s equations, eddy current approximations, scattering and radiation problems, inverse problems, finite element methods, boundary element methods, and isogeometric analysis.
Download or read book Shocks Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics written by Ferruccio Colombini and published by Springer. This book was released on 2017-04-25 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields.
Download or read book Quantum Computing in Solid State Systems written by Berardo Ruggiero and published by Springer Science & Business Media. This book was released on 2006-05-30 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Computation in Solid State Systems discusses experimental implementation of quantum computing for information processing devices; in particular observations of quantum behavior in several solid state systems are presented. The complementary theoretical contributions provide models of minimizing decoherence in the different systems. Most recent theoretical and experimental results on macroscopic quantum coherence of mesoscopic systems, as well as the realization of solid-state qubits and quantum gates are discussed. Particular attention is given to coherence effects in Josephson devices. Other solid state systems---including quantum dots, optical, ion, and spin devices---are also discussed.
Download or read book Spectral Geometry and Inverse Scattering Theory written by Huaian Diao and published by Springer Nature. This book was released on 2023-10-31 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse scattering problems are a vital subject for both theoretical and experimental studies and remain an active field of research in applied mathematics. This book provides a detailed presentation of typical setup of inverse scattering problems for time-harmonic acoustic, electromagnetic and elastic waves. Moreover, it provides systematical and in-depth discussion on an important class of geometrical inverse scattering problems, where the inverse problem aims at recovering the shape and location of a scatterer independent of its medium properties. Readers of this book will be exposed to a unified framework for analyzing a variety of geometrical inverse scattering problems from a spectral geometric perspective. This book contains both overviews of classical results and update-to-date information on latest developments from both a practical and theoretical point of view. It can be used as an advanced graduate textbook in universities or as a reference source for researchers in acquiring the state-of-the-art results in inverse scattering theory and their potential applications.
Download or read book Computational and Analytic Methods in Science and Engineering written by Christian Constanda and published by Springer Nature. This book was released on 2020-07-07 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume collects papers presented at a special session of the conference Computational and Mathematical Methods in Science and Engineering (CMMSE) held in Cadiz, Spain from June 30 - July 6, 2019. Covering the applications of integral methods to scientific developments in a variety of fields, ranging from pure analysis to petroleum engineering, the chapters in this volume present new results in both pure and applied mathematics. Written by well-known researchers in their respective disciplines, each chapter shares a common methodology based on a combination of analytic and computational tools. This approach makes the collection a valuable, multidisciplinary reference on how mathematics can be applied to various real-world processes and phenomena. Computational and Analytic Methods in Science and Engineering will be ideal for applied mathematicians, physicists, and research engineers.
Download or read book Inverse Scattering Theory and Transmission Eigenvalues written by Fioralba Cakoni and published by . This book was released on 2022-12-31 with total page 0 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 Issues in Applied Computing 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Applied Computing / 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Computer-Assisted Tomography. The editors have built Issues in Applied Computing: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Computer-Assisted Tomography in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Applied Computing: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Download or read book Issues in Mathematical Theory and Modeling 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Mathematical Theory and Modeling / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Mathematical Theory and Modeling. The editors have built Issues in Mathematical Theory and Modeling: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Mathematical Theory and Modeling in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Mathematical Theory and Modeling: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Download or read book Spectral Theory of Localized Resonances and Applications written by Youjun Deng and published by Springer Nature. This book was released on with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt:
