› › Time And Frequency Domain Scattering For The One Dimensional Wave Equation

Time-Domain Scattering

Author : P. A. Martin

Publisher : Cambridge University Press

Page : pages

File Size : 46,97 MB

Release : 2021-06-24

Category : Mathematics

ISBN : 1108880746

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Book Description

The wave equation, a classical partial differential equation, has been studied and applied since the eighteenth century. Solving it in the presence of an obstacle, the scatterer, can be achieved using a variety of techniques and has a multitude of applications. This book explains clearly the fundamental ideas of time-domain scattering, including in-depth discussions of separation of variables and integral equations. The author covers both theoretical and computational aspects, and describes applications coming from acoustics (sound waves), elastodynamics (waves in solids), electromagnetics (Maxwell's equations) and hydrodynamics (water waves). The detailed bibliography of papers and books from the last 100 years cement the position of this work as an essential reference on the topic for applied mathematicians, physicists and engineers.



Inverse Problems in Quantum Scattering Theory

Author : Khosrow Chadan

Publisher : Springer Science & Business Media

Page : 526 pages

File Size : 42,25 MB

Release : 2012-12-06

Category : Science

ISBN : 3642833179

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Book Description

The normal business of physicists may be schematically thought of as predic ting the motions of particles on the basis of known forces, or the propagation of radiation on the basis of a known constitution of matter. The inverse problem is to conclude what the forces or constitutions are on the basis of the observed motion. A large part of our sensory contact with the world around us depends on an intuitive solution of such an inverse problem: We infer the shape, size, and surface texture of external objects from their scattering and absorption of light as detected by our eyes. When we use scattering experiments to learn the size or shape of particles, or the forces they exert upon each other, the nature of the problem is similar, if more refined. The kinematics, the equations of motion, are usually assumed to be known. It is the forces that are sought, and how they vary from point to point. As with so many other physical ideas, the first one we know of to have touched upon the kind of inverse problem discussed in this book was Lord Rayleigh (1877). In the course of describing the vibrations of strings of variable density he briefly discusses the possibility of inferring the density distribution from the frequencies of vibration. This passage may be regarded as a precursor of the mathematical study of the inverse spectral problem some seventy years later.



Seismic Signatures and Analysis of Reflection Data in Anisotropic Media

Author : I. Tsvankin

Publisher : Elsevier

Page : 472 pages

File Size : 19,3 MB

Release : 2005-06-13

Category : Science

ISBN : 9780080446189

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Book Description

Following the breakthrough in the last decade in identifying the key parameters for time and depth imaging in anisotropic media and developing practical methodologies for estimating them from seismic data, Seismic Signatures and Analysis of Reflection Data in Anisotropic Media primarily focuses on the far reaching exploration benefits of anisotropic processing. This volume provides the first comprehensive description of reflection seismic signatures and processing methods in anisotropic media. It identifies the key parameters for time and depth imaging in transversely isotropic media and describes practical methodologies for estimating them from seismic data. Also, it contains a thorough discussion of the important issues of uniqueness and stability of seismic velocity analysis in the presence of anisotropy. The book contains a complete description of anisotropic imaging methods, from the theoretical background to algorithms to implementation issues. Numerous applications to synthetic and field data illustrate the improvements achieved by the anisotropic processing and the possibility of using the estimated anisotropic parameters in lithology discrimination. Focuses on the far reaching exploration benefits of anisotropic processing First comprehensive description of reflection seismic signatures and processing methods in anisotropic media



Electromagnetic Modelling and Measurements for Analysis and Synthesis Problems

Author : B. de Neumann

Publisher : Springer Science & Business Media

Page : 457 pages

File Size : 43,57 MB

Release : 2012-12-06

Category : Technology & Engineering

ISBN : 9401132321

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Book Description

In this volume is presented the proceedings of a NATO Advanced Study Institute (ASI) on the theme of Electromagnetic Modelling and Measurements for Analysis and Synthesis Problems. The ASI was held at 11 Ciocco, Castelvecchio Pascoli, Tuscany, Italy, August 10th - 21st, 1987. It has been my good fortune to act as co-director of two of Jozef's previous ASIs, and so I am well acquainted with the JKS format for ASIs. As participants will realise, I did not attend this ASI, and so I only have a partial appreciation of the programme. In particular it has not been possible to include transcripts of any panel discussions which may have taken place. Readers may recall that such transcripts have formed a most interesting and useful part of previous ASI proceedings edited by Jozef Skwirzynski, and helped to convey the spirit of the meetings. Unfortunately it has proved impossible to locate the tapes, despite the best efforts of Jozef's assistant, Barry Stuart. A further dificulty has arisen through the untimely death of Jozef's former deputy and colleague at GEC Research, Ed Pacello, who assisted Jozef with the organisation of the precursor of this ASI. The following is taken from original material relating to the aims of the Advanced Study Institute: "PURPOSE OF THE INSTITUTE This Institute is concerned with computer modelling and with experimental measurements as two complementary tools for both analysis and synthesis of electromagnetics (EM), infra-red (IR) and optical problems.



Mathematical Foundations of Imaging, Tomography and Wavefield Inversion

Author : Anthony J. Devaney

Publisher : Cambridge University Press

Page : 537 pages

File Size : 37,78 MB

Release : 2012-06-21

Category : Science

ISBN : 1139510142

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Book Description

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.



Parity-time Symmetry and Its Applications

Author : Demetrios Christodoulides

Publisher : Springer

Page : 585 pages

File Size : 39,5 MB

Release : 2018-11-28

Category : Science

ISBN : 9811312478

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Book Description

This book offers a comprehensive review of the state-of-the-art theoretical and experimental advances in linear and nonlinear parity-time-symmetric systems in various physical disciplines, and surveys the emerging applications of parity-time (PT) symmetry. PT symmetry originates from quantum mechanics, where if the Schrodinger operator satisfies the PT symmetry, then its spectrum can be all real. This concept was later introduced into optics, Bose-Einstein condensates, metamaterials, electric circuits, acoustics, mechanical systems and many other fields, where a judicious balancing of gain and loss constitutes a PT-symmetric system. Even though these systems are dissipative, they exhibit many signature properties of conservative systems, which make them mathematically and physically intriguing. Important PT-symmetry applications have also emerged. This book describes the latest advances of PT symmetry in a wide range of physical areas, with contributions from the leading experts. It is intended for researchers and graduate students to enter this research frontier, or use it as a reference book.



The Finite Element Method in Electromagnetics

Author : Jian-Ming Jin

Publisher : John Wiley & Sons

Page : 728 pages

File Size : 48,77 MB

Release : 2015-02-18

Category : Science

ISBN : 1118842022

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Book Description

A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The Finite Element Method in Electromagnetics, Third Edition explains the method’s processes and techniques in careful, meticulous prose and covers not only essential finite element method theory, but also its latest developments and applications—giving engineers a methodical way to quickly master this very powerful numerical technique for solving practical, often complicated, electromagnetic problems. Featuring over thirty percent new material, the third edition of this essential and comprehensive text now includes: A wider range of applications, including antennas, phased arrays, electric machines, high-frequency circuits, and crystal photonics The finite element analysis of wave propagation, scattering, and radiation in periodic structures The time-domain finite element method for analysis of wideband antennas and transient electromagnetic phenomena Novel domain decomposition techniques for parallel computation and efficient simulation of large-scale problems, such as phased-array antennas and photonic crystals Along with a great many examples, The Finite Element Method in Electromagnetics is an ideal book for engineering students as well as for professionals in the field.



Energy Research Abstracts

Author :

Publisher :

Page : 596 pages

File Size : 30,60 MB

Release : 1989

Category : Power resources

ISBN :

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Book Description

Semiannual, with semiannual and annual indexes. References to all scientific and technical literature coming from DOE, its laboratories, energy centers, and contractors. Includes all works deriving from DOE, other related government-sponsored information, and foreign nonnuclear information. Arranged under 39 categories, e.g., Biomedical sciences, basic studies; Biomedical sciences, applied studies; Health and safety; and Fusion energy. Entry gives bibliographical information and abstract. Corporate, author, subject, report number indexes.



Theory and Computation of Electromagnetic Fields

Author : Jian-Ming Jin

Publisher : John Wiley & Sons

Page : 756 pages

File Size : 15,43 MB

Release : 2015-08-26

Category : Science

ISBN : 1119108098

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Book Description

Reviews the fundamental concepts behind the theory and computation of electromagnetic fields The book is divided in two parts. The first part covers both fundamental theories (such as vector analysis, Maxwell’s equations, boundary condition, and transmission line theory) and advanced topics (such as wave transformation, addition theorems, and fields in layered media) in order to benefit students at all levels. The second part of the book covers the major computational methods for numerical analysis of electromagnetic fields for engineering applications. These methods include the three fundamental approaches for numerical analysis of electromagnetic fields: the finite difference method (the finite difference time-domain method in particular), the finite element method, and the integral equation-based moment method. The second part also examines fast algorithms for solving integral equations and hybrid techniques that combine different numerical methods to seek more efficient solutions of complicated electromagnetic problems. Theory and Computation of Electromagnetic Fields, Second Edition: Provides the foundation necessary for graduate students to learn and understand more advanced topics Discusses electromagnetic analysis in rectangular, cylindrical and spherical coordinates Covers computational electromagnetics in both frequency and time domains Includes new and updated homework problems and examples Theory and Computation of Electromagnetic Fields, Second Edition is written for advanced undergraduate and graduate level electrical engineering students. This book can also be used as a reference for professional engineers interested in learning about analysis and computation skills.



Electromagnetic Inverse Profiling

Author : A. G. Tijhuis

Publisher : VSP

Page : 498 pages

File Size : 47,41 MB

Release : 1987-12

Category : Science

ISBN : 9789067640930

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Book Description

This monograph is concerned with the direct-scattering of electromagnetic waves by one- and two-dimensional objects, and the use of this technique in one-dimensional inverse profiling. It discusses results of research into the method of this technique and its application to specific problems. Several techniques are presented for solving transient electromagnetic direct-scattering problems. These problems are solved indirectly, via a Fourier or Laplace transformation to the real- or complex-frequency domain, as well as directly in the time domain. For the one-dimensional case it is described how the special features of the respective techniques are also exploited to tackle the inverse problem of determining obstacle properties from the scattered field excited by a known incident field. The problems of both identification and of inverse profiling are addressed. For a range of specific problems representative numerical results are presented and discussed. Particular attention is devoted to the numerical implementation and to the physical interpretation of the theoretical numerical results obtained. With respect to inverse-scattering the emphasis is on the band-limiting effects that may arise due to approximation errors in the various inversion schemes employed.