Wave Propagation in Complex Media

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Publisher : Springer Science & Business Media
ISBN 13 : 1461216788
Total Pages : 301 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Wave Propagation in Complex Media by : George Papanicolaou

Download or read book Wave Propagation in Complex Media written by George Papanicolaou and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications WAVE PROPAGATION IN COMPLEX MEDIA is based on the proceedings of two workshops: • Wavelets, multigrid and other fast algorithms (multipole, FFT) and their use in wave propagation and • Waves in random and other complex media. Both workshops were integral parts of the 1994-1995 IMA program on "Waves and Scattering." We would like to thank Gregory Beylkin, Robert Burridge, Ingrid Daubechies, Leonid Pastur, and George Papanicolaou for their excellent work as organizers of these meetings. We also take this opportunity to thank the National Science Foun dation (NSF), the Army Research Office (ARO, and the Office of Naval Research (ONR), whose financial support made these workshops possible. A vner Friedman Robert Gulliver v PREFACE During the last few years the numerical techniques for the solution of elliptic problems, in potential theory for example, have been drastically improved. Several so-called fast methods have been developed which re duce the required computing time many orders of magnitude over that of classical algorithms. The new methods include multigrid, fast Fourier transforms, multi pole methods and wavelet techniques. Wavelets have re cently been developed into a very useful tool in signal processing, the solu tion of integral equation, etc. Wavelet techniques should be quite useful in many wave propagation problems, especially in inhomogeneous and nonlin ear media where special features of the solution such as singularities might be tracked efficiently.

Waves and Imaging through Complex Media

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Publisher : Springer Science & Business Media
ISBN 13 : 9401009759
Total Pages : 452 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Waves and Imaging through Complex Media by : P. Sebbah

Download or read book Waves and Imaging through Complex Media written by P. Sebbah and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advances in wave propagation in random media are certainly consequences of new approaches to fundamental issues, as well as of a strong interest in potential applications. A collective effort has been made to present in this book the state of the art in fundamental concepts, as well as in biomedical imaging techniques. As an example, the recent introduction of wave chaos, and more specifically random matrix theory - an old tool from nuclear physics - to the study of multiple scattering, has pointed the way to a deeper understanding of wave coherence in complex media. At the same time, efficient new approaches for retrieving information from random media promise to allow wave imaging of small tumors in opaque tissues. Review chapters are written by experts in the field, with the aim of making the book accessible to the widest possible scientific audience: graduate students and research scientists in theoretical and applied physics, optics, acoustics, and biomedical physics.

Wave Propagation, Scattering And Emission In Complex Media

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Publisher : World Scientific
ISBN 13 : 9814483117
Total Pages : 476 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Wave Propagation, Scattering And Emission In Complex Media by : Ya-qiu Jin

Download or read book Wave Propagation, Scattering And Emission In Complex Media written by Ya-qiu Jin and published by World Scientific. This book was released on 2005-01-26 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains review papers presented at the International Workshop on Wave Propagation, Scattering and Emission on Theory, Experiment, Simulation and Inversion (WPSE). The papers are of high quality, covering broad areas: a new mechanism of interaction of electromagnetic waves with complex media, remote sensing information, computational electromagnetics, etc. This book summarizes the most significant progress in wave propagation, encompassing theory, experiment, simulation, and inversion. It will also serve as a good reference for scientists in future research.List of Foreign Invited Speakers: Henry Bertoni (Brooklyn Polytechnic University), Lawrence Carin (Duke U), Al Chang (NASA, Goddard), Margaret Cheney (Rensselaer Polytech Institute), Weng Chew (U of Illinois at Urbana Champaign), Shane Cloude (AEL Consultants, UK), Adrian Fung (U of Texas at Arlington), Al Gasiewski (Environmental Tech Lab, NOAA), Martti Hallikainen (Helsinki U of Technology), Akira Ishimaru (U of Washington), Magdy Iskander (U of Hawaii), J A Kong (MIT), Roger Lang (George Washington U), Alex Maradudin (U of California at Irvine), Eric Michielssen (U of Illinois at Urbana Champaign), Eni Njoku (Caltech, Jet Propulsion Lab), Carey Rappaport (Northeastern U), Marc Saillard (Institut Fresnel), Kamal Sarabandi (U of Michigan), David R Smith (U of California at San Diego), Mitsuo Tateiba (Kyushu University), George Uslenghi (U of Illinois at Chicago), and Werner Wiesbeck (Karlsruhe U).

Waves in Complex Media

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Publisher : Cambridge University Press
ISBN 13 : 1107037506
Total Pages : 713 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Waves in Complex Media by : Luca Dal Negro

Download or read book Waves in Complex Media written by Luca Dal Negro and published by Cambridge University Press. This book was released on 2022-05-19 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: An interdisciplinary introduction to the structural and scattering properties of complex photonic media, focusing on deterministic aperiodic structures and their conceptual roots in geometry and number theory. An essential tool for students at the graduate or advanced undergraduate level.

Diffuse Waves in Complex Media

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Publisher : Springer Science & Business Media
ISBN 13 : 9401145725
Total Pages : 462 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Diffuse Waves in Complex Media by : Jean-Pierre Fouque

Download or read book Diffuse Waves in Complex Media written by Jean-Pierre Fouque and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: The NATO Advanced Study Institute on Diffuse Waves in Complex Media was held at the "Centre de Physique des Houches" in France from March 17 to 27, 1998. The Schools' scientific content, wave propagation in heterogeneous me dia, has covered many areas of fundamental and applied research. On the one hand, the understanding of wave propagation has considerably improved during the last thirty years. New developments and concepts such as, speckle correlations, weak and strong localization, time reversal, near-field propagation are under active research. On the other hand, wave propagation in random media is now being investigated in many different fields such as applied mathematics, acoustics, optics, atomic physics, geo physics or medical sciences. Each community often uses its own langage to describe the same phenomena. The aim of the School was to gather worldwide specialists to illuminate various aspects of wave propagation in random media. This volume presents fourteen expository articles corresponding to courses and seminars given during the School. They are arranged as follows. The first three articles deal with the phenomena of localization of waves: B. van Tiggelen (p. 1) gives a critical review of the physics of localization, J. Lacroix (p. 61) presents the mathematical theory and A. Klein (p. 73) describes recent results for randomized periodic media.

Wave Propagation and Radiation in Gyrotropic and Anisotropic Media

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Publisher : Springer Science & Business Media
ISBN 13 : 1441960244
Total Pages : 222 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Wave Propagation and Radiation in Gyrotropic and Anisotropic Media by : Abdullah Eroglu

Download or read book Wave Propagation and Radiation in Gyrotropic and Anisotropic Media written by Abdullah Eroglu and published by Springer Science & Business Media. This book was released on 2010-09-02 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: As technology matures, communication system operation regions shift from mic- wave and millimeter ranges to sub-millimeter ranges. However, device perf- mance at very high frequencies suffers drastically from the material de?ciencies. As a result, engineers and scientists are relentlessly in search for the new types of materials, and composites which will meet the device performance requirements and not present any de?ciencies due to material electrical and magnetic properties. Anisotropic and gyrotropic materials are the class of the materials which are very important in the development high performance microwave devices and new types composite layered structures. As a result, it is a need to understand the wave propagation and radiation characteristics of these materials to be able to realize them in practice. This book is intended to provide engineers and scientists the required skill set to design high frequency devices using anisotropic, and gyrotropic materials by providing them the theoretical background which is blended with the real world engineering application examples. It is the author’s hope that this book will help to ?ll the gap in the area of applied electromagnetics for the design of microwave and millimeter wave devices using new types of materials. Each chapter in the book is designed to give the theory ?rst on the subject and solidify it with application examples given in the last chapter. The application examples for the radiation problems are given at the end of Chap. 5 and Chap. 6 for anisotropic and gyrotropic materials, respectively, after the theory section.

Advances in Electromagnetics of Complex Media and Metamaterials

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Publisher : Springer Science & Business Media
ISBN 13 : 9400710674
Total Pages : 479 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Advances in Electromagnetics of Complex Media and Metamaterials by : Saïd Zouhdi

Download or read book Advances in Electromagnetics of Complex Media and Metamaterials written by Saïd Zouhdi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: The NATO Advanced Research Workshop Bianisotropics 2002 was held in th Marrakesh, Morocco, during 8-11 May 2002. This was the 9 International Conference on Electromagnetics of Complex Media, belonging to a series of meetings where the focus is on electromagnetics of chiral, bianisotropic, and other materials that may respond to electric and magnetic field excitations in special manner. The first of these meetings was held in Espoo, Finland (1993), and the following venues were Gomel, Belarus (1993), Perigueux, France (1994), State College, Pennsylvania, USA (1995), the rivers and channels between St. Petersburg and Moscow in Russia (1996), Glasgow, Scotland (1997), Brunswick, Germany (1998), and Lisbon, Portugal (2000). The present book contains full articles of several of the presentations that were given in the Marrakesh conference. In Bianisotropics 2002, 8 re view lectures, 14 invited lectures and 68 contributed talks and posters were presented. Of these presentations, after a double review process, 28 contributions have achieved their final form on the pages to follow. From the contributions ofthe meeting, also another publication is being planned: a Special Issue of the journal Electromagnetics will be devoted to complex materials. Guest editors for this issue are Keith W. Whites and Said Zouhdi. The chairmen of Bianisotropics 2002conference were Said Zouhdi (Pierre et Marie Curie University - Paris) and Mohamed Arsalane (Cadi Ayyad University - Marrakesh), who were assisted by Scientists from Moroccan Universities and the International Bianisotropics Conference Committee.

Wave Scattering in Complex Media: From Theory to Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 9401002274
Total Pages : 622 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Wave Scattering in Complex Media: From Theory to Applications by : Bart A. van Tiggelen

Download or read book Wave Scattering in Complex Media: From Theory to Applications written by Bart A. van Tiggelen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of lectures on a variety of modern subjects in wave scattering, including fundamental issues in mesoscopic physics and radiative transfer, recent hot topics such as random lasers, liquid crystals, lefthanded materials and time-reversal, as well as modern applications in imaging and communication. There is a strong emphasis on the interdisciplinary aspects of wave propagation, including light and microwaves, acoustic and elastic waves, propagating in a variety of "complex" materials (liquid crystals, media with gain, natural media, magneto-optical media, photonic and phononic materials, etc.). It addresses many different items in contemporary research: mesoscopic fluctuations, localization, radiative transfer, symmetry aspects, and time-reversal. It also discusses new (potential) applications in telecommunication, soft matter and imaging.

Imaging of Complex Media with Acoustic and Seismic Waves

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Publisher : Springer Science & Business Media
ISBN 13 : 354044680X
Total Pages : 339 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Imaging of Complex Media with Acoustic and Seismic Waves by : Mathias Fink

Download or read book Imaging of Complex Media with Acoustic and Seismic Waves written by Mathias Fink and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this interdisciplinary book, leading experts in underwater acoustics, seismology, acoustic medical imaging and non-destructive testing present basic concepts as well as the recent advances in imaging. The different subjects tackled show significant similarities.

Waves and Fields in Inhomogenous Media

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Publisher : John Wiley & Sons
ISBN 13 : 0780347498
Total Pages : 646 pages
Book Rating : 4.7/5 (83 download)

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Book Synopsis Waves and Fields in Inhomogenous Media by : Weng Cho Chew

Download or read book Waves and Fields in Inhomogenous Media written by Weng Cho Chew and published by John Wiley & Sons. This book was released on 1999-02-02 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electrical Engineering/Electromagnetics Waves and Fields in Inhomogeneous Media A Volume in the IEEE Press Series on Electromagnetic Waves Donald G. Dudley, Series Editor ".it is one of the best wave propagation treatments to appear in many years." Gerardo G. Tango, CPG, Consulting Seismologist-Acoustician, Covington, LA This comprehensive text thoroughly covers fundamental wave propagation behaviors and computational techniques for waves in inhomogeneous media. The author describes powerful and sophisticated analytic and numerical methods to solve electromagnetic problems for complex media and geometry as well. Problems are presented as realistic models of actual situations which arise in the areas of optics, radio wave propagation, geophysical prospecting, nondestructive testing, biological sensing, and remote sensing. Key topics covered include: * Analytical methods for planarly, cylindrically and spherically layered media * Transient waves, including the Cagniard-de Hoop method * Variational methods for the scalar wave equation and the electromagnetic wave equation * Mode-matching techniques for inhomogeneous media * The Dyadic Green's function and its role in simplifying problem-solving in inhomogeneous media * Integral equation formulations and inverse problems * Time domain techniques for inhomogeneous media This book will be of interest to electromagnetics and remote sensing engineers, physicists, scientists, and geophysicists. This IEEE Press reprinting of the 1990 version published by Van Nostrand Reinhold incorporates corrections and minor updating. Also in the series. Mathematical Foundations for Electromagnetic Theory by Donald G. Dudley, University of Arizona at Tucson This volume in the series lays the mathematical foundations for the study of advanced topics in electromagnetic theory. Important subjects covered include linear spaces, Green's functions, spectral expansions, electromagnetic source representations, and electromagnetic boundary value problems. 1994 Hardcover 264 pp ISBN 0-7803-1022-5 IEEE Order No. PC3715 About the Series The IEEE Press Series on Electromagnetic Waves consists of new titles as well as reprints and revisions of recognized classics that maintain long-term archival significance in electromagnetic waves and applications. Designed specifically for graduate students, practicing engineers, and researchers, this series provides affordable volumes that explore electromagnetic waves and applications beyond the undergraduate level.

The Topology of 4-Manifolds

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Publisher : Springer
ISBN 13 : 354046171X
Total Pages : 114 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis The Topology of 4-Manifolds by : Robion C. Kirby

Download or read book The Topology of 4-Manifolds written by Robion C. Kirby and published by Springer. This book was released on 2006-11-14 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the classical theorems about simply connected smooth 4-manifolds: intersection forms and homotopy type, oriented and spin bordism, the index theorem, Wall's diffeomorphisms and h-cobordism, and Rohlin's theorem. Most of the proofs are new or are returbishings of post proofs; all are geometric and make us of handlebody theory. There is a new proof of Rohlin's theorem using spin structures. There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions. The book should be useful to beginning researchers in 4-manifolds.

Ultrasonic Wave Propagation in Non Homogeneous Media

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Publisher : Springer Science & Business Media
ISBN 13 : 3540891056
Total Pages : 427 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Ultrasonic Wave Propagation in Non Homogeneous Media by : Alain Leger

Download or read book Ultrasonic Wave Propagation in Non Homogeneous Media written by Alain Leger and published by Springer Science & Business Media. This book was released on 2009-01-30 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non Destructive Testing and Non Destructive Evaluation using Ultrasounds covers an important field of applications and requires a wide range of fundamental theoretical, numerical and experimental investigations. In the present volume, the reader will find some relevant research results on wave propagation in complex materials and structures which are concerned with today’s problems on composites, bonding, guided waves, contact or damage, imaging and structural noise. The fifth meeting of the Anglo-French Research Group on "Wave propagation in non homogeneous media with a view to Non Destructive testing" was held in Anglet, France, June 2-6, 2008.

Waves in Layered Media

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Publisher : Elsevier
ISBN 13 : 0323163246
Total Pages : 574 pages
Book Rating : 4.3/5 (231 download)

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Book Synopsis Waves in Layered Media by : Leonid Brekhovskikh

Download or read book Waves in Layered Media written by Leonid Brekhovskikh and published by Elsevier. This book was released on 2012-12-02 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Waves in Layered Media focuses on the theory of the propagation of elastic and electromagnetic waves in layered media. This book presents a complete report of Soviet researches on wave propagation through layered media. Organized into six chapters, this book starts with an overview of the theory of wave reflection from layers and interfaces. This text then examines the some of the representations and methods, which are common to different branches of physics. Other chapters define the reflection reduction of optical waves as the lowering of the reflection coefficient at the air–glass boundaries by depositing thin layers of several materials on the glass. This book discusses as well the field of a concentrated source situated in a layered-inhomogeneous medium, which is one of the main problems in modern radiophysics, acoustics, and the physics of the Earth's crust. The final chapter deals with wave propagation in layered-inhomogeneous media. This book is a valuable resource for engineers, scientists, and physicists.

Waves in Layered Media

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Publisher : Elsevier
ISBN 13 : 0323161626
Total Pages : 520 pages
Book Rating : 4.3/5 (231 download)

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Book Synopsis Waves in Layered Media by : L Brekhovskikh

Download or read book Waves in Layered Media written by L Brekhovskikh and published by Elsevier. This book was released on 2012-12-02 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Waves in Layered Media discusses different theories about the relationship between waves and media. The book specifically covers several factors that can affect the behavior and formation of various kinds of waves in different types of media. Comprised of nine chapters, the book establishes the fundamentals by first tackling simplest concepts, such as the behavior plane wave and discretely layered media. The succeeding chapters cover much more complex ideas, such as the refraction and reflection of waves, spherical wave, and wave in inhomogeneous media. The book will be a great asset to researchers whose work involves acoustics, or to professionals whose line of work involves sound waves.

Metamaterials

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Publisher : BoD – Books on Demand
ISBN 13 : 9535130994
Total Pages : 294 pages
Book Rating : 4.5/5 (351 download)

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Book Synopsis Metamaterials by : Alejandro Lucas Borja

Download or read book Metamaterials written by Alejandro Lucas Borja and published by BoD – Books on Demand. This book was released on 2017-04-26 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metamaterials have become one of the most important emerging technologies in the scientific community due to its unusual electromagnetic properties. Consequently, during the last years, a huge deal of efforts has been concentrated in order to design functional components and devices based on metamaterials for many potential applications. The main objective of this book is to present in-depth analysis of the theory, properties, and realizations of novel devices that could be integrated within modern and future communication systems. The book contains 11 chapters written by acknowledged experts, researchers, academics, and microwave engineers, providing comprehensive information and covering a wide range of topics on several aspects of microwaves and optics, including polarization conversion, asymmetric transmission, transmission lines, filters, plasmonic lenses, tunable metamaterials, light manipulation, absorbers, and antennas, among others. This book is suitable for scholars from large scientific domain and therefore given to engineers, scientists, graduates, and other interested professionals as a reference on these artificial materials of tomorrow.

Electromagnetic Wave Propagation, Radiation, and Scattering

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Publisher : John Wiley & Sons
ISBN 13 : 1119079535
Total Pages : 968 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Electromagnetic Wave Propagation, Radiation, and Scattering by : Akira Ishimaru

Download or read book Electromagnetic Wave Propagation, Radiation, and Scattering written by Akira Ishimaru and published by John Wiley & Sons. This book was released on 2017-08-09 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most methodical treatments of electromagnetic wave propagation, radiation, and scattering—including new applications and ideas Presented in two parts, this book takes an analytical approach on the subject and emphasizes new ideas and applications used today. Part one covers fundamentals of electromagnetic wave propagation, radiation, and scattering. It provides ample end-of-chapter problems and offers a 90-page solution manual to help readers check and comprehend their work. The second part of the book explores up-to-date applications of electromagnetic waves—including radiometry, geophysical remote sensing and imaging, and biomedical and signal processing applications. Written by a world renowned authority in the field of electromagnetic research, this new edition of Electromagnetic Wave Propagation, Radiation, and Scattering: From Fundamentals to Applications presents detailed applications with useful appendices, including mathematical formulas, Airy function, Abel’s equation, Hilbert transform, and Riemann surfaces. The book also features newly revised material that focuses on the following topics: Statistical wave theories—which have been extensively applied to topics such as geophysical remote sensing, bio-electromagnetics, bio-optics, and bio-ultrasound imaging Integration of several distinct yet related disciplines, such as statistical wave theories, communications, signal processing, and time reversal imaging New phenomena of multiple scattering, such as coherent scattering and memory effects Multiphysics applications that combine theories for different physical phenomena, such as seismic coda waves, stochastic wave theory, heat diffusion, and temperature rise in biological and other media Metamaterials and solitons in optical fibers, nonlinear phenomena, and porous media Primarily a textbook for graduate courses in electrical engineering, Electromagnetic Wave Propagation, Radiation, and Scattering is also ideal for graduate students in bioengineering, geophysics, ocean engineering, and geophysical remote sensing. The book is also a useful reference for engineers and scientists working in fields such as geophysical remote sensing, bio–medical engineering in optics and ultrasound, and new materials and integration with signal processing.

Electromagnetics of Time Varying Complex Media

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Publisher : CRC Press
ISBN 13 : 1351834002
Total Pages : 416 pages
Book Rating : 4.3/5 (518 download)

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Book Synopsis Electromagnetics of Time Varying Complex Media by : Dikshitulu K. Kalluri

Download or read book Electromagnetics of Time Varying Complex Media written by Dikshitulu K. Kalluri and published by CRC Press. This book was released on 2018-09-03 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Completely revised and updated to reflect recent advances in the fields of materials science and electromagnetics, Electromagnetics of Time Varying Complex Media, Second Edition provides a comprehensive examination of current topics of interest in the research community—including theory, numerical simulation, application, and experimental work. Written by a world leader in the research of frequency transformation in a time-varying magnetoplasma medium, the new edition of this bestselling reference discusses how to apply a time-varying medium to design a frequency and polarization transformer. This authoritative resource remains the only electromagnetic book to cover time-varying anisotropic media, Frequency and Polarization Transformer based on a switched magnetoplasma medium in a cavity, and FDTD numerical simulation for time-varying complex medium. Providing a primer on the theory of using magnetoplasmas for the coherent generation of tunable radiation, early chapters use a mathematical model with one kind of complexity—eliminating the need for high-level mathematics. Using plasma as the basic medium to illustrate various aspects of the transformation of an electromagnetic wave by a complex medium, the text highlights the major effects of each kind of complexity in the medium properties. This significantly expanded edition includes: Three new parts: (a) Numerical Simulation: FDTD Solution, (b) Application: Frequency and Polarization Transformer, and (c) Experiments A slightly enhanced version of the entire first edition, plus 70% new material Reprints of papers previously published by the author—providing researchers with complete access to the subject The text provides the understanding of research techniques useful in electro-optics, plasma science and engineering, microwave engineering, and solid state devices. This complete resource supplies an accessible treatment of the effect of time-varying parameters in conjunction with one or more additional kinds of complexities in the properties of particular mediums.