Canonical Problems in Scattering and Potential Theory Part 1

Canonical Problems in Scattering and Potential Theory Part 1
Author: S.S. Vinogradov
Publisher: CRC Press
Total Pages: 393
Release: 2001-05-30
Genre: Mathematics
ISBN: 0849387078


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Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical scatterers

Canonical Problems in Scattering and Potential Theory - Two volume set

Canonical Problems in Scattering and Potential Theory - Two volume set
Author: S.S. Vinogradov
Publisher: Chapman and Hall/CRC
Total Pages: 912
Release: 2002-04-26
Genre: Mathematics
ISBN: 9781584881643


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Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical scatterers with comprising edges and other complex cavity features. It is an authoritative account of mathematical developments over the last two decades that provides benchmarks against which solutions obtained by numerical methods can be verified. The first volume, Canonical Structures in Potential Theory, develops the mathematics, solving mixed boundary potential problems for structures with cavities and edges. The second volume, Acoustic and Electromagnetic Diffraction by Canonical Structures, examines the diffraction of acoustic and electromagnetic waves from several classes of open structures with edges or cavities. Together these volumes present an authoritative and unified treatment of potential theory and diffraction-the first complete description quantifying the scattering mechanisms in complex structures.

Canonical Problems in Scattering and Potential Theory

Canonical Problems in Scattering and Potential Theory
Author: S.S. Vinogradov
Publisher: Chapman and Hall/CRC
Total Pages: 392
Release: 2001-05-30
Genre: Mathematics
ISBN: 9781584881629


Download Canonical Problems in Scattering and Potential Theory Book in PDF, Epub and Kindle

Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical scatterers with comprising edges and other complex cavity features. It is an authoritative account of mathematical developments over the last two decades that provides benchmarks against which solutions obtained by numerical methods can be verified. The first volume, Canonical Structures in Potential Theory, develops the mathematics, solving mixed boundary potential problems for structures with cavities and edges. The second volume, Acoustic and Electromagnetic Diffraction by Canonical Structures, examines the diffraction of acoustic and electromagnetic waves from several classes of open structures with edges or cavities. Together these volumes present an authoritative and unified treatment of potential theory and diffraction-the first complete description quantifying the scattering mechanisms in complex structures.

Canonical Problems in Scattering and Potential Theory Part II

Canonical Problems in Scattering and Potential Theory Part II
Author: S.S. Vinogradov
Publisher: CRC Press
Total Pages: 307
Release: 2002-04-29
Genre: Mathematics
ISBN: 1000738132


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Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical scatterers

Optical Waveguide Theory

Optical Waveguide Theory
Author: Yury Shestopalov
Publisher: Springer Nature
Total Pages: 269
Release: 2022-03-26
Genre: Science
ISBN: 9811905843


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This book addresses the most advanced to-date mathematical approach and numerical methods in electromagnetic field theory and wave propagation. It presents the application of developed methods and techniques to the analysis of waves in various guiding structures —shielded and open metal-dielectric waveguides of arbitrary cross-section, planar and circular waveguides filled with inhomogeneous dielectrics, metamaterials, chiral media, anisotropic media and layered media with absorption. It also looks into spectral properties of wave propagation for the waveguide families being considered, and the relevant mathematical techniques such as spectral theory of non-self-adjoint operator-valued functions are described, including rigorous proofs of the existence of various types of waves. Further, numerical methods constructed on the basis of the presented mathematical approach and the results of numerical modeling for various structures are also described in depth. The book is beneficial to a broad spectrum of readers ranging from pure and applied mathematicians in electromagnetic field theory to researchers and engineers who are familiar with mathematics. Further, it is also useful as a supplementary text for upper-level undergraduate students interested in learning more advanced topics of mathematical methods in electromagnetics.

Modern Theory of Gratings

Modern Theory of Gratings
Author: Yuriy K. Sirenko
Publisher: Springer
Total Pages: 404
Release: 2010-07-23
Genre: Science
ISBN: 1441912002


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The advances in the theory of diffraction gratings and the applications of these results certainly determine the progress in several areas of applied science and engineering. The polarization converters, phase shifters and filters, quantum and solid-state oscillators, open quasi optical dispersive resonators and power compressors, slow-wave structures and patter forming systems, accelerators and spectrometer; that is still far from being a complete list of devices exploiting the amazing ability of periodic structures to perform controlled frequency, spatial, and polarization selection of signals. Diffraction gratings used to be and still are one of the most popular objects of analysis in electromagnetic theory. The further development of the theory of diffraction gratings, in spite of considerable achievements, is still very important presently. The requirements of applied optics and microwave engineering present the theory of diffraction gratings with many new problems which force us to search for new methods and tools for their resolution. Just in such way there appeared recently new fields, connected with the analysis, synthesis and definition of equivalent parameters of artificial materials – layers and coatings, having periodic structure and possessing features, which can be found in natural materials only in extraordinary or exceptional situations. In this book the authors present results of the electromagnetic theory of diffraction gratings that may constitute the base of further development of this theory which can meet the challenges provided by the most recent requirements of fundamental and applied science. The following issues will be considered in the book Authentic methods of analytical regularization, that perfectly match the requirements of analysis of resonant scattering of electromagnetic waves by gratings; Spectral theory of gratings, providing a reliable foundation for the analysis of spatial – frequency transformations of electromagnetic fields occurring in open periodic resonators and waveguides; Parametric Fourier method and C-method, that are oriented towards the efficient numerical analysis of transformation properties of fields in the case of arbitrary profile periodic boundary between dielectric media and multilayered conformal arrays; Rigorous methods for analysis of transient processes and time-spatial transformations of electromagnetic waves in resonant situations, based on development and incorporation in standard numerical routines of FDTD of so called explicit absorbing boundary conditions; New approaches to the solution of homogenization problems – the key problem arising in construction of metamaterials and meta surfaces; New physical results about the resonance scattering of pulse and monochromatic waves by periodic structures, including structures with chiral or left-handed materials; Methods and the results of the solutions of several actual applied problems of analysis and synthesis of pattern creating gratings, power compressors, resonance radiators of high capacity short radio pulses, open electromagnetic structures for the systems of resonant quasi optics and absorbing coatings.

Advanced Electromagnetic Waves

Advanced Electromagnetic Waves
Author: Saad Bashir
Publisher: BoD – Books on Demand
Total Pages: 280
Release: 2015-11-18
Genre: Technology & Engineering
ISBN: 9535122053


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This book endeavors to give the reader a strong base in the advanced theory of electromagnetic waves and its applications, while keeping pace with research in various other disciplines that apply electrostatics/electrodynamics theory. The treatment is highly mathematical, which tends to obscure the principles involved.