Spectral Theory Of Guided Waves

Author : A.S Silbergleit,Y Kopilevich
Publisher : CRC Press
Page : 340 pages
File Size : 48,5 Mb
Release : 1996-01-01
Category : Science
ISBN : 0750303816

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Spectral Theory of Guided Waves by A.S Silbergleit,Y Kopilevich Pdf

Spectral Theory of Guided Waves represents a distillation of the authors' (and others) efforts over several years to rigorously discuss many of the properties of guided waves. The bulk of the book deals with the properties of eigenwaves of regular waveguiding systems and relates these to a variety of physical situations and applications to illustrate their generality. The book also includes considerable discussion of the basic properties of normal waves with quadratic operator pencils. Unique in its coverage of these subjects, the book will be of interest to engineers, applied mathematicians, and physicists with a working knowledge of functional analysis and spectral theory.

Author : A.S Silbergleit,Y Kopilevich
Publisher : CRC Press
Page : 310 pages
File Size : 47,7 Mb
Release : 2021-08-02
Category : Science
ISBN : 9781000445275

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Spectral Theory of Guided Waves by A.S Silbergleit,Y Kopilevich Pdf

Spectral Theory of Guided Waves represents a distillation of the authors' (and others) efforts over several years to rigorously discuss many of the properties of guided waves. The bulk of the book deals with the properties of eigenwaves of regular waveguiding systems and relates these to a variety of physical situations and applications to illustrate their generality. The book also includes considerable discussion of the basic properties of normal waves with quadratic operator pencils. Unique in its coverage of these subjects, the book will be of interest to engineers, applied mathematicians, and physicists with a working knowledge of functional analysis and spectral theory.

Author : Ricardo Weder
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461244301

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Spectral and Scattering Theory for Wave Propagation in Perturbed Stratified Media by Ricardo Weder Pdf

The propagation of acoustic and electromagnetic waves in stratified media is a subject that has profound implications in many areas of applied physics and in engineering, just to mention a few, in ocean acoustics, integrated optics, and wave guides. See for example Tolstoy and Clay 1966, Marcuse 1974, and Brekhovskikh 1980. As is well known, stratified media, that is to say media whose physical properties depend on a single coordinate, can produce guided waves that propagate in directions orthogonal to that of stratification, in addition to the free waves that propagate as in homogeneous media. When the stratified media are perturbed, that is to say when locally the physical properties of the media depend upon all of the coordinates, the free and guided waves are no longer solutions to the appropriate wave equations, and this leads to a rich pattern of wave propagation that involves the scattering of the free and guided waves among each other, and with the perturbation. These phenomena have many implications in applied physics and engineering, such as in the transmission and reflexion of guided waves by the perturbation, interference between guided waves, and energy losses in open wave guides due to radiation. The subject matter of this monograph is the study of these phenomena.

Author : Manfred Möller,Vyacheslav Pivovarchik
Publisher : Birkhäuser
Page : 412 pages
File Size : 55,8 Mb
Release : 2015-06-11
Category : Mathematics
ISBN : 9783319170701

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Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications by Manfred Möller,Vyacheslav Pivovarchik Pdf

The theoretical part of this monograph examines the distribution of the spectrum of operator polynomials, focusing on quadratic operator polynomials with discrete spectra. The second part is devoted to applications. Standard spectral problems in Hilbert spaces are of the form A-λI for an operator A, and self-adjoint operators are of particular interest and importance, both theoretically and in terms of applications. A characteristic feature of self-adjoint operators is that their spectra are real, and many spectral problems in theoretical physics and engineering can be described by using them. However, a large class of problems, in particular vibration problems with boundary conditions depending on the spectral parameter, are represented by operator polynomials that are quadratic in the eigenvalue parameter and whose coefficients are self-adjoint operators. The spectra of such operator polynomials are in general no more real, but still exhibit certain patterns. The distribution of these spectra is the main focus of the present volume. For some classes of quadratic operator polynomials, inverse problems are also considered. The connection between the spectra of such quadratic operator polynomials and generalized Hermite-Biehler functions is discussed in detail. Many applications are thoroughly investigated, such as the Regge problem and damped vibrations of smooth strings, Stieltjes strings, beams, star graphs of strings and quantum graphs. Some chapters summarize advanced background material, which is supplemented with detailed proofs. With regard to the reader’s background knowledge, only the basic properties of operators in Hilbert spaces and well-known results from complex analysis are assumed.

Author : V. P. Shestopalov
Publisher : IET
Page : 420 pages
File Size : 51,7 Mb
Release : 1996
Category : Mathematics
ISBN : 0852968760

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Spectral Theory and Excitation of Open Structures by V. P. Shestopalov Pdf

Open resonators, open waveguides and open diffraction gratings are used extensively in modern millimetre and submillemetre technology, spectroscopy and radio engineering. In this book, the physical processes in these open electromagnetic structures are analysed using a specially constructed spectral theory.

Author : Yury Shestopalov,Yury Smirnov,Eugene Smolkin
Publisher : Springer Nature
Page : 269 pages
File Size : 49,8 Mb
Release : 2022-03-26
Category : Science
ISBN : 9789811905841

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Optical Waveguide Theory by Yury Shestopalov,Yury Smirnov,Eugene Smolkin Pdf

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.

Author : Wieslaw Ostachowicz,Pawel Kudela,Marek Krawczuk,Arkadiusz Zak
Publisher : John Wiley & Sons
Page : 267 pages
File Size : 41,8 Mb
Release : 2011-12-30
Category : Science
ISBN : 9781119966746

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Guided Waves in Structures for SHM by Wieslaw Ostachowicz,Pawel Kudela,Marek Krawczuk,Arkadiusz Zak Pdf

Understanding and analysing the complex phenomena related to elastic wave propagation has been the subject of intense research for many years and has enabled application in numerous fields of technology, including structural health monitoring (SHM). In the course of the rapid advancement of diagnostic methods utilising elastic wave propagation, it has become clear that existing methods of elastic wave modeling and analysis are not always very useful; developing numerical methods aimed at modeling and analysing these phenomena has become a necessity. Furthermore, any methods developed need to be verified experimentally, which has become achievable with the advancement of measurement methods utilising laser vibrometry. Guided Waves in Structures for SHM reports on the simulation, analysis and experimental investigation related propagation of elastic waves in isotropic or laminated structures. The full spectrum of theoretical and practical issues associated with propagation of elastic waves is presented and discussed in this one study. Key features: Covers both numerical and experimental aspects of modeling, analysis and measurement of elastic wave propagation in structural elements formed from isotropic or composite materials Comprehensively discusses the application of the Spectral Finite Element Method for modelling and analysing elastic wave propagation in diverse structural elements Presents results of experimental measurements employing advanced laser technologies, validating the quality and correctness of the developed numerical models Accompanying website (www.wiley.com/go/ostachowicz) contains demonstration versions of commercial software developed by the authors for modelling and analyzing elastic wave propagation using the Spectral Finite Element Method Guided Waves in Structures for SHM provides a state of the art resource for researchers and graduate students in structural health monitoring, signal processing and structural dynamics. This book should also provide a useful reference for practising engineers within structural health monitoring and non-destructive testing.

Author : E. Khruslov,L. Pastur,D. Shepelsky
Publisher : American Mathematical Society
Page : 266 pages
File Size : 46,9 Mb
Release : 2014-09-26
Category : Mathematics
ISBN : 9781470416836

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Spectral Theory and Differential Equations by E. Khruslov,L. Pastur,D. Shepelsky Pdf

This volume is dedicated to V. A. Marchenko on the occasion of his 90th birthday. It contains refereed original papers and survey articles written by his colleagues and former students of international stature and focuses on the areas to which he made important contributions: spectral theory of differential and difference operators and related topics of mathematical physics, including inverse problems of spectral theory, homogenization theory, and the theory of integrable systems. The papers in the volume provide a comprehensive account of many of the most significant recent developments in that broad spectrum of areas.

Author : Joseph A. Ball,Yuli Eidelman,J. William Helton,Vadim Olshevsky,James Rovnyak
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 44,8 Mb
Release : 2007-12-22
Category : Mathematics
ISBN : 9783764385392

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Recent Advances in Matrix and Operator Theory by Joseph A. Ball,Yuli Eidelman,J. William Helton,Vadim Olshevsky,James Rovnyak Pdf

This volume comprises the proceedings of the International Workshop on Operator Theory and Its Applications held at the University of Connecticut in July 2005.

Author : David F. Parker,Gerard A. Maugin
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642835087

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Recent Developments in Surface Acoustic Waves by David F. Parker,Gerard A. Maugin Pdf

The topic of surface waves lies at the interface between a number of disci plines - physics, theoretical and applied mechanics, electroacoustics, ap plied mathematics, surface science and seismology. This volume, based on papers delivered at European Mechanics Colloquium 226, reflects this diversity in approach and background, while showing strong links between phenomena arising from different fields. The emphasis is on recent de velopments such as nonlinear and other nonclassical effects,which have great importance for both pure science and for applications such as signal processing, nondestructive evaluation and seismic studies. In recent years there has been considerable progress in the mathe matical treatment of nonlinear effects, of viscoelastic and of more novel constitutive effects which modify the predictions of linear elastic and piezo electric theory for surface acoustic wave (SAW) propagation. A number of these themes serve to group the contents of this volume. Part I contains recent advances in the rigorous mathematical treatment of nonlinearity, together with a paper giving experimental results showing the need for further theoretical development. Part II deals with anisotropic elasticity, showing that even the linear theory presents many possible behaviours, which are still not fully categorized.

Author : Edward F. Kuester
Publisher : CRC Press
Page : 611 pages
File Size : 40,8 Mb
Release : 2020-09-19
Category : Technology & Engineering
ISBN : 9781498730891

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Theory of Waveguides and Transmission Lines by Edward F. Kuester Pdf

This book covers the principles of operation of electromagnetic waveguides and transmission lines. The approach is divided between mathematical descriptions of basic behaviors and treatment of specific types of waveguide structures. Classical (distributed-network) transmission lines, their basic properties, their connection to lumped-element networks, and the distortion of pulses are discussed followed by a full field analysis of waveguide modes. Modes of specific kinds of waveguides - traditional hollow metallic waveguides, dielectric (including optical) waveguides, etc. are discussed. Problems of excitation and scattering of waveguide modes are addressed, followed by discussion of real systems and performance.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 45,6 Mb
Release : 1995-12-31
Category : Electronic
ISBN : 1468489275

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Spectral Theory and Wave Processes. by Anonim Pdf

Author : Pavel Kurasov,Ari Laptev,Sergey Naboko,Barry Simon
Publisher : Springer Nature
Page : 627 pages
File Size : 50,6 Mb
Release : 2020-07-14
Category : Mathematics
ISBN : 9783030315313

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Analysis as a Tool in Mathematical Physics by Pavel Kurasov,Ari Laptev,Sergey Naboko,Barry Simon Pdf

Boris Pavlov (1936-2016), to whom this volume is dedicated, was a prominent specialist in analysis, operator theory, and mathematical physics. As one of the most influential members of the St. Petersburg Mathematical School, he was one of the founders of the Leningrad School of Non-self-adjoint Operators. This volume collects research papers originating from two conferences that were organized in memory of Boris Pavlov: “Spectral Theory and Applications”, held in Stockholm, Sweden, in March 2016, and “Operator Theory, Analysis and Mathematical Physics – OTAMP2016” held at the Euler Institute in St. Petersburg, Russia, in August 2016. The volume also includes water-color paintings by Boris Pavlov, some personal photographs, as well as tributes from friends and colleagues.

Author : Peter Kuchment
Publisher : American Mathematical Soc.
Page : 232 pages
File Size : 40,9 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821832868

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Waves in Periodic and Random Media by Peter Kuchment Pdf

Science and engineering have been great sources of problems and inspiration for generations of mathematicians. This is probably true now more than ever as numerous challenges in science and technology are met by mathematicians. One of these challenges is understanding propagation of waves of different nature in systems of complex structure. This book contains the proceedings of the research conference, ``Waves in Periodic and Random Media''. Papers are devoted to a number of related themes, including spectral theory of periodic differential operators, Anderson localization and spectral theory of random operators, photonic crystals, waveguide theory, mesoscopic systems, and designer random surfaces. Contributions are written by prominent experts and are of interest to researchers and graduate students in mathematical physics.

Author : P.A. Kuchment
Publisher : Birkhäuser
Page : 363 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034885737

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Floquet Theory for Partial Differential Equations by P.A. Kuchment Pdf

Linear differential equations with periodic coefficients constitute a well developed part of the theory of ordinary differential equations [17, 94, 156, 177, 178, 272, 389]. They arise in many physical and technical applications [177, 178, 272]. A new wave of interest in this subject has been stimulated during the last two decades by the development of the inverse scattering method for integration of nonlinear differential equations. This has led to significant progress in this traditional area [27, 71, 72, 111 119, 250, 276, 277, 284, 286, 287, 312, 313, 337, 349, 354, 392, 393, 403, 404]. At the same time, many theoretical and applied problems lead to periodic partial differential equations. We can mention, for instance, quantum mechanics [14, 18, 40, 54, 60, 91, 92, 107, 123, 157-160, 192, 193, 204, 315, 367, 412, 414, 415, 417], hydrodynamics [179, 180], elasticity theory [395], the theory of guided waves [87-89, 208, 300], homogenization theory [29, 41, 348], direct and inverse scattering [175, 206, 216, 314, 388, 406-408], parametric resonance theory [122, 178], and spectral theory and spectral geometry [103 105, 381, 382, 389]. There is a sjgnificant distinction between the cases of ordinary and partial differential periodic equations. The main tool of the theory of periodic ordinary differential equations is the so-called Floquet theory [17, 94, 120, 156, 177, 267, 272, 389]. Its central result is the following theorem (sometimes called Floquet-Lyapunov theorem) [120, 267].