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Mathematical Modeling In Diffraction Theory

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Mathematical Modeling in Diffraction Theory

Mathematical Modeling in Diffraction Theory Book
Author : Alexander G. Kyurkchan,Nadezhda I. Smirnova
Publisher : Elsevier
Release : 2015-09-19
ISBN : 0128037482
Language : En, Es, Fr & De

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Book Description :

Mathematical Modeling in Diffraction Theory: Based on A Priori Information on the Analytical Properties of the Solution provides the fundamental physical concepts behind the theory of wave diffraction and scattered wave fields as well as its application in radio physics, acoustics, optics, radio astronomy, biophysics, geophysics, and astrophysics. This book provides a coherent discussion of several advanced topics that have the potential to push forward progress in this field. It begins with examples illustrating the importance of taking a priori information into account when developing algorithms for solving diffraction problems, with subsequent chapters discussing the basic analytical representations of wave fields, the auxiliary current and source methods for solving the problems of diffraction at compact scatterers, the null field and matrix methods that are widely used to solve problems in radio-physics, radio-astronomy, and biophysics, and the continued boundary condition and pattern equation method. Provides ideas and techniques for obtaining a priori information on analytical properties of wave fields and provides methods for solving diffraction problems Includes numerous concrete examples of localization of singularities of analytical continuation of wave fields Presents a qualitative explanation of the formation of visions of objects Formulates the concept of “invisible objects Supplies appropriate computer programs for all presented methods

Mathematical Modeling in Diffraction Theory

Mathematical Modeling in Diffraction Theory Book
Author : Alexander Kyurkchan,Nadezhda I. Smirnova
Publisher : Elsevier
Release : 2015-10-01
ISBN : 9780128037287
Language : En, Es, Fr & De

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Book Description :

Mathematical Modeling in Diffraction Theory: Based on A Priori Information on the Analytical Properties of the Solution provides the fundamental physical concepts behind the theory of wave diffraction and scattered wave fields as well as its application in radio physics, acoustics, optics, radio astronomy, biophysics, geophysics, and astrophysics. This book provides a coherent discussion of several advanced topics that have the potential to push forward progress in this field. It begins with examples illustrating the importance of taking a priori information into account when developing algorithms for solving diffraction problems, with subsequent chapters discussing the basic analytical representations of wave fields, the auxiliary current and source methods for solving the problems of diffraction at compact scatterers, the null field and matrix methods that are widely used to solve problems in radio-physics, radio-astronomy, and biophysics, and the continued boundary condition and pattern equation method. Provides ideas and techniques for obtaining a priori information on analytical properties of wave fields and provides methods for solving diffraction problems Includes numerous concrete examples of localization of singularities of analytical continuation of wave fields Presents a qualitative explanation of the formation of visions of objects Formulates the concept of "invisible" objects Supplies appropriate computer programs for all presented methods

Seismic Diffraction

Seismic Diffraction Book
Author : Tijmen Jan Moser,Michael A. Pelissier
Publisher : SEG Books
Release : 2016-06-30
ISBN : 1560803177
Language : En, Es, Fr & De

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Book Description :

The use of diffraction imaging to complement the seismic reflection method is rapidly gaining momentum in the oil and gas industry. As the industry moves toward exploiting smaller and more complex conventional reservoirs and extensive new unconventional resource plays, the application of the seismic diffraction method to image sub-wavelength features such as small-scale faults, fractures and stratigraphic pinchouts is expected to increase dramatically over the next few years. “Seismic Diffraction” covers seismic diffraction theory, modeling, observation, and imaging. Papers and discussion include an overview of seismic diffractions, including classic papers which introduced the potential of diffraction phenomena in seismic processing; papers on the forward modeling of seismic diffractions, with an emphasis on the theoretical principles; papers which describe techniques for diffraction mathematical modeling as well as laboratory experiments for the physical modeling of diffractions; key papers dealing with the observation of seismic diffractions, in near-surface-, reservoir-, as well as crustal studies; and key papers on diffraction imaging.

On the Kraus Levine Diffraction Model A Mathematical Theory of Conic Tip Diffraction

On the Kraus Levine Diffraction Model  A Mathematical Theory of Conic Tip Diffraction Book
Author : Joel Carroll,NAVAL UNDERSEA CENTER SAN DIEGO CALIF.
Publisher : Unknown
Release : 1973
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

In 1961, Kraus and Levine developed a mathematical model for diffraction by an elliptic cone, which included a plane angular sector as the degenerate case. Satterwhite and Kouyoumjian relied heavily upon this development as a basis for much of the work in their 1970 report which deals with the degenerate case. The report is an outgrowth of the Kraus-Levine model in an effort to further clarify the analytical theory. In particular, special attention has been given to a class of integrals which arises in the development of the Green's functions. Also, several examples of Lame polynomials are exhibited. (Author).

A Celebration of Mathematical Modeling

A Celebration of Mathematical Modeling Book
Author : Dan Czamanski,Joseph Bishop Keller,Dan Givoli,Marcus J. Grote,George C. Papanicolaou,George Papanicolaou
Publisher : Springer Science & Business Media
Release : 2004-04-30
ISBN : 9781402018428
Language : En, Es, Fr & De

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Book Description :

This volume celebrates the eightieth birthday of the famous applied mathematician Joseph B. Keller. The book contains 12 chapters, each on a specific area of mathematical modeling, written by established researchers who have collaborated with J.B. Keller during his long career. These chapters, all inspired by J.B. Keller, deal with a variety of application fields and together span the broad subject of mathematical modeling. The models discussed in the book describe the behavior of various systems such as those related to finance, waves, microorganisms, shocks, DNA, flames, contact, optics, fluids, bubbles and jets. The book also contains a preface written by the Editors, a full list of J.B. Keller's publications, and a comprehensive index. The book is intended for mathematicians, scientists and engineers, as well as graduate students in these fields, who are interested in mathematical models of physical phenomena.

Numerical Simulation of Water Waves

Numerical Simulation of Water Waves Book
Author : Jianhua Tao
Publisher : Springer Nature
Release : 2020-03-30
ISBN : 9811528411
Language : En, Es, Fr & De

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Book Description :

This book discusses the numerical simulation of water waves, which combines mathematical theories and modern techniques of numerical simulation to solve the problems associated with waves in coastal, ocean, and environmental engineering. Bridging the gap between practical mathematics and engineering, the book describes wave mechanics, establishment of mathematical wave models, modern numerical simulation techniques, and applications of numerical models in engineering. It also explores environmental issues related to water waves in coastal regions, such as pollutant and sediment transport, and introduces numerical wave flumes and wave basins. The material is self-contained, with numerous illustrations and tables, and most of the mathematical and engineering concepts are presented or derived in the text. The book is intended for researchers, graduate students and engineers in the fields of hydraulic, coastal, ocean and environmental engineering with a background in fluid mechanics and numerical simulation methods.

Mathematical Modeling in Optical Science

Mathematical Modeling in Optical Science Book
Author : Gang Bao,Lawrence Cowsar,Wen Masters
Publisher : SIAM
Release : 2001-01-01
ISBN : 9780898717594
Language : En, Es, Fr & De

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Book Description :

This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of mathematical models and the design and analysis of new computational approaches. The book contains cutting-edge discourses on emerging technology in optics that provides significant challenges and opportunities for applied mathematicians, researchers, and engineers.

Wave Propagation and Diffraction

Wave Propagation and Diffraction Book
Author : Igor T. Selezov,Yuriy G. Kryvonos,Ivan S. Gandzha
Publisher : Springer
Release : 2017-09-05
ISBN : 9811049238
Language : En, Es, Fr & De

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Book Description :

This book presents two distinct aspects of wave dynamics – wave propagation and diffraction – with a focus on wave diffraction. The authors apply different mathematical methods to the solution of typical problems in the theory of wave propagation and diffraction and analyze the obtained results. The rigorous diffraction theory distinguishes three approaches: the method of surface currents, where the diffracted field is represented as a superposition of secondary spherical waves emitted by each element (the Huygens–Fresnel principle); the Fourier method; and the separation of variables and Wiener–Hopf transformation method. Chapter 1 presents mathematical methods related to studying the problems of wave diffraction theory, while Chapter 2 deals with spectral methods in the theory of wave propagation, focusing mainly on the Fourier methods to study the Stokes (gravity) waves on the surface of inviscid fluid. Chapter 3 then presents some results of modeling the refraction of surf ace gravity waves on the basis of the ray method, which originates from geometrical optics. Chapter 4 is devoted to the diffraction of surface gravity waves and the final two chapters discuss the diffraction of waves by semi-infinite domains on the basis of method of images and present some results on the problem of propagation of tsunami waves. Lastly, it provides insights into directions for further developing the wave diffraction theory.

Mathematical Modeling in Optical Science

Mathematical Modeling in Optical Science Book
Author : Gang Bao,Lawrence Cowsar,Wen Masters
Publisher : SIAM
Release : 2001-01-01
ISBN : 0898714753
Language : En, Es, Fr & De

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Book Description :

This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of mathematical models and the design and analysis of new computational approaches. The book contains cutting-edge discourses on emerging technology in optics that provides significant challenges and opportunities for applied mathematicians, researchers, and engineers. Each of the three topics is presented through a series of survey papers to provide a broad overview focusing on the mathematical models. Chapters present model problems, physical principles, mathematical and computational approaches, and engineering applications corresponding to each of the three areas. Although some of the subject matter is classical, the topics presented are new and represent the latest developments in their respective fields.

Laser Interaction with Biological Material

Laser Interaction with Biological Material Book
Author : Kirill Kulikov
Publisher : Springer Science & Business Media
Release : 2013-09-16
ISBN : 331901739X
Language : En, Es, Fr & De

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Book Description :

This book covers the principles of laser interaction with biological cells and tissues of varying degrees of organization. The problems of biomedical diagnostics are considered. Scattering of laser irradiation of blood cells is modeled for biological structures (dermis, epidermis, vascular plexus). An analytic theory is provided which is based on solving the wave equation for the electromagnetic field. It allows the accurate analysis of interference effects arising from the partial superposition of scattered waves. Treated topics of mathematical modeling are: optical characterization of biological tissue with large-scale and small-scale inhomogeneities in the layers, heating blood vessel under laser irradiation incident on the outer surface of the skin and thermo-chemical denaturation of biological structures at the example of human skin.

Issues in Logic Operations and Computational Mathematics and Geometry 2013 Edition

Issues in Logic  Operations  and Computational Mathematics and Geometry  2013 Edition Book
Author : Anonim
Publisher : ScholarlyEditions
Release : 2013-05-01
ISBN : 1490110119
Language : En, Es, Fr & De

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Book Description :

Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Random Structures and Algorithms. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Random Structures and Algorithms 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 Logic, Operations, and Computational Mathematics and Geometry: 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/.

Spectral Theory and Excitation of Open Structures

Spectral Theory and Excitation of Open Structures Book
Author : V. P. Shestopalov,Youri V. Shestopalov
Publisher : IET
Release : 1996
ISBN : 9780852968765
Language : En, Es, Fr & De

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Book Description :

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 analyzed using a specially constructed spectral theory. The solution of electromagnetic problems in open structures requires a different approach from that used for closed structures because of radiation loss, edges, multiconnected cross-sections and the need to take into account the behavior of electromagnetic fields at infinity. This book, which is written by two authorities in the field of mathematical modeling, should be of interest to all engineers concerned with the analysis of electrodynamic structures.

Mathematical Models of Information and Stochastic Systems

Mathematical Models of Information and Stochastic Systems Book
Author : Philipp Kornreich
Publisher : CRC Press
Release : 2018-10-03
ISBN : 1420058843
Language : En, Es, Fr & De

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Book Description :

From ancient soothsayers and astrologists to today’s pollsters and economists, probability theory has long been used to predict the future on the basis of past and present knowledge. Mathematical Models of Information and Stochastic Systems shows that the amount of knowledge about a system plays an important role in the mathematical models used to foretell the future of the system. It explains how this known quantity of information is used to derive a system’s probabilistic properties. After an introduction, the book presents several basic principles that are employed in the remainder of the text to develop useful examples of probability theory. It examines both discrete and continuous distribution functions and random variables, followed by a chapter on the average values, correlations, and covariances of functions of variables as well as the probabilistic mathematical model of quantum mechanics. The author then explores the concepts of randomness and entropy and derives various discrete probabilities and continuous probability density functions from what is known about a particular stochastic system. The final chapters discuss information of discrete and continuous systems, time-dependent stochastic processes, data analysis, and chaotic systems and fractals. By building a range of probability distributions based on prior knowledge of the problem, this classroom-tested text illustrates how to predict the behavior of diverse systems. A solutions manual is available for qualifying instructors.

Modern Theory of Gratings

Modern Theory of Gratings Book
Author : Yuriy K. Sirenko,Staffan Ström
Publisher : Springer
Release : 2010-07-23
ISBN : 1441912002
Language : En, Es, Fr & De

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Book Description :

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.

Sinusoids

Sinusoids Book
Author : Prem K. Kythe
Publisher : CRC Press
Release : 2014-07-08
ISBN : 1482221071
Language : En, Es, Fr & De

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Book Description :

A Complete Treatment of Current Research Topics in Fourier Transforms and Sinusoids Sinusoids: Theory and Technological Applications explains how sinusoids and Fourier transforms are used in a variety of application areas, including signal processing, GPS, optics, x-ray crystallography, radioastronomy, poetry and music as sound waves, and the medical sciences. With more than 200 illustrations, the book discusses electromagnetic force and sychrotron radiation comprising all kinds of waves, including gamma rays, x-rays, UV rays, visible light rays, infrared, microwaves, and radio waves. It also covers topics of common interest, such as quasars, pulsars, the Big Bang theory, Olbers’ paradox, black holes, Mars mission, and SETI. The book begins by describing sinusoids—which are periodic sine or cosine functions—using well-known examples from wave theory, including traveling and standing waves, continuous musical rhythms, and the human liver. It next discusses the Fourier series and transform in both continuous and discrete cases and analyzes the Dirichlet kernel and Gibbs phenomenon. The author shows how invertibility and periodicity of Fourier transforms are used in the development of signals and filters, addresses the general concept of communication systems, and explains the functioning of a GPS receiver. The author then covers the theory of Fourier optics, synchrotron light and x-ray diffraction, the mathematics of radioastronomy, and mathematical structures in poetry and music. The book concludes with a focus on tomography, exploring different types of procedures and modern advances. The appendices make the book as self-contained as possible.

Mathematical Models of Higher Orders

Mathematical Models of Higher Orders Book
Author : Vadim A. Krysko,Jan Awrejcewicz,Maxim V. Zhigalov,Valeriy F. Kirichenko,Anton V. Krysko
Publisher : Springer
Release : 2019-02-11
ISBN : 3030047148
Language : En, Es, Fr & De

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Book Description :

This book offers a valuable methodological approach to the state-of-the-art of the classical plate/shell mathematical models, exemplifying the vast range of mathematical models of nonlinear dynamics and statics of continuous mechanical structural members. The main objective highlights the need for further study of the classical problem of shell dynamics consisting of mathematical modeling, derivation of nonlinear PDEs, and of finding their solutions based on the development of new and effective numerical techniques. The book is designed for a broad readership of graduate students in mechanical and civil engineering, applied mathematics, and physics, as well as to researchers and professionals interested in a rigorous and comprehensive study of modeling non-linear phenomena governed by PDEs.

Research Grants Index

Research Grants Index Book
Author : National Institutes of Health (U.S.). Division of Research Grants
Publisher : Unknown
Release : 1966
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Research Grants Index book written by National Institutes of Health (U.S.). Division of Research Grants, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Modeling and Analysis of Transient Processes in Open Resonant Structures

Modeling and Analysis of Transient Processes in Open Resonant Structures Book
Author : Yuriy K. Sirenko,Staffan Ström,Nataliya P. Yashina
Publisher : Springer
Release : 2007-04-03
ISBN : 0387325778
Language : En, Es, Fr & De

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Book Description :

This book describes a systematic approach to scattering of transient fields which can be introduced in undergraduate or graduate courses. The initial boundary value problems considered describe the transient electromagnetic fields formed by open periodic, compact, and waveguide resonators. The methods developed and the mathematical and physical results obtained provide a basis on which a modern theory for the scattering of resonant non-harmonic waves can be developed.

The Generalized Multipole Technique for Light Scattering

The Generalized Multipole Technique for Light Scattering Book
Author : Thomas Wriedt,Yuri Eremin
Publisher : Springer
Release : 2018-03-09
ISBN : 3319748904
Language : En, Es, Fr & De

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Book Description :

This book presents the Generalized Multipole Technique as a fast and powerful theoretical and computation tool to simulate light scattering by nonspherical particles. It also demonstrates the considerable potential of the method. In recent years, the concept has been applied in new fields, such as simulation of electron energy loss spectroscopy and has been used to extend other methods, like the null-field method, making it more widely applicable. The authors discuss particular implementations of the GMT methods, such as the Discrete Sources Method (DSM), Multiple Multipole Program (MMP), the Method of Auxiliary Sources (MAS), the Filamentary Current Method (FCM), the Method of Fictitious Sources (MFS) and the Null-Field Method with Discrete Sources (NFM-DS). The Generalized Multipole Technique is a surface-based method to find the solution of a boundary-value problem for a given differential equation by expanding the fields in terms of fundamental or other singular solutions of this equation. The amplitudes of these fundamental solutions are determined from the boundary condition at the particle surface. Electromagnetic and light scattering by particles or systems of particles has been the subject of intense research in various scientific and engineering fields, including astronomy, optics, meteorology, remote sensing, optical particle sizing and electromagnetics, which has led to the development of a large number of modelling methods based on the Generalized Multipole Technique for quantitative evaluation of electromagnetic scattering by particles of various shapes and compositions. The book describes these methods in detail.

Energy Research Abstracts

Energy Research Abstracts Book
Author : Anonim
Publisher : Unknown
Release : 1993
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Energy Research Abstracts book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.