Equations of Mathematical Diffraction Theory, Sumbatyan, Mezhlum A. , Scalia, Antonio

Автор: Igor T. Selezov; Yuriy G. Kryvonos; Ivan S. Gandzh
Название: Wave Propagation and Diffraction
ISBN: 9811352674 ISBN-13(EAN): 9789811352676
Издательство: Springer
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Цена: 130430.00 T
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Описание: 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 surface 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.

Автор: Alexander Komech; Anatoli Merzon
Название: Stationary Diffraction by Wedges
ISBN: 3030266982 ISBN-13(EAN): 9783030266981
Издательство: Springer
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Цена: 41920.00 T
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Описание: This book presents a new and original method for the solution of boundary value problems in angles for second-order elliptic equations with constant coefficients and arbitrary boundary operators. This method turns out to be applicable to many different areas of mathematical physics, in particular to diffraction problems in angles and to the study of trapped modes on a sloping beach. Giving the reader the opportunity to master the techniques of the modern theory of diffraction, the book introduces methods of distributions, complex Fourier transforms, pseudo-differential operators, Riemann surfaces, automorphic functions, and the Riemann–Hilbert problem.The book will be useful for students, postgraduates and specialists interested in the application of modern mathematics to wave propagation and diffraction problems.

Автор: Galina Filipuk, Andrzej Kozlowski
Название: Analysis with Mathematica®: Volume 1: Single Variable Calculus
ISBN: 3110590131 ISBN-13(EAN): 9783110590135
Издательство: Walter de Gruyter
Цена: 74320.00 T
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Описание: A computer algebra system such as Mathematica is able to do much more than just numerics: This text shows how to tackle real mathematical problems from basic analysis. The reader learns how Mathematica represents domains, qualifiers and limits to implement actual proofs – a requirement to unlock the huge potential of Mathematica for a variety of applications.

Автор: Wazwaz Abdul-Majid
Название: First Course In Integral Equations, A (Second Edition)
ISBN: 9814675121 ISBN-13(EAN): 9789814675123
Издательство: World Scientific Publishing
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Цена: 42240.00 T
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Описание: This second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations.

Автор: Calvin H. Wilcox
Название: Scattering Theory for Diffraction Gratings
ISBN: 0387909249 ISBN-13(EAN): 9780387909240
Издательство: Springer
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Цена: 88500.00 T
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Описание: The scattering of acoustic and electromagnetic waves by periodic sur- faces plays a role in many areas of applied physics and engineering. Trains of surface waves on the oceans are natural diffraction gratings which influence the scattering of electromagnetic waves and underwater sound.

Автор: Jean-Pierre Croisille; Gilles Lebeau
Название: Diffraction by an Immersed Elastic Wedge
ISBN: 3540668101 ISBN-13(EAN): 9783540668107
Издательство: Springer
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Цена: 27910.00 T
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Автор: Dumitru Baleanu and Antonio Mendes Lopes
Название: Handbook of Fractional Calculus with Applications
ISBN: 3110570920 ISBN-13(EAN): 9783110570922
Издательство: Walter de Gruyter
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Цена: 149590.00 T
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Описание: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This eighth volume collects authoritative chapters covering several applications of fractional calculus in engineering, life and social sciences, including applications in signal and image analysis, and chaos.

Автор: Habib Ammari , Brian Fitzpatrick, Hyeonbae Kang et al
Название: Mathematical and computational methods in photonics and phononics /
ISBN: 1470448009 ISBN-13(EAN): 9781470448004
Издательство: Mare Nostrum (Eurospan)
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Цена: 116210.00 T
Наличие на складе: Нет в наличии.
Описание: The fields of photonics and phononics encompass the fundamental science of light and sound propagation and interactions in complex structures, as well as its technological applications. This book reviews new and fundamental mathematical tools, computational approaches, and inversion and optimal design methods to address challenging problems in photonics and phononics.An emphasis is placed on analyzing sub-wavelength resonators, super-focusing and super-resolution of electromagnetic and acoustic waves, photonic and phononic crystals, electromagnetic cloaking, and electromagnetic and elastic metamaterials and metasurfaces. Throughout this book, the authors demonstrate the power of layer potential techniques for solving challenging problems in photonics and phononics when they are combined with asymptotic analysis. This book might be of interest to researchers and graduate students working in the fields of applied and computational mathematics, partial differential equations, electromagnetic theory, elasticity, integral equations, and inverse and optimal design problems in photonics and phononics.

Автор: Schоnlieb
Название: Partial Differential Equation Methods for Image Inpainting
ISBN: 1107001005 ISBN-13(EAN): 9781107001008
Издательство: Cambridge Academ
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Цена: 81300.00 T
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Описание: This book is concerned with digital image processing techniques that use partial differential equations (PDEs) for the task of image 'inpainting', an artistic term for virtual image restoration or interpolation, whereby missing or occluded parts in images are completed based on information provided by intact parts. Computer graphic designers, artists and photographers have long used manual inpainting to restore damaged paintings or manipulate photographs. Today, mathematicians apply powerful methods based on PDEs to automate this task. This book introduces the mathematical concept of PDEs for virtual image restoration. It gives the full picture, from the first modelling steps originating in Gestalt theory and arts restoration to the analysis of resulting PDE models, numerical realisation and real-world application. This broad approach also gives insight into functional analysis, variational calculus, optimisation and numerical analysis and will appeal to researchers and graduate students in mathematics with an interest in image processing and mathematical analysis.

Автор: Serovajsky
Название: Sequential Models of Mathematical Physics
ISBN: 1138601039 ISBN-13(EAN): 9781138601031
Издательство: Taylor&Francis
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Цена: 117390.00 T
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Описание: In Sequential Models of Mathematical Physics, the author considers the justification of the process of constructing mathematical models.

Автор: Angela Slavova, Petar Popivanov
Название: Nonlinear Waves: A Geometrical Approach
ISBN: 9813271604 ISBN-13(EAN): 9789813271609
Издательство: World Scientific Publishing
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Цена: 84480.00 T
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Описание:

This volume provides an in-depth treatment of several equations and systems of mathematical physics, describing the propagation and interaction of nonlinear waves as different modifications of these: the KdV equation, Fornberg-Whitham equation, Vakhnenko equation, Camassa-Holm equation, several versions of the NLS equation, Kaup-Kupershmidt equation, Boussinesq paradigm, and Manakov system, amongst others, as well as symmetrizable quasilinear hyperbolic systems arising in fluid dynamics.

Readers not familiar with the complicated methods used in the theory of the equations of mathematical physics (functional analysis, harmonic analysis, spectral theory, topological methods, a priori estimates, conservation laws) can easily be acquainted here with different solutions of some nonlinear PDEs written in a sharp form (waves), with their geometrical visualization and their interpretation. In many cases, explicit solutions (waves) having specific physical interpretation (solitons, kinks, peakons, ovals, loops, rogue waves) are found and their interactions are studied and geometrically visualized. To do this, classical methods coming from the theory of ordinary differential equations, the dressing method, Hirota's direct method and the method of the simplest equation are introduced and applied. At the end, the paradifferential approach is used.

This volume is self-contained and equipped with simple proofs. It contains many exercises and examples arising from the applications in mechanics, physics, optics and, quantum mechanics.

Автор: Lars H?rmander; Anders Melin
Название: Partial Differential Equations and Mathematical Physics
ISBN: 1461268974 ISBN-13(EAN): 9781461268970
Издательство: Springer
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Цена: 139750.00 T
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Описание: On March 17-19 and May 19-21,1995, analysis seminars were organized jointly at the universities of Copenhagen and Lund, under the heading "Danish-Swedish Analysis Seminar". The main topic was partial differen- tial equations and related problems of mathematical physics. The lectures given are presented in this volume, some as short abstracts and some as quite complete expositions or survey papers. They span over a large vari- ety of topics. The most frequently occurring theme is the use of microlocal analysis which is now important also in the study of non-linear differential equations although it originated entirely within the linear theory. Perhaps it is less surprising that microlocal analysis has proved to be useful in the study of mathematical problems of classical quantum mechanics, for it re- ceived a substantial input of ideas from that field. The scientific committee for the invitation of speakers consisted of Gerd Grubb in Copenhagen, Lars Hormander and Anders MeHn in Lund, and Jo- hannes Sjostrand in Paris. Lars Hormander and Anders Melin have edited the proceedings. They were hosts of the seminar days in Lund while Gerd Grubb was the host in Copenhagen. Financial support was obtained from the mathematics departments in Copenhagen and Lund, CNRS in France, the Danish and Swedish Na- tional Research Councils, Gustaf Sigurd Magnuson's foundation at the Royal Swedish Academy of Sciences, and the Wenner-Gren foundation in Stockholm. We want to thank all these organisations for their support.