Wave Scattering By Small Bodies Creating Materials With A Desired Refraction Coefficient And Other Applications

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Wave Scattering By Small Bodies: Creating Materials With A Desired Refraction Coefficient And Other Applications

$Download Wave Scattering By Small Bodies: Creating Materials With A Desired Refraction Coefficient And Other Applications PDF Online Free$

Author : Alexander G Ramm
Publisher : World Scientific
ISBN 13 : 9811276501
Total Pages : 291 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Wave Scattering By Small Bodies: Creating Materials With A Desired Refraction Coefficient And Other Applications by : Alexander G Ramm

Download or read book Wave Scattering By Small Bodies: Creating Materials With A Desired Refraction Coefficient And Other Applications written by Alexander G Ramm and published by World Scientific. This book was released on 2023-09-21 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a research monograph. An asymptotically exact solution of the many-body scattering problem is given under the assumption a ≪ d ≪ λ, where a is the characteristic size of a small particle, d is the smallest distance between particles and λ is the wavelength in the medium in which the particles are embedded. Scattering of scalar and electromagnetic waves is considered. Heat transfer theory in the medium in which many small bodies are embedded is developed. Quantum-mechanical theory of scattering by many potentials with small support is constructed.On the basis of these theoretical results, important applications are presented. First, a method for creating materials with a desired refraction coefficient is given. Secondly, a method for creating wave-focusing materials is developed. Technological problems to be solved for practical usage of these applied results are discussed.This book contains the contents of the author's earlier monograph, published in 2013. New appendices, based on the author's review papers published after 2013, are added.

Chaos Theory: Modeling, Simulation And Applications - Selected Papers From The 3rd Chaotic Modeling And Simulation International Conference (Chaos2010)

Download Chaos Theory: Modeling, Simulation And Applications - Selected Papers From The 3rd Chaotic Modeling And Simulation International Conference (Chaos2010) PDF Online Free

Author : Christos H Skiadas
Publisher : World Scientific
ISBN 13 : 9814460478
Total Pages : 468 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Chaos Theory: Modeling, Simulation And Applications - Selected Papers From The 3rd Chaotic Modeling And Simulation International Conference (Chaos2010) by : Christos H Skiadas

Download or read book Chaos Theory: Modeling, Simulation And Applications - Selected Papers From The 3rd Chaotic Modeling And Simulation International Conference (Chaos2010) written by Christos H Skiadas and published by World Scientific. This book was released on 2011-05-31 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: The work done in chaotic modeling and simulation during the last decades has changed our views of the world around us and has introduced new scientific tools, methods and techniques. Advanced topics of these achievements are included in this volume on Chaos Theory which focuses on Chaotic Modeling, Simulation and Applications of the nonlinear phenomena. This volume includes the best papers presented in the 3rd International Conference on CHAOS. This interdisciplinary conference attracted people from many scientific fields dealing with chaos, nonlinear dynamics, fractals and the works presented and the papers included here are of particular interest that could provide a broad understanding of chaos in its various forms.The chapters relate to many fields of chaos including Dynamical and Nonlinear Systems, Attractors and Fractals, Hydro-Fluid Dynamics and Mechanics, Chaos in Meteorology and Cosmology, Chaos in Biology and Genetics, Chaotic Control, Chaos in Economy and Markets, and Computer Composition and Chaotic Simulations, including related applications.

Topics on Chaotic Systems

Author : Charilaos Skiadas
Publisher : World Scientific
ISBN 13 : 9814271330
Total Pages : 435 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Topics on Chaotic Systems by : Charilaos Skiadas

Download or read book Topics on Chaotic Systems written by Charilaos Skiadas and published by World Scientific. This book was released on 2009 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes the best papers presented at the CHAOS 2008 International Conference on Chaotic Modeling, Simulation and Applications. It provides a valuable collection of new ideas, methods, and techniques in the field of nonlinear dynamics, chaos, fractals and their applications in general science and in engineering sciences. It touches on many fields such as chaos, dynamical systems, nonlinear systems, fractals and chaotic attractors. It also covers mechanics, hydrofluid dynamics, chaos in meteorology and cosmology, Hamiltonian and quantum chaos, chaos in biology and genetics, chaotic control, and chaos in economy and markets, and chaotic simulations; thus, containing cutting-edge interdisciplinary research with high-interest applications. These contributions present new solutions by analyzing the relevant data and through the use of recent advances in different fields, especially in chaotic simulation methods and techniques.

Mathematical Analysis and Applications

Author : Michael Ruzhansky
Publisher : John Wiley & Sons
ISBN 13 : 1119414342
Total Pages : 764 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Mathematical Analysis and Applications by : Michael Ruzhansky

Download or read book Mathematical Analysis and Applications written by Michael Ruzhansky and published by John Wiley & Sons. This book was released on 2018-05-11 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

Chaos Theory

Author : Charilaos Skiadas
Publisher : World Scientific
ISBN 13 : 9814350346
Total Pages : 467 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Chaos Theory by : Charilaos Skiadas

Download or read book Chaos Theory written by Charilaos Skiadas and published by World Scientific. This book was released on 2011 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithmic sound composition using coupled cellular automata / Jaime Serquera and Eduardo R. Miranda -- Efficient large-scale forcing in finite-difference simulations of steady isotropic turbulence / Ryo Onishi, Yuya Baba and Keiko Takahashi -- Rendering statistical significance of information flow measures / Angeliki Papana and Dimitris Kugiumtzis. Complexity theory and physical unification : from microscopic to macroscopic level / G.P. Pavlos [und weitere] -- Regular variation, Paretian distributions, and the interplay of light and heavy tails in the fractality of asymptotic models / Dinis D. Pestana, Sandra M. Aleixo and J. Leonel Rocha -- Tools for investigation of dynamics of DC-DC converters within Matlab/Simulink / Dmitry Pikulin -- Chaos as compositional order / Eleri Angharad Pound -- Beta(p, q)-Cantor sets - determinism and randomness / J. Leonel Rocha, Sandra M. Aleixo and Dinis D. Pestana -- Predicting chaos with second method of Lyapunov / Vladimir B. Ryabov -- Analysis of homoclinic bifurcation in Duffing oscillator under two-frequency excitation : peculiarity of using Melnikov method in combination with averaging technique / Vladimir Ryabov and Kenta Fukushima -- Exploring life expectancy limits : first exit time modeling, parameter analysis and forecasts / Christos H. Skiadas and Charilaos Skiadas -- Composing chaotic music from the letter m / Anastasios D. Sotiropoulos -- On the timbre of chaotic algorithmic sounds / Dimitrios A. Sotiropoulos, Anastasios D. Sotiropoulos and Vaggelis D. Sotiropoulos -- The rainbow effect on composing chaotic algorithmic music / Vaggelis D. Sotiropoulos -- A highly chaotic attractor for a dual-channel single-attractor, private communication system / Banlue Srisuchinwong and Buncha Munmuangsaen -- Manifestation of chaos in collective models of nuclei / Pavel Stransky [und weitere] -- Importance of the chaos for computational processes of collective intelligence in social structures / Tadeusz (Ted) Szuba -- Complex signal generators based on capacitors and on piezoelectric loads / Horia-Nicolai L. Teodorescu and Victor P. Cojocaru -- Drift waves' synchronization by using an external signal. The stabilization of a chaotic plasma turbulence / C.L. Xaplanteris and E. Filippaki -- Chaos game technique as a tool for the analysis of natural geomorphological features / G. Zibret and T. Verbovsek -- Dynamics of a steel turning process / Grzegorz Litak and Rafal Rusinek

Numerical Simulations of Physical and Engineering Processes

Author : Jan Awrejcewicz
Publisher : BoD – Books on Demand
ISBN 13 : 9533076208
Total Pages : 616 pages
Book Rating : 4.5/5 (33 download)

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Book Synopsis Numerical Simulations of Physical and Engineering Processes by : Jan Awrejcewicz

Download or read book Numerical Simulations of Physical and Engineering Processes written by Jan Awrejcewicz and published by BoD – Books on Demand. This book was released on 2011-09-26 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Simulations of Physical and Engineering Process is an edited book divided into two parts. Part I devoted to Physical Processes contains 14 chapters, whereas Part II titled Engineering Processes has 13 contributions. The book handles the recent research devoted to numerical simulations of physical and engineering systems. It can be treated as a bridge linking various numerical approaches of two closely inter-related branches of science, i.e. physics and engineering. Since the numerical simulations play a key role in both theoretical and application oriented research, professional reference books are highly needed by pure research scientists, applied mathematicians, engineers as well post-graduate students. In other words, it is expected that the book will serve as an effective tool in training the mentioned groups of researchers and beyond.

Creating Materials with a Desired Refraction Coefficient

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Author : Alexander G. Ramm
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1681747111
Total Pages : 79 pages
Book Rating : 4.6/5 (817 download)

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Book Synopsis Creating Materials with a Desired Refraction Coefficient by : Alexander G. Ramm

Download or read book Creating Materials with a Desired Refraction Coefficient written by Alexander G. Ramm and published by Morgan & Claypool Publishers. This book was released on 2017-12-20 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: Creating Materials with a Desired Refraction Coefficient' provides a recipe for creating materials with a desired refraction coefficient, and the many-body wave scattering problem for many small impedance bodies is solved. The physical assumptions make the multiple scattering effects essential. On the basis of this theory, a recipe for creating materials with a desired refraction coefficient is given. Technological problems are formulated which, when solved, make the theory practically applicable. The Importance of a problem of producing a small particle with a desired boundary impedance is emphasized, and inverse scattering with non-over-determined scattering data is considered.

Handbook of Applications of Chaos Theory

Author : Christos H. Skiadas
Publisher : CRC Press
ISBN 13 : 1466590440
Total Pages : 934 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Handbook of Applications of Chaos Theory by : Christos H. Skiadas

Download or read book Handbook of Applications of Chaos Theory written by Christos H. Skiadas and published by CRC Press. This book was released on 2017-12-19 with total page 934 pages. Available in PDF, EPUB and Kindle. Book excerpt: In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors from around the world show how chaos theory is used to model unexplored cases and stimulate new applications. Accessible to scientists, engineers, and practitioners in a variety of fields, the book discusses the intermittency route to chaos, evolutionary dynamics and deterministic chaos, and the transition to phase synchronization chaos. It presents important contributions on strange attractors, self-exciting and hidden attractors, stability theory, Lyapunov exponents, and chaotic analysis. It explores the state of the art of chaos in plasma physics, plasma harmonics, and overtone coupling. It also describes flows and turbulence, chaotic interference versus decoherence, and an application of microwave networks to the simulation of quantum graphs. The book proceeds to give a detailed presentation of the chaotic, rogue, and noisy optical dissipative solitons; parhelic-like circle and chaotic light scattering; and interesting forms of the hyperbolic prism, the Poincaré disc, and foams. It also covers numerous application areas, from the analysis of blood pressure data and clinical digital pathology to chaotic pattern recognition to economics to musical arts and research.

Symmetry Problems

Author : Alexander G. Ramm
Publisher : Springer Nature
ISBN 13 : 303102415X
Total Pages : 71 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Symmetry Problems by : Alexander G. Ramm

Download or read book Symmetry Problems written by Alexander G. Ramm and published by Springer Nature. This book was released on 2022-06-01 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and other symmetry problems for partial differential equations. It goes on to study some other symmetry problems related to the potential theory. Among these is the problem of "invisible obstacles." In Chapter 5, it provides a solution to the Navier‒Stokes problem in ℝ³. The author proves that this problem has a unique global solution if the data are smooth and decaying sufficiently fast. A new a priori estimate of the solution to the Navier‒Stokes problem is also included. Finally, it delivers a solution to inverse problem of the potential theory without the standard assumptions about star-shapeness of the homogeneous bodies.

Antenna Synthesis through the Characteristics of Desired Amplitude

Author : Mykhaylo I. Andriychuk
Publisher : Cambridge Scholars Publishing
ISBN 13 : 1527539822
Total Pages : 166 pages
Book Rating : 4.5/5 (275 download)

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Book Synopsis Antenna Synthesis through the Characteristics of Desired Amplitude by : Mykhaylo I. Andriychuk

Download or read book Antenna Synthesis through the Characteristics of Desired Amplitude written by Mykhaylo I. Andriychuk and published by Cambridge Scholars Publishing. This book was released on 2019-09-12 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the synthesis problems that arise in the theory and design of radiating systems (antennas). The characteristics of desired amplitude are data placed into a synthesis problem. A synthesis problem belongs to a class of inverse problems and its aim is to determine a distribution of current or fields in an antenna, which produces the amplitude radiation characteristic as close as possible to the desired one. Freedom of choice of phase distribution of the desired radiation pattern (RP) is used as an additional possibility of better approximation to such RPs. This book studies various different types of antennas and arrays as the radiation systems under consideration. A special class of problems related to acoustic and electromagnetic scattering on a set of bodies (particles) of small size is also discussed, while the constructive procedures of creating inhomogeneous materials with specific properties are proposed.

The Foundations of Chaos Revisited: From Poincaré to Recent Advancements

Author : Christos Skiadas
Publisher : Springer
ISBN 13 : 3319297015
Total Pages : 261 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis The Foundations of Chaos Revisited: From Poincaré to Recent Advancements by : Christos Skiadas

Download or read book The Foundations of Chaos Revisited: From Poincaré to Recent Advancements written by Christos Skiadas and published by Springer. This book was released on 2016-04-29 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions from a number of pioneering researchers in the field, this collection is aimed not only at researchers and scientists in nonlinear dynamics but also at a broader audience interested in understanding and exploring how modern chaos theory has developed since the days of Poincaré. This book was motivated by and is an outcome of the CHAOS 2015 meeting held at the Henri Poincaré Institute in Paris, which provided a perfect opportunity to gain inspiration and discuss new perspectives on the history, development and modern aspects of chaos theory. Henri Poincaré is remembered as a great mind in mathematics, physics and astronomy. His works, well beyond their rigorous mathematical and analytical style, are known for their deep insights into science and research in general, and the philosophy of science in particular. The Poincaré conjecture (only proved in 2006) along with his work on the three-body problem are considered to be the foundation of modern chaos theory.

Imaging, Multi-scale and High Contrast Partial Differential Equations

Author : Habib Ammari
Publisher : American Mathematical Soc.
ISBN 13 : 1470419238
Total Pages : 148 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Imaging, Multi-scale and High Contrast Partial Differential Equations by : Habib Ammari

Download or read book Imaging, Multi-scale and High Contrast Partial Differential Equations written by Habib Ammari and published by American Mathematical Soc.. This book was released on 2016-03-23 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Seoul ICM 2014 Satellite Conference on Imaging, Multi-scale and High-Contrast PDEs, held from August 7-9, 2014, in Daejeon, Korea. The mathematical analysis of partial differential equations modelling materials, or tissues, presenting multiple scales has been a very active area of research. The study of the corresponding imaging or reconstruction problem is a more recent area. If the material parameters of the partial differential equation present high contrast ratio, then the solution to the PDE becomes particularly challenging to analyze and compute. On the other hand, imaging in highly heterogeneous media poses significant challenges to the mathematical community. The focus of this volume is on recent progress towards complete understanding of the direct problem with high contrast or high frequencies, and unified approaches to the inverse and imaging problems for both small and large contrast or frequencies. Of particular importance in imaging are shape representation techniques and regularization approaches. Special attention is devoted to new models and problems coming from physics leading to innovative imaging and signal processing methods.

Scattering By Obstacles And Potentials

Author : Ramm Alexander G
Publisher : World Scientific
ISBN 13 : 9813220988
Total Pages : 620 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Scattering By Obstacles And Potentials by : Ramm Alexander G

Download or read book Scattering By Obstacles And Potentials written by Ramm Alexander G and published by World Scientific. This book was released on 2017-11-23 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is important as it contains results many of which are not available in the literature, except in the author's papers. Among other things, it gives uniqueness theorems for inverse scattering problems when the data are non-over-determined, numerical method for solving inverse scattering problems, a method (MRC) for solving direct scattering problem. Contents: Scattering by ObstaclesScattering by PotentialsModified Rayleigh Conjecture (MRC) Method Readership: Researchers and graduate students in mathematics, computational mathematics, physics, acoustics, mechanical engineering. Keywords: Wave Scattering;Scattering by Obstacles;Scattering by PotentialsReview: Key Features: It contains material part of which is not available in the literature (except in the author's papers)Most of the results belong to the authorNew material is added to the author's earlier monograph "Scattering by obstacles"

Scattering of Acoustic and Electromagnetic Waves by Small Impedance Bodies of Arbitrary Shapes

Author : Alexander G. Ramm
Publisher :
ISBN 13 : 9781606506219
Total Pages : 0 pages
Book Rating : 4.5/5 (62 download)

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Book Synopsis Scattering of Acoustic and Electromagnetic Waves by Small Impedance Bodies of Arbitrary Shapes by : Alexander G. Ramm

Download or read book Scattering of Acoustic and Electromagnetic Waves by Small Impedance Bodies of Arbitrary Shapes written by Alexander G. Ramm and published by . This book was released on 2013-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, mathematicians, engineers, physicists, and materials scientists will learn how to create material with a desired refraction coefficient. For example, how to create material with negative refraction or with desired wave-focusing properties. The methods for creating these materials are based on the many-body wave scattering theory developed by the author. The book offers new analytical formulas that allow one to calculate acoustic and electromagnetic waves, scattered by one and many small impedance bodies of an arbitrary shape under various boundary conditions. Equations for the effective (self-consistent) field in media consisting of many small impedance particles are derived. Numerical methods for solving many-body wave scattering problems are developed for small impedance scatterers.

Wave Scattering by Small Bodies of Arbitrary Shapes

Author : Alexander G. Ramm
Publisher : World Scientific
ISBN 13 : 9812561862
Total Pages : 314 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Wave Scattering by Small Bodies of Arbitrary Shapes by : Alexander G. Ramm

Download or read book Wave Scattering by Small Bodies of Arbitrary Shapes written by Alexander G. Ramm and published by World Scientific. This book was released on 2005 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents analytical formulas which allow one to calculate the S-matrix for the acoustic and electromagnetic wave scattering by small bodies or arbitrary shapes with arbitrary accuracy. Equations for the self-consistent field in media consisting of many small bodies are derived. Applications of these results to ultrasound mammography and electrical engineering are considered.The above formulas are not available in the works of other authors. Their derivation is based on a mathematical theory for solving integral equations of electrostatics, magnetostatics, and other static fields. These equations are at a simple characteristic value. Convergent iterative processes are constructed for stable solution of these equations. The theory completes the classical work of Rayleigh on scattering by small bodies by providing analytical formulas for polarizability tensors for bodies of arbitrary shapes.

Mathematical Analysis and Applications

Author : Michael Ruzhansky
Publisher : John Wiley & Sons
ISBN 13 : 1119414334
Total Pages : 1050 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Mathematical Analysis and Applications by : Michael Ruzhansky

Download or read book Mathematical Analysis and Applications written by Michael Ruzhansky and published by John Wiley & Sons. This book was released on 2018-04-11 with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

Wave Scattering from Rough Surfaces

Author : Alexander G. Voronovich
Publisher : Springer Science & Business Media
ISBN 13 :
Total Pages : 250 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Wave Scattering from Rough Surfaces by : Alexander G. Voronovich

Download or read book Wave Scattering from Rough Surfaces written by Alexander G. Voronovich and published by Springer Science & Business Media. This book was released on 1994 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diverse areas of physics and its applications deal with wave scattering at rough surfaces: optics, acoustics, remote sensing, radio astronomy, physics of solids, diffraction theory, radio and wave-propagation techniques, etc. The mathe matical description of relevant problems is rather universal and theoretical methods analysing this phenomenon form a definite area of mathematical physics. It was founded by Lord Rayleigh at the beginning of the 20th century and has been intensively developed since 1950 in response to practical needs. Modern theory involves, along with the classical methods, some new ap proaches with much more extensive possibilities. The theoretical methods describing wave scattering at rough surfaces repre sent the subject of this book. Having studied this area over many years, the author came to the conclusion that most of the results found in this theory can easily be obtained and comprehended in the framework of a rather universal scheme and this became the motive for writing the present monograph. The first half of the book deals with the classical results. However, several new problems are considered in connection with the methods used here (for example, some applications of the Rayleigh hypothesis and its relation to the Lippman argument). The second half is fully devoted to recent results presented in papers but not yet in books. For this reason the author hopes that the present book will be of interest to both newcomers and experts in this area.