In this unique volume the authors review the development of the subject, virtually from its inception. Details of much of the research work carded out in the linearized theory of water waves concerning problems of water wave scattering by barriers is incorporated.

The theory of water waves is most varied and is a fascinating topic. It includes a wide range of natural phenomena in oceans, rivers, and lakes. It is mostly concerned with elucidation of some general aspects of wave motion including the prediction of behaviour of waves in the presence of obstacles of some special configurations that are of interes

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.

The Fourier transform technique has been widely used in electrical engineer ing, which covers signal processing, communication, system control, electro magnetics, and optics. The Fourier transform-technique is particularly useful in electromagnetics and optics since it provides a convenient mathematical representation for wave scattering, diffraction, and propagation. Thus the Fourier transform technique has been long applied to the wave scattering problems that are often encountered in microwave antenna, radiation, diffrac tion, and electromagnetic interference. In order to u~derstand wave scattering in general, it is necessary to solve the wave equation subject to the prescribed boundary conditions. The purpose of this monograph is to present rigorous so lutions to the boundary-value problems by solving the wave equation based on the Fourier transform. In this monograph the technique of separation of vari ables is used to solve the wave equation for canonical scattering geometries such as conducting waveguide structures and rectangular/circular apertures. The Fourier transform, mode-matching, and residue calculus techniques are applied to obtain simple, analytic, and rapidly-convergent series solutions. The residue calculus technique is particularly instrumental in converting the solutions into series representations that are efficient and amenable to nu merical analysis. We next summarize the steps of analysis method for the scattering problems considered in this book. 1. Divide the scattering domain into closed and open regions. 2. Represent the scattered fields in the closed and open regions in terms of the Fourier series and transform, respectively. 3.

Part 1: SCATTERING OF WAVES BY MACROSCOPIC TARGET -- Interdisciplinary aspects of wave scattering -- Acoustic scattering -- Acoustic scattering: approximate methods -- Electromagnetic wave scattering: theory -- Electromagnetic wave scattering: approximate and numerical methods -- Electromagnetic wave scattering: applications -- Elastodynamic wave scattering: theory -- Elastodynamic wave scattering: Applications -- Scattering in Oceans -- Part 2: SCATTERING IN MICROSCOPIC PHYSICS AND CHEMICAL PHYSICS -- Introduction to direct potential scattering -- Introduction to Inverse Potential Scattering -- Visible and Near-visible Light Scattering -- Practical Aspects of Visible and Near-visible Light Scattering -- Nonlinear Light Scattering -- Atomic and Molecular Scattering: Introduction to Scattering in Chemical -- X-ray Scattering -- Neutron Scattering -- Electron Diffraction and Scattering -- Part 3: SCATTERING IN NUCLEAR PHYSICS -- Nuclear Physics -- Part 4: PARTICLE SCATTERING -- State of the Art of Peturbative Methods -- Scattering Through Electro-weak Interactions (the Fermi Scale) -- Scattering Through Strong Interactions (the Hadronic or QCD Scale) -- Part 5: SCATTERING AT EXTREME PHYSICAL SCALES -- Scattering at Extreme Physical Scales -- Part 6: SCATTERING IN MATHEMATICS AND NON-PHYSICAL SCIENCES -- Relations with Other Mathematical Theories -- Inverse Scattering Transform and Non-linear Partial Differenttial Equations -- Scattering of Mathematical Objects.

These Conference Proceedings are intended to summarise the latest developments in diffraction and scattering theory as reported at the IU TAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity held in Manchester, England on 16-20 July 2000. This in formal meeting was organised to discuss mathematical advances, both from the theoretical and more applied points of view. However, its pri mary goal was to bring together groups of researchers working in dis parate application areas, but who nevertheless share common models, phenomenological features arising in such problems, and common math ematical tools. To this end, we were delighted to have four Plenary Speakers, Professors Allan Pierce, Ed Kerschen, Roger Grimshaw and John Willis FRS, who are undisputed leaders in the four thematic ar eas of our meeting (these are respectively acoustics, aeroacoustics, water or other free surface waves, elasticity). These Proceedings should offer an excellent vehicle for continuing the dialogue between these groups of researchers. The participants were invited because of their expertise and recent contributions to this field. Collectively, there were around 90 contrib utors to the Symposium from some 13 countries located all around the world. These included 45 speakers, 35 co-authors and about 10 other delegates. Individuals came from many of the major international cen tres of excellence in the field of scattering theory.

Waves represent an important topic of study in physics, mathematics, and engineering. This volume is a resource book for those interested in understanding the physics underlying nanotechnology and mesoscopic phenomena. It aims to bridge the gap between the textbooks and research frontiers in wave related topics.

This one-of-a-kind book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas. Rays, Waves, and Scattering is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technical material), and several informative appendixes. Provides a panoramic look at wave motion in many different contexts Features problems and exercises throughout Includes numerous appendixes, some on topics not often covered An ideal reference book for practitioners Can also serve as a supplemental text in classical applied mathematics, particularly wave theory and mathematical methods in physics and engineering Accessible to anyone with a strong background in ordinary differential equations, partial differential equations, and functions of a complex variable

This volume contains a selection of papers presented at the 2008 Conference on Frontiers of Applied and Computational Mathematics (FACM'08), held at the New Jersey Institute of Technology (NJIT), May 19-21, 2008. The papers reflect the conference themes of mathematical biology, mathematical fluid dynamics, applied statistics and biostatistics, and waves and electromagnetics. Some of the world's most distinguished experts in the conference focus areas provide a unique and timely perspective on leading-edge research, research trends, and important open problems in several fields, making it a “must read” for active mathematical scientists.Included are major new contributions by a distinguished trio of plenary speakers: Frank Hoppensteadt contributes a thought-provoking paper on the evolving relationship between applied mathematics and the computer; Pranab Sen explores exciting new trends in computational biology and informatics; and Jean-Marc Vanden-Broeck describes his recent research on 3D free surface flows. There are also many innovative contributions by a prestigious group of invited mini-symposium speakers, making this an indispensable collection for professionals and graduate students in the mathematical sciences and related fields.Finally, the 75th birthday dedication to Daljit S Ahluwalia — for his many contributions to building a world-class mathematical sciences department at NJIT — adds to making this a one-of-a-kind volume.