Provides a review of developments in the fields of direct and inverse electromagnetic wave scattering. Contributions from leading researchers in these fields from all over the world are gathered in this book to discuss the state of the topic and directions for future research, starting from the fundamental structure of wave scattering problems and finishing with an assessment of the impact of this structure in applications

This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. The second edition includes material on Newton’s method for the inverse obstacle problem, an elegant proof of uniqueness for the inverse medium problem, a discussion of the spectral theory of the far field operator and a method for determining the support of an inhomogeneous medium from far field data.

This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. The second edition includes material on Newton’s method for the inverse obstacle problem, an elegant proof of uniqueness for the inverse medium problem, a discussion of the spectral theory of the far field operator and a method for determining the support of an inhomogeneous medium from far field data.

Electromagnetic Scattering is a collection of studies that aims to discuss methods, state of the art, applications, and future research in electromagnetic scattering. The book covers topics related to the subject, which includes low-frequency electromagnetic scattering; the uniform asymptomatic theory of electromagnetic edge diffraction; analyses of problems involving high frequency diffraction and imperfect half planes; and multiple scattering of waves by periodic and random distribution. Also covered in this book are topics such as theories of scattering from wire grid and mesh structures; t ...

This classic book provides a rigorous treatment of the Riesz?Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. Readers will benefit from a full discussion of the mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions, an in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves, and an introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.

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.

The 'factorization method', discovered by Professor Kirsch, is a relatively new method for solving certain types of inverse scattering problems and problems in tomography. The text introduces the reader to this promising approach and discusses the wide applicability of this method by choosing typical examples.

Inverse scattering theory has been a particularly active and successful field in applied mathematics and engineering for the past twenty years. The increasing demands of imaging and target identification require new powerful and flexible techniques besides the existing weak scattering approximation or nonlinear optimization methods. One class of such methods comes under the general description of qualitative methods in inverse scattering theory. This textbook is an easily-accessible "class-tested" introduction to the field. It is accessible also to readers who are not professional mathematicians, thus making these new mathematical ideas in inverse scattering theory available to the wider scientific and engineering community.

The purpose of this text is to present the theory and mathematics of inverse scattering, in a simple way, to the many researchers and professionals who use it in their everyday research. While applications range across a broad spectrum of disciplines, examples in this text will focus primarly, but not exclusively, on acoustics. The text will be especially valuable for those applied workers who would like to delve more deeply into the fundamentally mathematical character of the subject matter.Practitioners in this field comprise applied physicists, engineers, and technologists, whereas the theory is almost entirely in the domain of abstract mathematics. This gulf between the two, if bridged, can only lead to improvement in the level of scholarship in this highly important discipline. This is the book's primary focus.

The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years. This, therefore, is the first book devoted to ellipsoidal harmonics. Topics are drawn from geometry, physics, biosciences and inverse problems. It contains classical results as well as new material, including ellipsoidal bi-harmonic functions, the theory of images in ellipsoidal geometry and vector surface ellipsoidal harmonics, which exhibit an interesting analytical structure. Extended appendices provide everything one needs to solve formally boundary value problems. End-of-chapter problems complement the theory and test the reader's understanding. The book serves as a comprehensive reference for applied mathematicians, physicists, engineers and for anyone who needs to know the current state of the art in this fascinating subject.