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Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical scatterers with comprising edges and other complex cavity features. It is an authoritative account of mathematical developments over the last two decades that provides benchmarks against which solutions obtained by numerical methods can be verified.
The first volume, Canonical Structures in Potential Theory, develops the mathematics, solving mixed boundary potential problems for structures with cavities and edges. The second volume, Acoustic and Electromagnetic Diffraction by Canonical Structures, examines the diffraction of acoustic and electromagnetic waves from several classes of open structures with edges or cavities. Together these volumes present an authoritative and unified treatment of potential theory and diffraction-the first complete description quantifying the scattering mechanisms in complex structures.
Table of Contents
Mathematical Aspects of Wave Scattering. The Equations of Acoustic and Electromagnetic Waves Solution of Helmholtz Equation: Separation of Variables Electromagnetic Fields of Elementary Sources. Green's Functions Representation of Incident Electromagnetic Waves Formulation of Wave Scattering Theory for Structures with Edges Single- or Double-Layer Surface Potentials and Dual Series Equations Survey of Methods for Scattering Acoustic Diffraction from a Circular Hole in a Thin Spherical Shell Plane wave Diffraction from a Soft or Hard Spherical Cap Rigorous Theory of the Spherical Helmholtz Resonator Quasi-Eigen Oscillations: Spectrum of the Open Spherical Shell Total and Sonar Cross-Sections Wide band Calculation of Mechanical Force The Receiving Spherical Reflector Antenna. Focal Region Analysis The Transmitting Spherical Reflector Antenna Acoustic Diffraction from Various Spherical Cavities The Hard Spherical Barrel and Soft Slotted Spherical Shell The Soft Spherical Barrel and Hard Slotted Spherical Shell Helmholtz Resonators: Barrelled or Slotted Spherical Shells Quasi-Eigen Oscillations of the Spherical Cavity Total and Sonar Cross-Sections; Mechanical Force Factor Electromagnetic Diffraction from a Perfectly Conducting Spherical Cavity. Electric or Magnetic Dipole Excitation. PlaneWave Diffraction from a Circular Hole in a Thin Metallic Sphere Reflectivity of an Open Spherical Shell The Receiving Spherical Reflector Antenna: Focal Region Analysis The Transmitting Spherical Reflector Antenna Electromagnetic Diffraction from Various Spherical Cavities EM Plane Wave Scattering by Two Concentric Spherical Shells Dipole Excitation: Slot Antennae Dipole Excitation of Doubly-Connected Spherical Shells Plane Wave Diffraction from a Perfectly Conducting Slotted Spherical Shell Magnetic Dipole Excitation of an Open Spherical Resonator Open Resonators Composed of Spherical and Disc Mirrors Spherical Cavities with Spherical Dielectric Inclusions Resonant Cavity Heating of a Small Lossy Dielectric Sphere Reflectivity of a Partially Screened Dielectric Sphere The Luneberg Lens Reflector Diffraction from Spheroidal Cavities Acoustic Scattering by a Rigid Thin Prolate Spheroidal Shell with a Circular Hole. Rigorous Theory of the Spheroidal Helmholtz Resonator . Axial Electric Dipole Excitation of Ametallic Spheroidal Cavity with One Hole: The Spheroidal Antenna Axial Magnetic Dipole Excitation of a Metallic Spheroidal Cavity with One Hole Axial Electric Dipole Excitation of a Spheroidal Cavity with Two Symmetrically Located Holes Impedance Loading of the Spheroidal Barrel Metallic Spheroid Embedded in a Spheroidal Cavity with Two Circular Holes: Shielded Dipole Antenna SelectedWave-ScatteringProblems for Different Structures Plane Wave Diffraction from Infinitely Long Strips Axially Slotted Infinitely Long Circular Cylinders Diffraction Problems for Circular Discs Diffraction from Elliptic Plates Wave Scattering Problems for Hollow Finite Cylinders Wave Scattering Problems for Some Periodic Structures Periodic Structure of a Hollow Finite Cylinders Shielded Microstrip Lines A Spheroidal Functions References
Professor Sergei S. Vinogradov holds the post of Leading Scientist at the Institute of Radiophysics and Electronics, Kharkov, Ukraine.
Paul D. Smith is Professor of Applied Mathematics at the University of Dundee, Scotland.
Dr. Elena D. Vinogradova is also at the University of Dundee as a Visiting Scientist from the Institute of Radiophysics and Electronics, Kharkov, Ukraine.
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CHOICE – Outstanding Academic Title – Award Winner
CHOICE – 2018 Outstanding Academic Title – Award Winner
Shingo Research and Professional Publication Award Winner
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