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Canonical Problems in Scattering and Potential Theory Part II

Acoustic and Electromagnetic Diffraction by Canonical Structures

By S.S. Vinogradov, P. D. Smith, E.D. Vinogradova

Series Editor: Alan Jeffrey, Haim Brezis, Ronald G. Douglas

Published April 29th 2002 by Chapman and Hall/CRC – 520 pages

Series: Monographs and Surveys in Pure and Applied Mathematics

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Description

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.

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

Name: Canonical Problems in Scattering and Potential Theory Part II: Acoustic and Electromagnetic Diffraction by Canonical Structures (Hardback) – Chapman and Hall/CRC 
Description: By S.S. Vinogradov, P. D. Smith, E.D. VinogradovaSeries Editor: Alan Jeffrey, Haim Brezis, Ronald G. Douglas. 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...
Categories: Differential Equations, Applied Mathematics, Mathematics & Statistics for Engineers