Canonical Problems in Scattering and Potential Theory Part II: Acoustic and Electromagnetic Diffraction by Canonical Structures

Series:
Monographs and Surveys in Pure and Applied Mathematics
Published:
April 29, 2002 by Chapman and Hall/CRC - 520 Pages
Author(s):
S.S. Vinogradov, University of Dundee, Scotland, UK; P. D. Smith, University of Dundee, Dundee, Ireland Dundee University, Dundee, UK; E.D. Vinogradova, University of Dundee, Scotland, UK

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$139.95
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ISBN 9781584881636
Cat# C1631
 

Features

  • Presents groundbreaking advances in determining diffraction from various canonical scatterers
  • Develops the mathematics of canonical structures in potential theory and solves mixed boundary potential problems for structures with cavities and edges
  • Uses the Abel integral transform and the method of Regularization to present a unified treatment of potential theory and diffraction
  • Describes many applications of real physical and engineering significance and provides physical interpretation of explicit mathematical solutions

    • Summary

    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

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