Canonical Problems in Scattering and Potential Theory Part II: Acoustic and Electromagnetic Diffraction by Canonical Structures, 1st Edition (Hardback) book cover

Canonical Problems in Scattering and Potential Theory Part II

Acoustic and Electromagnetic Diffraction by Canonical Structures, 1st Edition

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

Chapman and Hall/CRC

520 pages | 170 B/W Illus.

Purchasing Options:$ = USD
Hardback: 9781584881636
pub: 2002-04-29
SAVE ~$35.00
Currently out of stock
$175.00
$140.00
x
eBook (VitalSource) : 9780429123696
pub: 2002-04-29
from $28.98


FREE Standard Shipping!

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.

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

About the Authors/Editors

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.

About the Series

Monographs and Surveys in Pure and Applied Mathematics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations