Canonical Problems in Scattering and Potential Theory - Two Volume Set

Canonical Problems in Scattering and Potential Theory - Two Volume Set

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

ISBN-10: 158488164X

ISBN-13: 9781584881643

Pub. Date: 04/26/2002

Publisher: Taylor & Francis

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 Studies diffraction of acoustic and electromagnetic waves from open structures with edges and cavities Uses the Abel

Overview

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 Studies diffraction of acoustic and electromagnetic waves from open structures with edges and cavities 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 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.

Product Details

ISBN-13:
9781584881643
Publisher:
Taylor & Francis
Publication date:
04/26/2002
Series:
500 Tips Series
Pages:
912
Product dimensions:
9.40(w) x 12.30(h) x 4.40(d)

Table of Contents

PART I: CANONICAL STRUCTURES IN POTENTIAL THEORY
Mathematical Aspects of Potential Theory
Dual or Triple Series and Integral Equations
Electrostatic Potential Theory for Open Spherical Shells and Cavities
Open Spheroidal Conducting Shells and Cavities
Charged Toroidal Shells and Cavities
Potential Theory for Conical Structures with Edges
Two-Dimensional Potential Theory
Rigorous Solution Methods for more Complicated Structures
APPENDICES

PART II: ACOUSTIC AND ELECTROMAGNETIC DIFFRACTION BY CANONICAL STRUCTURES
Mathematical Aspects of Wave Scattering
Acoustic Diffraction from a Circular Hole in a Thin Spherical Shell
Acoustic Diffraction from a Spherical Shell with Two Holes or an Equatorial Slot
Electromagnetic Diffraction from a Circular Hole in a Perfectly Conducting Spherical Shell
Electromagnetic Diffraction from a Spherical Shell with Two Circular Holes or an Equatorial Slot
Spherical Cavities with Dielectric Inclusions of Spherical Shape
Diffraction from Spheroidal Cavities
Applications of the Abel Integral Transform to Diffraction by Other Classes of Canonical Scatterers
Conclusion.

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