1st Edition
Canonical Problems in Scattering and Potential Theory - Two volume set
912 Pages
by
Chapman & Hall
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... Read more
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.
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.
Biography
S.S. Vinogradov, P. D. Smith, E.D. Vinogradova
