Vinogradov / Smith / Vinogradova Canonical Problems in Scattering and Potential Theory Part II

Acoustic and Electromagnetic Diffraction by Canonical Structures
Erscheinungsjahr 2002
ISBN: 978-0-8493-8706-7
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 520 Seiten

Reihe: Monographs and Surveys in Pure and Applied Mathematics

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.

Zielgruppe

Mathematicians, physicists, and electrical engineers in scattering theory

Autoren/Hrsg.

Vinogradov, S.S.

Smith, P. D.

Vinogradova, E.D.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis

Inhaltsverzeichnis

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