Canonical Problems in Scattering and Potential Theory Part 1: Canonical Structures in Potential Theory (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. Annotation Describes an analytical technique for determining diffraction from classes of canonical scatterers with edges and other complex cavity features. Develops the mathematics for solving mixed boundary value potential problems for structures with cavities and edges, and develops the theory of special functions, dual series, and functional analysis using transformations connected with Abel's integral equation to invert a singular part of the operator defining the potential. Chapter topics include electrostatic potential theory for open spherical and spheroidal shells, charged toroidal shells, and potential theory for conical structures with edges. Vinogradov is a scientist at the Institute of Radiophysics and Electronics in Ukraine. Annotation c. Book News, Inc., Portland, OR (booknews.com) This two-volume set describes a breakthrough in analytical techniques or accurately determining diffraction from classes of canonical scatterers. It is an authoritative account of mathematical developments over the last two decades, delivered in an accessible, concrete style rather than in abstract, formal one.Part 2: Acoustic and Electromagnetic Diffraction by Canonical Structures examines the diffraction of acoustic and electromagnetic waves from several classes of open structure with edges or cavities. Together these volumes present an authoritative and unified treatment of potential theory and diffraction. pt. 1. Canonical structures in potential theory pt. 2. Acoustic and electromagnetic diffraction by canonical structures.