Wave Scattering by Small Bodies of Arbitrary Shapes

Wave Scattering by Small Bodies of Arbitrary Shapes

by Alexander G. Ramm
     
 

ISBN-10: 9812561862

ISBN-13: 9789812561862

Pub. Date: 05/18/2005

Publisher: World Scientific Publishing Company, Incorporated

This book presents analytical formulas which allow one to calculate the S-matrix for the acoustic and electromagnetic wave scattering by small bodies or arbitrary shapes with arbitrary accuracy. Equations for the self-consistent field in media consisting of many small bodies are derived. Applications of these results to ultrasound mammography and electrical…  See more details below

Overview

This book presents analytical formulas which allow one to calculate the S-matrix for the acoustic and electromagnetic wave scattering by small bodies or arbitrary shapes with arbitrary accuracy. Equations for the self-consistent field in media consisting of many small bodies are derived. Applications of these results to ultrasound mammography and electrical engineering are considered.The above formulas are not available in the works of other authors. Their derivation is based on a mathematical theory for solving integral equations of electrostatics, magnetostatics, and other static fields. These equations are at a simple characteristic value. Convergent iterative processes are constructed for stable solution of these equations. The theory completes the classical work of Rayleigh on scattering by small bodies by providing analytical formulas for polarizability tensors for bodies of arbitrary shapes.

Product Details

ISBN-13:
9789812561862
Publisher:
World Scientific Publishing Company, Incorporated
Publication date:
05/18/2005
Pages:
312
Product dimensions:
6.10(w) x 9.32(h) x 0.89(d)

Table of Contents

1Basic problems1
2Iterative processes for solving Fredholm's integral equations for static problems13
3Calculating electric capacitance25
4Numerical examples43
5Calculating polarizability tensors53
6Iterative methods : mathematical results69
7Wave scattering by small bodies93
8Fredholm alternative and a characterization of Fredholm operators125
9Boundary-value problems in rough domains137
10Low frequency asymptotics163
11Finding small inhomogeneities from scattering data193
12Modified Rayleigh conjecture and applications201
App. AOptimal with respect of accuracy algorithms for calculation of multidimensional weakly singular integrals and applications to calculation of capacitances of conductors of arbitrary shapes221

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