In this paper we review the results of the author on the theory of scalar and
vector wave scattering by small bodies of an arbitrary shape with the emphasis
on practical applicability of the formulas obtained and on the mathematical
rigor of the theory. For the scalar wave scattering by a single body, our main
results can be described as follows: (1) Analytical formulas for the scattering
amplitude for a small body of an arbitrary shape are obtained; dependence of
the scattering amplitude on the boundary conditions is described. (2) An
analytical formula for the scattering matrix for electromagnetic wave
scattering by a small body of an arbitrary shape is given. Applications of
these results are outlined (calculation of the properties of a rarefied medium;
inverse radio measurement problem; formulas for the polarization tensors and
capacitance). (3) The multi-particle scattering problem is analyzed and
interaction of the scattered waves is taken into account. For the
self-consistent field in a medium consisting of many particles ~ 10^{23},
integral-differential equations are found. The equations depend on the boundary
conditions on the particle surfaces. These equations offer a possibility of
solving the inverse problem of finding the medium properties from the
scattering data. For about 5 to 10 bodies the fundamental integral equations of
the theory can be solved numerically to study the interaction between the
bodies.
Publié le : 2000-11-20
Classification:
Mathematical Physics,
Mathematics - Analysis of PDEs,
Mathematics - Numerical Analysis,
65J10, 65R20, 78A45
@article{0011034,
author = {Ramm, A. G.},
title = {Wave scattering by small bodies of arbitrary shapes},
journal = {arXiv},
volume = {2000},
number = {0},
year = {2000},
language = {en},
url = {http://dml.mathdoc.fr/item/0011034}
}
Ramm, A. G. Wave scattering by small bodies of arbitrary shapes. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0011034/