On the justification of the Foldy--Lax approximation for the acoustic scattering by small rigid bodies of arbitrary shapes
We are concerned with the acoustic scattering problem by many small rigid obstacles of
arbitrary shapes. We give a sufficient condition on the number M and the diameter a of the
obstacles as well as the minimum distance d between them under which the Foldy--Lax
approximation is valid. Precisely, if we use single layer potentials for the representation of
the scattered fields, as is done sometimes in the literature, then this condition is (M-
1)ad^2<c, with an appropriate constant c, while if we use double layer potentials, then a …
arbitrary shapes. We give a sufficient condition on the number M and the diameter a of the
obstacles as well as the minimum distance d between them under which the Foldy--Lax
approximation is valid. Precisely, if we use single layer potentials for the representation of
the scattered fields, as is done sometimes in the literature, then this condition is (M-
1)ad^2<c, with an appropriate constant c, while if we use double layer potentials, then a …
On the justification of the Foldy-Lax approximation for the acoustic scattering by small rigid bodies of arbitrary shapes
D Prasad Challa, M Sini - arXiv e-prints, 2013 - ui.adsabs.harvard.edu
We are concerned with the acoustic scattering problem by many small rigid obstacles of
arbitrary shapes. We give a sufficient condition on the number $ M $ and the diameter $ a $
of the obstacles as well as the minimum distance $ d $ between them under which the Foldy-
Lax approximation is valid. Precisely, if we use single layer potentials for the representation
of the scattered fields, as it is done sometimes in the literature, then this condition is $(M-
1)\frac {a}{d^ 2}< c $, with an appropriate constant $ c $, while if we use double layer …
arbitrary shapes. We give a sufficient condition on the number $ M $ and the diameter $ a $
of the obstacles as well as the minimum distance $ d $ between them under which the Foldy-
Lax approximation is valid. Precisely, if we use single layer potentials for the representation
of the scattered fields, as it is done sometimes in the literature, then this condition is $(M-
1)\frac {a}{d^ 2}< c $, with an appropriate constant $ c $, while if we use double layer …
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