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The Transmission Acoustic Scattering Problem for Bi-Spheres in Low-Frequency Regime
Arnaoudov, Iani
Venkov, George
2006
Abstract
An acoustically soft sphere covered by a penetrable eccentric spherical shell disturbs the propagation of an incident
plane wave field. It is shown that there exists exactly one bispherical coordinate system that describes the given geometry.
The incident wave is assumed to have a wavelength which is
much larger than the characteristic dimension of the scatterer
and thus the low-frequency approximation method is applicable to
the scattering problem. The incomplete R-separation of variables
in bispherical coordinates and the normal differentiation involved
in the transmission boundary conditions lead to a three-term recurrence relation for the series coefficients corresponding to the
scattered fields. Thus, the potential boundary-value problem for
the leading low-frequency approximations is reduced to infinite
tridiagonal linear systems, which are solved analytically.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
38 (2006)
Publisher
EUT Edizioni Università di Trieste
Source
I. Arnaoudov, G. Venkov, "The Transmission Acoustic Scattering Problem for Bi-Spheres in Low-Frequency Regime", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 38 (2006), pp. 73-93
Languages
en
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