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Low‐frequency scattering by a penetrable body with an eccentric soft or hard core
Author(s) -
LucasLekatsas John,
Kostopoulos Vassilis
Publication year - 2009
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1117
Subject(s) - scattering , plane wave , mathematics , scattering amplitude , field (mathematics) , mathematical analysis , wavelength , coordinate system , amplitude , radius , scattering theory , geometry , optics , physics , computer security , computer science , pure mathematics
A plane wave is scattered by an acoustically soft or hard sphere, covered by a penetrable non‐concentric spherical lossless shell that disturbs the propagation of the incident wave field. The dimensions of the coated sphere are much smaller than the wavelength of the incident field. Low‐frequency theory reduces this scattering problem to a sequence of potential problems, which can be solved iteratively. Exactly one bispherical coordinate system exists that fits the given geometry of the obstacle. For the case of a soft and hard core, the exact low‐frequency coefficients of the zeroth and the first‐order for the near field as well as the first‐ and second‐order coefficients for the normalized scattering amplitude are obtained and the cross sections are calculated. Discussion of the results and their physical meaning is included. Copyright © 2009 John Wiley & Sons, Ltd.