Algebraic aspects of multiple scattering by two parallel cylinders: Classification and physical interpretation of scattering resonances

Acoustic scattering by a pair of identical parallel cylinders is studied by emphasizing the role of the symmetries of the scatterer. Incident and scat tered fields are expanded over the different irreducible representations of C-2 nu, the symmetry group of the scatterer. Then, from the boundary condi tions, one obtains an infinite set of four linear complex algebraic equatio ns (each one associated with a representation) where the unknown coefficien ts of the scattered fields are uncoupled. This method significantly simplif ies the numerical treatment of the problem. As a consequence, positions of the scatterer resonances are determined in the complex plane of the reduced frequency and a partial algebraic classification of the resonances is obta ined for various boundary conditions (soft cylinders, hard cylinders and el astic cylinders immersed in water). A physical interpretation of certain re sonances in terms of trapped geometrical paths is provided. (C) 1999 Academ ic Press.