Mathematical Sciences: Multiple Scattering by Elastic Spheres in an Elastic Half-Space Bounded by an Elastic Penetrable Interface

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Dr. Phanord will extend to elasticity the work done by Richard Solakiewicz under the guidance of Professor Victor Twersky on acoustic scattering by an obstacle in a half-space bounded by a penetrable interface. With the elastic extension of the solution for the single object in isolation, Dr. Phanord will construct the multiple scattering solution for a distribution of identical spheres. He will use the self-consistent procedure to obtain integral equations for the multiple scattering amplitudes of the composite media in terms of the scattering amplitudes of the single obstacle. From the ensemble average of the integral equations and the equivalent medium approach, he will derive a pair of dispersion relations which provide a means to obtain the bulk propagation parameters of the composite media from those of the isolated single scatterer. To compute multiple scattering cross-sections, Dr. Phanord will establish new reciprocity relations corresponding to multiple elastic scattering for different combinations of the incident waves.