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

Phanord博士将把Richard Solakiewicz在Victor Twersky教授的指导下所做的工作扩展到弹性领域，该工作涉及由可穿透界面限制的半空间中障碍物的声波散射。在孤立地对单个物体的解进行弹性扩展的情况下，Phanord博士将为相同球体的分布构造多重散射解。他将使用自洽程序来获得复合介质的多重散射幅度的积分方程式，它是关于单个障碍物的散射幅度的。从积分方程组的系综平均和等效介质方法，他将导出一对色散关系，它提供了一种从孤立的单个散射体的整体传播参数获得复合介质的整体传播参数的方法。为了计算多个散射截面，Phanord博士将为不同的入射波组合建立对应于多个弹性散射的新的互易关系。

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.