Решение задачи дифракции на теле вращения, расположенном в диэлектрическом слое

Two methods for solving the problem of diffraction of the plane wave by the dielectric body of revolution located in the homogeneous dielectric layer are proposed. Two methods are compared using the example of the scattering of the plane wave by the homogeneous spheroid and the circular cylinder of finite dimensions located in the layer. The results of calculating the pattern for the case of diffraction by the finite circular cylinder which is immersed in the layer and has variable material characteristics are presented. The wavelength dependences of the pattern for plasmon particles located in the layered medium are obtained.

GRAVITATIONAL COLLAPSE OF HOMOGENEOUS SPHEROIDS

We present a simplified description of the gravitational collapse of a uniformly rotating neutron stellar core, which can represent the final stage of the protoneutron star formed after the supernova type II explosion. The system is treated as a compressible homogeneous spheroid and the collapse time-evolution is extracted from an effective Lagrangian description of the system geometric parameters. A sudden mass quadripole change of the system at the final stage of the collapse is shown during the core bounce.