Moving forcing effects in a two-phase medium

Abstract

AbstractAn unbounded two-phase medium is transmitting radiation from a group of uniformly moving, two-dimensional forcing effects. The emission process is governed by two matrix differential equations for both interior regions, accompanied by a common set of boundary conditions along the communicating interface. Anticipating possible hyperbolic modes, in co-existence with elliptic modes during the eventual steady state, a radiation condition is initially applied. This radiation condition, together with a particular boundedness criterion, decides the precise number of boundary equations required. An exact solution is established for moving forcing effects having arbitrary spatial distributions. Those aligned along the interface correspond to sheet sources. Superimposed are additional source sheets virtually induced by the action of internal forcing effects, converting their combined incident field into reflection and refraction. A peculiar feature is the invariant propagation along characteristics of certain hyperbolic modes, under the essential presence of elliptic modes, as real Hilbert transforms (in the sense of principal values) of a net interface source density.