Theoretical study of thermal diffusivity of superlattices in measurements using “mirage” technique

A complete theoretical treatment for the determination of thermal diffusivity of superlattices by the mirage technique has been performed. An effective medium approximation model of the thermal conductivity and thermal diffusivity of both sublayers is presented, which is different from the simple models with the thermal diffusivity or thermal conductivity in series or parallel. The numerical calculation of the transverse component of the probe beam deflection in the mirage effect shows that the results obtained from the complete thermal-wave theory and the medium approximation model, for the optically and thermally thick superlattices, are in good agreement with each other. However, the further study on the thermally thin superlattices shows that either the series or the parallel model of the thermal conductivity should be chosen according to whether the thermal impedance of the superlattice is larger or less than that of substrate, respectively.     

Finite-element analysis of planar dielectric waveguide discontinuities

The finite element method is combined with the mode-matching method and the multi-mode network method to analyze the scattering and radiation characteristics of a class of planar dielectric waveguide discontinuities. Unlike the conventional method to treat the radiation as a source-field problem, in the present approach, the dispersion characteristics of dielectric guided-wave structures are calculated first, and then the radiation problem is transferred to the propagation problem of a series of surface-waves and space waves from the viewpoint of scattering, thus the analysis is tremendously simplified.     

On Segal-Wilson's construction for the τ-functions of the constrained KP hierarchies

In this Letter, we study the constrained KP hierarchies by employing Segal-Wilson's theory on the -functions of the KP hierarchy. We first describe the elements of the Grassmannian which correspond to solutions of the constrained KP hierarchy, and then we show how to construct its rational and soliton solutions from these elements of the Grassmannian.