THE ANALYSIS OF THERMAL RESISTANCE OF THREE-DIMENSIONAL FRACTAL NETWORKS EMBEDDED IN A SPHERE

This paper presents a preliminary work to evaluate the thermal resistance of a spherical medium. In the sphere, a three-dimensional pore fractal network combined with electrical double layers is constructed to represent the pore structure of medium. The construction and structural parameters of a network are illustrated in detail. The thermal resistance of a sphere is primarily associated with structural parameters of network, pore structure parameters of medium, thermal conductivities of solid phase and pore channels. In this work, the evolution of thermal resistance with the fractal network is analyzed comprehensively. Besides, the evolution mechanisms of thermal resistance with pore structure parameters of medium are revealed. The influences of types of porous materials on thermal resistance are systematically studied.

A FREE BOUNDARY MODEL FOR OXYGEN DIFFUSION IN A SPHERICAL MEDIUM

The goal of this article is to find a correct approximated solution using a polynomial of sixth degree for the free boundary problem corresponding to the diffusion of oxygen in a spherical medium with simultaneous absorption at a constant rate, and to show some mistakes in previously published solutions.

Optical spectral singularities and coherent perfect absorption in a two-layer spherical medium

An optical spectral singularity is a zero-width resonance that corresponds to lasing at threshold gain. Its time-reversal causes coherent perfect absorption of light and forms the theoretical basis of antilasing. In this article, we explore optical spectral singularities of a two-layer spherical medium. In particular, we examine the cases that a gain medium is coated by a thin layer of high-refractive index glass and a spherical glass covered by a layer of gain material. In the former case, the coating reduces the minimum radius required for exciting spectral singularities and gives rise to the formation of clusters of spectral singularities separated by wide spectral gaps. In the latter case, the coating leads to a doubling of the number of spectral singularities.