A numerical scheme for the solution of axisymmetric radiative transfer problems in irregular domains filled by media with opaque and transparent diffuse and specular boundaries

This paper presents a new numerical scheme of the discrete ordinates method for the solution of axisymmetric radiative transfer problems in irregular domains filled by media with opaque and transparent diffuse and specular (Fresnel) boundaries and interfaces. New test problems of radiative transfer, which describe radiative transfer in domains with Fresnel interfaces, are proposed in this paper. These problems admit analytic solutions and can be used as benchmark ones. The proposed scheme is applied to the solution of the problems. Numerical results show that the presence of Fresnel interfaces leads to an appreciably larger error in numerical solution. This is connected with the “discontinuity” of the Fresnel reflectivity, which, through numerical diffusion, leads to the distortion of numerical solution. Modification of the scheme allows to reduce the numerical error.     

INITIAL BOUNDARY VALUE PROBLEMS FOR PARABOLIC EQUATIONS IN LIPSCHITZ CYLINDERS

ＩＮＩＴＩＡＬ ＢＯＵＮＤＡＲＹ ＶＡＬＵＥ ＰＲＯＢＬＥＭＳ ＦＯＲ ＰＡＲＡＢＯＬＩＣ ＥＱＵＡＴＩＯＮＳ ＩＮ ＬＩＰＳＣＨＩＴＺ ＣＹＬＩＮＤＥＲＳ ￥ＧＡＯＷＥＮＪＩＥＡｂｓｔｒａｃｔ：Ｔｈｅｉｎｉｔｉａｌ－Ｄｉｒｉｃｈｌｅｔａｎｄｉｎｉｔ...     

Rudolph diagrams and an analytic realization of the Vitushkin covering

An example of a three-sheeted covering over the ball in ² is constructed. The covering is the union of a four-dimensional ball with an analytic disk. The projection of the ball is a local homeomorphism ramified along the disk, whose projection is a part of an algebraic curve.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 206–224, August, 1996.This research was partially supported by the Russian Foundation for Basic Research under grant No. 93-011-225.     

The limit-periodic finite-difference operator onl 2(ℤ) associated with iterations of quadratic polynomials

The limit-periodic discrete operator of the Schrödinger type on the axis associated with iterations of quadratic polynomials is investigated. It is proved that this operator has a singularly continuous simple spectrum. Connections with the Sinai-Bowen-Ruelle measure and the conformai map onto a special comblike domain are established.     

Morphology of polyphosphazenes: Oriented and unoriented

The purpose of this work is to obtain a better understanding of the morphology of polyphosphazenes and to establish some general morphological characteristics. Solution cast, stretched and annealed films of poly(bistrifluoroethoxyphosphazene), PBFP, and poly(bisphenoxyphosphazene), PBPP, have been investigated by electron and optical microscopy. Thin and thick films were prepared using different solvents. Films were cast and stretched below as well as above T(1), the thermotropic transition of each polymer. In the case of PBFP its T(1) transition was established through birefringent-temperature measurements and orientational changes were measured as a result of heat cycling stepwise through T(1). Thin specimens were oriented on electron microscope grids using a mechanical stretcher; thicker films were drawn by hand at various temperatures, too. Orientation was effectively induced through casting on hot liquid surfaces at temperatures > T(1). PBPP exhibits a layer (domain) morphology of high crystallinity and orientation under these conditions. Dislocations or stacking faults can be recorded in darkfield in PBPP but the low stability of PBFP to the electron beam does not permit dark-field images to be recorded. Optical microscopy was used to record cast film textures.Paper presented at: Frühjahrstagung der Deutschen Physikalischen Gesellschaft und der Polymer-Gruppe Schweiz, Lausanne 18.–20. März, 1985.Dedicated to Professor H.-G. Kilian's 60th birthday.     

On the Continuity of Stochastic Exit Time Control Problems

We determine a weaker sufficient condition than that of Theorem 5.2.1 in Fleming and Soner (2006) for the continuity of the value functions of stochastic exit time control problems.     

The Dirichlet problem for Hessian quotient equations in exterior domains

In this paper, we obtain the uniqueness and existence of viscosity solutions with prescribed asymptotic behavior at infinity to Hessian quotient equations in exterior domains.     

Uniform estimates for transmission problems with high contrast in heat conduction and electromagnetism

In this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains, with a special emphasis for the case when the ratio between these coefficients is large. In the most part of the work, the interface between the two subdomains is supposed to be Lipschitz. We first study a scalar transmission problem which is handled through a converging asymptotic series. Then we derive uniform a priori estimates for Maxwell transmission problem set on a domain made up of a dielectric and a highly conducting material. The technique is based on an appropriate decomposition of the electric field, whose gradient part is estimated thanks to the first part. As an application, we develop an argument for the convergence of an asymptotic expansion as the conductivity tends to infinity.     

Positive solutions for a class of multiparameter ordinary elliptic systems

Using a fixed point theorem due to M.A. Krasnosel'skii, the upper-lower solutions method and fixed point index theory, we study existence, non-existence and multiplicity of positive solutions for a class of systems of second-order ordinary differential equations. We give a new notion of superlinearity for nonlinearities. Observe that the nonlinearities may even be, in some sense, singular. As an application, we show multiplicity results for a class of semilinear elliptic systems in both bounded annular domains and exterior domains. In addition, we apply our results to fourth-order boundary value problems.