A.R. Degheidy

The Pomraning-Eddington approximation to diffusion of light in turbid materials

Abstract The source-free diffusion problem of light in turbid media with generalized boundary conditions is considered. The intensity of light is considered as a sum of collimated and diffused radiance. In this way the problem is transformed to a source problem with a collimated source (problem 1). This problem is solved in terms of the corresponding source-free problem of simple boundary conditions (problem 2). The Pomraning-Eddington method is used to solve problem 2. Two coupled first-order differential equations are obtained involving the energy density and the radiation net flux. Weight functions are introduced in order to force the boundary conditions to be fulfilled. Numerical results are given and compared with previous calculations. The calculations show that the accuracy depends on the choice of the weight function.

Stochastic radiative transfer in a finite plane-parallel medium with general boundary conditions

Abstract The time-independent radiative transfer problem in a scattering and absorbing planar random medium with general boundary conditions and internal energy source is considered. The medium is assumed to consist of two randomly mixed immiscible fluids, with the mixing statistics described as a two-state homogeneous Markov process. The problem is solved in terms of the solution of the corresponding free-source problem with simple boundary conditions which is solved using Pomraning–Eddington approximation in the deterministic case. A formalism, developed to treat radiative transfer in statistical mixtures, is used to obtain the ensemble-averaged solution. The average partial heat fluxes are calculated in terms of the albedoes of the source-free problem. Results are obtained for isotropic and anisotropic scattering for specular and diffused reflecting boundaries.

Time-dependent radiation transfer in a semi-infinite stochastic medium with Rayleigh scattering

The time-dependent radiation transfer in a semi-infinite stochastic medium of binary Markovian mixture with Rayleigh scattering is presented. A formalism, developed to treat radiation transfer in statistical mixtures, is used to obtain the ensemble-averaged solution. The average reflectivity, radiant energy and net flux are computed for specular-reflecting boundary. For the sake of comparison, we use two different weight functions in our calculations.

Effect of pressure and temperature on electronic structure of GaN in the zinc-blende structure

The effect of the hydrostatic pressure and the temperature on the electronic structure in GaN semiconductor has been calculated using the local empirical pseudopotential method. The variation of the direct and indirect energy gaps with the pressure up to 120 kbar and with the temperature up to 500 K has been done. The calculated fundamental energy gap at different pressures and different temperatures are calculated and compared with the available experimental data which show excellent agreement. The effect of pressure and temperature on the refractive index of the considered materials has also been studied.

EFFECTS OF FRESNEL AND DIFFUSED REFLECTIVITIES ON LIGHT TRANSPORT IN A HALF-SPACE MEDIUM

Abstract Radiation transfer problem for isotropically scattering, non-absorbing half-space medium with angular-dependent (specular) and constant diffuse reflecting boundary is considered. The angular-dependent reflectivity of the boundary is considered as Fresnel’s reflection probability function. Some physical and engineering quantities of interest such as angular distribution of radiation, total density of radiation and extrapolated endpoint are computed for various values of refractive index and diffuse reflecting coefficient using variational method. For sake of comparisons, results with average and effective reflectivities are carried out for different values of refractive indices. Our results for non-diffuse reflectivity are compared with the available data given for specular Fresnel’s reflectivity which show excellent agreement.

Radiative transfer in a spherical medium

Abstract The problem of radiative transfer in a spherical medium is solved by inspection once the slab solution is known. In this work we try to solve the Pseudo-slab problem using a set of trial functions that depend on Cases eigenvalues plus a linear combination of exponential integral functions. The proposed trial functions are used in the integral equation which transforms it to a system of algebraic equations in the expansion coefficients. These expansion coefficients are used to calculate the albedo and the partial heat flux for isotropic scattering in a homogeneous spherical medium.

Variational approach to the milne problem with a specular and diffuse reflecting boundary

Abstract An approximate solution of the Milne integral equation for specular and diffuse reflecting boundary is deduced by using variational calculus. An approximate, (four variable parameters) expression, for the particle density and emergent angular distribution has been proposed. Numerical results for extrapolated endpoint, particle density and angular distribution in a region close to the boundary are calculated. The percentage difference for extrapolated endpoint, taking the exact values as a reference, is approximately 1.4 × 10−10 for a non-reflecting medium and does not exceed 0.01% for all degrees of blackness in the diffusion reflection. The results for a combination of specular and diffuse reflections are also given.

EFFICIENT AND ACCURATE METHOD FOR RADIATION TRANSFER PROBLEMS

Abstract An efficient method of analysis, which utilizes trial functions based on Cases eigenvalues, is developed for solving radiation transfer in an absorbing and scattering homogeneous semi-infinite plane-parallel medium subjected to externally incident radiation. Expressions for the forward and backward intensities, reflectivity and total radiation intensity are included. Numerical results are given and compared involving different forms of the externally incident radiation on the boundary surface. It is shown that the solution converges rapidly to the exact results and that lower-order solutions predict values of the physical parameters that are accurate to five figures in all values of the single-scattering albedos in the range 0.1 ≤ ω ≤ 1. The method has been also used to get approximate formulae for calculating Chandrasekhars characteristic H-functions and their moments.

A three-center shell model for ternary fission

We propose a generalization of the phenomenological shell model based on the harmonic oscillator potential with spin-orbit term andl2-corrections to systems made up of three clusters. The centers of these may be in arbitrary geometrical configurations and the clusters may be of different masses. The method of determining the eigenstates of the single-particle Hamiltonian is sketched and results for the cluster structure of light nuclei and the ternary fission of a superheavy system are presented.

Polarized radiation transfer in a semi-infinite random medium

The problem of radiation transfer in a semi-infinite plane-parallel random medium with polarized Rayleigh scattering phase function is considered. The random medium is assumed to consist of two immiscible mixed materials with specular reflecting boundary. The mixing statistics of the two components of the medium is described by the two-state homogeneous Markovian statistics. A formalism, developed to treat radiative transfer in statistical mixtures, is used to obtain the ensemble averaged solution. Three different weight functions are used to obtain the numerical results for the ensemble-average for reflectivity, radiant energy, and net flux of the medium.