The energy-dependent radiation transfer in a homogeneous finite cylinder

Radiation transfer problem in the slowing-down region for cylindrical geometry with diffuse reflectivity and internal source is connected with source-free problem with isotropic boundary condition. Modelled kernels are used to represent the slowing-down kernel. Calculations are performed for the radiation flux at the boundary of the cylinder. Numerical results are obtained using the bi-variation technique.     

Anisotropic radiation transfer in a sphere with internal source

In this work we connect the problem of anisotropic radiation transfer in a sphere with diffuse reflectivity and containing an energy source with the problem of source free amisotropic radiation transfer with isotropic boundary condition. Exact equation for radiation heat flux for the first problem is obtained in terms of the source, the flux and the albedo of the second problem. Modeled kernel is used to represent the anisotropy of the phase function. Numerical results are given.     

Radiation transfer due to a point-source in an inhomogeneous finite sphere

A simple method for solving the radiation transfer due to a point source in an isotropically-scattering sphere with space-dependent albedo is presented. The results are compared with the only other available results obtained by Thynell and Özisik (1986) for inhomogeneous sphere. The present method is applicable for a wider class of albedo functions.     

Polarized radiation transfer in finite atmospheric media

The problem of monoenergetic polarized radiation transfer in a plane-parallel finite atmospheric medium is proposed. Pomraning–Eddington approximation is used to obtain the analytical solution for both the total intensity and the difference function of the polarized radiation. The medium is assumed to have specular reflecting boundaries with angular-dependent externally incident flux. For the sake of comparison, two different forms of the weight function, which introduced to force the boundary conditions to be fulfilled, are used. Numerical results of the reflectivity and transmissivity are obtained for the different degrees of polarization.     

Statistical description of the radiation field in a homogeneous medium of finite optical thickness

The problem of finding statistical averages which characterize the radiation field in a semi-infinite atmosphere has been discussed by the author in a series of papers. In this paper some of the results obtained there are generalized to media of finite optical thickness. The average number of scattering events undergone by a photon during its random walk in an atmosphere and the average time required for this are determined. Three different types of averages are considered, depending on the photon characteristics over which the averages are taken. Special attention is devoted to the asymptotic behavior of these quantities for media with large optical depths taking the influence of continuum absorption into account. __________ Translated from Astrofizika, Vol. 49, No. 2, pp. 263–275 (May 2006).     

Radiative transfer in a homogeneous magnetized plasma

On the ground of the proper wave representation the general theory is developed of radiative transfer in a homogeneous plasma with the strong magnetic field ( _B /1). The linear and nonlinear equations are derived which generalize the corresponding equations of scalar radiative transfer theory in isotropic media. The solutions of some problems are given for the cases when the magnetic field is perpendicular to the surface: diffuse reflection of radiation from a semiinfinite medium, provided the sources are placed far from the surface (Milne's problem) and have constant intensity, increase linearly or quadratically with the optical depths, or decrease exponentially from the surface.     

Radiation transfer in a sphere with internal source

From the presence of superhumps in its outburst light curve, the dwarf nova BR Lup is shown to be a member of the SU UMa sub-class of cataclysmic variables. Its orbital period is estimated to be 0.0789 d.     

An exact solution of time-dependent equation of transfer of trapped radiation in a finite absorbing medium

Milne's time-dependent equation of transfer of trapped radiation in finite absorbing medium has been exactly solved by a combination of Das Gupta's modified form of the Wiener-Hopf technique and method of solving boundary value problems in the theory of heat conduction as adopted by Chandrasekhar (1950) to solve the same equation approximately in combination with his method of discrete ordinates. Milne himself had earlier obtained an approximate solution of his equation.     

Stochastic transfer of polarized radiation in finite cloudy atmospheric media with reflective boundaries

The problem of monoenergetic radiative transfer in a finite planar stochastic atmospheric medium with polarized (vector) Rayleigh scattering is proposed. The solution is presented for an arbitrary absorption and scattering cross sections. The extinction function of the medium is assumed to be a continuous random function of position, with fluctuations about the mean taken as Gaussian distributed. The joint probability distribution function of these Gaussian random variables is used to calculate the ensemble-averaged quantities, such as reflectivity and transmissivity, for an arbitrary correlation function. A modified Gaussian probability distribution function is also used to average the solution in order to exclude the probable negative values of the optical variable. Pomraning-Eddington approximation is used, at first, to obtain the deterministic analytical solution for both the total intensity and the difference function used to describe the polarized radiation. The problem is treated with specular reflecting boundaries and angular-dependent externally incident flux upon the medium from one side and with no flux from the other side. For the sake of comparison, two different forms of the weight function, which introduced to force the boundary conditions to be fulfilled, are used. Numerical results of the average reflectivity and average transmissivity are obtained for both Gaussian and modified Gaussian probability density functions at the different degrees of polarization.     

Gravitational instability of a homogeneous gas cloud with radiation

The problem of the gravitational instability of an inviscid plasma cloud is investigated by taking into account radiative effects. It is shown that, on given conditions, the radiation stabilizes the system.     

The solution of a time-dependent equation of transfer in nonconservative finite media

A time-dependent nonconservative radiative transfer equation in a finite media has been solved. Firstly, the time-dependent function is converted into a time-independent function by the use of a Laplace transform and the transformed equation is then solved by a method using linear operator theory.