M. Sallah

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.

Radiative transfer in random media with Rayleigh scattering

Abstract This paper considers radiation transfer through a finite plane-parallel random medium consisting of two immiscible mixed materials. The mixing statistics of the two components of the medium is assumed to be described by the two-state homogeneous Markovian statistics. The problem treats a medium contains an internal source and has diffusely- and specularly-reflecting boundaries obeying Rayleigh scattering law. The problem with this generalized boundary conditions is solved in terms of the solution of the corresponding free source problem with simple boundary conditions. Pomraning–Eddington approach is used to obtain an explicit solution of the simple problem in the deterministic case. A formalism, developed to treat radiative transfer in statistical mixtures, is used to obtain the ensemble-averaged solution. Numerical results for the ensemble-average partial heat fluxes of the problem under consideration are obtained using three different weight functions for the sake of comparison.

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.

Time-dependent neutron transport in a semi-infinite random medium

Abstract The time-dependent neutron transport in a semi-infinite random medium of binary Markovian mixture with linear anisotropic scattering is proposed. A formalism, developed to treat radiative 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. Results are obtained for isotropic and anisotropic scattering.

Transport Of Neutral Particles In A Finite Continuous Stochastic Medium With Gaussian Statistics

The stationary solution of the one-speed transport equation in a finite stochastic medium with linear anisotropic scattering is considered. The solution is presented for an arbitrary absorption and scattering cross sections. The total cross section of medium is assumed to be a continuous random function of position, with fluctuations about the mean taken as Gaussian distributed. The Pomraning-Eddington technique is used at first to solve the problem in the deterministic case. Two correlated random variables appear in the solution; namely, the optical space variable and the optical thickness of the medium. The dual Gaussian-probability density function of these two random variables is derived from which the ensemble-averaged solution is calculated for an arbitrary correlation function. The first and the second statistical moments of some quantities of interest, such as radiant energy, net flux, reflectivity, and transmissivity, are calculated. The problem is treated with specular-refecting boundaries and an incident flux of particles on the medium from the left and with no flux from the right.

On Galerkin Technique for Transient Radiative Heat Transfer in Finite Thin Media

The transient radiative heat transfer problem in an absorbing and isotropically scattering plane-parallel medium is proposed. The medium is considered to be nonemitting and the boundaries are nonreflecting and nonrefracting, exposed to an external incident flux. The transient problem is transformed into a stationary-like one. Then, Galerkin technique is extended to obtain the analytical solution for the transient radiative heat transfer problem. The transient reflectivity and transmissivity of the medium are calculated for various values of optical thickness and scattering albedo at different times. The results are in fair agreement with those available in the literature using Pomraning-Eddington approximation.

Kinematic dust viscosity effect on linear and nonlinear dust-acoustic waves in space dusty plasmas with nonthermal ions

Linear and nonlinear dust-acoustic (DA) waves are studied in a collisionless, unmagnetized and dissipative dusty plasma consisting of negatively charged dust grains, Boltzmann-distributed electrons, and nonthermal ions. The normal mode analysis is used to obtain a linear dispersion relation illustrating the dependence of the wave damping rate on the carrier wave number, the dust viscosity coefficient, the ratio of the ion temperature to the electron temperatures, and the nonthermal parameter. The plasma system is analyzed nonlinearly via the reductive perturbation method that gives the KdV-Burgers equation. Some interesting physical solutions are obtained to study the nonlinear waves. These solutions are related to soliton, a combination between a shock and a soliton, and monotonic and oscillatory shock waves. Their behaviors are illustrated and shown graphically. The characteristics of the DA solitary and shock waves are significantly modified by the presence of nonthermal (fast) ions, the ratio of the ion temperature to the electron temperature, and the dust kinematic viscosity. The topology of the phase portrait and the potential diagram of the KdV-Burgers equation is illustrated, whose advantage is the ability to predict different classes of traveling wave solutions according to different phase orbits. The energy of the soliton wave and the electric field are calculated. The results in this paper can be generalized to analyze the nature of plasma waves in both space and laboratory plasma systems.

Nonlinear Dust Acoustic Waves in Dissipative Space Dusty Plasmas with Superthermal Electrons and Nonextensive Ions

The nonlinear characteristics of the dust acoustic (DA) waves are studied in a homogeneous, collisionless, unmagnetized, and dissipative dusty plasma composed of negatively charged dusty grains, superthermal electrons, and nonextensive ions. Sagdeev pseudopotential technique has been employed to study the large amplitude DA waves. It (Sagdeev pseudopotential) has an evidence for the existence of compressive and rarefractive solitons. The global features of the phase portrait are investigated to understand the possible types of solutions of the Sagdeev form. On the other hand, the reductive perturbation technique has been used to study small amplitude DA waves and yields the Korteweg-de Vries-Burgers (KdV-Burgers) equation that exhibits both soliton and shock waves. The behavior of the obtained results of both large and small amplitude is investigated graphically in terms of the plasma parameters like dust kinematic viscosity, superthermal and nonextensive parameters.

Pure-triplet scattering for radiative transfer in binary discrete random finite media with reflective boundaries and internal source of radiation

The stochastic solution of the monoenergetic radiative transfer equation in a finite slab random medium with pure-triplet anisotropic scattering is considered. The random medium is assumed to consist of two randomly mixed immiscible fluids labelled by 1 and 2. The extinction function, the scattering kernel, and the internal source of radiation are treated as discrete random variables, which obey the same statistics. The theoretical model used here for stochastic media transport assumes Markovian processes and exponential chord length statistics. The boundaries of the medium under consideration are considered to have specular and diffuse reflectivities with an internal source of radiation inside the medium. The ensemble-average partial heat fluxes are obtained in terms of the average albedos of the corresponding source-free problem, whose solution is obtained by using the Pomraning–Eddington approximation. Numerical results are calculated for the average forward and backward partial heat fluxes for different values of the single scattering albedo with variation of the parameters that characterize the random medium. Compared to the results obtained by Adams et al. in the case of isotropic scattering based on the Monte Carlo technique, it can be demonstrated that we have good comparable data.