Related papers: Radiative Transfer in Spheres I. Analytical Soluti…
Linear kinetic transport equations play a critical role in optical tomography, radiative transfer and neutron transport. The fundamental difficulty hampering their efficient and accurate numerical resolution lies in the high dimensionality…
We study the mathematical character of the angular moment equations of radiative transfer in spherical symmetry and conclude that the system is hyperbolic for general forms of the closure relation found in the literature. Hyperbolicity and…
We introduce the classical stellar atmosphere problem and describe in detail its numerical solution. The problem consists of the solution of the radiation transfer equations under the constraints of hydrostatic, radiative and statistical…
This work is aimed at the study and analysis of the heat transport on a metal bar of length $L$ with a solid-solid interface. The process is assumed to be developed along one direction, across two homogeneous and isotropic materials.…
A spectral element method (SEM) is developed to solve polarized radiative transfer in multidimensional participating medium. The angular discretization is based on the discrete-ordinates approach, and the spatial discretization is conducted…
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
In this paper we present a framework which provides an analytical (i.e., infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits…
(Abridged) We describe a new algorithm for solving the coupled frequency-integrated transfer equation and the equations of magnetohydrodynamics when the light-crossing time is only marginally shorter than dynamical timescales. The transfer…
The charge transfer from an adatom to a semiconductor substrate of one-dimensional quantum dot array is evaluated theoretically. Due to the Van Hove singularity in the density of electron states at the band edges, the charge transfer decay…
We suggest a technique based on the transfer of topological charge from applied laser radiation to directional and coherent optical fields generated in ladder-type excited atomic media to identify the major processes responsible for their…
A full symmetry classification is given for models of energy transport in radiant plasma when the mass density is spatially variable and the diffusivity is nonlinear. A systematic search for conservation laws also leads to some potential…
Many questions in physical cosmology regarding the thermal and ionization history of the intergalactic medium are now successfully studied with the help of cosmological hydrodynamical simulations. Here we present a numerical method that…
A spectral decomposition method is used to obtain solutions to a class of nonlinear differential equations. We extend this approach to the analysis of the fractional form of these equations and demonstrate the method by applying it to the…
Two-stream radiative transfer is a workhorse in the Earth, planetary and exoplanetary sciences due to its simplicity and ease of implementation. However, a longstanding limitation of the two-stream approximation is its inaccuracy in the…
We solve the classic albedo and Milne problems of plane-parallel illumination of an isotropically-scattering half-space when generalized to a Euclidean domain $\mathbb{R}^d$ for arbitrary $d \ge 1$. A continuous family of pseudo-problems…
A numerically exact path integral treatment of the absorption and emission spectra of open quantum systems is presented that requires only the straightforward solution of a stochastic differential equation. The approach converges rapidly…
The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are given as spatial-temporal homogeneous and isotropic random…
We address the problem of angular momentum transport in stellar radiative interiors with a novel semi-analytic spectral technique, using an eigenfunction series expansion, that can be used to derive benchmark solutions in hydromagnetic…
Non-LTE radiative transfer is a key tool for modern astrophysics: it is the means by which many key synthetic observables are produced, thus connecting simulations and observations. Radiative transfer models also inform our understanding of…
We propose a method for transformating linear and nonlinear hypersingular integral equations into ordinary differential equations. Linear and nonlinear polyhypersingular integral equations are transformed into partial differential…