Related papers: Solution of the radiative transfer equation in the…
The main purpose of this paper is to obtain analytical solutions for radiative transfer equations related to the vertical structure of accretion discs with finite optical depth. In the non-gray atmosphere, we employ the optical-depth…
This work presents efficient solution techniques for radiative transfer in the smoothed particle hydrodynamics discretization. Two choices that impact efficiency are how the material and radiation energy are coupled, which determines the…
A numerical scheme is proposed for the solution of the three-dimensional radiative transfer equation with variable optical depth. We show that time-dependent ray tracing is an attractive choice for simulations of astrophysical ionization…
A finite element method for solving the resonance line transfer problem in moving media is presented. The algorithm works in three spatial dimensions on unstructured grids which are adaptively refined by means of an a posteriori error…
The discontinuous Galerkin finite element method (DG-FEM) is successfully applied to treat a broad variety of transport problems numerically. In this work, we use the full capacity of the DG-FEM to solve the radiative transfer equation in…
Superluminal propagation is an intrinsic problem in the diffusion equation and has not been effectively addressed for a long time. In this work, a rigorous solution to this issue is obtained under the assumption that particles undergo a…
A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…
Observations and magnetohydrodynamic simulations of solar and stellar atmospheres reveal an intermittent behavior or steep gradients in physical parameters, such as magnetic field, temperature, and bulk velocities. The numerical solution of…
We proposed in a previous paper [Opt. Commun. 228, 33 (2003)] a modified radiative transfer equation to describe radiative transfer in a medium with a spatially varying refractive index. The present paper is devoted to the demonstration…
Analytic solutions to the nonlinear radiation diffusion equation with an instantaneous point source for a non-homogeneous medium with a power law spatial density profile, are presented. The solutions are a generalization of the well known…
The difficulty of description of the radiative transfer in disordered photonic crystals arises from the necessity to consider on the equal footing the wave scattering by periodic modulations of the dielectric function and by its random…
Radiative transfer in curved spacetimes has become increasingly important to understanding high-energy astrophysical phenomena and testing general relativity in the strong field limit. The equations of radiative transfer are physically…
The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients of order three. We prove that this difference equation can be solved in general. Consequently we can find an exact solution to the…
The radiative transport equation accurately describes light transport in participating media such as biological tissues, though analytic solutions are known only for simple geometries. We present a pseudospectral technique to efficiently…
We present a field-theoretic framework to characterize the distribution of transmission eigenvalues for coherent wave propagation through disordered media. The central outcome is a transport equation for a matrix-valued radiance, analogous…
In this work we study the radiative transfer equation in the forward-peaked regime in free space. Specifically, it is shown that the equation is well-posed by proving instantaneous regularization of weak solutions for arbitrary initial…
An analytic solution for a Fokker-Planck equation that describes propagation of energetic particles through a scattering medium is obtained. The solution is found in terms of an infinite series of mixed moments of particle distribution. The…
We describe a novel adaptive ray tracing scheme to solve the equation of radiative transfer around point sources in hydrodynamical simulations. The angular resolution adapts to the local hydrodynamical resolution and hence is of use for…
We obtain a nonperturbative, analytical solution to integral equation of scattering theory by assuming the field within the scattering object is a spherical wave with a scattering amplitude equal to that of the far field. This approximation…
We present an algorithm for solving the radiative transfer problem on massively parallel computers using adaptive mesh refinement and domain decomposition. The solver is based on the method of characteristics which requires an adaptive…