Related papers: Radiative Transfer in Spheres I. Analytical Soluti…
A nonlinear algebraic equation system of 5 variables is numerically solved, which is derived from the application of the Fourier transform to a differential equation system that allows modeling the behavior of the temperatures and the…
An improvement modification of the Spectral Approach (SA) used for approximating the nonclassical neutral particle transport equation is described in this work. The main focus of the modified SA lies on a slight modification of the…
Solution of the Cox-Thompson inverse scattering problem at fixed energy [1,2,3] is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are…
The high-precision solution of the radial Dirac equation is fundamental to relativistic quantum chemistry, essential for reliable pseudopotential generation and all-electron electronic structure methods. However, standard basis-set…
We study the standard spectral line radiative transfer equation for media consisting of resonant atoms and non-resonant components (the dust grains and the atoms without considered spectral transition). Our goal is to study the intensity…
This review presents basic equations for the solution of the NLTE radiative transfer problem for trace elements and methods for its solution are summarized. The importance of frequency coupling in radiative transfer in stellar atmospheres…
We classify entire positive singular solutions to a family of critical sixth order equations in the punctured space with a non-removable singularity at the origin. More precisely, we show that when the origin is a non-removable singularity,…
Analytical solution of precise equations that describe the rf-coupling of two cavities through a co-axial cylindrical hole are given for various limited cases. For their derivation we have used the method of solution of an infinite set of…
The linearly-polarized solar limb spectrum that is produced by scattering processes contains a wealth of information on the physical conditions and magnetic fields of the solar outer atmosphere, but the modeling of many of its strongest…
Case's method obtains solutions to the radiative transport equation as superpositions of elementary solutions when the specific intensity depends on one spatial variable. In this paper, we find elementary solutions when the specific…
Spatial solitary waves in colloidal suspensions of spherical dielectric nanoparticles are considered. The interaction of the nanoparticles is modelled as a hard-sphere gas, with the Carnahan-Starling formula used for the gas…
We compare four different methods to calculate radiative transfer through a magnetized stellar atmosphere, and apply them to the case of magnetic white dwarfs. All methods are numerically stable enough to allow determination of the magnetic…
When integrating the radiative transfer equation for polarized light, the necessity of high-order numerical methods is well known. In fact, well-performing high-order formal solvers enable higher accuracy and the use of coarser spatial…
Radial basis functions are typically used when discretization sche-mes require inhomogeneous node distributions. While spawning from a desire to interpolate functions on a random set of nodes, they have found successful applications in…
We study in this work an integral formulation for the radiative transfer equation (RTE) in anisotropic media with truncated approximation to the scattering phase function. The integral formulation consists of a coupled system of integral…
In the central part of this paper, we revisit the classical study of the H-function defined as the unique solution, regular in the right complex half-plane, of a Cauchy integral equation. We take advantage of our work on the N-function…
When dealing with the steady-state multiscale radiative transfer equation (RTE) with heterogeneous coefficients, spatially localized low-rank structures are present in the angular space. This paper introduces an adaptive tailored finite…
Based on the classical Lorentz model of the index of refraction, a new method is presented for the extraction of the complex index of refraction from the extinction efficiency of homogeneous and layered dielectric spheres that…
A consolidated mathematical formulation of the spherically symmetric mass-transfer problem is presented, with the quasi-stationary approximating equations derived from a perturbation point of view for the leading-order effect. For the…
Considering two-body integral equations we show how they can be dimensionally reduced by integrating exactly over the azimuthal angle of the intermediate momentum. Numerical solution of the resulting equation is feasible without employing a…