Related papers: Exact solutions for radiative transfer with partia…
Approximate methods to estimate solutions to the radiative transfer equation are essential for the understanding of atmospheres of exoplanets and brown dwarfs. The simplest and most popular choice is the "two-stream method" which is often…
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…
This paper investigates the problem of reconstructing a random source from statistical phaseless data for the two-dimensional Helmholtz equation. The major challenge of this problem is non-uniqueness, which we overcome through a reference…
In Radiative transfer, the intensities of radiation from the bounding faces of finite slab are obtained in terms of X- and Y- functions of Chandrasekhar . Those are non linear non homogeneous coupled integral equations . Those non linear…
We propose a direct imaging method based on the reverse time migration to reconstruct extended obstacles in the half space with finite aperture elastic scattering data at a fixed frequency. We prove the resolution of the reconstruction…
We present a numerical tool for solving the non-relativistic Kohn-Sham problem for spherically-symmetric atoms. It treats the Schr\"{o}dinger equation as an integral equation relying heavily on convolutions. The solver supports different…
We simulate convection near the solar surface, where the continuum optical depth is of order unity. Hence, to determine the radiative heating and cooling in the energy conservation equation, we must solve the radiative transfer equation…
This paper presents a direct solution technique for the scattering of time-harmonic waves from a bounded region of the plane in which the wavenumber varies smoothly in space.The method constructs the interior Dirichlet-to-Neumann (DtN) map…
We consider the inverse scattering problem to reconstruct a local perturbation of a given inhomogeneous periodic layer in $\mathbb{R}^d$, $d=2,3$, using near field measurements of the scattered wave on an open set of the boundary above the…
A simple transformation converts a solution of a partial differential equation with a Dirichlet boundary condition to a function satisfying a Robin (generalized Neumann) condition. In the simplest cases this observation enables the exact…
We propose an explicit-implicit scheme for numerically solving Special Relativistic Radiation Hydrodynamic (RRHD) equations, which ensures a conservation of total energy and momentum (matter and radiation). In our scheme, 0th and 1st moment…
The inverse scattering transform is developed to solve the Maxwell-Bloch system of equations that describes two-level systems with inhomogeneous broadening, in the case of optical pulses that do not vanish at infinity in the future. The…
We present describe a new computer code that solves the radiative transfer problem on multi-resolution grids. If the cloud model is from an MHD simulation on a regular cartesian grid, criteria based for example on local density or velocity…
Fundamental rules and definitions of Fractional Differintegrals are outlined. Factorizing 1-D and 2-D Helmholtz equations four fractional eigenfunctions are determined. The functions exhibit incident and reflected plane waves as well as…
Exact bound state solutions and the corresponding wave functions of the Schr\"odinger equation for some non-central potentials including Makarov potential, modified-Kratzer plus a ring-shaped potential, double ring-shaped Kratzer potential,…
We present new exact solutions of the Landau-Lifshitz and higher-order Landau-Lifshitz equations describing particle motion, with radiation reaction, in intense electromagnetic fields. Through these solutions and others we compare the…
A new numerical method to solve an inverse source problem for the Helmholtz equation in inhomogenous media is proposed. This method reduces the original inverse problem to a boundary value problem for a coupled system of elliptic PDEs, in…
We study a model that intermediates among the wave, heat, and transport equations. The approach considers the propagation of initial disturbances in a one-dimensional medium that can vibrate. The medium is nonlinear in such a form that…
A solution of the radiative-transfer problem in arbitrary velocity fields introduced in a previous paper, has limitations in its applicability. For large-scale applications, the methods described also require large memory sets that are…
In this paper we present a spectral decomposition of solutions to relativistic wave equations described on horizon penetrating hyperboloidal slices within a given Schwarzschild-black-hole background. The wave equa- tion in question is…