Related papers: Radiative Transfer in Spheres I. Analytical Soluti…
Remote sensing hyperspectral and more generally spectral instruments are common tools to decipher surface features in Earth and Planetary science. While linear mixture is the most common approximation for compounds detection (mineral,…
A new approach is proposed for the quantum mechanical problem of the falling of a particle to a singularly attracting center, basing on a black-hole concept of the latter. The singularity r^{-2} in the potential of the radial Schroedinger…
We study inversion of the spherical Radon transform with centers on a sphere (the data acquisition set). Such inversions are essential in various image reconstruction problems arising in medical, radar and sonar imaging. In the case of…
A novel explicit analytical solution is reported for the transmission and recovery of information signals using a simple communication scheme. Analytical solutions are obtained for the normalized state equations of coupled second-order…
Analytical solutions in fluid dynamics can be used to elucidate the physics of complex flows and to serve as test cases for numerical models. In this work, we present the analytical solution for the acoustic boundary layer that develops…
We derive from first principles a one-way radiative transfer equation for the wave intensity resolved over directions (Wigner transform of the wave field) in random media. It is an initial value problem with excitation from a source which…
We study the ballistic adsorption of a polydisperse mixture of spheres onto a line. Within a mean-field approximation, the problem can be analytically solved by means of a kinetic equation for the gap distribution. In the mean-field…
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…
Existence and uniqueness of radially symmetric self-similar very singular solutions are proved for the singular diffusion equation with gradient absorption {equation*} \partial_t u -\Delta_{p}u+|\nabla u|^q=0, \ \hbox{in} \…
The standard Advection-Dominated Accretion Flow (ADAF) is studied using a set of self-similar analytical solutions in the spherical coordinates. Our new solutions are useful for studying ADAFs without dealing with the usual mathematical…
Radiative transfer is a fundamental process in astrophysics, essential for both interpreting observations and modeling thermal and dynamical feedback in simulations via ionizing radiation and photon pressure. However, numerically solving…
An analytical linear solution of the fully compressible Euler equations is found, in the particular case of a stationary two dimensional flow that passes over an orographic feature with small height-width ratio. A method based on the…
A new second order form of radiative transfer equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order radiative transfer equation [J. Comput. Phys. 214 (2006) 12-40 (where it was…
The cutoff method, which cuts off the values of a function less than a given number, is studied for the numerical computation of nonnegative solutions of parabolic partial differential equations. A convergence analysis is given for a broad…
A method is presented for the evaluation of integrals on tetrahedra where the integrand has an integrable singularity at one vertex. The approach uses a transformation to spherical polar coordinates which explicitly eliminates the…
We solve exactly the problem of a finite slab receiving an isotropic radiation on one side and no radiation on the other side. This problem - to be more precise the calculation of the source function within the slab - was first formulated…
Solutions to fractional models inherently exhibit non-smooth behavior, which significantly deteriorates the accuracy and therefore efficiency of existing numerical methods. We develop a two-stage data-infused computational framework for…
We consider the numerical approximation of boundary conditions in radiative transfer problems by a perfectly matched layer approach. The main idea is to extend the computational domain by an absorbing layer and to use an appropriate…
General dynamical transport of classical particles in disordered quasi-1D samples is viewed in the framework of scattering approach. Simple equation for the transfer-matrix is obtained within this unified picture. In the case of diffusive…
The absorption cross section of rotating black holes in the Randall-Sundrum brane-world scenario for massless scalar waves is obtained via the partial-wave method. A variety of incidence directions with respect to the black hole rotation…