Solutions to the multidimensional linear transport equation by the spectral method

MT Vilhena, LB Barichello, JR Zabadal… - Progress in Nuclear …, 1999 - Elsevier
The spectral method is used to develop a solution for multidimensional transport problems
for neutral particles in cartesian geometry. The procedure is based on the expansion of the …

The searchlight problem with isotropic scattering

GB Rybicki - Journal of Quantitative Spectroscopy and Radiative …, 1971 - Elsevier
A solution to Chandrasekhar's searchlight problem with isotropic scattering is presented for
semi-infinite and finite geometries. The scattering and transmission functions for the Fourier …

Singular eigenfunctions for the three-dimensional radiative transport equation

M Machida - Journal of the Optical Society of America A, 2013 - opg.optica.org
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 …

Analytical solutions of the neutron transport equation in arbitrary convex geometry

AG Gibbs - Journal of Mathematical Physics, 1969 - pubs.aip.org
The integral equation describing the transport of monoenergetic, isotropically scattered
neutrons in a one‐, two‐, or three‐dimensional body of arbitrary convex shape, containing …

Three-dimensional radiative transfer with polarization in a multiple scattering medium exposed to spatially varying radiation

DW Mueller Jr, AL Crosbie - Journal of Quantitative Spectroscopy and …, 1997 - Elsevier
The present investigation of three-dimensional radiative transfer accounts for polarization
and multiple scattering by using the vector transport equation. The intensity vector is …

Three‐dimensional linear transport theory

KM Case, RD Hazeltine - Journal of Mathematical Physics, 1970 - pubs.aip.org
A recent technique for extending the singular eigenfunction method in linear transport theory
to prob~ ems which are not strictly I-dimensional is compared to a more naive approach …

Two-dimensional radiative equilibrium: a semi-infinite medium subjected to cosine varying radiation

WF Breig, AL Crosbie - Journal of Quantitative Spectroscopy and Radiative …, 1973 - Elsevier
Exact numerical solutions are presented for the radiative flux and emissive power at the
boundary of a semi-infinite, two-dimensional, planar, absorbing-emitting, gray medium …

Analytical solutions for the neutron transport using the spectral methods

A Kadem - … journal of mathematics and mathematical sciences, 2006 - Wiley Online Library
We present a method for solving the two‐dimensional equation of transfer. The method can
be extended easily to the general linear transport problem. The used technique allows us to …

How to construct three-dimensional transport theory using rotated reference frames

M Machida - Journal of Computational and Theoretical Transport, 2016 - Taylor & Francis
Full article: How to Construct Three-Dimensional Transport Theory Using Rotated Reference
Frames Skip to Main Content Taylor and Francis Online homepage Browse Search Publish …

Numerical algorithms of the radiative transport equation using rotated reference frames for optical tomography with structured illumination

M Machida - Journal of Quantitative Spectroscopy and Radiative …, 2019 - Elsevier
We consider optical tomography with structured illumination in spatial-frequency domain
using the three-dimensional radiative transport equation. Without the diffusion …