The radiative transport equation in flatland with separation of variables

TL;DR

This paper extends the singular-eigenfunction approach used for the linear Boltzmann equation from three-dimensional space with planar symmetry to two-dimensional flatland, providing a new perspective on solving the radiative transport equation.

Contribution

It introduces the application of the separation of variables and singular-eigenfunction method to the radiative transport equation in flatland, a two-dimensional setting, which was not previously explored.

Findings

Successful formulation of the eigenfunction approach in flatland

New analytical solutions for the radiative transport equation in two dimensions

Enhanced understanding of transport phenomena in flatland geometry

Abstract

The linear Boltzmann equation can be solved with separation of variables in one dimension, i.e., in three-dimensional space with planar symmetry. In this method, solutions are given by superpositions of eigenmodes which are sometimes called singular eigenfunctions. In this paper, we explore the singular-eigenfunction approach in flatland or two-dimensional space.