Isotropic Scattering in a Flatland Half-Space

Abstract

We solve the Milne, constant-source and albedo problems for isotropic scattering in a two-dimensional "Flatland" half-space via the Wiener-Hopf method. The Flatland $H$-function is derived and benchmark values and some identities unique to Flatland are presented. A number of the derivations are supported by Monte Carlo simulation.

final version, accepted to JCTT

References in corpus (4)

• Photon Management in Two-Dimensional Disordered Media
• Collision densities and mean residence times for $d$-dimensional exponential flights
• Rigorous asymptotic and moment-preserving diffusion approximations for generalized linear Boltzmann transport in arbitrary dimension
• The radiative transport equation in flatland with separation of variables

Cited by in corpus (2)

• A reciprocal formulation of non-exponential radiative transfer. 1: Sketch and motivation
• Radiative transfer in half spaces of arbitrary dimension