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.

Keywords:

• Wiener–Hopf
• Flatland
• H-function
• Milne problem

Acknowledgments

We thank Norm McCormick for pointing out several important related works (Bal et al. 2000; Stewart, Kuščer, and McCormick 1966).