Isotropic Scattering in a Flatland Half-Space

TL;DR

This paper analyzes isotropic scattering in a two-dimensional Flatland half-space, deriving the Flatland H-function, solving classical radiative transfer problems, and validating results with Monte Carlo simulations.

Contribution

It introduces the Flatland H-function and provides solutions to the Milne, constant-source, and albedo problems specific to Flatland geometry, supported by simulations.

Findings

Derived the Flatland H-function and related identities.

Solved classical scattering problems in Flatland geometry.

Validated solutions with Monte Carlo simulations.

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.