Radiative Albedo from a Linearly Fibered Half Space

TL;DR

This paper investigates radiative transfer in fiber-reinforced composites with linear scattering, using analytical methods to solve the half-space albedo problem and exploring potential extensions of classical eigenfunction techniques.

Contribution

It introduces a simplified cylindrical scattering model for fiber composites and applies Wiener-Hopf and discrete ordinates methods to solve the albedo problem, suggesting further development of eigenfunction approaches.

Findings

Good agreement between Wiener-Hopf and discrete ordinates solutions

Simplified cylindrical scattering model captures key phenomena

Potential for extending eigenfunction methods to this context

Abstract

A growing acceptance of fiber reinforced composite materials imparts some relevance to exploring the effects which a predominantly linear scattering lattice may have upon interior radiant transport. Indeed, a central feature of electromagnetic wave propagation within such a lattice, if sufficiently dilute, is ray confinement to cones whose half-angles are set by that between lattice and the incident ray. When such propagation is subordinated to a viewpoint of photon transport, one arrives at a somewhat simplified variant of the Boltzmann equation with spherical scattering demoted to its cylindrical counterpart. With a view to initiating a hopefully wider discussion of such phenomena, we follow through in detail the half-space albedo problem. This is done first along canonical lines that harness the Wiener-Hopf technique, and then once more in a discrete ordinates setting via flux decomposition along the eigenbasis of the underlying attenuation/scattering matrix. Good agreement is seen to prevail. We further suggest that the Case singular eigenfunction apparatus could likewise be evolved here in close analogy to its original, spherical scattering model.