Eur. Phys. J. Plus (2018) 133: 178
https://doi.org/10.1140/epjp/i2018-12004-4

Regular Article

Radiative albedo from a linearly fibered half-space

Allwave Corporation, 3860 Del Amo Boulevard, Suite 404, 90503, Torrance, CA, USA

^* e-mail: jan.grzesik@hotmail.com

Received: 24 February 2018
Accepted: 6 April 2018
Published online: 9 May 2018

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 radiative 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 an unpolarized intensity 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. A cursory contact with related problems in the astrophysical literature suggests, in addition, that the basic physical fidelity of our scalar radiative transfer equation (RTE) remains open to improvement by passage to a (4×1) Stokes vector, (4×4) matricial setting.