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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Howard R. Gordon, Opt. Express 19, 4673 (2011)
Endrik Krügel, The Physics of Interstellar Dust (Institute of Physics Publishing, Bristol and Philadelphia, 2003)
H.C. van de Hulst, Light Scattering by Small Particles (Dover Publications, Inc., New York, 1981)
S. Chandrasekhar, Radiative Transfer (Oxford University Press, New York, 1950)
V.V. Sobolev, A Treatise on Radiative Transfer (D. Van Nostrand Company, Inc., Princeton, New Jersey, 1963) translated by S.I. Gaposchkin
M.I. Mishchenko, Kinem. Phys. Cel. Bod. 3, 53 (1987)
M.I. Mishchenko, E.G. Yanovitskii, Kinem. Phys. Cel. Bod. 4, 19 (1988)
M.I. Mishchenko, J.M. Dlugach, E.G. Janovitskij, J. Quant. Spectrosc. Radiat. Transf. 47, 401 (1992)
M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic Press, New York, 1969) pp. 255--265
M. Barabas, J. Opt. Soc. Am. A4, 2240 (1987)
S.C. Lee, J. Appl. Phys. 68, 4952 (1990)
S.C. Lee, J. Opt. Soc. Am. A13, 2256 (1996)
Siu-Chun Lee, Jan A. Grzesik, J. Opt. Soc. Am. A15, 163 (1998)
J.A. Grzesik, Progr. Electromagn. Res. 40, 255 (2003)
M. Kerker, D.D. Cooke, J.M. Carlin, J. Opt. Soc. Am. 60, 1236 (1970)
K.M. Case, Rev. Mod. Phys. 29, 651 (1957)
Kenneth M. Case, Paul Frederick Zweifel, Linear Transport Theory (Addison-Wesley Publishing Company, Reading, Massachusetts, 1967)
Leung Tsang, Jin Au Kong, Kung-Hau Ding, Scattering of Electromagnetic Waves, Theories and Applications (John Wiley & Sons, Inc., New York, 2000) pp. 107--166, 259--286
Michael I. Mishchenko, Radiative transfer theory: from Maxwell’s equations to practical applications, in Wave Scattering from Complex Media: From Theory to Applications, edited by B.A. van Tiggelen, S.E. Skipetrov (Academic Publishers, Dordrecht, The Netherlands, 2003) pp. 367--414
Michael I. Mishchenko, J. Quant. Spectrosc. Radiat. Transf. 146, 4 (2014)
B. Davison, Neutron Transport Theory, with the collaboration of J.B. Sykes (Oxford University Press, 1958) p. 67
J.A. Grzesik, Two-dimensional radiation transport across fibrous media, in 1997 IEEE Antennas and Propagation Society Symposium and URSI Radio Science Meeting, Montréal, Canada, July 13-18, 1997
T.W. Tong, C.L. Tien, ASME J. Heat Transf. 105, 70 (1983)
S.C. Lee, J. Quant. Spectrosc. Radiat. Transf. 36, 253 (1986)
Tom J. Love Jr., An Investigation of radiant heat transfer in absorbing, emitting, and scattering media (University of Oklahoma Research Institute, Norman, Oklahoma, 1963)
Stephen Whitaker, Ind. Eng. Chem. Fund. 19, 210 (1980)
Robert Siegel, John R. Howell, Thermal Radiation Heat Transfer, second edition (Hemisphere Publishing Corporation, New York, 1981)
Michael F. Modest, Radiative Heat Transfer, third edition (Academic Press/Elsevier, New York, 2013) cf. pp. 387--439
Author information
Authors and Affiliations
Corresponding author
Additional information
This article is published with open access at Springerlink.com
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Grzesik, J.A. Radiative albedo from a linearly fibered half-space. Eur. Phys. J. Plus 133, 178 (2018). https://doi.org/10.1140/epjp/i2018-12004-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2018-12004-4