Photon transport problems involving a point source

A. Belleni-Morante, W. Lamb, A.C. McBride

Research output: Contribution to journalArticle

Abstract

We consider both a direct and an inverse problem of photon transport in an interstellar cloud with a point photon source. By using a non-rigorous (but physically reasonable) procedure, we prove that the direct problem has a unique solution and that the inverse problem also has a unique solution, under the assumptions that a single value of the photon far-field is known and the scattering cross-section is suitably small. Finally, we show in a rigorous way that the direct problem has a unique distributional solution if the point source is modelled by a Dirac δ functional.
LanguageEnglish
Pages77-93
Number of pages16
JournalAnalysis and Applications
Volume5
Issue number1
DOIs
Publication statusPublished - 2007

Fingerprint

Point Source
Photon
Photons
Inverse problems
Unique Solution
Inverse Problem
Far Field
Paul Adrien Maurice Dirac
Cross section
Scattering

Keywords

  • photon transport
  • direct and inverse problems
  • distributional solutions
  • physics
  • numerical mathematics

Cite this

Belleni-Morante, A. ; Lamb, W. ; McBride, A.C. / Photon transport problems involving a point source. In: Analysis and Applications. 2007 ; Vol. 5, No. 1. pp. 77-93.
@article{2a6e0e0191ca40ffa4f33ee1e488298e,
title = "Photon transport problems involving a point source",
abstract = "We consider both a direct and an inverse problem of photon transport in an interstellar cloud with a point photon source. By using a non-rigorous (but physically reasonable) procedure, we prove that the direct problem has a unique solution and that the inverse problem also has a unique solution, under the assumptions that a single value of the photon far-field is known and the scattering cross-section is suitably small. Finally, we show in a rigorous way that the direct problem has a unique distributional solution if the point source is modelled by a Dirac δ functional.",
keywords = "photon transport, direct and inverse problems, distributional solutions, physics, numerical mathematics",
author = "A. Belleni-Morante and W. Lamb and A.C. McBride",
year = "2007",
doi = "10.1142/S0219530507000894",
language = "English",
volume = "5",
pages = "77--93",
journal = "Analysis and Applications",
issn = "0219-5305",
number = "1",

}

Photon transport problems involving a point source. / Belleni-Morante, A.; Lamb, W.; McBride, A.C.

In: Analysis and Applications, Vol. 5, No. 1, 2007, p. 77-93.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Photon transport problems involving a point source

AU - Belleni-Morante, A.

AU - Lamb, W.

AU - McBride, A.C.

PY - 2007

Y1 - 2007

N2 - We consider both a direct and an inverse problem of photon transport in an interstellar cloud with a point photon source. By using a non-rigorous (but physically reasonable) procedure, we prove that the direct problem has a unique solution and that the inverse problem also has a unique solution, under the assumptions that a single value of the photon far-field is known and the scattering cross-section is suitably small. Finally, we show in a rigorous way that the direct problem has a unique distributional solution if the point source is modelled by a Dirac δ functional.

AB - We consider both a direct and an inverse problem of photon transport in an interstellar cloud with a point photon source. By using a non-rigorous (but physically reasonable) procedure, we prove that the direct problem has a unique solution and that the inverse problem also has a unique solution, under the assumptions that a single value of the photon far-field is known and the scattering cross-section is suitably small. Finally, we show in a rigorous way that the direct problem has a unique distributional solution if the point source is modelled by a Dirac δ functional.

KW - photon transport

KW - direct and inverse problems

KW - distributional solutions

KW - physics

KW - numerical mathematics

UR - http://dx.doi.org/10.1142/S0219530507000894

U2 - 10.1142/S0219530507000894

DO - 10.1142/S0219530507000894

M3 - Article

VL - 5

SP - 77

EP - 93

JO - Analysis and Applications

T2 - Analysis and Applications

JF - Analysis and Applications

SN - 0219-5305

IS - 1

ER -