Document Type
Article
Publication Date
2004
Abstract
The stationary linear transport equation models the scattering and absorption of a low-density beam of neutrons as it passes through a body. In Euclidean space, to a first approximation, particles travel in straight lines. Here we study the analogous transport equation for particles in an ambient field described by a Riemannian metric where, again to first approximation, particles follow geodesics of the metric. We consider the problem of determining the scattering and absorption coefficients from knowledge of the albedo operator on the boundary of the domain. Under certain restrictions, the albedo operator is shown to determine the geodesic ray transform of the absorption coefficient; for “simple” manifolds this transform is invertible and so the coefficient itself is determined. In dimensions 3 or greater, we show that one may then obtain the collision (or scattering) kernel.
Publication Title
Pacific Journal of Mathematics
Volume
216
Issue
2
First Page
303
Last Page
326
Required Publisher's Statement
Mathematical Sciences Publishers
DOI: 10.2140/pjm.2004.216.303
Recommended Citation
McDowall, Stephen R., "An Inverse Problem for the Transport Equation in the Presence of a Riemannian Metric" (2004). Mathematics Faculty Publications. 35.
https://cedar.wwu.edu/math_facpubs/35
Subjects - Topical (LCSH)
Functions, Inverse; Inversion (Geophysics); Geometry, Riemannian
Genre/Form
articles
Type
Text
Rights
Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.
Language
English
Format
application/pdf
