Modelling uncertainties in phase-space boundary integral models of ray propagation

Bajars, J. ORCID: 0000-0001-7601-8694 and Chappell, D.J. ORCID: 0000-0001-5819-0271, 2020. Modelling uncertainties in phase-space boundary integral models of ray propagation. Communications in Nonlinear Science and Numerical Simulation, 80: 104973. ISSN 1007-5704

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A recently proposed phase-space boundary integral model for the stochastic propagation of ray densities is presented and, for the first time, explicit connections between this model and parametric uncertainties arising in the underlying physical model are derived. In particular, an asymptotic analysis for a weak noise perturbation of the propagation speed is used to derive expressions for the probability distribution of the phase-space boundary coordinates after transport along uncertain, and in general curved, ray trajectories. Furthermore, models are presented for incorporating geometric uncertainties in terms of both the location of an edge within a polygonal domain, as well as small scale geometric fluctuations giving rise to rough boundary reflections. Uncertain source terms are also considered in the form of stochastically distributed point sources and uncertain boundary data. A series of numerical experiments is then performed to illustrate these uncertainty models in two-dimensional convex polygonal domains.

Item Type: Journal article
Publication Title: Communications in Nonlinear Science and Numerical Simulation
Creators: Bajars, J. and Chappell, D.J.
Publisher: Elsevier
Date: January 2020
Volume: 80
ISSN: 1007-5704
S1007570419302928Publisher Item Identifier
Rights: © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license. (
Divisions: Schools > School of Science and Technology
Record created by: Linda Sullivan
Date Added: 04 Sep 2019 10:17
Last Modified: 04 Sep 2019 10:17

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