A boundary integral formalism for stochastic ray tracing in billiards

Chappell, David and Tanner, Gregor (2014) A boundary integral formalism for stochastic ray tracing in billiards. Chaos, 24 . 043137/1-043137/10. ISSN 1089-7682

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Abstract

Determining the flow of rays or non-interacting particles driven by a force or velocity field is fundamental to modelling many physical processes. These include particle flows arising in fluid mechanics and ray flows arising in the geometrical optics limit of linear wave equations. In many practical applications, the driving field is not known exactly and the dynamics are determined only up to a degree of uncertainty. This paper presents a boundary integral framework for propagating flows including uncertainties, which is shown to systematically interpolate between a deterministic and a completely random description of the trajectory propagation. A simple but efficient discreti- sation approach is applied to model uncertain billiard dynamics in an integrable rectangular domain.

Item Type: Article
Additional Information: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in A boundary integral formalism for stochastic ray tracing in billiards David J. Chappell and Gregor Tanner Chaos: An Interdisciplinary Journal of Nonlinear Science 24, 043137 (2014); doi: 10.1063/1.4903064 and may be found at http://aip.scitation.org/doi/10.1063/1.4903064.
Keywords: Trajectory models, Phase space methods, Boundary integral methods, Integral equations, Ray tracing
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1063/1.4903064
Depositing User: Tanner, Prof Gregor
Date Deposited: 25 Sep 2017 12:33
Last Modified: 14 Oct 2017 08:23
URI: http://eprints.nottingham.ac.uk/id/eprint/46597

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