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A boundary integral formalism for stochastic ray tracing in billiards

Chappell, David; Tanner, Gregor

Authors

David Chappell david.chappell@ntu.ac.uk

GREGOR TANNER GREGOR.TANNER@NOTTINGHAM.AC.UK
Professor of Applied Mathematics



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.

Journal Article Type Article
Journal Chaos
Print ISSN 1054-1500
Electronic ISSN 1089-7682
Publisher AIP Publishing
Peer Reviewed Peer Reviewed
Volume 24
Article Number 043137
APA6 Citation Chappell, D., & Tanner, G. (in press). A boundary integral formalism for stochastic ray tracing in billiards. Chaos, 24, https://doi.org/10.1063/1.4903064
DOI https://doi.org/10.1063/1.4903064
Keywords Trajectory models, Phase space methods, Boundary integral methods, Integral equations, Ray tracing
Publisher URL http://aip.scitation.org/doi/10.1063/1.4903064
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
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.

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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