A boundary integral formalism for stochastic ray tracing in billiards

Chappell, David; Tanner, Gregor

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.

Citation

Chappell, D., & Tanner, G. (in press). A boundary integral formalism for stochastic ray tracing in billiards. Chaos, 24, Article 043137. https://doi.org/10.1063/1.4903064

• Journal Article Type: Article
• Acceptance Date: Nov 19, 2014
• Online Publication Date: Dec 5, 2014
• Deposit Date: Sep 25, 2017
• Publicly Available Date: Sep 25, 2017
• Journal: Chaos
• Print ISSN: 1054-1500
• Electronic ISSN: 1089-7682
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 24
• Article Number: 043137
• DOI: https://doi.org/10.1063/1.4903064
• Keywords: Trajectory models, Phase space methods, Boundary integral methods, Integral equations, Ray tracing
• Public URL: https://nottingham-repository.worktribe.com/output/741521
• Publisher URL: http://aip.scitation.org/doi/10.1063/1.4903064
• 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.