title: A boundary integral formalism for stochastic ray tracing in billiards.
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 discretisation approach is applied to model uncertain billiard dynamics in an integrable rectangular domain.
authors.affiliation: School of Science and Technology, Nottingham Trent University, Clifton Campus, Nottingham NG11 8NS, United Kingdom.
authors.forename: David J
authors.initials: DJ
authors.lastname: Chappell
authors.affiliation: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
authors.forename: Gregor
authors.initials: G
authors.lastname: Tanner