A boundary integral formalism for stochastic ray tracing in billiards
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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Published: |
AIP Publishing
2014
|
| Subjects: | |
| Online Access: | https://eprints.nottingham.ac.uk/46597/ |
| _version_ | 1848797363698663424 |
|---|---|
| author | Chappell, David Tanner, Gregor |
| author_facet | Chappell, David Tanner, Gregor |
| author_sort | Chappell, David |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:02:41Z |
| format | Article |
| id | nottingham-46597 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:02:41Z |
| publishDate | 2014 |
| publisher | AIP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-465972020-05-04T16:59:07Z https://eprints.nottingham.ac.uk/46597/ A boundary integral formalism for stochastic ray tracing in billiards Chappell, David Tanner, Gregor 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. AIP Publishing 2014-12-05 Article PeerReviewed 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 Trajectory models Phase space methods Boundary integral methods Integral equations Ray tracing http://aip.scitation.org/doi/10.1063/1.4903064 doi:10.1063/1.4903064 doi:10.1063/1.4903064 |
| spellingShingle | Trajectory models Phase space methods Boundary integral methods Integral equations Ray tracing Chappell, David Tanner, Gregor A boundary integral formalism for stochastic ray tracing in billiards |
| title | A boundary integral formalism for stochastic ray tracing in billiards |
| title_full | A boundary integral formalism for stochastic ray tracing in billiards |
| title_fullStr | A boundary integral formalism for stochastic ray tracing in billiards |
| title_full_unstemmed | A boundary integral formalism for stochastic ray tracing in billiards |
| title_short | A boundary integral formalism for stochastic ray tracing in billiards |
| title_sort | boundary integral formalism for stochastic ray tracing in billiards |
| topic | Trajectory models Phase space methods Boundary integral methods Integral equations Ray tracing |
| url | https://eprints.nottingham.ac.uk/46597/ https://eprints.nottingham.ac.uk/46597/ https://eprints.nottingham.ac.uk/46597/ |