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DC Field | Value | Language |
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dc.contributor.author | VANPOUCKE, Danny E.P. | - |
dc.contributor.author | WENMACKERS, Sylvia | - |
dc.date.accessioned | 2022-01-17T09:13:56Z | - |
dc.date.available | 2022-01-17T09:13:56Z | - |
dc.date.issued | 2021 | - |
dc.date.submitted | 2022-01-17T06:29:37Z | - |
dc.identifier.citation | Chaos (Woodbury, N.Y.), 31 (12) (Art N° 123131) | - |
dc.identifier.uri | http://hdl.handle.net/1942/36495 | - |
dc.description.abstract | We present a method for assigning probabilities to the solutions of initial value problems that have a Lipschitz singularity. To illustrate the method, we focus on the following toy example: d(2)r(t)/dt(2) = r(a), r ( t = 0 ) = 0, and d r ( t )/d t divide r ( t = 0 ) = 0, with a & ISIN; ] 0 , 1 [. This example has a physical interpretation as a mass in a uniform gravitational field on a frictionless, rigid dome of a particular shape; the case with a = 1 / 2 is known as Norton's dome. Our approach is based on (1) finite difference equations, which are deterministic; (2) elementary techniques from alpha-theory, a simplified framework for non-standard analysis that allows us to study infinitesimal perturbations; and (3) a uniform prior on the canonical phase space. Our deterministic, hyperfinite grid model allows us to assign probabilities to the solutions of the initial value problem in the original, indeterministic model. | - |
dc.description.sponsorship | We are grateful to an anonymous referee for a very instructive report that greatly helped us to improve the presentation of our methodology, to Vieri Benci for helpful discussions on this topic, and to Christian Maes for feedback on an earlier version. Part of S.W.’s work was supported by the Research Foundation Flanders (Fonds Wetenschappelijk Onderzoek, FWO) (Grant No. G066918N). | - |
dc.language.iso | en | - |
dc.publisher | AMER INST PHYSICS | - |
dc.rights | 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0063388 Open access | - |
dc.title | Assigning probabilities to non-Lipschitz mechanical systems | - |
dc.type | Journal Contribution | - |
dc.identifier.issue | 12 | - |
dc.identifier.volume | 31 | - |
local.format.pages | 14 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.notes | Wenmackers, S (corresponding author), Katholieke Univ Leuven, Inst Philosophy, Ctr Log & Philosophy Sci CLPS, Kardinaal Mercierpl 2,Bus 3200, B-3000 Leuven, Belgium. | - |
dc.description.notes | sylvia.wenmackers@kuleuven.be | - |
local.publisher.place | 1305 WALT WHITMAN RD, STE 300, MELVILLE, NY 11747-4501 USA | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
local.bibliographicCitation.artnr | 123131 | - |
dc.identifier.doi | 10.1063/5.0063388 | - |
dc.identifier.pmid | 34972340 | - |
dc.identifier.isi | 000739120300004 | - |
dc.contributor.orcid | Vanpoucke, Danny/0000-0001-5919-7336 | - |
local.provider.type | wosris | - |
local.description.affiliation | [Vanpoucke, Danny E. P.] UHasselt, Fac Sci, Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium. | - |
local.description.affiliation | [Wenmackers, Sylvia] Katholieke Univ Leuven, Inst Philosophy, Ctr Log & Philosophy Sci CLPS, Kardinaal Mercierpl 2,Bus 3200, B-3000 Leuven, Belgium. | - |
local.uhasselt.international | no | - |
item.fulltext | With Fulltext | - |
item.accessRights | Open Access | - |
item.fullcitation | VANPOUCKE, Danny E.P. & WENMACKERS, Sylvia (2021) Assigning probabilities to non-Lipschitz mechanical systems. In: Chaos (Woodbury, N.Y.), 31 (12) (Art N° 123131). | - |
item.validation | ecoom 2023 | - |
item.contributor | VANPOUCKE, Danny E.P. | - |
item.contributor | WENMACKERS, Sylvia | - |
crisitem.journal.issn | 1054-1500 | - |
crisitem.journal.eissn | 1089-7682 | - |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
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Assigning probabilities to non-Lipschitz mechanical systems.pdf | Published version | 3.85 MB | Adobe PDF | View/Open |
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