{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T06:30:20Z","timestamp":1790836220351,"version":"4.1.0"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2014,1]]},"abstract":"<jats:p>A method is presented to compute minimizers (instantons) of action functionals using arclength parametrization of Hamilton's equations. This method can be interpreted as a local variant of the geometric minimum action method introduced to compute minimizers of the Freidlin--Wentzell action functional that arises in the context of large deviation theory for stochastic differential equations. The method is particularly well suited to calculate expectations dominated by noise-induced excursions from deterministically stable fixpoints. Its simplicity and computational efficiency are illustrated here using several examples: a finite-dimensional stochastic dynamical system (an Ornstein--Uhlenbeck model) and two models based on stochastic partial differential equations: the $\\phi^4$-model and the stochastically driven Burgers equation.<\/jats:p>","DOI":"10.1137\/130939158","type":"journal-article","created":{"date-parts":[[2014,4,24]],"date-time":"2014-04-24T13:02:47Z","timestamp":1398344567000},"page":"566-580","source":"Crossref","is-referenced-by-count":25,"title":["Arclength Parametrized Hamilton's Equations for the Calculation of Instantons"],"prefix":"10.1137","volume":"12","author":[{"given":"T.","family":"Grafke","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R.","family":"Grauer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T.","family":"Sch\u00e4fer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E.","family":"Vanden-Eijnden","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2014,4,24]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.78.1452"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"J. Cardy, G. Falkovich, and K. Gawedzki,\n                      Non-equilibrium Statistical Mechanics and Turbulence\n                      , Cambridge University Press, Cambridge, UK, 2008.","DOI":"10.1017\/CBO9780511812149"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.64.026306"},{"key":"atypb4","first-page":"247","volume":"1","author":"C","year":"1976","journal-title":"J. Phys. C"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.66.052301"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3036"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1063\/1.2720838"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/15\/10\/011"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.80.041116"},{"key":"atypb10","doi-asserted-by":"crossref","unstructured":"M. I. Freidlin and A. D. Wentzell,\n                      Random Perturbations of Dynamical Systems\n                      , Springer-Verlag, New York, 1998.","DOI":"10.1007\/978-1-4612-0611-8"},{"key":"atypb11","unstructured":"C. Gardiner,\n                      Stochastic Methods: A Handbook for the Natural and Social Sciences\n                      , 4th ed., Springer-Verlag, Berlin, 2009."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/46\/6\/062002"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20238"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.100.140601"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01316547"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.8.423"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/10\/5\/011"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2004.12.025"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1063\/1.2833040"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1214\/07-AOP348"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/j.parco.2013.08.004"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1063\/1.2830717"}],"container-title":["Multiscale Modeling &amp; Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/130939158","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:38:44Z","timestamp":1787233124000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/130939158"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,1]]}},"alternative-id":["10.1137\/130939158"],"URL":"https:\/\/doi.org\/10.1137\/130939158","relation":{},"ISSN":["1540-3459","1540-3467"],"issn-type":[{"value":"1540-3459","type":"print"},{"value":"1540-3467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1]]}}}