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Arclength parametrized Hamilton's equations for the calculation of instantons
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Grafke, Tobias, Grauer, R., Schäfer, T. and Vanden-Eijnden, E. (2014) Arclength parametrized Hamilton's equations for the calculation of instantons. Multiscale Modeling & Simulation, 12 (2). pp. 566-580. doi:10.1137/130939158 ISSN 1540-3459.
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Official URL: http://dx.doi.org/10.1137/130939158
Abstract
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.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Multiscale Modeling & Simulation | ||||||||
Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||||||
ISSN: | 1540-3459 | ||||||||
Official Date: | 2014 | ||||||||
Dates: |
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Volume: | 12 | ||||||||
Number: | 2 | ||||||||
Page Range: | pp. 566-580 | ||||||||
DOI: | 10.1137/130939158 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Open Access Version: |
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