Tipping Points in Stochastically Perturbed Linear Filippov Systems
In this thesis, we study noise-induced tipping in a piecewise-smooth, linear, one-dimensional periodically forced system perturbed by weak additive noise. This problem is motivated by a recent model of energy flux in Arctic sea ice. We determine the most probable tipping events using path integral t...
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Wake Forest University
2018
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ftwakeforestuniv:oai:wakespace.lib.wfu.edu:10339/90720 2023-05-15T15:00:08+02:00 Tipping Points in Stochastically Perturbed Linear Filippov Systems Zanetell, Jessica 2018 http://hdl.handle.net/10339/90720 en eng Wake Forest University http://hdl.handle.net/10339/90720 Thesis 2018 ftwakeforestuniv 2022-08-02T09:02:41Z In this thesis, we study noise-induced tipping in a piecewise-smooth, linear, one-dimensional periodically forced system perturbed by weak additive noise. This problem is motivated by a recent model of energy flux in Arctic sea ice. We determine the most probable tipping events using path integral techniques. Specifically, we calculate local minimizes of the Onsager-Machlup functional using solutions to the corresponding Euler-Lagrange equations and a gradient flow applied to the functional. We also prove an extension of Kramer's law to determine bounds for the expected tipping time. Using these methods, we determine the most probable transition path from a frozen state to an unfrozen state and determine the seasons that are most susceptible to tipping. Thesis Arctic Sea ice WakeSpace Scholarship (Wake Forest University) Arctic Lagrange ENVELOPE(-62.597,-62.597,-64.529,-64.529) |
institution |
Open Polar |
collection |
WakeSpace Scholarship (Wake Forest University) |
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ftwakeforestuniv |
language |
English |
description |
In this thesis, we study noise-induced tipping in a piecewise-smooth, linear, one-dimensional periodically forced system perturbed by weak additive noise. This problem is motivated by a recent model of energy flux in Arctic sea ice. We determine the most probable tipping events using path integral techniques. Specifically, we calculate local minimizes of the Onsager-Machlup functional using solutions to the corresponding Euler-Lagrange equations and a gradient flow applied to the functional. We also prove an extension of Kramer's law to determine bounds for the expected tipping time. Using these methods, we determine the most probable transition path from a frozen state to an unfrozen state and determine the seasons that are most susceptible to tipping. |
format |
Thesis |
author |
Zanetell, Jessica |
spellingShingle |
Zanetell, Jessica Tipping Points in Stochastically Perturbed Linear Filippov Systems |
author_facet |
Zanetell, Jessica |
author_sort |
Zanetell, Jessica |
title |
Tipping Points in Stochastically Perturbed Linear Filippov Systems |
title_short |
Tipping Points in Stochastically Perturbed Linear Filippov Systems |
title_full |
Tipping Points in Stochastically Perturbed Linear Filippov Systems |
title_fullStr |
Tipping Points in Stochastically Perturbed Linear Filippov Systems |
title_full_unstemmed |
Tipping Points in Stochastically Perturbed Linear Filippov Systems |
title_sort |
tipping points in stochastically perturbed linear filippov systems |
publisher |
Wake Forest University |
publishDate |
2018 |
url |
http://hdl.handle.net/10339/90720 |
long_lat |
ENVELOPE(-62.597,-62.597,-64.529,-64.529) |
geographic |
Arctic Lagrange |
geographic_facet |
Arctic Lagrange |
genre |
Arctic Sea ice |
genre_facet |
Arctic Sea ice |
op_relation |
http://hdl.handle.net/10339/90720 |
_version_ |
1766332250185531392 |