TY - JOUR
T1 - Non-equilibrium transitions in multiscale systems with a bifurcating slow manifold
AU - Grafke, Tobias
AU - Vanden-Eijnden, Eric
N1 - Funding Information:
EVE is supported in part by the Materials Research Science and Engineering Center (MRSEC) program of the National Science Foundation (NSF) under award number DMR-1420073 and by NSF under award number DMS-1522767.
Publisher Copyright:
© 2017 IOP Publishing Ltd and SISSA Medialab srl.
PY - 2017/9/25
Y1 - 2017/9/25
N2 - Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed within the realm of large deviation theory. It is shown that these non-equilibrium transitions make use of a reaction channel created by the bifurcation structure of the slow manifold, leading to vastly increased transition rates. Several examples are used to illustrate these findings, including an insect outbreak model, a system modeling phase separation in the presence of evaporation, and a system modeling transitions in active matter self-assembly. The last example involves a spatially extended system modeled by a stochastic partial differential equation.
AB - Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed within the realm of large deviation theory. It is shown that these non-equilibrium transitions make use of a reaction channel created by the bifurcation structure of the slow manifold, leading to vastly increased transition rates. Several examples are used to illustrate these findings, including an insect outbreak model, a system modeling phase separation in the presence of evaporation, and a system modeling transitions in active matter self-assembly. The last example involves a spatially extended system modeled by a stochastic partial differential equation.
KW - active matter
KW - large deviations in non-equilibrium systems
KW - metastable states
KW - stochastic processes
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U2 - 10.1088/1742-5468/aa85cb
DO - 10.1088/1742-5468/aa85cb
M3 - Article
AN - SCOPUS:85032278334
SN - 1742-5468
VL - 2017
JO - Journal of Statistical Mechanics: Theory and Experiment
JF - Journal of Statistical Mechanics: Theory and Experiment
IS - 9
M1 - 093208
ER -