Koltai, P. and Renger, M. (2018) From Large Deviations to Semidistances of Transport and Mixing: Coherence Analysis for Finite Lagrangian Data. Journal of Nonlinear Science, 28 (5). pp. 19151957. ISSN 14321467 (online)

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Official URL: https://dx.doi.org/10.1007/s0033201894710
Abstract
One way to analyze complicated nonautonomous flows is through trying to understand their transport behavior. In a quantitative, setoriented approach to transport and mixing, finite time coherent sets play an important role. These are timeparametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as a measure of transport and mixing for purely advective (i.e., deterministic) flows, (semi)distances that arise under vanishing perturbations in the sense of large deviations. Analogously, for given finite Lagrangian trajectory data we derive a discretetimeandspace semidistance that comes from the “best” approximation of the randomly perturbed process conditioned on this limited information of the deterministic flow. It can be computed as shortest path in a graph with timedependent weights. Furthermore, we argue that coherent sets are regions of maximal farness in terms of transport and mixing, and hence they occur as extremal regions on a spanning structure of the state space under this semidistance—in fact, under any distance measure arising from the physical notion of transport. Based on this notion, we develop a tool to analyze the state space (or the finite trajectory data at hand) and identify coherent regions. We validate our approach on idealized prototypical examples and wellstudied standard cases.
Item Type:  Article 

Additional Information:  SFB 1114 Preprint in arXiv:1709.02352 (Titel der Publikation weicht ab von PreprintTitle: From large deviations to transport semidistances: coherence analysis for finite Lagrangian data) 
Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group 
ID Code:  2257 
Deposited By:  BioComp Admin 
Deposited On:  16 Jul 2018 08:56 
Last Modified:  11 Jan 2019 11:16 
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