A fractional kinetic process describing the intermediate time behaviour of cellular flows

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Title: A fractional kinetic process describing the intermediate time behaviour of cellular flows
Author(s): Hairer, M
Iyer, G
Koralov, L
Novikov, A
Pajor-Gyulai, Z
Item Type: Journal Article
Abstract: This paper studies the intermediate time behaviour of a small random perturbation of a periodic cellular flow. Our main result shows that on time scales shorter than the diffusive time scale, the limiting behaviour of trajectories that start close enough to cell boundaries is a fractional kinetic process: A Brownian motion time changed by the local time of an independent Brownian motion. Our proof uses the Freidlin-Wentzell framework, and the key step is to establish an analogous averaging principle on shorter time scales. As a consequence of our main theorem, we obtain a homogenization result for the associated advection-diffusion equation. We show that on intermediate time scales the effective equation is a fractional time PDE that arises in modelling anomalous diffusion.
URI: http://hdl.handle.net/10044/1/55157
Copyright Statement: © The Authors
Keywords: math.PR
math.PR
math-ph
math.AP
math.MP
60H10, 60H30, 60F17, 26A33, 35R11, 76R50
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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