14
IRUS TotalDownloads
Altmetric
A fractional kinetic process describing the intermediate time behaviour of cellular flows
File | Description | Size | Format | |
---|---|---|---|---|
1607.01859v1.pdf | Accepted version | 1.47 MB | Adobe PDF | View/Open |
Title: | A fractional kinetic process describing the intermediate time behaviour of cellular flows |
Authors: | 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. |
Issue Date: | 1-Mar-2018 |
URI: | http://hdl.handle.net/10044/1/55157 |
Copyright Statement: | © The Authors |
Keywords: | math.PR math-ph math.AP math.MP 60H10, 60H30, 60F17, 26A33, 35R11, 76R50 |
Notes: | 47 pages |
Appears in Collections: | Pure Mathematics Faculty of Natural Sciences Mathematics |