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Duncan, A. B.; Kalliadasis, S.; Pavliotis, G. A. and Pradas, M.
(2016).
DOI: https://doi.org/10.1103/PhysRevE.94.032107
Abstract
We consider the problem of an overdamped Brownian particle moving in multiscale potential with N + 1 characteristic length scales: the macroscale and N separated microscales. We show that the coarse-grained dynamics is given by an overdamped Langevin equation with respect to the free energy and with a space-dependent diffusion tensor, the calculation of which requires the solution of N fully coupled Poisson equations. We study in detail the structure of the bifurcation diagram for one-dimensional problems, and we show that the multiscale structure in the potential leads to hysteresis effects and to noise-induced transitions. Furthermore, we obtain an explicit formula for the effective diffusion coefficient for a self-similar separable potential, and we investigate the limit of infinitely many small scales.
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About
- Item ORO ID
- 47509
- Item Type
- Journal Item
- ISSN
- 2470-0053
- Project Funding Details
-
Funded Project Name Project ID Funding Body Not Set EP/H034587 EPSRC Not Set EP/J009636 EPSRC Not Set EP/K008595 EPSRC Not Set EP/L020564 EPSRC Not Set EP/L024926 EPSRC Not Set 247031 ERC - Academic Unit or School
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Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Copyright Holders
- © 2016 American Physical Society
- Depositing User
- Marc Pradas