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Mean field limits for interacting diffusions in a two-scale potential
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Gomes, Susana N. and Pavliotis, G. A. (2018) Mean field limits for interacting diffusions in a two-scale potential. Journal of Nonlinear Science, 28 (3). pp. 905-941. doi:10.1007/s00332-017-9433-y ISSN 0938-8974.
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Official URL: https://doi.org/10.1007/s00332-017-9433-y
Abstract
In this paper, we study the combined mean field and homogenization limits for a system of weakly interacting diffusions moving in a two-scale, locally periodic confining potential, of the form considered in Duncan et al. (Brownian motion in an N-scale periodic potential, arXiv:1605.05854, 2016b). We show that, although the mean field and homogenization limits commute for finite times, they do not, in general, commute in the long time limit. In particular, the bifurcation diagrams for the stationary states can be different depending on the order with which we take the two limits. Furthermore, we construct the bifurcation diagram for the stationary McKean–Vlasov equation in a two-scale potential, before passing to the homogenization limit, and we analyze the effect of the multiple local minima in the confining potential on the number and the stability of stationary solutions.
Item Type: | Journal Article | ||||||||||||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Mean field theory, Multiscale modeling, Bifurcation theory, Phase transformations (Statistical physics) | ||||||||||||||||||
Journal or Publication Title: | Journal of Nonlinear Science | ||||||||||||||||||
Publisher: | Springer | ||||||||||||||||||
ISSN: | 0938-8974 | ||||||||||||||||||
Official Date: | June 2018 | ||||||||||||||||||
Dates: |
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Volume: | 28 | ||||||||||||||||||
Number: | 3 | ||||||||||||||||||
Page Range: | pp. 905-941 | ||||||||||||||||||
DOI: | 10.1007/s00332-017-9433-y | ||||||||||||||||||
Status: | Peer Reviewed | ||||||||||||||||||
Publication Status: | Published | ||||||||||||||||||
Reuse Statement (publisher, data, author rights): | This is a post-peer-review, pre-copyedit version of an article published in Journal of Nonlinear Science. The final authenticated version is available online at: http://dx.doi.org/[insert DOI]”. | ||||||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||||||||
Date of first compliant deposit: | 28 October 2019 | ||||||||||||||||||
Date of first compliant Open Access: | 30 October 2019 | ||||||||||||||||||
RIOXX Funder/Project Grant: |
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