Mean field limits for interacting diffusions in a two-scale potential

File Description SizeFormat 
10.1007%2Fs00332-017-9433-y.pdfPublished version2.52 MBAdobe PDFDownload
Title: Mean field limits for interacting diffusions in a two-scale potential
Author(s): Noronha Moreira Antunes Gomes, ST
Pavliotis, GA
Item Type: Journal Article
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 [13]. 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.
Publication Date: 1-Jun-2018
Date of Acceptance: 6-Dec-2017
URI: http://hdl.handle.net/10044/1/54615
DOI: https://dx.doi.org/10.1007/s00332-017-9433-y
ISSN: 0938-8974
Publisher: Springer Verlag
Start Page: 905
End Page: 941
Journal / Book Title: Journal of Nonlinear Science
Volume: 28
Issue: 3
Copyright Statement: © The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/L025159/1
EP/L020564/1
EP/L024926/1
EP/P031587/1
Keywords: Bifurcation diagram
Curie–Weiss model
Desai–Zwanzig model
Interacting particles
McKean–Vlasov equation
Multiscale diffusions
Phase transitions
0102 Applied Mathematics
Fluids & Plasmas
Publication Status: Published
Online Publication Date: 2017-12-19
Appears in Collections:Mathematics
Statistics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



Items in Spiral are protected by copyright, with all rights reserved, unless otherwise indicated.

Creative Commons