Imperial College London
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Professor Grigorios A. Pavliotis

Faculty of Natural Sciences, Department of Mathematics

Professor of Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8564g.pavliotis Website

 
 
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Location

 

736aHuxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Gomes:2020:10.1137/19M1258116,
author = {Gomes, SN and Pavliotis, GA and Vaes, U},
doi = {10.1137/19M1258116},
journal = {SIAM: Multiscale Modeling and Simulation},
pages = {1343--1370},
title = {Mean field limits for interacting diffusions with colored noise: phase transitions and spectral numerical methods},
url = {http://dx.doi.org/10.1137/19M1258116},
volume = {18},
year = {2020}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - In this paper we consider systems of weakly interacting particles driven by colored noise in a bistable potential, and we study the effect of the correlation time of the noise on the bifurcation diagram for the equilibrium states. We accomplish this by solving the corresponding McKean--Vlasov equation using a Hermite spectral method, and we verify our findings using Monte Carlo simulations of the particle system. We consider both Gaussian and non-Gaussian noise processes, and for each model of the noise we also study the behavior of the system in the small correlation time regime using perturbation theory. The spectral method that we develop in this paper can be used for solving linear and nonlinear, local and nonlocal (mean field) Fokker--Planck equations, without requiring that they have a gradient structure.
AU  - Gomes,SN
AU  - Pavliotis,GA
AU  - Vaes,U
DO  - 10.1137/19M1258116
EP  - 1370
PY  - 2020///
SN  - 1540-3459
SP  - 1343
TI  - Mean field limits for interacting diffusions with colored noise: phase transitions and spectral numerical methods
T2  - SIAM: Multiscale Modeling and Simulation
UR  - http://dx.doi.org/10.1137/19M1258116
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000576464000007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://epubs.siam.org/doi/10.1137/19M1258116
UR  - http://hdl.handle.net/10044/1/88275
VL  - 18
ER  -
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