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Mean field limits for interacting diffusions with colored noise: phase transitions and spectral numerical methods

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Title: Mean field limits for interacting diffusions with colored noise: phase transitions and spectral numerical methods
Authors: Gomes, SN
Pavliotis, GA
Vaes, U
Item Type: Journal Article
Abstract: 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.
Issue Date: 2-Sep-2020
Date of Acceptance: 28-Apr-2020
URI: http://hdl.handle.net/10044/1/88275
DOI: 10.1137/19M1258116
ISSN: 1540-3459
Publisher: Society for Industrial and Applied Mathematics
Start Page: 1343
End Page: 1370
Journal / Book Title: SIAM: Multiscale Modeling and Simulation
Volume: 18
Issue: 3
Copyright Statement: © 2020, Society for Industrial and Applied Mathematics
Keywords: Science & Technology
Physical Sciences
Mathematics, Interdisciplinary Applications
Physics, Mathematical
Mathematics
Physics
McKean-Vlasov PDEs
nonlocal Fokker-Planck equations
interacting particles
Desai-Zwanzig model
colored noise
Hermite spectral methods
phase transitions
MARKOVIAN BROWNIAN-MOTION
STOCHASTIC-SYSTEMS
MODEL
CONVERGENCE
FLUCTUATIONS
EQUILIBRIUM
EQUATIONS
DYNAMICS
BEHAVIOR
Science & Technology
Physical Sciences
Mathematics, Interdisciplinary Applications
Physics, Mathematical
Mathematics
Physics
McKean-Vlasov PDEs
nonlocal Fokker-Planck equations
interacting particles
Desai-Zwanzig model
colored noise
Hermite spectral methods
phase transitions
MARKOVIAN BROWNIAN-MOTION
STOCHASTIC-SYSTEMS
MODEL
CONVERGENCE
FLUCTUATIONS
EQUILIBRIUM
EQUATIONS
DYNAMICS
BEHAVIOR
math.NA
math.NA
cond-mat.stat-mech
cs.NA
35Q70, 35Q83, 35Q84, 65N35, 65M70, 82B26
0102 Applied Mathematics
Applied Mathematics
Publication Status: Published
Online Publication Date: 2020-09-02
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics