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Mean field limits for interacting diffusion with colored noise : phase transitions and spectral numerical methods
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Gomes , Susana, Pavliotis, G. A. and Vaes, U. (2020) Mean field limits for interacting diffusion with colored noise : phase transitions and spectral numerical methods. Multiscale Modeling and Simulation : A SIAM Interdisciplinary Journal, 18 (3). pp. 1343-1370. doi:10.1137/19M1258116 ISSN 1540-3459.
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WRAP-Mean-field-limits-interacting-diffusion-noise-transitions-spectral-numerical-Gomes-2020.pdf - Accepted Version - Requires a PDF viewer. Download (3222Kb) | Preview |
Official URL: https://doi.org/10.1137/19M1258116
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.
| 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): | Fokker-Planck equation , White noise theory, Gaussian processes, Phase transformations (Statistical physics) | |||||||||||||||||||||
| Journal or Publication Title: | Multiscale Modeling and Simulation : A SIAM Interdisciplinary Journal | |||||||||||||||||||||
| Publisher: | SIAM | |||||||||||||||||||||
| ISSN: | 1540-3459 | |||||||||||||||||||||
| Official Date: | 2020 | |||||||||||||||||||||
| Dates: |
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| Volume: | 18 | |||||||||||||||||||||
| Number: | 3 | |||||||||||||||||||||
| Page Range: | pp. 1343-1370 | |||||||||||||||||||||
| DOI: | 10.1137/19M1258116 | |||||||||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||||||||
| Publication Status: | Published | |||||||||||||||||||||
| Reuse Statement (publisher, data, author rights): | “First Published in Multiscale Modeling and Simulation : A SIAM Interdisciplinary Journal in [volume and number, or year], published by the Society for Industrial and Applied Mathematics (SIAM)” and the copyright notice as stated in the article itself (e.g., “Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.”) | |||||||||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||||||||
| Copyright Holders: | Copyright © by SIAM. Unauthorized reproduction of this article is prohibited | |||||||||||||||||||||
| Date of first compliant deposit: | 15 June 2020 | |||||||||||||||||||||
| Date of first compliant Open Access: | 16 June 2020 | |||||||||||||||||||||
| RIOXX Funder/Project Grant: |
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