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Dynamics of the Desai-Zwanzig model in multiwell and random energy landscapes
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Gomes, Susana N. M. A., Kalliadasis, Serafim, Pavliotis, Grigorios A. and Yatsyshin, Petr (2019) Dynamics of the Desai-Zwanzig model in multiwell and random energy landscapes. Physical Review E, 99 (3). 032109 . doi:10.1103/PhysRevE.99.032109 ISSN 2470-0045.
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Official URL: https://doi.org/10.1103/PhysRevE.99.032109
Abstract
We analyze a variant of the Desai-Zwanzig model [J. Stat. Phys. {\bf 19}1-24 (1978)]. In particular, we study stationary states of the mean field limit for a system of weakly interacting diffusions moving in a multi-well potential energy landscape, coupled via a Curie-Weiss type (quadratic) interaction potential. The location and depth of the local minima of the potential are either deterministic or random. We characterize the structure and nature of bifurcations and phase transitions for this system, by means of extensive numerical simulations and of analytical calculations for an explicitly solvable model. Our numerical experiments are based on Monte Carlo simulations, the numerical solution of the time-dependent nonlinear Fokker-Planck (McKean-Vlasov equation), the minimization of the free energy functional and a continuation algorithm for the stationary solutions.
| Item Type: | Journal Article | |||||||||||||||||||||
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| Subjects: | Q Science > QC Physics | |||||||||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Phase transitions (Statistical physics), Convex domains, Neural networks (Neurobiology) | |||||||||||||||||||||
| Journal or Publication Title: | Physical Review E | |||||||||||||||||||||
| Publisher: | American Physical Society | |||||||||||||||||||||
| ISSN: | 2470-0045 | |||||||||||||||||||||
| Official Date: | 6 March 2019 | |||||||||||||||||||||
| Dates: |
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| Volume: | 99 | |||||||||||||||||||||
| Number: | 3 | |||||||||||||||||||||
| Article Number: | 032109 | |||||||||||||||||||||
| DOI: | 10.1103/PhysRevE.99.032109 | |||||||||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||||||||
| Publication Status: | Published | |||||||||||||||||||||
| Reuse Statement (publisher, data, author rights): | © 2019 American Physical Society | |||||||||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||||||||
| Copyright Holders: | © 2019 American Physical Society | |||||||||||||||||||||
| RIOXX Funder/Project Grant: |
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