Dynamics of the Desai-Zwanzig model in multiwell and random energy landscapes
File(s)PhysRevE.99.032109.pdf (1.49 MB)
Published version
Author(s)
Gomes, Susana N
Kalliadasis, Serafim
Pavliotis, Grigorios A
Yatsyshin, Petr
Type
Journal Article
Abstract
We analyze a variant of the Desai-Zwanzig model [J. Stat. Phys. 19, 1 (1978)]. In particular, we study stationary states of the mean field limit for a system of weakly interacting diffusions moving in a multiwell 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.
Date Issued
2019-03
Date Acceptance
2019-02-04
Citation
Physical Review E, 2019, 99 (3)
ISSN
2470-0045
Publisher
American Physical Society (APS)
Journal / Book Title
Physical Review E
Volume
99
Issue
3
Copyright Statement
© 2019 American Physical Society.
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/L020564/1
EP/L024926/1
EP/P031587/1
Subjects
Science & Technology
Physical Sciences
Physics, Fluids & Plasmas
Physics, Mathematical
Physics
MEAN-FIELD MODEL
PHASE-TRANSITIONS
FLUCTUATIONS
OPTIMIZATION
CONVERGENCE
DIFFUSIONS
Publication Status
Published
OA Location
https://arxiv.org/pdf/1810.06371.pdf
Article Number
032109
Date Publish Online
2019-03-06