Stability of stationary states for mean field models with multichromatic interaction potentials
File(s)
Published version
Author(s)
Bertoli, Benedetta
Goddard, Benjamin D
Pavliotis, Grigorios A
Type
Journal Article
Abstract
We consider weakly interacting diffusions on the torus, for multichromatic interaction potentials. We
consider interaction potentials that are not H-stable, leading to phase transitions in the mean field limit.
We show that the mean field dynamics can exhibit multipeak stationary states, where the number of peaks
is related to the number of nonzero Fourier modes of the interaction. We also consider the effect of a
confining potential on the structure of nonuniform steady states. We approach the problem by means of
analysis, perturbation theory and numerical simulations for the interacting particle systems and the PDEs.
consider interaction potentials that are not H-stable, leading to phase transitions in the mean field limit.
We show that the mean field dynamics can exhibit multipeak stationary states, where the number of peaks
is related to the number of nonzero Fourier modes of the interaction. We also consider the effect of a
confining potential on the structure of nonuniform steady states. We approach the problem by means of
analysis, perturbation theory and numerical simulations for the interacting particle systems and the PDEs.
Date Issued
2024-10-01
Date Acceptance
2025-01-13
Citation
IMA Journal of Applied Mathematics, 2024, 89 (5), pp.833-859
ISSN
0272-4960
Publisher
Oxford University Press
Start Page
833
End Page
859
Journal / Book Title
IMA Journal of Applied Mathematics
Volume
89
Issue
5
Copyright Statement
© The Author(s) 2025. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/ 4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
License URL
Identifier
https://doi.org/10.1093/imamat/hxaf001
Subjects
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
0199 Other Mathematical Sciences
Applied Mathematics
Publication Status
Published
Date Publish Online
2025-01-13