A1 Refereed original research article in a scientific journal
Effective equilibrium states in the colored-noise model for active matter I. Pairwise forces in the Fox and unified colored noise approximations
Authors: Wittmann, Rene; Maggi, C.; Sharma, A.; Scacchi, A.; Brader, J. M.; Marconi, U. Marini Bettolo
Publisher: IOP PUBLISHING LTD
Publishing place: BRISTOL
Publication year: 2017
Journal: Journal of Statistical Mechanics: Theory and Experiment
Journal name in source: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Journal acronym: J STAT MECH-THEORY E
Article number: 113207
Number of pages: 26
ISSN: 1742-5468
DOI: https://doi.org/10.1088/1742-5468/aa8c1f
Abstract
The equations of motion of active systems can be modeled in terms of Ornstein-Uhlenbeck processes (OUPs) with appropriate correlators. For further theoretical studies, these should be approximated to yield a Markovian picture for the dynamics and a simplified steady-state condition. We perform a comparative study of the unified colored noise approximation (UCNA) and the approximation scheme by Fox recently employed within this context. We review the approximations necessary to define effective interaction potentials in the low-density limit and study the conditions for which these represent the behavior observed in two-body simulations for the OUPs model and active Brownian particles. The demonstrated limitations of the theory for potentials with a negative slope or curvature can be qualitatively corrected by a new empirical modification. In general, we find that in the presence of translational white noise the Fox approach is more accurate. Finally, we examine an alternative way to define a force-balance condition in the limit of small activity.
The equations of motion of active systems can be modeled in terms of Ornstein-Uhlenbeck processes (OUPs) with appropriate correlators. For further theoretical studies, these should be approximated to yield a Markovian picture for the dynamics and a simplified steady-state condition. We perform a comparative study of the unified colored noise approximation (UCNA) and the approximation scheme by Fox recently employed within this context. We review the approximations necessary to define effective interaction potentials in the low-density limit and study the conditions for which these represent the behavior observed in two-body simulations for the OUPs model and active Brownian particles. The demonstrated limitations of the theory for potentials with a negative slope or curvature can be qualitatively corrected by a new empirical modification. In general, we find that in the presence of translational white noise the Fox approach is more accurate. Finally, we examine an alternative way to define a force-balance condition in the limit of small activity.
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