Issue 25, 2017

Mode coupling theory for nonequilibrium glassy dynamics of thermal self-propelled particles

Abstract

We present a mode coupling theory study for the relaxation and glassy dynamics of a system of strongly interacting self-propelled particles, wherein the self-propulsion force is described by Ornstein–Uhlenbeck colored noise and thermal noises are included. Our starting point is an effective Smoluchowski equation governing the distribution function of particle positions, from which we derive a memory function equation for the time dependence of density fluctuations in nonequilibrium steady states. With the basic assumption of the absence of macroscopic currents and standard mode coupling approximation, we can obtain expressions for the irreducible memory function and other relevant dynamic terms, wherein the nonequilibrium character of the active system is manifested through an averaged diffusion coefficient [D with combining macron] and a nontrivial structural function S2(q) with q being the magnitude of wave vector q. [D with combining macron] and S2(q) enter the frequency term and the vertex term for the memory function, and thus influence both the short time and the long time dynamics of the system. With these equations obtained, we study the glassy dynamics of this thermal self-propelled particle system by investigating the Debye–Waller factor fq and relaxation time τα as functions of the persistence time τp of self-propulsion, the single particle effective temperature Teff as well as the number density ρ. Consequently, we find the critical density ρc for given τp shifts to larger values with increasing magnitude of propulsion force or effective temperature, in good accordance with previously reported simulation work. In addition, the theory facilitates us to study the critical effective temperature Tceff for fixed ρ as well as its dependence on τp. We find that Tceff increases with τp and in the limit τp → 0, it approaches the value for a simple passive Brownian system as expected. Our theory also well recovers the results for passive systems and can be easily extended to more complex systems such as active–passive mixtures.

Graphical abstract: Mode coupling theory for nonequilibrium glassy dynamics of thermal self-propelled particles

Article information

Article type
Paper
Submitted
29 Apr 2017
Accepted
19 May 2017
First published
05 Jun 2017

Soft Matter, 2017,13, 4464-4481

Mode coupling theory for nonequilibrium glassy dynamics of thermal self-propelled particles

M. Feng and Z. Hou, Soft Matter, 2017, 13, 4464 DOI: 10.1039/C7SM00852J

To request permission to reproduce material from this article, please go to the Copyright Clearance Center request page.

If you are an author contributing to an RSC publication, you do not need to request permission provided correct acknowledgement is given.

If you are the author of this article, you do not need to request permission to reproduce figures and diagrams provided correct acknowledgement is given. If you want to reproduce the whole article in a third-party publication (excluding your thesis/dissertation for which permission is not required) please go to the Copyright Clearance Center request page.

Read more about how to correctly acknowledge RSC content.

Social activity

Spotlight

Advertisements