TY - JOUR

T1 - Nonequilibrium mode-coupling theory for dense active systems of self-propelled particles

AU - Nandi, Saroj Kumar

AU - Gov, Nir S.

N1 - We are grateful to Madan Rao and Chandan Dasgupta for useful discussions, comments and a critical reading of the manuscript. SKN would like to thank G. Szamel, J. Kurchan, S. Ramaswamy and J. Prost for many important discussions, L. Berthier for comments and the Koshland Foundation for funding through a fellowship. NSG is the incumbent of the Lee and William Abramowitz Professorial Chair of Biophysics and this research was made possible in part by the generosity of the Harold Perlman family.

PY - 2017/11/4

Y1 - 2017/11/4

N2 - The physics of active systems of self-propelled particles, in the regime of a dense liquid state, is an open puzzle of great current interest, both for statistical physics and because such systems appear in many biological contexts. We develop a nonequilibrium mode-coupling theory (MCT) for such systems, where activity is included as a colored noise with the particles having a self-propulsion force f(0) and a persistence time tau(p). Using the extended MCT and a generalized fluctuation-dissipation theorem, we calculate the effective temperature T-eff of the active fluid. The nonequilibrium nature of the systems is manifested through a time-dependent T-eff that approaches a constant in the long-time limit, which depends on the activity parameters f0 and tp. We find, phenomenologically, that this long-time limit is captured by the potential energy of a single, trapped active particle (STAP). Through a scaling analysis close to the MCT glass transition point, we show that tau(a), the alpha-relaxation time, behaves as tau(a) similar to f(0) (-2 gamma), where gamma = 1.74 is the MCT exponent for the passive system. ta may increase or decrease as a function of tp depending on the type of active force correlations, but the behavior is always governed by the same value of the exponent g. Comparison with the numerical solution of the nonequilibrium MCT and simulation results give excellent agreement with scaling analysis.

AB - The physics of active systems of self-propelled particles, in the regime of a dense liquid state, is an open puzzle of great current interest, both for statistical physics and because such systems appear in many biological contexts. We develop a nonequilibrium mode-coupling theory (MCT) for such systems, where activity is included as a colored noise with the particles having a self-propulsion force f(0) and a persistence time tau(p). Using the extended MCT and a generalized fluctuation-dissipation theorem, we calculate the effective temperature T-eff of the active fluid. The nonequilibrium nature of the systems is manifested through a time-dependent T-eff that approaches a constant in the long-time limit, which depends on the activity parameters f0 and tp. We find, phenomenologically, that this long-time limit is captured by the potential energy of a single, trapped active particle (STAP). Through a scaling analysis close to the MCT glass transition point, we show that tau(a), the alpha-relaxation time, behaves as tau(a) similar to f(0) (-2 gamma), where gamma = 1.74 is the MCT exponent for the passive system. ta may increase or decrease as a function of tp depending on the type of active force correlations, but the behavior is always governed by the same value of the exponent g. Comparison with the numerical solution of the nonequilibrium MCT and simulation results give excellent agreement with scaling analysis.

U2 - https://doi.org/10.1039/c7sm01648d

DO - https://doi.org/10.1039/c7sm01648d

M3 - مقالة

SN - 1744-683X

VL - 13

SP - 7609

EP - 7616

JO - Soft Matter

JF - Soft Matter

IS - 41

ER -