Transport coefficients of self-propelled particles. II. Numerics for vorticity fluctuations and the reverse perturbation method

TL;DR

This paper extends the reverse perturbation method to systems of interacting particles with stochastic dynamics, verifying it with MPCD and applying it to Vicsek models to measure transport coefficients and compare them with theoretical predictions.

Contribution

It introduces and validates the reverse perturbation method for stochastic particle systems and applies it to Vicsek models to analyze transport coefficients.

Findings

Excellent agreement between measured and theoretical shear viscosity in MPCD.

Transport coefficients in Vicsek models are slightly higher than mean-field predictions.

Mean-field assumptions may be less reliable in velocity-alignment systems like the Vicsek model.

Abstract

In Part I of this two-part series, the reverse perturbation method for shearing simple liquids [Phys. Rev. E 59, 4894 (1999)] was extended to systems of interacting particles with time-discrete stochastic dynamics. For verification, in this paper (Part II) the reverse perturbation method is first applied to a simple momentum-conserving liquid, modeled through the Multi-Particle Collision Dynamics (MPCD) technique [J. Chem. Phys. 110, 8605 (1999)]. For MPCD, excellent agreement between the measured shear viscosity and its theoretical prediction is found. Furthermore, this paper contains applications of the reverse perturbation method to agent-based simulations of the Vicsek-model [Phys. Rev. Lett. 75, 1226 (1995)] and its metric-free version. The extracted transport coefficients, the kinematic viscosity $\nu$ and the momentum amplification coefficient $\lambda$, were compared to theoretical predictions. To verify the transport coefficients, Green-Kubo relations were evaluated and transverse current correlations were measured in independent simulations. Not too far to the transition to collective motion, we find excellent agreement between the different measurements of the transport coefficients. However, the measured values of $\nu$ and $1-\lambda$ are always slightly higher than the mean-field predictions, even at large mean free paths and at state points quite far from the threshold to collective motion, that is, far in the disordered phase. These findings seem to indicate that the mean-field assumption of molecular chaos is much less reliable in systems with velocity-alignment rules such as the Vicsek model, compared to models obeying detailed balance such as MPCD.