Dynamics of self-organization in dense persistent active matter

TL;DR

This work investigates how a dense, two-dimensional athermal binary Lennard-Jones mixture subject to persistent active forces evolves from a disordered state into a self-organized, correlated steady state. Using large-scale simulations, it analyzes velocity and active-force correlations, their structure factors, and anisotropy to characterize domain growth and flow patterns. The authors find self-similar domain growth with a common length scale and distinct boundary morphologies: velocity domains exhibit Porod-like smooth boundaries (S_{vv}(k) ∝ k^{-3}), while active-force domains show rough boundaries (S_{ff}(k) ∝ k^{-2}); the steady-state flow is dominated by two opposing streams. These results reveal a non-equilibrium universality in active matter, providing a framework to compare with lane formation and offering potential guidance for experimental realizations of persistent-active fluids.

Abstract

We consider a two-dimensional athermal binary mixture of Lennard-Jones particles with persistent random active forces. The liquid phase of this system for active forces exceeding a threshold value exhibits self-organization with long-range spatial correlations of particle velocities and active forces. We study by simulations the development of these correlations from a random initial state. Several characteristics of the growth of correlations are measured and compared with those of phase-ordering kinetics of equilibrium systems after a quench from a disordered state. The motion of the particles in the long-time steady state is found to be dominated by two streams that flow in opposite directions.

Figures (8)

• Figure 1: Velocity (a)-(c), active force (d)-(f); both active force and velocity heatmaps correspond to the same state of a system of 38880 particles and $L=180$. The color of a dot representing a particle corresponds to the direction of the velocity/active force with the x-axis. The mapping of colors to angles is shown in the color-bar.
• Figure 2: The spatial correlation functions in linear scale in the main figure and the log-linear scale in the inset. (a)$~C_{vv}(r,t)$ versus $r$ (b) $~C_{fv}(r,t)$ versus $r$ (c) $~C_{ff}(r,t)$ versus $r$
• Figure 3: Spatial correlation functions plotted versus the scaled distance $r/R(t)$ at different times. Unscaled versions are shown in the insets (a) $C_{vv}\left(\frac{r}{R(t)}\right)$ versus $\frac{r}{R(t)}$ (b) $C_{fv}\left(\frac{r}{R(t)}\right)$ versus $\frac{r}{R(t)}$ (c) $C_{ff}\left(\frac{r}{R(t)}\right)$ versus $\frac{r}{R(t)}$ (d) $R(t)$ as a function of time $t$ for $C_{vv}$, $C_{fv}$, $C_{ff}$ and $C_{vv}^{(2)}$ on a log-log scale.
• Figure 4: The structure factors $F(k,t)$ plotted versus $k$ on log-log scale (a),(b) $~S_{vv}(k,t)$ versus $k$ in the steady state and (c),(d) $S_{ff}(k,t)$ versus $k$ in the steady state
• Figure 5: (a) Distribution of velocity angles, (b) Contour plot for $C_{vv}(r,\Theta)$ of the same configuration in the steady state.