Correlated and anti-correlated density dependent motility

TL;DR

This work studies density-dependent motility (DDM) as a quorum-sensing inspired mechanism in a soft-repulsive 2D particle system, comparing correlated and anti-correlated motility rules. Using Langevin dynamics with a local density $\rho_i$ and a critical threshold $\rho_c$, it maps steady states and phase transitions as functions of $\rho_c$ and the activity parameter $b$, revealing distinct phase diagrams: correlated DDM drives motility-induced phase separation and a later dilution of active regions, while anti-correlated DDM yields coexistence of a passive solid or glass with an active gas, including hexatic ordering in the passive phase at higher activity. The results illustrate how the sign of the density-dependence and activity shape clustering, ordering, and transitions, and point to future directions such as multi-threshold motility schemes, continuous motility functions, and extensions to three dimensions or non-spherical particles. These insights help illuminate quorum-sensing-like collective behavior in synthetic active matter and potentially biological contexts.

Abstract

I study via Langevin dynamics simulations two opposite cases of systems of particles that alternate their identity according to density dependent motility (DDM) rules and interact via a soft repulsive potential. In the correlated case, dilute regions are passive and dense regions are active, while in the anti-correlated case, dilute regions are active and dense regions are passive. I classify the emerging steady states, explain the principal phase transitions, and finally suggest directions for further investigation.

Figures (7)

• Figure 1: Correlated versus anti-correlated density dependent motility. In the correlated case, dilute regions are passive and dense regions are active. In the anti-correlated case, dilute regions are active and dense regions are passive. When the local density of a particle increases, it can participate in one of three events, marked by $e_1$, $e_2$ and $e_3$.
• Figure 2: Snapshots for the correlated case at $b=5, 50$ and $\rho_c=0.20, 0.25, 0.35$. Passive (active) particles are colored in gray (black). The fraction of active particles is indicated on the top-left corner of each snapshot.
• Figure 3: Phase diagram for the correlated case. The transition from "active fluid" to "fluid-fluid" is marked by a red line and the transition from "fluid-fluid" to "passive fluid" is marked by a blue line. The sub-transition from "active majority" to "passive majority" is marked by the black dashed line. Insets (i) and (ii) show the tendency of the principal phase lines.
• Figure 4: Correlated case: systems in the "active majority" state at $\rho_c=0.225$. Particles colored according to local density as indicated in the colormap. As $b$ increases, the active clusters are smaller.
• Figure 5: Snapshots for the anti-correlated case $b=5, 50$ and $\rho_c=0.2, 0.3, 0.4$. Passive (active) particles are colored in gray (black). The fraction of active particles is indicated on the top-left corner of each snapshot. The system gradually phase separates into a cluster of passive particles coexisting with an active gas.