Active jamming: Self-propelled soft particles at high density

We study numerically the phases and dynamics of a dense collection of self-propelled particles with soft repulsive interactions in two dimensions. The model is motivated by recent in vitro experiments on confluent monolayers of migratory epithelial and endothelial cells. The phase diagram exhibits a liquid phase with giant number fluctuations at low packing fraction $\phi$ and high self-propulsion speed $v_0$ and a jammed phase at high $\phi$ and low $v_0$. The dynamics of the jammed phase is controlled by the low-frequency modes of the jammed packing.

Figure 1

Sample snapshots of the system in the liquid phase ($\phi =0.6$, left) and in the jammed phase ($\phi =0.95$, right) for $v_0=0.025$. The glued boundary is shown in dark gray. The red (dark gray) arrows represent the instantaneous velocity field, with $v=v_0$ corresponding to an arrow of length 1 in units of the particle diameter. Please see Supplemental Material [23] for movies of these two runs.

Figure 2

Left: Mean-square displacement vs time as a function of density at $v_0=0.025$, showing a transition from rotational diffusion at low $\phi$, to polar alignment for $\phi <0.8$ and to the jammed state around $\phi =0.842$. Right: Phase diagram in the $\phi$-$v_0$ plane, showing the transition from the liquid state (blue or light gray) to the solid state (red or dark gray). The dots are simulated ($\phi$,$v_0$) pairs shaded white to black proportional to the fraction of jammed runs.

Figure 3

Scaled number fluctuations for $N_t=10000$ and a cut through the phase diagram at $v_0=0.025$. We observe three regimes: gaslike fluctuations at low density (green, top three curves), giant number fluctuations at intermediate density (red, middle five curves), and strongly suppressed fluctuations in the jammed phase (blue, bottom curves). The dashed line corresponds to $\Delta N/N^{1/2}=1$.

Figure 4

Left: Density of states of the mean positions (dashed) and time-averaged projection of the displacements on the modes (solid, scaled for visibility) for $\phi =0.86$. Inset: Scaling of peak with system size $N_t$ at $v_0=0.025$; the line has a slope of $-0.3$. Right: Time projection of the displacement on the modes $a_{\nu }\left(t\right)$ for four representative modes in the undamped and damped regions ($\phi =0.86$, $v_0=0.025$). Inset: Measured oscillation frequency ${\omega }^{\prime }$ as a function of $\omega$.