Impact fragmentation of model flocks

Predicting the bulk material properties of active matter is challenging since these materials are far from equilibrium and standard statistical-mechanics approaches may fail. We report a computational study of the surface properties of a well known active matter system: aggregations of self-propelled particles that are coupled via an orientational interaction and that resemble bird flocks. By simulating the impact of these models flocks on an impermeable surface, we find that they fragment into subflocks with power-law mass distributions, similar to shattering brittle solids but not to splashing liquid drops. Thus, we find that despite the interparticle interactions, these model flocks do not possess an emergent surface tension.

Figure 1

Morphology of flock impacts for various simulation parameters. Flocks are shown from the side (top row; the solid line shows the impermeable wall) and from above (bottom row). In all cases, the flocks move along the $X$ axis, and begin in a cylindrical configuration, as shown in (a) and (b). Postimpact configurations are shown for (c, d) $n_0=1$ and $v=0.1$, (e, f) $n_0=1$ and $v=0.5$, (g, h) $n_0=1$ and $v=1$, and (i, j) $n_0=2$ and $v=1$.

Figure 2

(a) Flattening parameter ${\varphi }_F$, as defined in the text, as a function of $n_0$ and $v$. Low-speed flocks tend to compress into the plane of the wall, while high-speed flocks tend to rebound strongly. (b) Asymmetry parameter ${\varphi }_S$ as a function of $n_0$ and $v$ [note that the in-plane axes are oriented differently in (a) and (b) to show the variation better]. Low-speed flocks maintain their overall polarization better during impact and tend to move in a single direction after impact. Each data point represents the ensemble average of 300 simulations.

Figure 3

Number of distinct clusters (for a fixed population size of 1000 particles) after impact as a function of $n_0$ and $v$. High-speed, low-density flocks tend to shatter into many fragments, while low-speed flocks maintain group cohesion. Each data point represents the ensemble average of 300 simulations.

Figure 4

Sample distributions of cluster sizes for (a) $n_0=0.1$ and $v=0.1$, (b) $n_0=0.1$ and $v=1$, (c) $n_0=1$ and $v=0.1$, (d) $n_0=1$ and $v=1$, and (e) $n_0=0.5$ and $v=0.5$. The dashed lines are power-law fits.

Figure 5

Power-law exponents for the cluster-size distributions as a function of $n_0$ and $v$. The black circles mark the curves shown in Fig. 4. Each data point represents the ensemble average of 100 simulations.