Swarming and Swirling in Self-Propelled Polar Granular Rods

Using experiments with anisotropic vibrated rods and quasi-2D numerical simulations, we show that shape plays an important role in the collective dynamics of self-propelled (SP) particles. We demonstrate that SP rods exhibit local ordering, aggregation at the side walls, and clustering absent in round SP particles. Furthermore, we find that at sufficiently strong excitation SP rods engage in a persistent swirling motion in which the velocity is strongly correlated with particle orientation.

Figure 1

The distributions of displacements in a time interval $\tau$ (a) parallel and (b) perpendicular to the axis of the polar rod ($\Gamma =2$). Inset: schematic of the polar rod. The arrow shows the direction of net motion.

Figure 2

(a) Rods migrate and aggregate at the boundaries of a container for modest excitations ($N=500$, $\Gamma =2$). (b) Aggregation reduces and a homogeneous distribution is observed as excitation is increased. ($N=500$, $\Gamma =4$.) (c) Area fraction $\rho (r/R)$ as a function of distance $r$ from the center of the container with radius $R$ for $N=900$ averaged over 100 frames at 10 frames per second; open symbols: the results of numerical simulations for the same system parameters; (d) simulations show a decrease of clustering as $A_r$ is reduced ($\Gamma =2$).

Figure 3

(a) The standard deviation of the number of rods $\Delta n$ versus mean number of rods $n$ inside a circular area at the center of the container ($\Gamma =3$). Open symbols correspond to the simulations for a larger system size $R_L=2.5R_S$ but the same density. A fit to the data gives a slope $0.66\pm 0.05$, which indicates clustering. (b),(c) Local orientational order parameter $Q$ for nearest neighbors from simulation data for polar and apolar particles as a function of (b) density and (c) aspect ratio.

Figure 4

Swirling in time-averaged velocity obtained by computing particle displacements after $\tau =5\mathrm{s}$: (a) experiment ($\Gamma =3$, $N=900$), (b) numerics ($F_0=1.0$, $\rho =0.68$), and (c) example of swirls observed in a larger numerical system ($N=5500$, $R_L=2.5R_S$). (d) Spatial velocity correlation function $C(r)$ as a function of distance between two rods ($\Gamma =3$, $\rho =0.31$, $\rho =0.65$); results of simulations are shown for small ($R_S=34.2d$) and large ($R_L=2.5R_S$) system sizes and for the same density $\rho =0.68$. (e) The distribution of the angle between rod orientation and its velocity.