Clogging Transition of Vibration-Driven Vehicles Passing through Constrictions

We report experimental results on the competitive passage of elongated self-propelled vehicles rushing through a constriction. For the chosen experimental conditions, we observe the emergence of intermittencies similar to those reported previously for active matter passing through narrow doors. Noteworthy, we find that, when the number of individuals crowding in front of the bottleneck increases, there is a transition from an unclogged to a clogged state characterized by a lack of convergence of the mean clog duration as the measuring time increases. It is demonstrated that this transition—which was reported previously only for externally vibrated systems such as colloids or granulars—appears also for self-propelled agents. This suggests that the transition should also occur for the flow through constrictions of living agents (e.g., humans and sheep), an issue that has been elusive so far in experiments due to safety risks.

Figure 1

VDV photograph and snapshot of the system during a typical run. The dimensions are $d_1=200\mathrm{mm}$, $d_2=180\mathrm{mm}$, $d_3=100\mathrm{mm}$, and $L=30\mathrm{mm}$. Red arrows indicate the feedback path followed by the VDVs. ${\alpha }_i$ is the angle between agent $i$ and the axis of the enclosure.

Figure 2

(a) Number of evacuated agents as a function of the elapsed time for different number of agents in the arena. Dashed lines stand for independent realizations and solid lines for mean values. (b) Complementary CDF of $\mathrm{\Delta }t$ for independent realizations with $N=36$ agents. Symbols stand for experimental data and the solid line for the fitted power law. (c) Complementary CDF of the burst duration for independent realizations with $N=36$ agents. Successive bursts are set apart when the time lapse between two consecutive VDVs is longer than 5 s.

Figure 3

(a) PL exponent $\gamma$ for each experimental realization estimated using semiparametric bootstrap methods [25]. Error bars were defined as the 95% confidence intervals. (b) Fraction of time $\mathrm{\Phi }$ that the system is flowing as a function of the time window $T_W$ in which this magnitude is calculated.

Figure 4

(a) Radial distribution function and (b) radial orientational function for different $N$.