Absence of jamming in ant trails: Feedback control of self-propulsion and noise

We present a model of ant traffic considering individual ants as self-propelled particles undergoing single-file motion on a one-dimensional trail. Recent experiments on unidirectional ant traffic in well-formed natural trails showed that the collective velocity of ants remains approximately unchanged, leading to the absence of jamming even at very high densities [John et al., Phys. Rev. Lett. 102, 108001 (2009)]. Assuming a feedback control mechanism of self-propulsion force generated by each ant using information about the distance from the ant in front, our model captures all the main features observed in the experiment. The distance headway distribution shows a maximum corresponding to separations within clusters. The position of this maximum remains independent of average number density. We find a non-equilibrium first-order transition, with the formation of an infinite cluster at a threshold density where all the ants in the system suddenly become part of a single cluster.

Figure 1

Average velocity with density. The symbols $\circ$ with error bars denote our simulation results, while the small $▵$ symbols denote data extracted from Fig. 3 of Ref. [22]. The dashed line is the mean filed estimate $\langle v\rangle =f_0(1-\rho /{\rho }_f)$. Inset: The fundamental diagram showing current as a function of density. The dashed line is a plot of mean field estimate $\langle j\rangle =\rho \langle v\rangle$.

Figure 2

Distribution functions. (a) Probability distribution of velocity of each particle at densities $\rho =0.1,0.3,0.5,0.7,0.9$. The points are obtained from simulation, and the lines show expected Gaussian distributions with varying peaks and widths. (b)–(d) Simulation results for probability distributions of distance headways, at densities $\rho =0.2,0.5,0.7$.

Figure 3

Cluster-size distributions $P\left(n\right)$ at various densities $\rho$ denoted in the legend. The largest possible cluster size is $n=N=4096$. The semi-log plots show exponential tails of the distributions $exp(-n/n_c)$.

Figure 4

Typical cluster size $n_c$ as a function of overall density $\rho$, shows sharp increase in $n_c$ at $\rho >0.9$, indicating a non-equilibrium first-order transition.