Universal cover-time distributions of random motion in bounded granular gases

Abstract

The exhaustive random exploration of a complex domain is a fundamental issue in many natural, social, and engineering systems. The key characterizing quantity is the cover time, which is the time to visit every site in the system. One prototypical experimental platform is the confined granular gas, where the random motion of granular particles mimics the wandering of random walkers in a confined region. Here, we investigate the cover-time distribution of the random motion of tracer particles in granular gases confined in four containers to account for different boundary and angle effects and examine whether the cover time of the heterogeneous random motion of the granular gases can be rescaled into the universal Gumbel distribution according to a recent theory [Dong et al., arXiv:2210.05122 (2022)]. It is found that for long cover times, the experimental results are in full accord, while for short cover times, the agreement is reasonable, with noticeable deviations that can be attributed to spatial correlations of the sites in the covering process. Our results, thus, call for further theoretical investigations in order to take into full account these nonideal issues.