Cover-time distribution of random processes in granular gases

Abstract

Random processes have attracted much attention due to their broad applications. Despite the many varieties of random processes, it is proposed that there can be universal properties, e.g., the cover-time distributions for noncompact random walks. In this work, we investigate experimentally the cover-time distribution in random processes of granular gases. In particular, the trajectory of a tracer particle in the granular gases is read out by a high-speed camera, which forms a random process that is specific to granular gas systems. Analysis of the covering process of this trajectory is then carried out to get the cover-time distribution. The direct results of cover-time distribution deviates from the universal law, which can be attributed to two main factors: the attracting effect at the boundary and the nonperiodic boundary condition due to the fixed boundaries. By efficiently removing these effects step by step, the cover-time distribution recovers to the universal law approximately, which also reveals that the attracting effect at the boundary is the most dominant factor leading to the discrepancy. We have carried out three distinct experiments with different granular gas circumstances, and all agreed well with the universal distribution after removing the boundary effects.