First-passage dynamics by aggregating particles

Abstract

Using the Langevin dynamics simulations, we study the first-passage problem in a system where particles aggregate into clusters. We consider N Brownian particles strongly attracting each other so that upon encountering, they form bound states. We find that the search time, the mean time for a target to be found for the first time by particles, exhibits non-monotonic behavior with the number of particles N. At small N, the search time decreases with N, while as increasing N further, it turns to grow with N. The non-monotonic behavior can be understood by a thicker power law distribution of the first-passage time on typical time scales of aggregations.