Time scale of directional change of active Brownian particles

Abstract

For active Brownian particles (ABPs), the time scale τR=DR−1 has been widely used, with DR the rotational diffusion coefficient. Since the only independent non-dimensional number is Pe=v0DT−1/2DR−1/2 with v0 the self-propulsion velocity and DT the translational diffusion coefficient, any time scale of the ABP statistics should be the order of PeατR. In the present contribution, we show that by introducing the concept of relative angle Θ along with its expectation Φ(τ), a novel time scale with α=−1 can be observed, which indicates that the phenomenon of directional change is sensitive to Pe. This time scale corresponds to the transition time from the active overdamped particles (i.e., DT=0) to the PBPs under a background uniform velocity (i.e., DR=0). The direction change of both particle types can be estimated by using simplified analytical models. Comparisons with Navier-Stokes turbulence and football players indicate that the statistical similarity between ABPs and the latter is high.