Diffusion dynamics of an overdamped active ellipsoidal Brownian particle in two dimensions

Shape asymmetry is the most abundant in nature and has attracted considerable interest in recent research. The phenomenon is widely recognized: a free ellipsoidal Brownian particle displays anisotropic diffusion during short time intervals, which subsequently transitions to an isotropic diffusion pattern over longer timescales. We have further expanded this concept to incorporate active ellipsoidal particles characterized by an initial self-propelled velocity. This paper provides analytical and simulation results of diffusion dynamics of an active ellipsoidal particle. The active ellipsoidal particle manifests three distinct regimes in its diffusion dynamics over time. In the transient regime, it displays diffusive behavior followed by a super-diffusive phase, and in the longer time duration, it transitions to purely diffusive dynamics. We investigated the diffusion dynamics of a free particle as well as a particle in a harmonic trap, and a particle subject to a constant field force. Moreover, we have studied the rotational diffusion dynamics and torque production resulting from an external constant force field. Furthermore, our investigation extends to the examination of the scaled average velocity of an ellipsoidal active particle, considering both a constant force field and a one-dimensional ratchet.