  Shape asymmetry is the most abundant in nature and attracted great 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
time scales. 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 diffusion dynamics for the free particle as well as the particle
in a harmonic trap, and the 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.
