  The active Brownian particle (ABP) model describes a swimmer, synthetic or
living, whose direction of swimming is a Brownian motion. The swimming is due
to a propulsion force, and the fluctuations are typically thermal in origin. We
present a 2D model where the fluctuations arise from nonthermal noise in a
propelling force acting at a single point, such as that due to a flagellum. We
take the overdamped limit and find several modifications to the traditional ABP
model. Since the fluctuating force causes a fluctuating torque, the diffusion
tensor describing the process has a coupling between translational and
rotational degrees of freedom. An anisotropic particle also exhibits a
noise-induced induced drift. We show that these effects have measurable
consequences for the long-time diffusivity of active particles, in particular
adding a contribution that is independent of where the force acts.
