Active Ornstein-Uhlenbeck particles: a versatile model for self-propelled motion

Active Brownian Particles (ABPs), characterized by a constant self-propulsion velocity along the current orientaion, are commonly perceived as the standard model for dry active motion. As an alternative, Active Ornstein-Uhlenbeck Particles (AOUPs) model the persistent motion through a Gaussian process, which is particularly appealing in view of calculating exact solutions and developing approximate theories, and are thus sometimes perceived as an approximation to ABPs.

Here, we introduce a parental active model (PAM) based on a general stochastic process with fluctuating self-propulsion velocity, within which both ABPs and AOUPs emerge as limiting cases, i.e., they are rather sisters than cousins. We then demonstrate that a position-dependent swim-velocity field can be consistently introduced for any self-propulsion mechanism. As an application, we discuss the effects of varying self propulsion in external confinement and predict the stationary properties using effective interactions.

Both ABPs and AOUPs have been originally developed to model the overdamped dynamics of microscopic active particles. However, the recent interest in macroscopic active systems generates the need to develop manageable theoretical descriptions of inertial effects. For AOUPs with translational inertia we provide exact analytical solutions for dynamical correlation functions considering an active dimer, a time-dependent mass and various external forces. Finally, we discuss effects of rotational inertia.