Time-dependent propulsion of fully inertial active stochastic particles: theory and simulations

Up to now, studies on fully inertial (adding mass and moment of inertia) active Brownian particles (IABPs) have only considered a constant propulsion force. This work overcomes this by studying IABPs but with a time-dependent propulsion and analytically characterizes this system by finding its mean-square displacement and effective diffusion for any periodic time-dependent propulsion speed. To exemplify the periodic general expressions, three particular self-propulsion signals are addressed, expressly, a cosine, a square-wave, and a zig-zag propulsion force. Langevin dynamics simulations are also employed to validate the analytical findings.