Dynamics of active particles with space-dependent swim velocity

Abstract

We study the dynamical properties of an active particle subject to a swimming speed explicitly depending on the particle position. The oscillating spatial profile of the swim velocity considered in this paper takes inspiration from experimental studies based on Janus particles whose speed can be modulated by an external source of light. We suggest and apply an appropriate model of an active Ornstein Uhlenbeck particle (AOUP) to the present case. This allows us to predict the stationary properties, by finding the exact solution of the steady-state probability distribution of particle position and velocity. From this, we obtain the spatial density profile and show that its form is consistent with the one found in the framework of other popular models. The reduced velocity distribution highlights the emergence of non-Gaussianity in our generalized AOUP model which becomes more evident as the spatial dependence of the velocity profile becomes more pronounced. Then, we focus on the time-dependent properties of the system. Velocity autocorrelation functions are studied in the steady-state combining numerical and analytical methods derived under suitable approximations. We observe a non-monotonic decay in the temporal shape of the velocity autocorrelation function which depends on the ratio between the persistence length and the spatial period of the swim velocity. Finally, we numerically and analytically study the mean square displacement and the long-time diffusion coefficient. The ballistic regime, observed in the small-time region, is deeply affected by the properties of the swim velocity landscape which induces also a crossover to a sub-ballistic but superdiffusive regime for intermediate times. Finally, the long-time diffusion coefficient decreases as the amplitude of the swim velocity oscillations increases because the diffusion is mainly determined by those regions where the particles are slow.

The Parental Active Model: a unifying stochastic description of self-propulsion

“…In conclusion, the PAM both unifies ABPs and AOUPs and provides a crucial step towards more realistic modeling of overdamped (dry) active motion in general, which should in future work be employed to provide an improved fit of experimental swim-velocity distributions. Investigating the effect of the swim-velocity fluctuations could represent an interesting perspective for circle swimming [92][93][94][95][96][97] , systems with spatial-dependent swim velocity [98][99][100][101][102][103] , and inertial dynamics [104][105][106][107][108] even affecting the orientational degrees of freedom 109,110 . The generalization of PAM to these cases could be responsible for new intriguing phenomena which will be investigated in future works.…”