Time-dependent inertia of self-propelled particles: the Langevin rocket

Abstract

Many self-propelled objects are large enough to exhibit inertial effects but still suffer from environmental fluctuations. The corresponding basic equations of motion are governed by active Langevin dynamics which involve inertia, friction and stochastic noise for both the translational and orientational degrees of freedom coupled via the self-propulsion along the particle orientation. In this paper, we generalize the active Langevin model to time-dependent parameters and explicitly discuss the effect of time-dependent inertia for achiral and chiral particles. Realizations of this situation are manifold ranging from minirockets which are self-propelled by burning their own mass, dust particles in plasma which lose mass by evaporating material to walkers with expiring activity. Here we present analytical solutions for several dynamical correlation functions such as the mean-square displacement and the orientational and velocity autocorrelation functions. If the parameters exhibit a slow power-law in time, we obtain anomalous superdiffusion with a non-trivial dynamical exponent. Finally we constitute the "Langevin rocket" model by including orientational fluctuations in the traditional Tsiolkovsky rocket equation. We calculate the mean reach of the Langevin rocket and discuss different mass ejection strategies to maximize it. Our results can be tested in experiments on macroscopic robotic or living particles or in self-propelled mesoscopic objects moving in media of low viscosity such as complex plasma.

Generalized Fluctuation-Dissipation relations holding in non-equilibrium dynamics

“…Even if many experimental systems of active matter have microscopic sizes [21] and usually move in environments with large viscosity (in such a way that inertial forces are negligible), recently, the effects of inertia [66] have been highlighted in many experimental active systems, such as vibro-robots [67], Hexbug crawlers and camphor surfers [68] and vibration-driven granular particles [69][70][71] (in the granular case, the response function has been also calculated experimentally [72]). To include the active force in these physical systems, the active Langevin model has been introduced [66,67,[73][74][75][76] so that the equation of motion of the active particle is described by its position, x, and velocity, v:…”

Barrier-mediated predator-prey dynamics

“…In future work we aim to extend our model to twodimensional landscapes [42,52,53], which might be realized by viscosity gradients [54][55][56] or external flow fields [57] and account for more realistic microswimmer models. Also, we will include inertial effects [58][59][60][61] to make a connection with macroscopic predator prey dynamics.…”

Active noise-driven particles under space-dependent friction in one dimension

“…Moreover inertial effects can be included in the particle dynamics [59][60][61][62]. Finally collective effects for many active-noise driven particles such as motility-induced phase separation should be explored [63,64].…”