Transport of underdamped active particles in ratchet potentials

Abstract

We study the rectified transport of underdamped active noninteracting particles in an asymmetric periodic potential. It is found that the ratchet effect of active noninteracting particles occurs in a single direction (along the easy direction of the substrate asymmetry) in the overdamped limit. However, when the inertia is considered, it is possible to observe reversals of the ratchet effect, where the motion is along the hard direction of the substrate asymmetry. By changing the friction coefficient or the self-propulsion force, the average velocity can change its direction several times. Therefore, by suitably tailoring the parameters, underdamped active particles with different self-propulsion forces can move in different directions and can be separated.

Inertial self-propelled particles

“…The understanding of these aspects requires a description taking into account the acceleration of the particles, in contrast with the one commonly employed to describe self-propelled systems. As recent studies have shown, inertia affects many properties of active particles, such as their pressure [13][14][15][16][17], transport properties [18,19], the stochastic energetics [20] and, even, anomalous responses to boundary driving [21]. Besides, inertial forces play an important role also at the collective level: i) affecting the clustering typical of active matter and, in particular, suppressing the phase-coexistence [22][23][24][25][26] and changing several features of the transition [27] ii) modifying some properties of dense phases of active matter [28], such as the active temperature in the homogeneous [29] and inhomogeneous phases [30].…”

Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions

“…We expect that this approach will be particularly useful in two contexts. Firstly, it will allow the study of systems that are not over-damped; as illustrated in Section V A, such systems can show substantially different behaviour from their over-damped counterparts 21 .…”

“…We now present the integrator itself. In each time step of size h, we perform half a step of the Verlet-type integrator for Hamiltonian dynamics, 20 followed by a full time step of the Ornstein-Uhlenbeck process in (21), and finally a second half step of the Verlet-type integrator. Starting from the initial conditions P 0 = p, R 0 = r, Q 0 = q, |q i | = 1, i = 1, .…”

“…We also note that the matrix exponent e −ξ(r,q)t from (21), which is used in the method (22), can be expressed as…”

“…The specific approach, which does not assume an over-damped limit, may be particularly useful in the following two contexts. First, one can study systems with HI in non-over-damped regimes, where it is known 21 that behaviour can significantly differ from the over-damped case. Second, the proposed method works well even when the damping parameter is very large and hence, using it, one can get a good approximation of the over-damped (Brownian) dynamics.…”