Interacting particles in a periodically moving potential: traveling wave and transport

Optimum transport in systems with time-dependent drive and short-ranged interactions

We consider a one-dimensional lattice gas model of hardcore particles with nearest-neighbor interaction in presence of a time-periodic external potential. We investigate how attractive or repulsive interaction affects particle transport and determine the conditions for optimum transport, i.e., the conditions for which the maximum dc particle current is achieved in the system. We find that the attractive interaction in fact hinders the transport, while the repulsive interaction generally enhances it. The net dc current is a result of the competition between the current induced by the periodic external drive and the diffusive current present in the system. When the diffusive current is negligible, particle transport in the limit of low particle density is optimized for the strongest possible repulsion. But when the particle density is large, very strong repulsion makes particle movement difficult in an overcrowded environment and, in that case, the optimal transport is obtained for somewhat weaker repulsive interaction. Our numerical simulations show reasonable agreement with our mean-field calculations. When the diffusive current is significantly large, the particle transport is still facilitated by repulsive interaction, but the conditions for optimality change. Our numerical simulations show that the optimal transport occurs at the strongest repulsive interaction for large particle density and at a weaker repulsion for small particle density.

Transverse dichotomic ratchet in a two-dimensional corrugated channel

A particle diffusing in a two-dimensional channel of varying width h(x) is considered. It is driven by a force of constant magnitude f, but random orientation across the channel. We suggest the projection technique to study the ratchet effect appearing in this system. Reducing the transverse coordinate, as well as the orientation of the force in the full-dimensional Fokker-Planck equation, we arrive at the generalized Fick-Jacobs equation, describing dynamics of the system in the longitudinal coordinate x only. The additional effective potential -γ(x), calculated within the mapping procedure, exhibits an increasing or decreasing part in the channel shaped by an asymmetric periodic h(x), which determines the appearing ratchet current. As shown on a specific example, random driving in the transverse direction is much more effective than that in the longitudinal direction, at least for quickly flipping orientation of the force. Also, the transverse and the longitudinal driving push the rectified current in opposite directions along the same channel.

Transport of particles driven by the traveling obstacle arrays

Transport of three types of particles (passive particles, active particles without polar interaction, and active particles with polar interaction) is numerically investigated in the presence of traveling obstacle arrays. The transport behaviors are different for different types of particles. For passive particles, there exists an optimal traveling speed (or the translational diffusion) at which the average velocity of particles takes its maximum value. For active particles without polar interaction, the average velocity of particles is a peaked function of the obstacle traveling speed. The average velocity decreases monotonically with increase of the rotational diffusion for large driving speed, while it is a peaked function of the rotational diffusion for small driving speed. For active particles with polar interaction, interestingly, within particular parameter regimes, active particles can move in the opposite direction to the obstacles. The average velocity of particles can change its direction by changing the system parameters (the obstacles driving speed, the polar interaction strength, and the rotational diffusion).

Currents and flux-inversion in photokinetic active particles

Many active particles, both of biological and synthetic origin, can have a light controllable propulsion speed, a property that in biology is commonly referred to as photokinesis. Here we investigate directed transport of photokinetic particles by traveling light patterns. We find general expressions for the current in the cases where the motility wave, induced by light, shifts very slowly or very quickly. These asymptotic formulas are independent of the shape of the wave and are valid for a wide class of active particle models. Moreover we derive an exact solution for the one-dimensional "run and tumble" model. Our results could be used to design time-varying illumination patterns for fast and efficient spatial reconfiguration of photokinetic colloids or bacteria.

Collective transport for active matter run-and-tumble disk systems on a traveling-wave substrate

We examine numerically the transport of an assembly of active run-and-tumble disks interacting with a traveling-wave substrate. We show that as a function of substrate strength, wave speed, disk activity, and disk density, a variety of dynamical phases arise that are correlated with the structure and net flux of disks. We find that there is a sharp transition into a state in which the disks are only partially coupled to the substrate and form a phase-separated cluster state. This transition is associated with a drop in the net disk flux, and it can occur as a function of the substrate speed, maximum substrate force, disk run time, and disk density. Since variation of the disk activity parameters produces different disk drift rates for a fixed traveling-wave speed on the substrate, the system we consider could be used as an efficient method for active matter species separation. Within the cluster phase, we find that in some regimes the motion of the cluster center of mass is in the opposite direction to that of the traveling wave, while when the maximum substrate force is increased, the cluster drifts in the direction of the traveling wave. This suggests that swarming or clustering motion can serve as a method by which an active system can collectively move against an external drift.

Symmetric exclusion processes on a ring with moving defects

We study symmetric simple exclusion processes (SSEP) on a ring in the presence of uniformly moving multiple defects or disorders-a generalization of the model we proposed earlier [Phys. Rev. E 89, 022138 (2014)PLEEE81539-375510.1103/PhysRevE.89.022138]. The defects move with uniform velocity and change the particle hopping rates locally. We explore the collective effects of the defects on the spatial structure and transport properties of the system. We also introduce an SSEP with ordered sequential (sitewise) update and elucidate the close connection with our model.

Pumping single-file colloids: Absence of current reversal

We consider the single-file motion of colloidal particles interacting via short-range repulsion and placed in a traveling wave potential that varies periodically in time and space. Under suitable driving conditions, a directed time-averaged flow of colloids is generated. We obtain analytic results for the model using a perturbative approach to solve the Fokker-Planck equations. The predictions show good agreement with numerical simulations. We find peaks in the time-averaged directed current as a function of driving frequency, wavelength, and particle density and discuss possible experimental realizations. Surprisingly, unlike a closely related exclusion dynamics on a lattice, the directed current in the present model does not show current reversal with density. A linear response formula relating current response to equilibrium correlations is also proposed.