Dichotomic ratchet in a two-dimensional corrugated channel

Ratchet effect and jamming in dense mixtures of active and passive colloids in narrow pores

Using the framework of generalized exclusion processes, we study mixtures of passive and active particles interacting by steric repulsion. The particles move in a pore with a periodically modulated aperture, which is modeled by a quasi-one-dimensional channel with a periodic tooth-shaped profile. Internal driving of the active particles induces a ratchet current of these particles. In the current-density diagram, we observe three main regimes: of free flow, of thermally activated processes, and of spinodal decomposition. When the density of particles is increased, we observe a transition to a jammed state, where the ratchet current is substantially reduced. In time evolution, the transition to a jammed state is seen as a sudden drop of current at a certain time. The probability distribution of these jamming times follows an exponential law. The average jamming time depends exponentially on the density of active particles. The coefficient in this exponential is nearly independent of the switching rate of the active particles as well as the presence or absence of passive particles. Due to the interaction, the current of active particles imposes a drag on the passive particles. In the limit of both large systems and long times, the current of passive particles always has the same direction as the ratchet current of active particles. However, during the evolution of the system, we observe a very slow (logarithmic in time) approach to the asymptotic value, sometimes accompanied by current reversal, i.e., the current of active and passive particles may go in opposite directions.

Effective dynamics of a particle diffusing in time-dependent confinement

A pointlike particle diffusing in a two-dimensional channel is considered. Its width h(x,t) varies not only with the longitudinal coordinate x, but also in time t. Reducing the transverse degree of freedom in the corresponding diffusion equation, we arrive at the effective one-dimensional dynamics along the channel, represented by the generalized Fick-Jacobs equation; its coefficients calculated recursively also depend on time. In contrast to the static confinement, the moving boundaries generate an effective force driving the particle in the channel, which can be explicitly expressed within our method. We analyze this force in two examples: deformation of the boundary advancing as the traveling wave and in the channel "breathing" with an amplitude varying in x.

Optimizing Work Extraction in the Presence of an Entropic Potential: An Entropic Stochastic Resonance

We study the nontrivial thermodynamic responses of an overdamped Brownian system driven by an unbiased driving force when the particle is confined inside a bilobal irregular structure. The spatial irregularity of the confinement results in an effective entropic bistable potential along the direction of transport. We calculate the thermodynamic response functions in terms of the averaged work done and the absorbed heat over a cycle of driving. We find that the thermodynamic responses are influenced by the nonlinearity of the effective entropic potential, the frequency of the external periodic driving force, and the random thermal fluctuations in a nontrivial way. In the presence of an optimal amount of thermal noise and a favoring driving frequency, the process exhibits a resonance-like precedent in terms of both output work and absorbed heat. We explore the conditions to get best synchronized work extraction (or absorbed heat), which can be utilized as a potential quantifier of an entropic stochastic resonance phenomenon. Finally, we identify a hallmark of entropy dominance over an analogous energy-driven scenario in terms of output work.

Ratchet effect in an asymmetric two-dimensional system of Janus particles

We consider a disk-like Janus particle self-driven by a force of constant magnitude f, but an arbitrary direction depending on the stochastic rotation of the disk. The particle diffuses in a two-dimensional channel of varying width 2h(x). We applied the procedure mapping the 2+1-dimensional Fokker-Planck equation onto the longitudinal coordinate x; the result is the Fick-Jacobs equation extended by the spatially dependent effective diffusion constant D(x) and an additional effective potential -γ(x), derived recursively within the mapping procedure. Unlike the entropic potential ∼lnh(x), γ(x) becomes an increasing or decreasing function also in periodic channels, depending on the asymmetry of h(x) and thus it visualizes the net force driving the ratchet current. We demonstrate the appearance of the ratchet effect on a trial asymmetric channel; our theory is verified by a numerical solution of the corresponding Fokker-Planck equation. Isotropic driving force f results in the monotonic decrease of the ratchet current with a growing ratio α=D_{R}/D_{T} of the rotation and the translation diffusion constants; asymptotically going ∼1/α^{2}. If we allow anisotropy of the force, we can observe the current reversal depending on α.

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.