It was recently shown that the use of feedback control can improve the performance of a flashing ratchet. We investigate the effect of a time delay in the implementation of feedback control in a closed-loop collective flashing ratchet, using Langevin dynamics simulations. Surprisingly, for a large ensemble, a well-chosen delay time improves the ratchet performance by allowing the system to synchronize into a quasi-periodic stable mode of oscillation that reproduces the optimal average velocity for a periodically flashing ratchet. For a small ensemble, on the other hand, finite delay times significantly reduce the benefit of feedback control for the time-averaged velocity, because the relevance of information decays on a time scale set by the diffusion time of the particles. Based on these results, we establish that experimental use of feedback control is realistic.
We consider a randomly flashing ratchet, where the potential acting can be switched to another at random. Using coupled Fokker-Planck equations, we formulate the expressions of quantities measuring dynamics and thermodynamics. Extended numerical calculations present how the potential landscapes and the transitions affect the motility and energetics. Load-dependent velocity and energetic efficiency of motor proteins, kinesin and dynein, further exemplify the randomly flashing ratchet model. We also discuss the system with two shifted sawtooth potentials.
We study a system of independent Brownian particles in a flashing ratchet potential that can be turned on or off depending on the position of the particles, with the aim of maximising the speed of the center of mass in the long run. First, an explanation on how to find the optimal protocol using Bellman's principle of optimality for any number of particles is given. Then the problem is numerically solved for a system of 2 particles. Simulations show that the optimal protocol performs better than the maximisation of instantaneous center-of-mass speed, a protocol known to give better results for…
The flashing Brownian ratchet is a stochastic process that alternates between two regimes, a one-dimensional Brownian motion and a Brownian ratchet, the latter being a one-dimensional diffusion process that drifts towards a minimum of a periodic asymmetric sawtooth potential. The result is directed motion. In the presence of a static homogeneous force that acts in the direction opposite that of the directed motion, there is a reduction (or even a reversal) of the directed motion effect. Such a process may be called a tilted flashing Brownian ratchet. We show how one can study this process nume…
Korea Advanced Institute of Science and Technology（韩国科学技术院）
A collective flashing ratchet transports Brownian particles using a spatially periodic, asymmetric, and time-dependent on-off switchable potential. The net current of the particles in this system can be substantially increased by feedback control based on the particle positions. Several feedback policies for maximizing the current have been proposed, but optimal policies have not been found for a moderate number of particles. Here, we use deep reinforcement learning (RL) to find optimal policies, with results showing that policies built with a suitable neural network architecture outperform th…
The study of Brownian ratchets has taught how time-periodic driving supports a time-periodic steady state that generates nonequilibrium transport. When a single particle is transported in one dimension, it is possible to rationalize the current in terms of the potential, but experimental efforts have ventured beyond that single-body case to systems with many interacting carriers. Working with a lattice model of volume-excluding particles in one dimension, we analyze the impact of interactions on a flashing ratchet's current. To surmount the many-body problem, we employ the time-dependent varia…
Ratchet effects can arise for single or collectively interacting Brownian particles on an asymmetric substrate when a net dc transport is produced by an externally applied ac driving force or by periodically flashing the substrate. Recently, a new class of active ratchet systems has been realized through the use of active matter, which are self-propelled units that can be biological or non-biological in nature. When active materials such as swimming bacteria interact with an asymmetric substrate, a net dc directed motion can arise even without external driving, opening a wealth of possibilitie…
The transport of a walker in rocking feedback-controlled ratchets are investigated. The walker consists of two coupled "feet" that allow the interchange of the order of the particles while the walker moves. In the underdamped case, the deterministic dynamics of the walker in a tilted asymmetric ratchet with an external periodic force is considered. It is found that the delayed feedback ratchets with a switching-on-and-off dependence of the states of the system can lead to the absolute negative mobility (ANM). In such a novel phenomenon the particles move against the bias. Moreover, the walker …
Here, we investigate the uncertainty of dynamical observables in classical systems manipulated by repeated measurements and feedback control; the precision should be enhanced in the presence of an external controller but limited by the amount of information obtained from the measurements. We prove that the entropy production and the information quantity constrain from below the fluctuation of arbitrary observables that are antisymmetric under time reversal. The information term is the sum of the mutual entropy production and the Kullback--Leibler divergence, which characterises the irreversibi…
