Thermodynamical and mechanical efficiency of a ratchet pump

Characteristics of the polymer transport in ratchet systems

Molecules with complex internal structure in time-dependent periodic potentials are studied by using short Rubinstein-Duke model polymers as an example. We extend our earlier work on transport in stochastically varying potentials to cover also deterministic potential switching mechanisms, energetic efficiency, and nonuniform charge distributions. We also use currents in the nonequilibrium steady state to identify the dominating mechanisms that lead to polymer transportation and analyze the evolution of the macroscopic state (e.g., total and head-to-head lengths) of the polymers. Several numerical methods are used to solve the master equations and nonlinear optimization problems. The dominating transport mechanisms are found via graph optimization methods. The results show that small changes in the molecule structure and the environment variables can lead to large increases of the drift. The drift and the coherence can be amplified by using deterministic flashing potentials and customized polymer charge distributions. Identifying the dominating transport mechanism by graph analysis tools is found to give insight in how the molecule is transported by the ratchet effect.

Brownian motors: current fluctuations and rectification efficiency

With this work, we investigate an often neglected aspect of Brownian motor transport, namely, the role of fluctuations of the noise-induced current and its consequences for the efficiency of rectifying noise. In doing so, we consider a Brownian inertial motor that is driven by an unbiased monochromatic, time-periodic force and thermal noise. Typically, we find that the asymptotic, time-, and noise-averaged transport velocities are small, possessing rather broad velocity fluctuations. This implies a corresponding poor performance for the rectification power. However, for tailored profiles of the ratchet potential and appropriate drive parameters, we can identify a drastic enhancement of the rectification efficiency. This regime is marked by persistent, unidirectional motion of the Brownian motor with few back-turns only. The corresponding asymmetric velocity distribution is then rather narrow, with a support that predominantly favors only one sign for the velocity.

Efficiency and current in a correlated ratchet

We present a detailed study of the transport and the efficiency of a ratchet system in a periodic potential in the presence of correlated noises. The current and the efficiency of the system are investigated. It is found that, when the potential is spatially symmetric, the correlation between the two noises can induce a net transport. The efficiency shows many interesting features as a function of the applied force, the noise intensity, the external load, etc. The efficiency can be maximized as a function of noise intensity (or temperature), which shows that the thermal fluctuation can facilitate the efficiency of energy transformation.

Directed particle diffusion under "burnt bridges" conditions

We study random walks on a one-dimensional lattice that contains weak connections, so-called "bridges." Each time the walker crosses the bridge from the left or attempts to cross it from the right, the bridge may be destroyed with probability p; this restricts the particle's motion and directs it. Our model, which incorporates asymmetric aspects in an otherwise symmetric hopping mechanism, is very akin to "Brownian ratchets" and to front propagation in autocatalytic A+B-->2A reactions. The analysis of the model and Monte Carlo simulations show that for large p the velocity of the directed motion is extremely sensitive to the distribution of bridges, whereas for small p the velocity can be understood based on a mean-field analysis. The single-particle model advanced by us here allows an almost quantitative understanding of the front's position in the A+B-->2A many-particle reaction.

Irreversible and reversible modes of operation of deterministic ratchets

We discuss a problem of optimization of the energetic efficiency of a simple rocked ratchet. We concentrate on a low-temperature case in which the particle's motion in a ratchet potential is deterministic. We show that the energetic efficiency of a ratchet working adiabatically is bounded from above by a value depending on the form of ratchet potential. The ratchets with strongly asymmetric potentials can achieve ideal efficiency of unity without approaching reversibility. On the other hand we show that for any form of the ratchet potential a set of time protocols of the outer force exists under which the operation is reversible and the ideal value of efficiency eta=1 is also achieved. The mode of operation of the ratchet is still quasistatic but not adiabatic. The high values of efficiency can be preserved even under elevated temperatures.

Broad-band colored noise: digital simulation and dynamical effects

We propose a broad-band colored noise, which allows the transition between "red" and "green" noises. A double-integral algorithm for solving the Langevin equation with this noise is developed. The steady currents of an overdamped particle moving in the correlation and diffusion ratchets are calculated. It is shown that the flow reverses sign when the external noise is filtered off in the region of low frequencies to a sufficient extent. The present noise is also compared with the Ornstein-Uhlenbeck colored noise and the harmonic noise.

Reversible fluctuation rectifier

The analysis of a Feynman's ratchet system [J. M. R. Parrondo and P. Español, Am. J. Phys. 64, 1125 (1996)] and of its electrical counterpart, a diode engine [I. M. Sokolov, Europhys. Lett. 44, 278 (1998)] has shown that "fluctuation rectifiers" consisting of a nonlinear element (ratchet, diode) and a linear element (vane, resistor) kept at different temperatures always show efficiency smaller than the Carnot value, thus indicating the irreversible mode of operation. We show that this irreversibility is not intrinsic for a system in simultaneous contact with two heat baths at different temperatures and that a fluctuation rectifier can work reversibly. This is illustrated by a model with two diodes switched in opposite directions, where the Carnot efficiency is achieved when backward resistivity of the diodes tends to infinity.