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The one-dimensional motion of a massless Brownian particle on a symmetric periodic substrate can be rectified by reinjecting its driving noise through a realistic recycling procedure. If the recycled noise is multiplicatively coupled to the substrate, the ensuing feedback system works like a passive Maxwell's daemon, capable of inducing a net current that depends on both the delay and the autocorrelation times of the noise signals. Extensive numerical simulations show that the underlying rectification mechanism is a resonant nonlinear effect: The observed currents can be optimized for an appropriate choice of the recycling parameters with immediate application to the design of nanodevices for particle transport.

This study examined whether epidurally delivered cortical electrical stimulation (CS) improves the efficacy of motor rehabilitative training and alters neuronal density and/or cell proliferation in perilesion cortex following ischemic sensorimotor cortex (SMC) lesions. Adult rats were pre-trained on a skilled reaching task and then received partial unilateral SMC lesions and implantation of electrodes over the remaining SMC. Ten to fourteen days later, rats received daily reach training concurrent with anodal or cathodal 100 Hz CS or no stimulation (NoCS) for 18 days. To label newly generated cells, bromodeoxyuridine (BrdU; 50 mg/kg) was administered every third day of training. Both anodal and cathodal CS robustly enhanced reaching performance compared to NoCS controls. Neuronal density in the perilesion cortex was significantly increased in the cathodal CS group compared to the NoCS group. There were no significant group differences in BrdU-labeled cell density in ipsilesional cortex. Staining with Fluoro-Jade-B indicated that neurons continue to degenerate near the infarct at the time when cortical stimulation and rehabilitation were initiated. These data indicate that epidurally delivered CS greatly improves the efficacy of rehabilitative reach training following SMC damage and raise the possibility that cathodal CS may influence neuronal survival in perilesion cortex.

Transport in one-dimensional symmetric devices can be activated by the combination of thermal noise and a biharmonic drive. For the study case of an overdamped Brownian particle diffusing on a periodic one-dimensional substrate, we distinguish two apparently different biharmonic regimes: (i) Harmonic mixing, where the two drive frequencies are commensurate and of the order of some intrinsic relaxation rate. Earlier predictions based on perturbation expansions seem inadequate to interpret our simulation results; (ii) Vibrational mixing, where one harmonic drive component is characterized by high frequency but finite amplitude-to-frequency ratio. Its effect on the device response to either a static or a low-frequency additional input signal is accurately reproduced by rescaling each spatial Fourier component of the substrate potential, separately. Contrary to common wisdom, based on the linear response theory, we show that extremely high-frequency modulations can indeed influence the response of slowly (or dc) operated devices, with potential applications in sensor technology and cellular physiology. Finally, the mixing of two high-frequency beating signal is also investigated both numerically and analytically.

The rectification of a massive Brownian particle moving on a periodic substrate can be achieved in the absence of spatial asymmetry, by having recourse to (at least) two periodic, zero-mean input signals. We determine the relevant drift current under diverse operation conditions, namely, additive and multiplicative couplings, adiabatic and fast oscillating drives, and propagating substrate modulations. Distinct rectification mechanisms result from the interplay of noise and commensuration of the input frequencies, mediated through the nonlinearity of the substrate. These mechanisms are then extended to characterize soliton transport along a directed multistable chain. As the side-wise soliton diffusion is ultimately responsible for the transverse diffusion of such chains, our approach provides a full account of the Brownian motion of both pointlike and linear objects on a periodic substrate.

A Brownian particle hopping in a symmetric double-well potential can be statistically confined into a single well by the simultaneous action of (a) two periodic input signals, one tilting the minima and the other one modulating the barrier height, and (b) an additive and a purely multiplicative random signal, generated by a unique source and thus preserving a certain degree of statistical correlation. The underlying gating mechanism is quite robust when compared, for instance, with biharmonic rocking. In view of technological implementation, asymmetric confinement through gating can be conveniently maximized by tuning the input signal parameters (correlation time, phase-time lag, amplitudes), thus revealing a resonant localization mechanism of general applicability.

We simulated numerically the time evolution of a one-kink bearing, damped elastic string sitting on noiseless periodic substrates of two types: (I) asymmetric, time independent, (II) symmetric, periodically deformable. An asymmetric kink subjected to an ac drive is shown to drift steadily with finite average speed independent of its initial kinetic conditions. In the overdamped regime the resulting net kink transport can be attributed to the rectification of the Brownian motion of a pointlike particle with oscillating mass. For intermediate to low damping completely different features show up, due to the finite size of the objects being transported; in particular, the kink current hits a maximum for an optimal value of the damping constant, resonates at the kink internal-mode frequency and, finally, reverses sign within a certain range of the drive parameters.

The rectification efficiency of an underdamped ratchet operated in the adiabatic regime increases according to a scaling current-amplitude curve as the damping constant approaches a critical threshold; below threshold the rectified signal becomes extremely irregular and eventually its time average drops to zero. Periodic (locked) and diffusive (fully chaotic) trajectories coexist on fine tuning the amplitude of the input signal. The transition from regular to chaotic transport in noiseless ratchets has been studied numerically.

Driven diffusion of a Brownian particle along a one-dimensional lattice is investigated numerically on decreasing its damping constant. The notions of multiple jumps, jump reversal, and backward-to-forward rates are discussed in detail. In particular, we conclude that in the underdamped limit backward jumps are suppressed relative to forward jumps more effectively than previously assumed. The dependence of such a drive-controlled mechanism on the damping constant and the temperature is interpreted analytically.