Singular features in noise-induced transport with dry friction

TL;DR

This paper introduces an exactly solvable nonlinear model demonstrating how dry friction and asymmetric noise can induce non-monotonic, singular transport phenomena, including a transition to unidirectional motion and velocity distribution discontinuities.

Contribution

It reveals that dissipation via dry friction can enhance transport and identifies a critical friction strength where a transition to unidirectional motion occurs.

Findings

Transport improves with increasing dry friction up to a critical point.

A cusp singularity marks the transition to unidirectional motion.

Velocity distribution exhibits discontinuities and delta peaks.

Abstract

We present an exactly solvable nonlinear model for the directed motion of an object due to zero-mean fluctuations on a uniform featureless surface. Directed motion results from the effect of dry (Coulombic) friction coupled to asymmetric surface vibrations with Poissonian shot noise statistics. We find that the transport of the object exhibits striking non-monotonic and singular features: transport actually improves for increasing dry friction up to a critical dry friction strength $\Delta^*$ and undergoes a transition to a unidirectional mode of motion at $\Delta^*$. This transition is indicated by a cusp singularity in the mean velocity of the object. Moreover, the stationary velocity distribution also contains singular features, such as a discontinuity and a delta peak at zero velocity. Our results highlight that dissipation can in fact enhance transport, which might be exploited in artificial small scale systems.