Singular features in noise-induced transport with dry friction

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 ${\Delta }^{\ast }$ and undergoes a transition to a unidirectional mode of motion at ${\Delta }^{\ast }$. 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.

6 pages, 2 figures

References in corpus (8)

• Brownian motors: noisy transport far from equilibrium
• Artificial Brownian motors: Controlling transport on the nanoscale
• Brownian motion with dry friction: Fokker-Planck approach
• Langevin equation with Coulomb friction
• Stick-slip motion of solids with dry friction subject to random vibrations and an external field
• The effect of Coulombic friction on spatial displacement statistics
• Path integral approach to random motion with nonlinear friction
• Rectification of motion in nonlinear media with asymmetric random drive

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