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arXiv · 1211.0241

Rectification of asymmetric surface vibrations with dry friction: an exactly solvable model

Adrian Baule·Peter Sollich
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Abstract

We consider a stochastic model for the directed motion of a solid object due to the rectification of asymmetric surface vibrations with Poissonian shot-noise statistics. The friction between the object and the surface is given by a piecewise-linear friction force. This models the combined effect of dynamic friction and singular dry friction. We derive an exact solution of the stationary Kolmogorov-Feller (KF) equation in the case of two-sided exponentially distributed amplitudes. The stationary density of the velocity exhibits singular features such as a discontinuity and a delta-peak singularity at zero velocity, and also contains contributions from non-integrable solutions of the KF equation. The mean velocity in our model generally varies non-monotonically as the strength of the dry friction is increased, indicating that transport improves for increased dissipation.

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Adrian Baule, Peter Sollich. 2012-11-01. Rectification of asymmetric surface vibrations with dry friction: an exactly solvable model. https://doi.org/10.1103/physreve.87.032112

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