Rectification of asymmetric surface vibrations with dry friction: an exactly solvable model
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.
Keywords
Cite
@article{arxiv.1211.0241,
title = {Rectification of asymmetric surface vibrations with dry friction: an exactly solvable model},
author = {Adrian Baule and Peter Sollich},
journal= {arXiv preprint arXiv:1211.0241},
year = {2015}
}
Comments
9 pages, 5 figures