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

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 nonintegrable solutions of the KF equation. The mean velocity in our model generally varies nonmonotonically as the strength of the dry friction is increased, indicating that transport improves for increased dissipation. DOI: 10.1103/PhysRevE.87.032112