  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.
