  We study the rolling motion of a small solid sphere on a surface patterned
rubber substrate in an external field with and without a noise. In the absence
of the noise, the ball does not move below a threshold force above which it
accelerates sub-linearly with the applied field. In the presence of a random
noise, the ball exhibits a stochastic rolling with a net drift, the velocity of
which increases non-linearly with the strength of the noise (K). From the
evolution of the displacement distribution, it is evident that the rolling is
controlled by a Coulomb like friction at a very low velocity, a super-linear
friction at an intermediate velocity and a linear kinematic friction at a large
velocity. This transition from a non-linear to a linear friction control of
motion can be discerned from another experiment in which the ball is subjected
to a small amplitude periodic asymmetric vibration in conjunction with a random
noise. Here, as opposed to that of a fixed external force, the rolling velocity
decreases with the increase of the strength of the noise suggesting a
progressive fluidization of the interface. Furthermore, the ball exhibits a
flow reversal with the increase of the amplitude of the asymmetric vibration,
which is indicative of a profile of friction that first descends and then
ascends with velocity. An approximate non-linear friction model with the
non-linearity decreasing with K is somewhat consistent with the evolution of
the displacement fluctuation that also explains the sigmoidal variation of the
drift velocity with the strength of the noise. This research sets the stage for
studying friction in a new way, in which it is submitted to a noise and then
its dynamic response is studied using the tools of statistical mechanics.
