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We study the rolling motion of a small solid sphere on a surface patternedrubber substrate in an external field with and without a noise. In the absenceof the noise, the ball does not move below a threshold force above which itaccelerates sub-linearly with the applied field. In the presence of a randomnoise, the ball exhibits a stochastic rolling with a net drift, the velocity ofwhich increases non-linearly with the strength of the noise (K). From theevolution of the displacement distribution, it is evident that the rolling iscontrolled by a Coulomb like friction at a very low velocity, a super-linearfriction at an intermediate velocity and a linear kinematic friction at a largevelocity. This transition from a non-linear to a linear friction control ofmotion can be discerned from another experiment in which the ball is subjectedto a small amplitude periodic asymmetric vibration in conjunction with a randomnoise. Here, as opposed to that of a fixed external force, the rolling velocitydecreases with the increase of the strength of the noise suggesting aprogressive fluidization of the interface. Furthermore, the ball exhibits aflow reversal with the increase of the amplitude of the asymmetric vibration,which is indicative of a profile of friction that first descends and thenascends with velocity. An approximate non-linear friction model with thenon-linearity decreasing with K is somewhat consistent with the evolution ofthe displacement fluctuation that also explains the sigmoidal variation of thedrift velocity with the strength of the noise. This research sets the stage forstudying friction in a new way, in which it is submitted to a noise and thenits dynamic response is studied using the tools of statistical mechanics.

Rolling motion of a rigid sphere on a structured rubber substrate aided by a random noise and an external bias