Brownian Forces in Sheared Granular Matter

We present results from a series of experiments on a granular medium sheared in a Couette geometry and show that their statistical properties can be computed in a quantitative way from the assumption that the resultant from the set of forces acting in the system performs a Brownian motion. The same assumption has been utilized, with success, to describe other phenomena, such as the Barkhausen effect in ferromagnets, and so the scheme suggests itself as a more general description of a wider class of driven instabilities.

Figure 1

The signals measured in experiments: (a) instantaneous velocity of the disk; (b) instantaneous torque exerted by the spring; (c) definition of duration and size of a slip event.

Figure 2

The experimentally measured distribution of disk velocities for different values of the driving angular velocity $V$. The lines are obtained from the numerical integration of Eqs. (1, 2, 3) using parameters value extracted from the experiments. The distributions for different drives are vertically shifted for clarity.

Figure 3

Slip sizes probability distribution, for different values of the driving angular velocity. The lines are the results from the numerical integration of Eqs. (1, 2, 3). The distributions for different drives are vertically shifted for clarity.

Figure 4

Slip durations probability distribution, for different values of the driving angular velocity. The lines are the results from the numerical integration of Eqs. (1, 2, 3). The distributions for different drives are vertically shifted for clarity.

Figure 5

Frictional torque: (a) average velocity dependence; (b) power spectrum of the random frictional torque.