Jamming patterns in a two-dimensional hopper

We report experimental studies of jamming phenomenon of monodisperse metal disks falling through a two-dimensional hopper when the hopper opening is larger than three times the size of the disks. For each jamming event, the configuration of the arch formed at the hopper opening is studied. The cumulative distribution functions f(d)(X) for hoppers of opening size d are measured. (Here X is the horizontal component of the arch vector, which is defined as the displacement vector from the center of the first disk to the center of the last disk in the arch.) We found that the distribution of fd(X) can be collasped into a master curve G(X) = f(d)(X)mu(d) that decays exponentially for X > 4. The scaling factor p(d) is a decreasing function of d and is approximately proportional to the jamming probability.