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 functionsfd(X) for hoppers of opening sized are measured. (HereX 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 offd(X) can be collasped into a master curveG(X) = fd(X)μ(d) that decays exponentially forX > 4. The scaling factorμ(d) is a decreasing function ofd and is approximately proportional to the jamming probability.