Jamming of granular flow in a two-dimensional Hopper

We study experimentally the jamming phenomenon of granular flow of monodisperse disks of D = 5 mm diameter in a two-dimensional hopper with opening R. The jamming probability J(d) is measured where d = R/D. We found that J(d) decreases from 1 to zero when d increases from 2 to 5. From observing the disk configurations of the arch in the jamming events, the jamming probability can be explained quantitatively by treating the arch as the trajectory of a restricted random walker.