Jamming of Granular Flow in a Two-Dimensional Hopper

We study experimentally the jamming phenomenon of granular flow of monodisperse disks of $D=5\mathrm{}\mathrm{mm}$ diameter in a two-dimensional hopper with opening $R$. The jamming probability $J\left(d\right)$ is measured where $d\equiv R/D$. We found that $J\left(d\right)$ 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.