  Gravity driven flows such as in hoppers and silos are susceptible to clogging
due to the formation of arches at the exit whose failure is the key to
re-initiation of flow. In vibrated hoppers, clog durations exhibit a broad
distribution, which poses a challenge for devising efficient unclogging
protocols. Using numerical simulations, we demonstrate that the dynamics of
arch shapes preceding failure can be modeled as a continuous time random walk
(CTRW) with a broad distribution of waiting times, which breaks ergodicity.
Treating arch failure as a first passage process of this random walk, we argue
that the distribution of unclogging times is determined by this waiting time
distribution. We hypothesize that this is a generic feature of unclogging, and
that specific characteristics, such as hopper geometry, and mechanical
properties of the grains modify the waiting time distribution.
