  Granular flows in small-outlet hoppers exhibit several characteristic but
poorly understood behaviors: temporary clogs (pauses) that last for an extended
period before flow spontaneously restarts, permanent clogs that last
indefinitely, and non-Gaussian, non-monotonic flow-rate statistics. These
aspects have been extensively studied independently, but a model of hopper flow
that includes all three has not been formulated. Here, we introduce such a
phenomenological model that provides a unifying dynamical explanation of all
three behaviors: a coupling between the flow rate and a hidden configurational
mode that controls the stability of clogs. In the theory, flow rate evolves
according to Langevin dynamics with multiplicative noise and an absorbing state
at zero flow, conditional on the hidden mode. The model fully reproduces the
statistics of pause and clog events taken from a large ($>40,000$ flows)
experimental dataset, including non-exponentially distributed clogging times
and non-Gaussian flow rate distribution, and explains the stretched-exponential
growth of the average clogging time with outlet size. Further, we highlight
several microscopic configurational features of this hidden mode, including
size and smoothness of the static arch structure formed during pauses and
clogs. Our work provides a unifying framework for several poorly understood
granular phenomena, and suggests numerous new paths toward further
understanding of this complex system.
