Flows in hoppers and silos are susceptible to clogging due to the formation of arches at the exit. The failure of these arches is the key to reinitiation of flow, yet the physical mechanism of failure is not well understood. Experiments on vibrated hoppers exhibit a broad distribution of the duration of clogs. Using numerical simulations of a hopper in two dimensions, we show that arches become trapped in locally stable shapes that are explored dynamically under vibrations. The shape dynamics, preceding failure, break ergodicity and can be modeled as a continuous-time random walk with a broad distribution of waiting, or trapping, times. We argue that arch failure occurs as a result of this random walk crossing a stability boundary, which is a first-passage process that naturally gives rise to a broad distribution of unclogging times.

We explore phase separation and kinetic arrest in active hard-core particles, in the limit of infinite persistence time of their active orientation. The passive limit of the model we consider, namely crossshaped particles on a square lattice, exhibits a first order transition from a fluid phase to a solid phase with increasing density. Quenches into the two-phase coexistence region exhibit a crossover from a simple fluid to an extremely slowly coarsening regime in which concentrated immobile clusters with local crystalline order emerge. These states represent an aging passive glass in this system. Adding persistent, yet small, active bias to the particle dynamics enhances and speeds up the aggregation of such clusters of immobile particles, creating states that resemble the passive glass at lower densities. For large active bias, the dense, immobile clusters proliferate until a spanning network bridges the system leading to percolation of an arrested phase, reminiscent of gelation in attracting colloids. Active particles remaining within the voids inside this network collect to form an interface which "wets" the surface of the arrested solid. We use an asymmetric simple exclusion process to map out a non-equilibrium phase diagram for this system. The phase diagram exhibits intriguing similarities to that of attracting colloids, however, we observe novel phases such as solid-liquid-void states that have no analogue in systems with zero activity.

We analyze the dynamics of an active tracer particle embedded in a thermal lattice gas. All particles are subject to exclusion up to third nearest neighbors on the square lattice, which leads to slow dynamics at high densities. For the case with no rotational diffusion of the tracer, we derive an analytical expression for the resulting drift velocity v of the tracer in terms of non-equilibrium density correlations involving the tracer particle and its neighbors, which we verify using numerical simulations. We show that the properties of the passive system alone do not adequately describe even this simple system of a single non-rotating active tracer. For large activity and low density, we develop an approximation for v. For the case where the tracer undergoes rotational diffusion independent of its neighbors, we relate its diffusion coefficient to the thermal diffusion coefficient and v. Finally we study dynamics where the rotation of the tracer is limited by the presence of neighboring particles. We find that the effect of this rotational locking may be quantitatively described in terms of a reduction of the rotation rate.

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