Phase-Slip Avalanches in the Superflow ofHe4through Arrays of Nanosize Apertures

In response to recent experiments by the Berkeley group, we construct a model of superflow through an array of nanosize apertures that incorporates two basic ingredients: (1) disorder associated with each aperture having its own random critical velocity, and (2) effective interaperture coupling, mediated through the bulk superfluid. As the disorder becomes weak there is a transition from a regime where phase slips are largely independent to a regime where interactions lead to system-wide avalanches of phase slips. We explore the flow dynamics in both regimes, and make connections to the experiments.