Sandpiles with Bistable Automata Rules: Towards a Minimal Model of Pedestal Formation and Structure

A sandpile with two stable and two unstable ranges of slopes is presented as a minimal model for the study of $H$-mode pedestal formation and dynamics. Pedestals are observed to form and expand inward with increasing deposition. Transport bifurcation is not critical to pedestal formation, though the pedestal structure obtained with a second, hard stability boundary is qualitatively different from that found in standard sandpiles. Nonperiodic particle ejection events are observed, but do not initiate pedestal collapse. Pedestal formation alters the spectrum of transport avalanches.