Avalanche dynamics in a deposition model with ‘‘sliding’’

We introduce a simple model of ‘‘avalanches’’ in which there is continuous deposition of mass on a ‘‘tilted’’ substrate, with avalanches occurring whenever the mass at a given site reaches a preassigned threshold value $h_c$. The avalanche is defined to sweep away all mass which is downhill from the initiation event. Basic dynamical features are studied, including the distribution of avalanche sizes and the time intervals between avalanches. For a one-dimensional ‘‘slope’’ of length L, the average &, and in the continuum limit the averaged steady-state mass distribution a distance &. Qualitatively similar results are found for avalanches on a two-dimensional substrate. Contrasts between the present avalanche model and models of self-organized criticality are discussed.