SELF-ORGANIZED CRITICALITY IN COMPUTER-MODELS OF SETTLING POWDERS

We present numerical simulations of powder flow in the regime of vacancy hopping, under gravity, in two dimensions, for simplicity. Bulk properties such as density and angle of rest are measured and correlated with the microscopic parameters of the model. Avalanches are identified as the damage spreading from a single new vacancy introduced. They are found to exhibit universal power-law distributions of both total size S and maximum height reached H, with pH(H) similar to H-(1.47+/-0.02) and P-S(S) similar to S--1.34+/-0.01. At height h, the average width of avalanches (reaching H greater than or equal to h) scales as [w] similar to h(0.46+/-0.09), consistent with the assumption that S similar to Hw(H). We also show that the distribution of w at fixed h can be scaled as a universal function of w/[w]. The average lateral deviation of the core of the avalanche from the avalanche origin, x(h), scales as [\x\] similar to h(0.33+/-0.09). We have investigated the correlation between successive avalanches precipitated from the same site. Both their survival to any given height and their horizontal displacements at fixed height are strongly correlated-implying that the critical behavior of the avalanches is dictated by organized structure in the powder.