SELF-ORGANIZED CRITICALITY IN COMPUTER-MODELS OF SETTLING POWDERS

We present numerical simulations of powder flow in the regime of vacan cy hopping, under gravity, in two dimensions, for simplicity. Bulk pro perties such as density and angle of rest are measured and correlated with the microscopic parameters of the model. Avalanches are identifie d as the damage spreading from a single new vacancy introduced. They a re found to exhibit universal power-law distributions of both total si ze S and maximum height reached H, with pH(H) similar to H-(1.47+/-0.0 2) and P-S(S) similar to S--1.34+/-0.01. At height h, the average widt h 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 simil ar 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 deviatio n 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 correlat ion between successive avalanches precipitated from the same site. Bot h their survival to any given height and their horizontal displacement s at fixed height are strongly correlated-implying that the critical b ehavior of the avalanches is dictated by organized structure in the po wder.