Mechanisms of avalanche dynamics and forms of scaling in sandpiles

The probability distributions of several avalanche quantities of the Bak-Ta ng-Wiesenfeld sandpile in two dimensions display multifractal scaling. This explains why this prototype model remained extremely problematic and contr oversial for such a long time after its introduction. Other models, like th e Manna model, obey instead standard finite size scaling and fall in differ ent universality classes. An analysis of time series for the waves into whi ch avalanches can be decomposed, shows that the different forms of scaling can be ascribed to the respective autocorrelation functions. The intermitte ncy of the Bak-Tang-Wiesenfeld sandpile is due to this autocorrelation bein g long range in time, unlike in the Manna case. A coarse graining of the wa ve rime series elucidates these differences and the mechanism leading to mu ltifractality. (C) 2001 Elsevier Science B.V. All rights reserved.