Mechanisms of avalanche dynamics and forms of scaling in sandpiles

The probability distributions of several avalanche quantities of the Bak–Tang–Wiesenfeld sandpile in two dimensions display multifractal scaling. This explains why this prototype model remained extremely problematic and controversial for such a long time after its introduction. Other models, like the Manna model, obey instead standard finite size scaling and fall in different universality classes. An analysis of time series for the waves into which avalanches can be decomposed, shows that the different forms of scaling can be ascribed to the respective autocorrelation functions. The intermittency of the Bak–Tang–Wiesenfeld sandpile is due to this autocorrelation being long range in time, unlike in the Manna case. A coarse graining of the wave time series elucidates these differences and the mechanism leading to multifractality.