Extended instability criteria in isotropic and anisotropic energy avalanches

We demonstrate that adding extended instability criteria to 3D critical-slope sand-pile models has the effect of considerably enhancing the self-organized critical state displayed by these models. We present two extended models, an isotropic one which displays large energy-avalanches, and an anisotropic one which shows much shorter and much more frequent energy bursts. We illuminate the multifractal nature of the self-organised critical state in both extended models by finding a nontrivial spectrum of generalised correlation dimensions from the time series and by showing that the power-law regions of the distributions functions for different lattice sizes show a scaling behaviour which is ruled by a generalised multifractal scaling transformation.