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 distribution functions for different lattice sizes show a scaling behaviour which is ruled by a generalised multifractal scaling transformation.

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