EXTENDED INSTABILITY CRITERIA IN ISOTROPIC AND ANISOTROPIC ENERGY AVALANCHES

We demonstrate that adding extended instability criteria to 3D critica l-slope sand-pile models has the effect of considerably enhancing the self-organized critical state displayed by these models. We present tw o extended models, an isotropic one which displays large energy-avalan ches, and an anisotropic one which shows much shorter and much more fr equent energy bursts. We illuminate the multifractal nature of the sel f-organised critical state in both extended models by finding a nontri vial spectrum of generalised correlation dimensions from the time seri es and by showing that the power-law regions of the distribution funct ions for different lattice sizes show a scaling behaviour which is rul ed by a generalised multifractal scaling transformation.