Universal Accretion Growth Using Sandpile Models

Abstract

The Bak Tang Weisenfeld (BTW) sandpile process is a model of a complex dynamical system with a large collection of particles or grains in a node that sheds load to their neighbours when they reach capacity. The cascades move around the system till it reaches stability with a critical point as an attractor. The BTW growth process shows self-organized criticality (SOC) with power- law distribution in cascade sizes having slope -5/3. This self-similarity of structure is synonymous with the fractal structure found in molecular clouds of Kolmogorov dimension 1.67 and by treating cascades as waves, scaling functions are found to be analogous to those observed for velocity structure functions in fluid turbulence. In this paper, we show that this is a naturally occuring universal process giving rise to scale - free structures with size limited only by the number of infalling grains. We also compare the BTW process with other sandpile models such as the Manna and Zhang processes. We find that the BTW sandpile model can be applied to a wide range of objects including molecular clouds, accretion disks and perhaps galaxies.