SCALING BEHAVIOR OF A DIRECTED SANDPILE AUTOMATA WITH RANDOM DEFECTS

In a recent paper [B. Tadic, U. Nowak, K. D. Usadel, R. Ramaswamy, and S. Padlewski, Phys. Rev. A 45, 8536 (1992)], the directed two-dimensional sandpile is modified to include a concentration p of randomly placed holes. For p>0, they observe a characteristic cutoff size for the duration (and mass) of avalanches. This breaks the formal power-law behavior that is a signature of self-organized criticality. The scaling of these characteristic sizes with the concentration of defects is observed empirically to follow a power law, and the exponents are numerically determined. In this Brief Report, it is shown that a previously described mean-field approximation can account for the observed exponents.