Abstract
We present results of large scale numerical simulations of the Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] sandpile model. We analyze the critical behavior of the model in Euclidean dimensions . We consider a dissipative generalization of the model and study the avalanche size and duration distributions for different values of the lattice size and dissipation. We find that the scaling exponents in significantly differ from mean-field predictions, thus suggesting an upper critical dimension . Using the relations among the dissipation rate and the finite lattice size , we find that a subset of the exponents displays mean-field values below the upper critical dimensions. This behavior is explained in terms of conservation laws.
- Received 18 February 1998
DOI:https://doi.org/10.1103/PhysRevE.57.R6241
©1998 American Physical Society