ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


конечно-размерный скейлинг

Two-dimensional self-organized critical sandpile models with anisotropic dynamics of the activity propagation

We numerically and analytically investigate two self-organized critical sandpile models with anisotropic dynamics of the activity propagation – Dhar–Ramaswamy and discrete Feder–Feder models. The full set of critical indices for these models is theoretically determined. We also give systematical statement of the finite-size scaling ansatz and of its use for the solving of self-organized critical systems.

Classical two-dimensional sandpile models

  I consider sandpile models being open nonlinear systems demonstrating the phenomenon of avalanche-like response to a single disturbance of steady state. I study thoroughly the five most known variants of the two-dimensional rules referred as the models of Dhar–Ramaswamy, Pastor-Satorras–Vespignani, Feder–Feder, Manna and Bak–Tang–Wiesenfeld. The analytical solutions obtained in various ways are known for the first four models and the reasons preventing the construction of a solution are known for the fifth one.