This article is cited in 1 paper

Two-dimensional self-organized critical Мanna model

A. V. Podlazov

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow

Abstract: We propose a full solution for Manna model, two-dimensional conservative sand pile model with isotropic rules of grains redistribution on average. We determined the general properties indices of avalanches distribution (size, area, perimeter, duration, the multiplicity of topplings) for the model both analytically and numerically. The solution is based on spatio-temporal decomposition of avalanches described in terms of toppling layers and waves and on division of the motion of grains into directed and undirected types. The former of the two is treated as the dynamics of active particles with some physical properties described.

Keywords: Self-organized criticality, scale invariance, power-series distribution, finitesize scaling, sandpile models, manna model, layers of toppling, waves of toppling.

UDC: 519.6