We propose a full solution for Manna model – two-dimensional conservative sandpile model with isotropic at the average rules of grains redistribution. Indices of the probability distributions of avalanches main characteristics (size, area, perimeter, duration, topplings multiplicity) are determined for this model both from theory and from simulations. The solution bases on the spatiotemporal decomposition of avalanches described in terms of toppling layers and waves. The motion of grains is divided into directed and undirected types. The former is treated as the dynamics of active particles with some physical properties described.

self-organized criticality, scale invariance, power laws, finite-size scaling, sandpile models, Manna model, layers of toppling, waves of toppling

Mathematical modelling in actual problems of science and technics