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Solution of the self-organized critical Manna model of arbitrary dimension

A. V. Podlazov


Abstract: I study the conservative isotropic self-organized critical sandpile model of Manna. I present for it the results of computer simulation in 3D and analytical solution for arbitrary space dimension. The solution bases on the formulation of an mesolevel model in terms of the excitation density, its correlation length, the average activity and the boundary width of avalanche region. Calculation of the critical indices is carried out in two independent ways: on the basis of stochastic differential equations and by reducing of the occurring processes to random walks.

Keywords: self-organized criticality, sandpiles, Manna model, BTW model, scale invariance, power laws, mesolevel models, Langevin equations, random walks.

DOI: 10.20948/prepr-2017-125