Solution of the one-dimensional self-organized critical Oslo model

A. V. Podlazov


Abstract: I study the Oslo model – a one-dimensional conservative strictly isotropic self-organized critical sandpile model. I obtain a complete analytical solution for it, and I also present confirming simulation results. The solution is based on a meso-level model. I consider the processes of this level as anomalous diffusion. To explain it, I consider various random walk mechanisms, one of which essentially takes into account the one-dimensional nature of the model.

Keywords: self-organized criticality, scale invariance, power-law distributions, sandpiles, Oslo model, Frette model, Mann model, meso-level models, anomalous diffusion, random walks.

DOI: 10.20948/prepr-2023-70