Conference material: "Horizons of mathematical modeling and theory of self-organization. On the occasion of the 95th anniversary of the birth of S.P. Kurdyumova"
Solution of the one-dimensional self-organized critical Oslo model
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 bases 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
