Predictability and Scaling in a BTW Sandpile on a Self-similar Lattice

Alexander Shapoval, Dayana Savostianova, Mikhail Shnirman

Abstract: This paper explores the predictability of a Bak–Tang–Wiesenfeld isotropic sandpile on a self-similar lattice, introducing an algorithm which predicts the occurrence of target events when the stress in the system crosses a critical level. The model exhibits the self-organized critical dynamics characterized by the power-law segment of the size-frequency event distribution extended up to the sizes $∼𝐿^\beta$, $\beta=\log_3 5$, where L is the lattice length. We establish numerically that there are large events which are observed only in a super-critical state and, therefore, predicted efficiently. Their sizes fill in the interval with the left endpoint scaled as $𝐿^\alpha$ and located to the right from the power-law segment: $\alpha≈2.24>\beta$. The right endpoint scaled as $𝐿^3$ represents the largest event in the model. The mechanism of predictability observed with isotropic sandpiles is shown here for the first time.