Novel Mechanism for Discrete Scale Invariance in Sandpile Models

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Abstract
Numerical simulations and a mean-field analysis of a sandpile model of earthquake aftershocks in 1d, 2d and 3d euclidean lattices determine that the average stress decays in a punctuated fashion after a main shock, with events occurring at characteristic times increasing as a geometrical series with a well-defined multiplicative factor which is a function of the stress corrosion exponent, the stress drop ratio and the degree of dissipation. These results are independent of the discrete nature of the lattice and stem from the interplay between the threshold dynamics and the power law stress relaxation.

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