Novel Mechanism for Discrete Scale Invariance in Sandpile Models

TL;DR

This paper introduces a new mechanism explaining discrete scale invariance in sandpile models of earthquake aftershocks, revealing how stress decay occurs in punctuated, geometrically spaced events across different dimensions.

Contribution

It presents a novel mechanism for discrete scale invariance in sandpile models, supported by simulations and mean-field analysis, linking stress decay patterns to model parameters.

Findings

Stress decays punctuated with characteristic times increasing geometrically.

Results are consistent across 1D, 2D, and 3D lattices.

Decay pattern is independent of lattice discreteness.

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.