Mapping the train model for earthquakes onto the stochastic sandpile model

Abstract

We perform a computational study of a variant of the ``train'' model for earthquakes [PRA 46, 6288 (1992)], where we assume a static friction that is a stochastic function of position rather than being velocity dependent. The model consists of an array of blocks coupled by springs, with the forces between neighbouring blocks balanced by static friction. We calculate the probability, P(s), of the occurrence of avalanches with a size s or greater, finding that our results are consistent with the phenomenology and also with previous models which exhibit a power law over a wide range. We show that the train model may be mapped onto a stochastic sandpile model and study a variant of the latter for non-spherical grains. We show that, in this case, the model has critical behaviour only for grains with large aspect ratio, as was already shown in experiments with real ricepiles. We also demonstrate a way to introduce randomness in a physically motivated manner into the model.

14 pages and 6 figures. Accepted in European Physical Journal B

References in corpus (5)

• Tracer Dispersion in a Self-Organized Critical System
• Transport in Sand Piles, Interface Depinning, and Earthquake Models
• Critical behavior of a one-dimensional fixed-energy stochastic sandpile
• Sliding blocks with random friction and absorbing random walks
• Self-Organized Criticality with Complex Scaling Exponents in the Train Model

Cited by in corpus (4)

• Chaos on the conveyor belt
• Avalanches in Tip-Driven Interfaces in Random Media
• A spring-block analogy for the dynamics of stock indexes
• Equivalence of the train model of earthquake and boundary driven Edwards-Wilkinson interface