Simple dynamical model with history dependence for a sandpile experiment

Abstract

A lattice dynamics model is proposed for the history dependence observed in sandpile experiments. The dependence of the stress distribution on the preparation of the sandpile is explained as a dependence of certain attractors on the preparation of the system. The model has three phases, but the history dependence is shown to exist only in the phase where a perturbation is amplified selectively rather than globally when propagating in the downflow direction. The condition for this history dependence is given in terms of the spatial Lyapunov exponent.