Avalanches, Scaling and Coherent Noise

We present a simple model of a dynamical system driven by externallyimposed coherent noise. Although the system never becomes critical in the sense of possessing spatial correlations of arbitrarily long range, it does organize into a stationary state characterized by avalanches with a power-law size distribution. We explain the behavior of the model within a time-averaged approximation, and discuss its potential connection to the dynamics of earthquakes, the Gutenberg-Richter law, and to recent experiments on avalanches in rice piles. Typeset using REVT E X I. INTRODUCTION There has in the last few years been considerable interest in extended systems which self-organize into a state exhibiting large scale fluctuations and intermittent dynamics. One of the earliest attempts to model systems of this type was made in 1987 by Bak, Tang, and Wiesenfeld, who proposed a simple lattice model for the avalanches produced by depositing grains of sand on an ever-growing sand pile [1]. Despite ha..