Self-organized criticality: An experiment with sandpiles

Abstract

In 1987, Bak, Tang, and Wiesenfeld introduced the notion of self-organized criticality (SOC) in the guise of a computer simulation: a ‘‘sandpile cellular automaton machine.’’ They supposed that a real, many-bodied, physical system in an external field assembles itself into a critical state. The system then relaxes about the critical state creating spatial and temporal self similarities which give rise to fractal objects and 1/f noise. Their computer modeling was of a system like a sandpile at its critical angle of repose. This provided a new paradigm for many-body dynamics. Understanding SOC may well allow substantial strides to occur in the theory of flow and transport. The simplest model system, one for which computer simulations and corresponding real experiments are feasible, is a ‘‘sandpile’’ near its critical angle of repose. The size and duration of avalanches occurring as subsequent ‘‘sand’’ grains are added can provide detailed information about the ‘‘sandpile’’ as a model of SOC, and for SOC as a basis for many-body dynamics. This article describes a fairly simple, junior-level experiment in this new field involving the measurement of the distribution of avalanche sizes which occur as grains of sand are added to a ‘‘sandpile.’’ The universality of the phenomena can be observed and a power law relationship can be deduced.