Simulation of Self-organized Criticality

Abstract

Many phenomena in nature exhibit anomalously large fluctuations exceeding what can not be explained as a consequence of statistically independent random events. These include earthquakes, turbulence in liquids, sand falling through an hour glass, light emitted from quasars, biological evolution, and even stock prices. Also, it has been pointed out that many structures in nature have self-similar scaling properties, that is they have the same appearance when viewed through a microscope no matter what the magnification is. The universe consists of clusters of galaxies, and clusters of clusters of galaxies, and so on. The distribution of earthquakes are clustered in a similar way. A turbulent liquid has vortices of all sizes. We have suggested that the large temporal fluctuations, and the spatial self-similarity are two sides of the same coin: self-organized criticality. The idea is that the systems operate persistently out of equilibrium at or near a threshold of instability. The systems evolve automatically to this critical state without any fine-tuning of external fields; hence the criticality is self-organized. This is in contrast with the criticality of equilibrium systems undergoing phase transition where large clusters exist only at a critical external field, such as temperature, pressure, or magnetic field.