AVALANCHES IN CONTINUUM DRIVEN DISSIPATIVE SYSTEMS

We show that continuum driven dissipative systems can have behavior analogous to that of cellular automata sandpile models. We discuss the conditions for this behavior, and argue that a system which can be shown to satisfy these criteria will exhibit a broad power law distribution of discrete energy dissipating avalanches. We give a one-dimensional example of such a system, and show that such behavior does result when these conditions are met. We then show that the statistical behavior of this system can be approximated by a much simpler cellular automaton. Finally, we argue that a general prescription for showing how certain real physical systems can be understood in this manner. © 1995 The American Physical Society.