1/fnoise, distribution of lifetimes, and a pile of sand

Abstract

A connection between the distribution of lifetimes and the power spectrum is derived. It is shown that the flow of sand down the slope in the cellular automaton model, considered recently by Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987)], has a 1/$f^2$ power spectrum in one and two dimensions. The flow over the rim of the system behaves similar to the transport in a real sand pile as measured by Jaeger, Liu, and Nagel [Phys. Rev. Lett. 62, 40 (1989)].