Dynamic scaling in stick-slip friction

Abstract

We introduce a generalized homogeneous function to describe the joint probability density for magnitude and duration of events in self-organized critical systems (SOC). It follows that the cumulative distributions of magnitude and of duration are power-laws with exponents $\alpha$ and $\tau$ respectively. A power-law relates duration and magnitude (exponent $\gamma$) on the average. The exponents satisfy the dynamic scaling relation $\alpha=\gamma\tau$. The exponents classify SOC systems into universality classes that do not depend on microscopic details provided that both $\alpha<1$ and $\tau<1$. We also present new experimental results on the stick-slip motion of a sandpaper slowly pulled across a carpet that are consistent with our criteria for SOC systems. Our experiments, as well as experiments by others, satisfy our dynamic scaling relation. We discuss the relevance of our results to earthquake statistics.