Self-organized criticality in a stick-slip process

Abstract

The force required to pull sandpaper across a carpet fluctuates. Slips (sudden drops of magnitude M of the force) are observed to have a probability N(M>m)\ensuremath{\sim}${\mathit{m}}^{\mathrm{\ensuremath{-}}\mathit{b}}$ with b\ensuremath{\simeq}0.8. The power spectrum of force fluctuations has a low-frequency 1/f behavior. Thus our system reaches a self-organized critical state with fractal scaling in both the spatial and the time domain. We introduce a new nonconservative cellular automaton that exhibits self-organized criticality and describes these observations well.