Model of spatiotemporal dynamics of stick-slip motion

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Abstract
We propose a model of spatiotemporal dynamics that, in contrast to many earthquake models, does not contain a velocity-weakening frictional force. Dissipation in this model occurs only through viscous forces acting in the presence of a nondissipative random potential. Both small localized and large delocalized events are observed. The scaling behavior of the event probability distribution is found to be nonuniversal and distinct from that found in earthquake models. The system loses instability as the strength of the pulling spring becomes large enough. It also shows transitions from behavior exhibiting a wide range of magnitudes of slipping events to showing a narrow range scale in which only large events occur for a certain range of parameters. Effects of varying system size, boundary conditions, and pulling speed were investigated. Most of our numerical results are in qualitative agreement with the rubber-sheet experiments of Vallette and Gollub [Phys. Rev. E 47, 820 (1993)].