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Simple models for ruptures along a heterogeneous earthquake fault zone arestudied, focussing on the interplay between the roles of disorder and dynamicaleffects. A class of models are found to operate naturally at a critical pointwhose properties yield power law scaling of earthquake statistics. Variousdynamical effects can change the behavior to a distribution of small eventscombined with characteristic system size events. The studies employ variousanalytic methods as well as simulations.Comment: 4 pages, RevTex, 3 figures (eps-files), uses eps

Statistics of Earthquakes in Simple Models of Heterogeneous Faults