  Simple models of earthquake faults are important for understanding the
mechanisms for their observed behavior, such as Gutenberg-Richter scaling and
the relation between large and small events, which is the basis for various
forecasting methods. Although cellular automaton models have been studied
extensively in the long-range stress transfer limit, this limit has not been
studied for the Burridge-Knopoff model, which includes more realistic friction
forces and inertia. We find that the latter model with long-range stress
transfer exhibits qualitatively different behavior than both the long-range
cellular automaton models and the usual Burridge-Knopoff model with nearest
neighbor springs, depending on the nature of the velocity-weakening friction
force. This result has important implications for our understanding of
earthquakes and other driven dissipative systems.
