Crossover behavior in the event size distribution of the Olami-Feder-Christensen model

Transient and stationary behavior of the Olami-Feder-Christensen model

Using long-term computer simulations and mean-field-like arguments, we investigate the transient time and the properties of the stationary state of the Olami-Feder-Christensen model as function of the coupling parameter alpha and the system size N. The most important findings are that the transient time increases with a nonuniversal exponent of the system size, and that the avalanche size distribution will not approach a power law with increasing system size.

Distribution of epicenters in the Olami-Feder-Christensen model

We show that the well established Olami-Feder-Christensen (OFC) model for the dynamics of earthquakes is able to reproduce a striking property of real earthquake data. Recently, it has been pointed out by Abe and Suzuki that the epicenters of earthquakes could be connected in order to generate a graph, with properties of a scale-free network of the Barabási-Albert type. However, only the nonconservative version of the Olami-Feder-Christensen model is able to reproduce this behavior. The conservative version, instead, behaves like a random graph. Besides indicating the robustness of the model to describe earthquake dynamics, those findings reinforce that conservative and nonconservative versions of the OFC model are qualitatively different. Also, we propose a completely different dynamical mechanism that, even without an explicit rule of preferential attachment, generates a scale-free network. The preferential attachment is in this case a "byproduct" of the long term correlations associated with the self-organized critical state.

Nonuniversality and scaling breakdown in a nonconservative earthquake model

We use extensive numerical simulations to test recent claims of universality in the nonconservative regime of the Olami-Feder-Christensen model. By studying larger systems and a wider range of dissipation levels than previously considered we conclude that there is no evidence of universality in the model with only limited regions of the event size distributions displaying power-law behavior. We further analyze the dimension of the largest events in the model, D(max), using a multiscaling method. This reveals that although D(max) initially increases with system size, for larger systems the dimension ultimately decreases with system size casting further doubt on the criticality of the model.