Self-organisation to criticality in a system without conservation law

Details Self-organisation to criticality in a system without conservation law Self-organisation to criticality in a system without conservation law

2002-04-23

arxiv.org/abs/cond-mat/0204490v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, 6 figures; accepted for publication in Journal of Physics A

Scientific paper

10.1088/0305-4470/35/22/301

We numerically investigate the approach to the stationary state in the nonconservative Olami-Feder-Christensen (OFC) model for earthquakes. Starting from initially random configurations, we monitor the average earthquake size in different portions of the system as a function of time (the time is defined as the input energy per site in the system). We find that the process of self-organisation develops from the boundaries of the system and it is controlled by a dynamical critical exponent z~1.3 that appears to be universal over a range of dissipation levels of the local dynamics. We show moreover that the transient time of the system $t_{tr}$ scales with system size L as $t_{tr} \sim L^z$. We argue that the (non-trivial) scaling of the transient time in the OFC model is associated to the establishment of long-range spatial correlations in the steady state.

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