Dresden 2006 – scientific programme
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DY: Dynamik und Statistische Physik
DY 10: Statistical Physics of Complex Networks I
DY 10.2: Talk
Monday, March 27, 2006, 10:00–10:15, H\"UL 186
Transient times and avalanche size distribution in the Olami-Feder-Christensen earthquake model — •Felix Wissel and Barbara Drossel — Institut f. Festkoerperphysik, Hochschulstrasse 8, 64287 Darmstadt
We present analytical and numerical results for the earthquake model by Olami, Feder and Christensen (OFC). First we discuss the transient time until the system is in the stationary state. By introducing the concept of effective sites and using a mean field ansatz for the toppling profile we explain the numerical data as function of the system size N and the coupling parameter α. In the limit α→ 0, our calculation and our simulation data suggest that the transient time diverges as T(N,α)∼ α−ν Nα−µ with exponents ν ≃ 0.5 and µ>0.5. By analyzing the correlation function, we then find that the pattern of "patches" (i.e., areas of similar force value) shows scaling behavior, and based on this result we argue that the avalanche size distribution in the thermodynamic limit of infinite system size is either a power law with α-dependent exponent τ or no power law at all. In any case, almost all topplings occur in the thermodynamic limit in avalanches of size one.