Supervisors info:
Νικόλαος Σαρλής, Αναπλ. Καθηγητής (επιβλέπων), Παναγιώτης Βαρώτσος, Καθηγητής, Ευθύμιος Σκορδάς Επικ. Καθηγητής
Summary:
In the present assignment, the transition to the self-organization of Olami -
Feder -
Christensen (OFC) Model is studied. This study took place with the help of
natural time χ
[Varotsos, 2001; Varotsos et al., 2011]. A new time field that can reveal
hidden dynamic
characteristics that exist in a time series. For assignment purposes, a two
dimensional cellular
automaton was used. At first place, the dispertion behavior in function with
the conventional time was studied, demonstrating that it can constitute the
evidence regarding when the system goes over the
transient regime to the steady state. The system adjusts to the steady state
when the quantity
k1 reaches approximately the value ku = 0:083. After that, two OFC model
versions were compared, the conservative and the nonconservative. We
demonstrated that in both versions, the system reaches the steady state. In the
contrary, the non-maintained version is characterised by the a absence of the
thermodynamic limit and, presumably, the non- conservative OFC model does not
seem to be
critical. More specifically, in the non-conservative OFC model, the development
of cohesive
structures (clusters) was observed. These structures were quantified and
studied. It was
shown that when the system enters the steady state , the parameters of these
structures, like
its population as well as the population of the blocks that compose them, are
stabilized to a
specific value. In addition, in the steady state, aforementioned parameters are
characterized by temporal long range correlations.
Keywords:
Natural time, OFC model, Self-organized criticallity, Clusters, Regime time
