Recently (Sarlis and Christopoulos (2012)) the threshold distribution function pthres(k)(x) of the coherent noise model for infinite number of agents after the k-th avalanche has been studied as a function of k, and hence natural time. An analytic expression of the expectation value E(Sk+1) for the size Sk+1 of the next avalanche has been obtained in the case that the coherent stresses are exponentially distributed with an average value σ. Here, by using a statistical ensemble of initially identical systems, we investigate the relaxation of the average E(Sk+1) versus k. For k values smaller than kmax(σ,f), the numerical results indicate that E(Sk+1) collapses to the q-exponential (Tsallis (1988)) as a function of k. For larger k values, the ensemble average can be effectively described by the time average threshold distribution function obtained by Newman and Sneppen (1996). An estimate k0(σ,f)(> kmax(σ,f)) of this transition is provided. This ensemble of coherent noise models may be considered as a simple prototype following q-exponential relaxation. The resulting q-values are compatible with those reported in the literature for the coherent noise model.
|Number of pages||10|
|Journal||Physica A: Statistical Mechanics and its Applications|
|Early online date||12 Apr 2014|
|Publication status||Published - 1 Aug 2014|