TY - JOUR

T1 - q-exponential relaxation of the expected avalanche size in the coherent noise model

AU - Christopoulos, S. R.G.

AU - Sarlis, N. V.

PY - 2014/8/1

Y1 - 2014/8/1

N2 - 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.

AB - 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.

KW - Coherent noise model

KW - Natural time

KW - Off-equilibrium dynamics

KW - q-exponential

UR - http://www.scopus.com/inward/record.url?scp=84898987878&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2014.03.090

DO - 10.1016/j.physa.2014.03.090

M3 - Article

AN - SCOPUS:84898987878

VL - 407

SP - 216

EP - 225

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

ER -