Abstract
Recently (Sarlis and Christopoulos (2012)) the threshold distribution function View the MathML source of the coherent noise model for infinite number of agents after the kth 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 View the MathML source, the numerical results indicate that 〈E(Sk+1)〉 collapses to the qexponential (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 View the MathML source of this transition is provided. This ensemble of coherent noise models may be considered as a simple prototype following qexponential relaxation. The resulting qvalues are compatible with those reported in the literature for the coherent noise model.
Original language  English 

Pages (fromto)  216–225 
Journal  Physica A: Statistical Mechanics and its Applications 
Volume  407 
Early online date  12 Apr 2014 
DOIs  
Publication status  Published  1 Aug 2014 
Keywords
 qexponential
 Coherent noise model
 Natural time
 Offequilibrium dynamics
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Stavros Christopoulos
 Institute for Future transport and Cities  Associate
 School of Mechanical, Aerospace and Automotive Engineering  Lecturer in Mechanical Engineering and Physics
Person: Teaching and Research