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

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  • Christopoulos, S.-R.G.
  • Sarlis, N.V.

Abstract

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.

Suggested Citation

  • Christopoulos, S.-R.G. & Sarlis, N.V., 2014. "q-exponential relaxation of the expected avalanche size in the coherent noise model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 216-225.
    • Handle: RePEc:eee:phsmap:v:407:y:2014:i:c:p:216-225
    DOI: 10.1016/j.physa.2014.03.090
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    Cited by:

    1. Loukidis, Andronikos & Pasiou, Ermioni D. & Sarlis, Nicholas V. & Triantis, Dimos, 2020. "Fracture analysis of typical construction materials in natural time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    2. Stergiopoulos, Ch. & Stavrakas, I. & Triantis, D. & Vallianatos, F. & Stonham, J., 2015. "Predicting fracture of mortar beams under three-point bending using non-extensive statistical modeling of electric emissions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 603-611.
    3. Zhang, Fode & Shi, Yimin & Wang, Ruibing, 2017. "Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 552-565.
    4. Stavros-Richard G. Christopoulos & Nicholas V. Sarlis, 2017. "An Application of the Coherent Noise Model for the Prediction of Aftershock Magnitude Time Series," Complexity, Hindawi, vol. 2017, pages 1-27, February.

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