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Portevin–Le Chatelier effect and Tsallis nonextensive statistics

Author

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  • Iliopoulos, A.C.
  • Nikolaidis, N.S.
  • Aifantis, E.C.

Abstract

In this paper, we estimate Tsallis’ entropic index q≡qstat (stat denotes stationary states) for various stress serration time series of Cu–15%Al alloys corresponding to different deformation temperatures and types (A, B, C) of Portevin–Le Chatelier (PLC) bands. Tsallis statistical analysis is also conducted on experimental data derived from correlation diagrams focusing on PLC type C bands’ spatial organization at the surface of various specimens. The results concerning the stress serrations analysis reveal the non-Gaussian (Tsallis q-Gaussian), nonextensive, sub-additive, character of the underlying dynamics of the PLC type-A bands (q>1) indicating dynamics at the edge of chaos, with global long range correlations and power law scaling. Similarly, for PLC type B bands, a Tsallis q-Gaussian, non-extensive, super-additive, statistical profile was found with q<1, while for the PLC type C bands, a near Boltzmann–Gibbs (BG) statistical character was verified indicating Gaussian dynamics with short (weak) range correlations. Finally, Tsallis q-index for the spatial data of PLC type C bands was found above unity (q>1) indicating that type C bands are not randomly nucleated in the specimen (e.g. yielding a Gaussian distribution) but there exist spatial coupling and long range deformation correlations in the PLC type C bands spatial localization.

Suggested Citation

  • Iliopoulos, A.C. & Nikolaidis, N.S. & Aifantis, E.C., 2015. "Portevin–Le Chatelier effect and Tsallis nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 509-518.
    • Handle: RePEc:eee:phsmap:v:438:y:2015:i:c:p:509-518
    DOI: 10.1016/j.physa.2015.07.007
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    References listed on IDEAS

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    1. Pavlos, G.P. & Iliopoulos, A.C. & Zastenker, G.N. & Zelenyi, L.M. & Karakatsanis, L.P. & Riazantseva, M.O. & Xenakis, M.N. & Pavlos, E.G., 2015. "Tsallis non-extensive statistics and solar wind plasma complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 113-135.
    2. Pavlos, G.P. & Karakatsanis, L.P. & Xenakis, M.N. & Sarafopoulos, D. & Pavlos, E.G., 2012. "Tsallis statistics and magnetospheric self-organization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3069-3080.
    3. Kugiumtzis, Dimitris & Tsimpiris, Alkiviadis, 2010. "Measures of Analysis of Time Series (MATS): A MATLAB Toolkit for Computation of Multiple Measures on Time Series Data Bases," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i05).
    4. Pavlos, G.P. & Karakatsanis, L.P. & Xenakis, M.N. & Pavlos, E.G. & Iliopoulos, A.C. & Sarafopoulos, D.V., 2014. "Universality of non-extensive Tsallis statistics and time series analysis: Theory and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 58-95.
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    Cited by:

    1. Ogunsua, B.O. & Laoye, J.A., 2018. "Tsallis non-extensive statistical mechanics in the ionospheric detrended total electron content during quiet and storm periods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 236-245.
    2. Iliopoulos, A.C. & Aifantis, E.C., 2018. "Tsallis q-triplet, intermittent turbulence and Portevin–Le Chatelier effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 498(C), pages 17-32.

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