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Tsallis q-triplet, intermittent turbulence and Portevin–Le Chatelier effect

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  • Iliopoulos, A.C.
  • Aifantis, E.C.

Abstract

In this paper, we extend a previous study concerning Portevin–LeChatelier (PLC) effect and Tsallis statistics (Iliopoulos et al., 2015). In particular, we estimate Tsallis’ q-triplet, namely {qstat, qsens, qrel} for two sets of stress serration time series concerning the deformation of Cu-15%Al alloy corresponding to different deformation temperatures and thus types (A and B) of PLC bands. The results concerning the stress serrations analysis reveal that Tsallis q- triplet attains values different from unity ({qstat, qsens, qrel} ≠ {1,1,1}). In particular, PLC type A bands’ serrations were found to follow Tsallis super-q-Gaussian, non-extensive, sub-additive, multifractal statistics indicating that the underlying dynamics are at the edge of chaos, characterized by global long range correlations and power law scaling. For PLC type B bands’ serrations, the results revealed a Tsallis sub-q-Gaussian, non-extensive, super-additive, multifractal statistical profile. In addition, our results reveal also significant differences in statistical and dynamical features, indicating important variations of the stress field dynamics in terms of rate of entropy production, relaxation dynamics and non-equilibrium meta-stable stationary states. We also estimate parameters commonly used for characterizing fully developed turbulence, such as structure functions and flatness coefficient (F), in order to provide further information about jerky flow underlying dynamics. Finally, we use two multifractal models developed to describe turbulence, namely Arimitsu and Arimitsu (A&A) [2000, 2001] theoretical model which is based on Tsallis statistics and p-model to estimate theoretical multifractal spectrums f(a). Furthermore, we estimate flatness coefficient (F) using a theoretical formula based on Tsallis statistics. The theoretical results are compared with the experimental ones showing a remarkable agreement between modeling and experiment. Finally, the results of this study verify, as well as, extend previous studies which stated that type B and type A PLC bands underlying dynamics are connected with distinct dynamical behavior, namely chaotic behavior for the first and self-organized critical (SOC) behavior for the latter, while they shed new light concerning the turbulent character of the PLC jerky flow.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:498:y:2018:i:c:p:17-32
    DOI: 10.1016/j.physa.2017.12.077
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    References listed on IDEAS

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    1. Tsallis, Constantino, 2004. "Dynamical scenario for nonextensive statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 1-10.
    2. Arimitsu, Toshihico & Arimitsu, Naoko, 2001. "Analysis of turbulence by statistics based on generalized entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 177-194.
    3. 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.
    4. Pavlos, G.P. & Karakatsanis, L.P. & Xenakis, M.N., 2012. "Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma, Part one: Sunspot dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6287-6319.
    5. 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.
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