• On the dynamical mechanism of cross-over from chaotic to turbulent states

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      https://www.ias.ac.in/article/fulltext/pram/064/03/0343-0352

    • Keywords

       

      Chaos; power law; Lyapunov spectrum; Portevin-Le Chatelier effect; slow manifold

    • Abstract

       

      The Portevin-Le Chatelier effect is one of the few examples of organization of defects. Here the spatio-temporal dynamics emerges from the cooperative behavior of the constituent defects, namely dislocations and point defects. Recent dynamical approach to the study of experimental time series reports an intriguing cross-over phenomenon from a low dimensional chaotic to an infinite dimensional scale invariant power-law regime of stress drops in experiments on CuAl single crystals and AlMg polycrystals, as a function of strain rate. We show that an extension of a dynamical model due to Ananthakrishna and coworkers for the Portevin-Le Chatelier effect reproduces this cross-over. At low and medium strain rates, the model shows chaos with the structure of the attractor resembling the reconstructed experimental attractor. At high strain rates, the model exhibits a power-law statistics for the magnitudes and durations of the stress drops as in experiments. Concomitantly, the largest Lyapunov exponent is zero. In this regime, there is a finite density of null exponents which itself follows a power law. This feature is similar to the Lyapunov spectrum of a shell model for turbulence. The marginal nature of this state is visualized through slow manifold approach.

    • Author Affiliations

       

      G Ananthakrishna1

      1. Materials Research Centre and Centre for Condensed Matter Theory, Indian Institute of Science, Bangalore - 560 012, India
    • Dates

       
  • Pramana – Journal of Physics | News

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