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

Ananthkrishna, G (2005) On the dynamical mechanism of cross-over from chaotic to turbulent states. In: Pramana-journal of Physics, 64 (3). pp. 343-352.


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The Portevin-Le Chatelier e®ect 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.

Item Type: Journal Article
Publication: Pramana-journal of Physics
Publisher: Indian Academy of Sciences
Keywords: Chaos; Power law; Lyapunov spectrum; Portevin-Le Chatelier effect; slowmanifold.
Department/Centre: Division of Chemical Sciences > Materials Research Centre
Date Deposited: 05 Apr 2007
Last Modified: 19 Sep 2010 04:35
URI: http://eprints.iisc.ac.in/id/eprint/9837

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