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.
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|
|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|
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