Dynamics of Crossover from a Chaotic to a Power Law State in Jerky Flow

Abstract

We study the dynamics of an intriguing crossover from a chaotic to a power law state as a function of strain rate within the context of a recently introduced model which reproduces the crossover. While the chaotic regime has a small set of positive Lyapunov exponents, interestingly, the scaling regime has a power law distribution of null exponents which also exhibits a power law. The slow manifold analysis of the model shows that while a large proportion of dislocations are pinned in the chaotic regime, most of them are pushed to the threshold of unpinning in the scaling regime, thus providing insight into the mechanism of crossover.

arXiv comment5 pages, 3 figures. In print in Phy. Rev. E Rapid Communications

References in corpus (5)

• Multifractal burst in the spatio-temporal dynamics of jerky flow
• Relaxation oscillations and negative strain rate sensitivity in the Portevin - Le Chatelier effect
• Chaotic and power law states in the Portevin-Le Chatelier effect
• Incomplete approach to homoclinicity in a model with bent-slow manifold geometry
• Lyapunov exponents and transport in the Zhang model of Self-Organized Criticality

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• Projecting Low Dimensional Chaos from Spatio-temporal Dynamics in a Model for Plastic Instability
• Scaling Behaviour and Complexity of the Portevin-Le Chatelier Effect