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

TL;DR

This paper investigates the transition from chaotic to power law behavior in jerky flow, revealing how dislocation dynamics shift and how Lyapunov exponents characterize different regimes.

Contribution

It introduces a model that captures the crossover from chaos to power law scaling and analyzes the underlying dislocation mechanisms involved.

Findings

Chaotic regime has a small set of positive Lyapunov exponents.

Scaling regime exhibits a power law distribution of null exponents.

Dislocations are mostly pinned in chaos, but near unpinning in the scaling regime.

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.