Relaxation with long-period oscillation in defect turbulence of planar nematic liquid crystals

TL;DR

This paper investigates defect turbulence in nematic liquid crystals, revealing long-period oscillations in structural relaxation caused by defect pair dynamics, analyzed through a combination of experiments and analytical methods.

Contribution

It introduces a novel analytical approach to separate and understand the two independent relaxation processes in defect turbulence.

Findings

Long-period oscillations in structural relaxation are observed.

Relaxation processes are analytically separated into macroscopic and fluctuation components.

Nonthermal fluctuations are modeled as independent Markov processes.

Abstract

Through experiments, we studied defect turbulence, a type of spatiotemporal chaos in planar systems of nematic liquid crystals, to clarify the chaotic advection of weak turbulence. In planar systems of large aspect ratio, structural relaxation which is characterized by the dynamic structure factor exhibits a long-period oscillation that is described well by a combination of a simple exponential relaxation and underdamped oscillation. The simple relaxation arises as a result of the roll modulation while the damped oscillation is manifest in the repetitive gliding of defect pairs in a local area. Each relaxation is derived analytically by the projection operator method that separates turbulent transport into a macroscopic contribution and fluctuations. The analysis proposes that the two relaxations are not correlated. The nonthermal fluctuations of defect turbulence are consequently separated into two independent Markov processes. Our approach sheds light on diversity and universality from a unified viewpoint for weak turbulence.