Director precession and nonlinear waves in nematic liquid crystals under elliptic shear

TL;DR

This paper investigates how elliptic shear induces director precession and nonlinear wave phenomena in nematic liquid crystals, revealing a transition from diffusive to dispersive waves and linking it to the Freedericks transition as a Hopf bifurcation.

Contribution

It provides an exact solution for director precession under elliptic shear and connects the wave behavior to the Freedericks transition, offering new insights into nonlinear wave dynamics in nematics.

Findings

Precession of the director is observed under elliptic shear.

Transition from diffusive to dispersive waves as the Freedericks transition is approached.

Exact flow alignment solutions predict precession reversal in non-flow aligning materials.

Abstract

Elliptic shear applied to a homeotropically oriented nematic above the electric bend Freedericks transition (FT) generates slow precession of the director. The character of the accompanying nonlinear waves changes from diffusive phase waves to dispersive ones exhibiting spirals and spatio-temporal chaos as the FT is approached from above. An exact solution of the flow alignment equations captures the observed precession and predicts its reversal for non-flow aligning materials. The FT transforms into a Hopf bifurcation opening the way to understand the wave phenomena.