Regular and Chaotic States in a Local Map Description of Sheared Nematic Liquid Crystals

TL;DR

This paper introduces a local map model that captures the full spectrum of dynamical behaviors, from regular to chaotic, in sheared nematic liquid crystals, aligning with previous differential equation models.

Contribution

It presents a novel quaternion-based local map that describes various dynamical states in sheared nematics, enabling simplified analysis and potential lattice model development.

Findings

Model reproduces kayaking, wagging, tumbling, and aligned states

Agrees with previous differential equation formulations

Provides a foundation for lattice models of complex spatio-temporal states

Abstract

We propose and study a local map capable of describing the full variety of dynamical states, ranging from regular to chaotic, obtained when a nematic liquid crystal is subjected to a steady shear flow. The map is formulated in terms of a quaternion parametrization of rotations of the local frame described by the axes of the nematic director, subdirector and the joint normal to these, with two additional scalars describing the strength of ordering. Our model yields kayaking, wagging, tumbling, aligned and coexistence states, in agreement with previous formulations based on coupled ordinary differential equations. Such a map can serve as a building block for the construction of lattice models of the complex spatio-temporal states predicted for sheared nematics.