A fundamental improvement to Ericksen-Leslie kinematics

TL;DR

This paper advances the Ericksen-Leslie liquid crystal theory by developing finite-energy line defect solutions, exploring static force balance, and connecting defect characterization with elasticity and vector field decompositions.

Contribution

It introduces a novel theoretical and computational framework for line defect solutions in liquid crystals, improving upon existing Ericksen-Leslie models.

Findings

Finite-energy line defect solutions in liquid crystals are demonstrated.

Static force balance can occur without flow or body forces.

Connections between defect theory, elasticity, and vector field decompositions are established.

Abstract

We demonstrate theory and computations for finite-energy line defect solutions in an improvement of Ericksen-Leslie liquid crystal theory. Planar director fields are considered in two and three space dimensions, and we demonstrate straight as well as loop disclination solutions. The possibility of static balance of forces in the presence of a disclination and in the absence of flow and body forces is discussed. The work exploits an implicit conceptual connection between the Weingarten-Volterra characterization of possible jumps in certain potential fields and the Stokes-Helmholtz resolution of vector fields. The theoretical basis of our work is compared and contrasted with the theory of Volterra disclinations in elasticity. Physical reasoning precluding a gauge-invariant structure for the model is also presented.