Euler-Poincar\'e approaches to nematodynamics

TL;DR

This paper unifies various nematodynamics theories using Euler-Poincaré reduction, showing their compatibility and extending results to flowing liquid crystals, thus providing a comprehensive mathematical framework.

Contribution

It introduces a unifying Euler-Poincaré framework for nematodynamics theories, including Ericksen-Leslie, Luhiller-Rey, and micropolar theory, and extends these to flowing liquid crystals.

Findings

All theories are compatible within the Euler-Poincaré framework.

Some theories allow for configurations with non-zero disclination density.

Results are extended to flowing liquid crystal systems.

Abstract

Nematodynamics is the orientation dynamics of flowless liquid-crystals. We show how Euler-Poincar\'e reduction produces a unifying framework for various theories, including Ericksen-Leslie, Luhiller-Rey, and Eringen's micropolar theory. In particular, we show that these theories are all compatible with each other and some of them allow for more general configurations involving a non vanishing discination density. All results are also extended to flowing liquid crystals.