Vector Formalism for Active Nematics in Two Dimensions

TL;DR

This paper introduces a vector formalism for 2D active nematics that overcomes limitations of tensor representations, providing a more accurate and stable theoretical framework for analyzing nematic alignment and flow in active matter.

Contribution

It proposes a vector order parameter approach for 2D nematics, addressing shortcomings of tensor-based models and enhancing stability analysis in active nematic systems.

Findings

Tensor representation has limitations in 2D nematics.

Vector formalism improves stability analysis.

Standard director theory fails to ensure passive system relaxation.

Abstract

Specific features of two-dimensional nematodynamics give rise to shortfalls of the tensor representation of the nematic order parameter commonly used in computations, especially in theory of active matter. The alternative representation in terms of the vector order parameter follows with small adjustments the classical director-based theory, but is applicable to 2D problems where both nematic alignment and deviation from the isotropic state are variable. Stability analysis of nematic alignment and flow is used as a testing ground. A director-based analysis demonstrates a shortfall of the standard theory, which does not ensure relaxation to equilibrium in a passive system. It also demonstrates the inadequacy of the director-based description, which misses a stabilizing effect of perturbations of the modulus ensuring stability of a passive system on scales far exceeding the healing length.