Stochastic effects on solution landscapes for nematic liquid crystals

TL;DR

This paper investigates how additive and multiplicative noise influence the solution landscapes of nematic liquid crystals, revealing noise-induced symmetry breaking and providing insights into the robustness of deterministic models.

Contribution

It introduces a stochastic framework using Q-Wiener processes to analyze the effects of noise on nematic liquid crystal solutions, highlighting the impact on symmetry and solution stability.

Findings

Noise can break the symmetry of the radial hedgehog solution.

Stochastic effects alter the solution landscape compared to deterministic predictions.

The framework tests the robustness of deterministic liquid crystal models.

Abstract

We study the effects of additive and multiplicative noise on the solution landscape of nematic liquid crystals confined to a square domain within the Landau-de Gennes framework, as well as the impact of additive noise on the symmetric radial hedgehog solution for nematic droplets. The introduction of random noise can be used to capture material uncertainties and imperfections, which are always present in physical systems. We implement random noise in our framework by introducing a Q-Wiener stochastic process to the governing differential equations. On the square, the solution landscape for the deterministic problem is well understood, enabling us to compare and contrast the deterministic predictions and the stochastic predictions, while we demonstrate that the symmetry of the radial hedgehog solution can be violated by noise. This approach of introducing noise to deterministic equations can be used to test the robustness and validity of predictions from deterministic liquid crystal models, which essentially capture idealised situations.