Landau-de Gennes numerical simulation of nematic liquid crystals utilizing radial basis functions

TL;DR

This paper introduces a radial basis function-based numerical simulation method for nematic liquid crystals, offering greater geometric flexibility and efficiency, and demonstrates its effectiveness through simulations of complex systems with defect resolution.

Contribution

It presents a novel RBF-based simulation approach for nematic liquid crystals, highlighting advantages over traditional methods and incorporating adaptive refinement for defect analysis.

Findings

Effective modeling of complex geometries

Enhanced computational efficiency

Successful resolution of defect structures

Abstract

Numerical simulations based on radial basis functions have been developed for systems with complex geometries and have been successfully applied across various fields, including seismology, coastal hydrodynamics, and biology. However, examples in liquid crystal modeling are limited. In this study, we present a Landau-de Gennes numerical simulation of nematic liquid crystals utilizing radial basis functions, emphasizing its advantages over traditional cubic grid calculations, such as enhanced geometric flexibility and improved computational efficiency. Through simulations of liquid crystal-colloid systems with diverse geometries, we demonstrate that our approach effectively captures the essential topological and energetic features of liquid crystal equilibrium structures. Additionally, we introduce an adaptive node refinement scheme that is crucial for resolving the fine structure of singular defects in nematic liquid crystals.