A genetic algorithm for the response of twisted nematic liquid crystals to an applied field

TL;DR

This paper introduces a genetic algorithm that efficiently computes the response of twisted nematic liquid crystals to external fields, offering a flexible alternative to traditional numerical methods and aligning well with experimental data.

Contribution

The paper presents a novel genetic algorithm approach for solving the integral equations governing liquid crystal behavior, avoiding the need for trial solutions and enhancing computational flexibility.

Findings

The algorithm produces fast, accurate solutions consistent with experimental observations.

It effectively handles complex boundary conditions and spatial variations.

The method outperforms traditional finite-difference approaches in flexibility and speed.

Abstract

When an external field is applied across a liquid-crystal cell, the twist and tilt distributions cannot be calculated analytically and must be extracted numerically. In the standard approach, the Euler-Lagrange equations are derived from the minimization of the free energy of the system and then solved via finite-difference methods, often implemented in commercial software. These tools iterate from initial solutions that are compatible with the boundary conditions, providing limited to no flexibility for customization. Here, we present a genetic algorithm that outputs fast and accurate solutions to the integral form of the equations. In our approach, the evolutionary routine is sequentially applied at each position within the bulk of the cell, thus overcoming the necessity of assuming trial solutions. The predictions of our routine strongly support the experimental observations on different instances of spatially varying twisted nematic liquid-crystal cells, patterned with different topologies on the two alignment layers.