JuliaCon 2025

Experimental data on liquid crystals (LCs) have revealed complex patterns that remain unexplained, including active nematics triggered by molecular motors and solitons generated by external electric fields. These studies raise questions about the effective parameters that transform such chaotic dynamics into coherent motion, with the goal of uncovering new applications and technologies. To address this challenging problem, we employ the GENERIC framework to construct a thermodynamically consistent model. Within this framework, the time-evolution equations for out-of-equilibrium systems are naturally described by the sum of energy and entropy contributions.

Using this approach, we systematically formulate a set of equations that describe the behavior of concentration-dependent (lyotropic) LCs. We solve these equations using a hybrid lattice Boltzmann code written in Julia, which combines: 1) finite differences (inspired by DiffEqOperators.jl) and 2) the Lattice Boltzmann method (from Trixi.jl); the time evolution is integrated using DifferentialEquations.jl.

We show that, in 2D, two passive isotropic droplets within a nematic environment can form stable defect cores with topological charges of +1/2 and -1/2, as observed in chromonic LC data. In 3D, the simulations predict different behaviors, such as the Fréedericksz' transition, due to the electric energies involved. Additionally, we investigate the effect of our solutions under different types of flow, arisen by these additional energy sources. Our findings demonstrate that the experimental results can be quantitatively predicted by the proposed GENERIC equations and our numerical approach.