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Explore liquid crystal modeling through thermodynamics and numerical methods in this conference talk that addresses complex patterns in experimental liquid crystal data, including active nematics and solitons. Learn how the GENERIC framework constructs thermodynamically consistent models by combining energy and entropy contributions to describe out-of-equilibrium systems. Discover the systematic formulation of equations for concentration-dependent lyotropic liquid crystals and their solution using a hybrid lattice Boltzmann code implemented in Julia. Examine the computational approach that integrates finite differences inspired by DiffEqOperators.jl, the Lattice Boltzmann method from Trixi.jl, and time evolution using DifferentialEquations.jl. Understand how 2D simulations demonstrate stable defect cores with topological charges of +1/2 and -1/2 in passive isotropic droplets within nematic environments, matching chromonic liquid crystal observations. Investigate 3D simulation predictions including the Fréedericksz transition due to electric energies and analyze solution behavior under different flow types arising from additional energy sources. See how experimental results can be quantitatively predicted using the proposed GENERIC equations and numerical methodology.
