In my master's thesis, I explore the influence of flexoelectricity and ions in active nematic liquid crystals through numerical simulations and theoretical analysis. First, by comparing analytical and numerical calculations in an isotropic liquid with ions in one and two dimensions, I demonstrate the difference between the constant potential and constant charge regimes. I focus on a system with a constant number of ions, which limits the choice of boundary conditions. In active nematics with flexoelectricity, I investigate the dynamics in a spherical droplet at various values of the flexoelectric constant and activity. I observe a range of dynamic regimes, which I describe and characterize, including active turbulence. I continue by studying the dynamics of active nematics with ions in different dynamic regimes, where I also observe the electric current in the system. I notice that the ions mostly follow the dynamics of director field and material flow without influencing it. I only observe a change in regime of active turbulence, where the ions enhance its stability at the expense of making static regimes less stable. The time-averaged electric current in the system is negligible in all regimes. Finally, I test the performance of numerical simulations at different Gibbs transfer energies and show that they affect the ion density in defect cores. The described master's thesis is aimed at understanding various electrostatic effects, including ions, on the dynamics of passive and active complex nematic liquids.
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