Abstract
We propose a practical finite element method for the simulation of uniaxial nematic liquid crystals with a constant order parameter. A monotonicity result for Q-tensor fields is derived under the assumption that the underlying triangulation is weakly acute. Using this monotonicity argument we show the stability of a gradient flow type algorithm and prove the convergence outputs to discrete stable configurations as the stopping parameter of the algorithm tends to zero. Numerical experiments with singularities illustrate the performance of the algorithm. Furthermore, we examine numerically the difference of orientable and non-orientable stable configurations of liquid crystals in a planar two dimensional domain and on a curved surface. As an application, we examine tangential line fields on the torus and show that there exist orientable and non-orientable stable states with comparing Landau-de Gennes energy and regions with different tilts of the molecules.
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The authors acknowledge support by the DFG through the Collaborative Research Center (SFB) 611 Singular Phenomena and Scaling in Mathematical Models.
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Bartels, S., Raisch, A. (2014). Simulation of Q-Tensor Fields with Constant Orientational Order Parameter in the Theory of Uniaxial Nematic Liquid Crystals. In: Griebel, M. (eds) Singular Phenomena and Scaling in Mathematical Models. Springer, Cham. https://doi.org/10.1007/978-3-319-00786-1_17
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DOI: https://doi.org/10.1007/978-3-319-00786-1_17
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