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A numerical investigation on configurational distortions in nematic liquid crystals. (English) Zbl 1226.76004
Summary: When subjected to magnetic or electric fields, nematic liquid crystals confined between two parallel glass plates and initially uniformly oriented may undergo homogeneous one-dimensional spatial distortions or periodic distortions. According to the experimental observations, periodic phases are stable configurations at intermediate intensity of the acting field, while homogeneous phases are stable at higher strengths.
We present a fully nonlinear finite element approach able to describe homogeneous and periodic configurational phases in a cell of confined nematic liquid crystal with strong planar anchoring boundary conditions. Stationary configurations are obtained by setting to zero the first variation of the discretized total energy of the system. Unstable configurations are identified by evaluating the behavior of the solution under small numerical perturbations. Numerical calculations are able to describe the evolution of the configurational distortions as a function of the applied field and are able to capture the critical points between homogeneous and periodic phases. The proposed approach has been proved to be an excellent tool to predict the existence of unstable or metastable distortions, characterized by higher energy levels.

76A15 Liquid crystals
82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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