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The structure of the half-integer rectilinear disclination line within the framework of the Landau-de Gennes effective theory of nematic liquid crystals is investigated. The consistent perturbative expansion is constructed for the case of $L_2 eq 0$. It turns out that such expansion can be performed around only a discrete subset of an infinite set of the degenerate zeroth order solutions. These solutions correspond to the positive and negative wedge disclination lines and to four configurations of the twist disclination line. The first order corrections to both the order parameter field as well as the free energy of the disclination lines have been found. The results for the free energy are compared with the ones obtained in the Frank-Oseen-Zocher director description.
Liquid crystal networks combine the orientational order of liquid crystals with the elastic properties of polymer networks, leading to a vast application potential in the field of responsive coatings, e.g., for haptic feedback, self-cleaning surfaces
In this paper, we study the connection between the Ericksen-Leslie equations and the Beris-Edwards equations in dimension two. It is shown that the weak solutions to the Beris-Edwards equations converge to the one to the Ericksen-Leslie equations as
We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains. Assuming smooth and uniaxial (e.g. homeotropic) boundary conditions and a corresponding physically relevant norm c
We show that Landau theory for the isotropic, nematic, smectic A, and smectic C phases generically, but not ubiquitously, implies de Vries behavior. I.e., a continuous AC transition can occur with little layer contraction; the birefringence decreases
We study energy minimization of a continuum Landau-de Gennes energy functional for nematic liquid crystals, in three-dimensional axisymmetric domains and in a restricted class of $mathbb{S}^1$-equivariant (i.e., axially symmetric) configurations. We