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We analyse a recent generalised free-energy for liquid crystals posited byVirga and falling in the class of quartic functionals in the spatial gradientsof the nematic director. We review some known interesting solutions, i. e.,uniform heliconical structures, and we find new liquid crystal configurations,which closely resemble some novel, experimentally detected, structures calledSkyrmion tubes. These new configurations are characterised by a localisedpattern given by the variation of the conical angle. We study the equilibriumdifferential equations and find numerical solutions and analyticalapproximations.

Non-uniform localised distortions in generalised elasticity for liquid crystals