Order reconstruction patterns in nematic liquid crystal wells

We numerically study structural transitions inside shallow nanoscale wells with square cross-section, filled with nematic liquid crystal material. We model the wells within the Landau-de Gennes theory for nematic liquid crystals, in the absence of any external fields. We obtain two qualitatively different states: (i) the DSD state for relatively large wells with lateral dimension greater than a numerically computed critical threshold and (ii) a novel, two-dimensional star-like biaxial order reconstruction (OR) pattern called the WORS pattern, for wells smaller than the critical threshold. We define quantitative criteria for the onset of the WORS pattern in terms of the biaxiality parameter. We systematically study the dependence of the critical threshold, for the appearance of the WORS pattern, on the temperature and the anchoring strength on the lateral well surfaces.