On a Molecular Based Q-Tensor Model for Liquid Crystals with Density Variations

In this paper, we study the new Q-tensor model previously derived from Onsager's molecular theory byHan et al. [Arch. Rational Mech. Anal., 215 (2015), pp. 741--809] for static liquid crystalmodeling. Taking density and Q-tensor as order parameters, the new Q-tensor model not only characterizesimportant phases while capturing density variation effects, but also remains computationally tractableand efficient. We report the results of two numerical applications of the model, namely theisotropic--nematic--smectic-A--smectic-C phase transitions and the isotropic--nematic interfaceproblem, in which density variations are indispensable. Meanwhile, we show the connections of the newQ-tensor model with classical models including generalized Landau--de Gennes models, generalized McMillanmodels, and the Chen--Lubensky model. The new Q-tensor model is the pivot and an appropriate trade-offbetween the classical models in three scales.