  In this article, we study the new Q-tensor model previously derived from
Onsager's molecular theory by Han \textit{et al.} [Arch. Rational Mech. Anal.,
215.3 (2014), pp. 741-809] for static liquid crystal modeling. Taking density
and Q-tensor as order parameters, the new Q-tensor model not only characterizes
important phases while capturing density variation effects, but also remains
computationally tractable and efficient. We report the results of two numerical
applications of the model, namely the isotropic--nematic--smectic-A--smectic-C
phase transitions and the isotropic--nematic interface problem, in which
density variations are indispensable. Meanwhile, we show the connections of the
new Q-tensor model with classical models including generalized Landau-de Gennes
models, generalized McMillan models, and the Chen-Lubensky model. The new
Q-tensor model is the pivot and an appropriate trade-off between the classical
models in three scales.
