Smectic liquid crystals are typical layered phases, which possess both orientational order and a periodic modulation of the center-of-mass density in the form of layers. They are of great interest in mathematics for the questions arising in their modeling and analysis. In this talk, we propose a new continuum model of smectics, solving for a real-valued smectic order parameter for the density variation and a tensor-valued nematic order parameter for the molecular orientation, leading to a new unified frameword of isotropic, nematic, both non-tilted and tilted smectics. The model is challenging to discretisedue to the high regularity of the density variation; to address this, a continuous interior penalty finite element discretisationis employed. Numerical analysis and experiments are performed to confirm the effectiveness of the proposed model and discretisation. The model numerically captures important defect structures in both two and three dimensions for both non-tilted and tilted cases of smectics. Finally, we explore the topological configurations on button-like confinements by means of real-space microscopy experiments of hard rods and two other complementary theories: Monte-Carlo simulation and density functional theory. This yields a consistent description of defect structures on a qualitative level.
