Insights on the smectic 'spacetime' microstructure

We numerically decompose the full four-dimensional microstructure of simulated smectics into domains, using an analogy to the theory of martensites. Smectic liquid crystals are remarkable, beautiful examples of materials microstructure, with ordered patterns of geometrically perfect ellipses and hyperbolas. The solution of the complex problem of filling three-dimensional space with domains of focal conics under constraining boundary conditions yields a set of strict rules, which are like the compatibility conditions in a martensitic crystal. In previous work, we presented the rules giving compatible conditions for the concentric circle domains found at two-dimensional smectic interfaces with planar boundary conditions. Here we discuss generalizations of our approach to describe the full four-dimensional smectic domains, where the variant symmetry group is the Weyl-Poincaré group of Lorentz boosts, translations, rotations, and dilatations. We will explore implications for the coarsening mechanism of focal conics, and possible effects of incorporating topological defects such as dislocations.