Smectic liquid crystals are composed of layers which can bend but otherwise maintain close to a uniform spacing. In such a material, the layer shapes are represented by a displacement giving their deviation from the ideal ground state configuration. The layered nature of this phase connects the bending energy of the layers to the spacing between the layers in a complex manner. A proper understanding of how the layers arrange themselves requires us to account for these connections. Similar difficulties arise in the elasticity of thin elastic sheets.
We have developed a method to explore deformations of the layers around particular configurations called edge dislocation (shown in the figure). To do so, we start with a focal texture – a possibly complex configuration of exactly equally-spaced layers. We are then able to relax the constraint of constant spacing by balancing the bending energy with the layer spacing using a technique called a BPS decomposition. It turns out the two methods are closely allied, allowing us to construct approximate layer configurations that were impossible before.
G. Alexander, R.D. Kamien and C.D. Santangelo, “Developed smectics: When exact solutions agree”, accepted to Physical Review Letters (2011). [ARXIV].