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The power of Poincare: Elucidating the hidden symmetries in focal conic domains
Gareth P. Alexander1, Bryan Gin-ge Chen1, Elisabetta A. Matsumoto1 and Randall D. Kamien1,2
1 Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA
2 School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA

Focal conic domains are typically the ``smoking gun'' by which smectic liquid crystalline phases are identified. The geometry of the equally-spaced smectic layers is highly generic but, at the same time, difficult to work with. In this talk we develop an approach to the study of focal sets in smectics which exploits a hidden Poincare symmetry revealed only by viewing the smectic layers as projections from one-higher dimension. We use this perspective to shed light upon several classic focal conic textures, including the concentric cyclides of Dupin, polygonal textures and tilt-grain boundaries.

[1] arXiv:1004.0465v1

"Jožef Stefan" Institute

University of Ljubljana
Faculty of Mathematics
and Physics

Center of Excellence