Weirdest Martensite: Smectic Liquid Crystal Microstructure and Weyl-Poincaré Invariance.
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 similar to the compatibility conditions in a martensitic crystal. Here we present the rules giving compatible conditions for the concentric circle domains found at two-dimensional smectic interfaces with planar boundary conditions. Using configurations generated by numerical simulations, we develop a clustering algorithm to decompose the planar boundaries into domains. The interfaces between different domains agree well with the smectic compatibility conditions. We also discuss generalizations of our approach to describe the full three-dimensional smectic domains, where the variant symmetry group is the Weyl-Poincaré group of Lorentz boosts, translations, rotations, and dilatations.
Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853-2501, USA.|Institute of Physics, University of São Paulo, São Paulo, São Paulo 05314-970, Brazil.
Danilo B
DB
Liarte
Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853-2501, USA.
Matthew
M
Bierbaum
Departamento de Matemática Aplicada, Universidade Estadual de Campinas, Campinas, São Paulo 13083-859, Brazil.
Ricardo A
RA
Mosna
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Randall D
RD
Kamien
Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853-2501, USA.
James P
JP
Sethna