Putting a liquid crystal on a curved background can introduce or alleviate geometrical frustration - an inability of the preferred local order to fill all of space. We study thin self-assembled columns constrained to lie on a curved, rigid substrate. The curvature presents no local obstruction to equally spaced columns in contrast with curved crystals for which the crystalline bonds are frustrated. Instead, the equal spacing of the columns implies that their normals lie on geodesics which converge (diverge) in regions of positive (negative) Gaussian curvature, in analogy to the focusing of light rays by a lens. We show that the out of plane bending of the cylinders acts as an effective ordering field. C.D. Santangelo, V. Vitelli, R.D. Kamien and D.R. Nelson, "Geometric Theory of Columnar Phases on Curved Substrates", Phys. Rev Lett. 99 (2007) 017801 (Editor's suggestion) [ARXIV] [PDF]

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Aspen workshop, "Interfaces, Topological Defects and Flexible Packings: Applied Geometry in Condensed Matter", accepted for Summer 2008. See here for details. I am currently looking for students. Interested students should contact me. Winner of the Glenn H. Brown Prize (2006) from the International Liquid Crystal Society (2006).

Seminar, Brown University, October 16