2. 1d Translational Order in Curved Substrate
Xiangjun Xing, Physics Department, Syracuse University
The physics of translational orders on curved substrate has received much attention recently. It has relevance to colloidal science and biophysics. The description of translational order in curved space however is rather nontrivial and necessitate modern differential geometry. We have studied the elasticity theory of smectic/coumnar order on curved substrate using modern differential geometry and topological methods.
Using differential form to describe translational order in curved space
Identify novel global dislocation of translational order in curved space and clarify its connection with the nontrivial topology of the underlying curved substrate
Identify important coupling between extrinsic curvature and nematic director field, which has been incorrectly ignored by other groups
Compute mean field phase diagram of smectic order on a torus, and identify two phases: an achiral phase where the nematic director is locked by the extrinsic curvature, and a chiral phase where the director continuously rotate as system parameters change. The transition is driven by the coupling between extrinsic curvature and nematic director.