The effect of curvature on cholesteric doughnuts
  The confinement of liquid crystals inside curved geometries leads to exotic structures, with applications ranging from bio-sensors to optical switches and privacy windows. Here we study how curvature affects the alignment of a cholesteric liquid crystal. We model the system on the mesoscale using the Landau-de Gennes model. Our study was performed in three stages, analysing different curved geometries from cylindrical walls and pores, to toroidal domains, in order to isolate the curvature effects. Our results show that the stresses introduced by the curvature influence the orientation of the liquid crystal molecules, and cause distortions in the natural periodicity of the cholesteric that depend on the radius of curvature and on the commensurability between the pitch and the dimensions of the system. In particular, the cholesteric layers of toroidal droplets exhibit a symmetry breaking not seen in cylindrical pores and that is driven by the additional curvature. 
Ana Fialho and Nelson R. Bernardino and Nuno M. Silvestre and   Margarida M. Telo da Gama
cond-mat.soft