Geometrically Frustrated Crystals: Elastic Theory and Dislocations
  Elastic theory of ring-(or cylinder-)shaped crystals is constructed and the generation of edge dislocations due to geometrical frustration caused by the bending is studied. The analogy to superconducting (or superfluid) vortex state is pointed out and the phase diagram of the ring-crystal, which depends on radius and thickness, is discussed. 
Masahiko Hayashi, Hiromichi Ebisawa and Kazuhiro Kuboki