 Award ID(s):
 2011754
 NSFPAR ID:
 10500454
 Publisher / Repository:
 APS
 Date Published:
 Journal Name:
 Physical Review E
 Volume:
 108
 Issue:
 5
 ISSN:
 24700045
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Conical surfaces, with a δ function of Gaussian curvature at the apex, are perhaps the simplest example of geometric frustration. We study twodimensional liquid crystals with pfold rotational symmetry (patics) on the surfaces of cones. For free boundary conditions at the base, we find both the ground state(s) and a discrete ladder of metastable states as a function of both the cone angle and the liquid crystal symmetry p. We find that these states are characterized by a set of fractional defect charges at the apex and that the ground states are in general frustrated due to effects of parallel transport along the azimuthal direction of the cone. We check our predictions for the groundstate energies numerically for a set of commensurate cone angles (corresponding to a set of commensurate Gaussian curvatures concentrated at the cone apex), whose surfaces can be polygonized as a perfect triangular or squaremesh, and find excellent agreement with our theoretical predictions.more » « less

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