Frustrated order on extrinsic geometries

Badel L. Mbanga, Gregory M. Grason, Christian D. Santangelo

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


We study, numerically and theoretically, defects in an anisotropic liquid that couple to the extrinsic geometry of a surface. Though the intrinsic geometry tends to confine topological defects to regions of large Gaussian curvature, extrinsic couplings tend to orient the order along the local direction of maximum or minimum bending. This additional frustration is generically unavoidable, and leads to complex ground-state thermodynamics. Using the catenoid as a prototype, we show, in contradistinction to the well-known effects of intrinsic geometry, that extrinsic curvature expels disclinations from the region of maximum curvature above a critical coupling threshold. On catenoids lacking an "inside-outside" symmetry, defects are expelled altogether above a critical neck size.

Original languageEnglish (US)
Article number017801
JournalPhysical Review Letters
Issue number1
StatePublished - Jan 3 2012
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy


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