Nematic Equilibria on a Two-Dimensional Annulus

A. H. Lewis, D. G. A. L. Aarts, P. D. Howell, A. Majumdar

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, in the Oseen–Frank theoretical framework. We analyze a radially invariant defect-free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral-like equilibrium which emerges as the defect-free state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect-free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.
Original languageEnglish (US)
Pages (from-to)438-466
Number of pages29
JournalStudies in Applied Mathematics
Issue number4
StatePublished - Jan 16 2017
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: We thank Dr. Oliver Dammone for valuable discussions. AL is supported by the Engineering and Physical Sciences Research Council (EPSRC) studentship. AM is supported by an EPSRC Career Acceleration Fellowship EP/J001686/1 and EP/J001686/2, an OCCAM Visiting Fellowship and the Keble Advanced Studies Centre. This publication is partly based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). In compliance with EPSRC's open access initiative, the data in this paper are available from
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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