Nematic equilibria on a two-dimensional annulus

Lewis, A. H. and Aarts, D. G. A. L. and Howell, P. D. and Majumdar, A. (2017) Nematic equilibria on a two-dimensional annulus. Studies in Applied Mathematics, 138 (4). pp. 438-466. ISSN 0022-2526 (https://doi.org/10.1111/sapm.12161)

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Abstract

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.

  • Item type:Article
    ID code:70988
    Dates:
    Date
    Event
    31 May 2017
    Published
    16 January 2017
    Published Online
    18 August 2016
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:18 Dec 2019 14:57
    Last modified:19 Apr 2024 00:24
    URI:https://strathprints.strath.ac.uk/id/eprint/70988
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