TY - JOUR
T1 - Nematic Equilibria on a Two-Dimensional Annulus
AU - Lewis, A. H.
AU - Aarts, D. G. A. L.
AU - Howell, P. D.
AU - Majumdar, A.
N1 - 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 https://doi.org/10.5287/bodleian:R59G8pEMv.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2017/1/16
Y1 - 2017/1/16
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/623570
UR - http://doi.wiley.com/10.1111/sapm.12161
UR - http://www.scopus.com/inward/record.url?scp=85018363977&partnerID=8YFLogxK
U2 - 10.1111/sapm.12161
DO - 10.1111/sapm.12161
M3 - Article
VL - 138
SP - 438
EP - 466
JO - Studies in Applied Mathematics
JF - Studies in Applied Mathematics
SN - 0022-2526
IS - 4
ER -