Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nematic liquid crystals on sinusoidal channels: the zigzag instability   Substrates which are chemically or topographically patterned induce a variety
of liquid crystal textures. The response of the liquid crystal to competing
surface orientations, typical of patterned substrates, is determined by the
anisotropy of the elastic constants and the interplay of the relevant lengths
scales, such as the correlation length and the surface geometrical parameters.
Transitions between different textures, usually with different symmetries, may
occur under a wide range of conditions. We use the Landau-de Gennes free energy
to investigate the texture of nematics in sinusoidal channels with parallel
anchoring bounded by nematic-air interfaces that favour perpendicular
(hometropic) anchoring. In micron size channels 5CB was observed to exhibit a
non-trivial texture characterized by a disclination line, within the channel,
which is broken into a zigzag pattern. Our calculations reveal that when the
elastic anisotropy of the nematic does not favour twist distortions the defect
is a straight disclination line that runs along the channel, which breaks into
a zigzag pattern with a characteristic period, when the twist elastic constant
becomes sufficiently small when compared to the splay and bend constants. The
transition occurs through a twist instability that drives the defect line to
rotate from its original position. The interplay between the energetically
favourable twist distortions that induce the defect rotation and the liquid
crystal anchoring at the surfaces leads to the zigzag pattern. We investigate
in detail the dependence of the periodicity of the zigzag pattern on the
geometrical parameters of the sinusoidal channels, which in line with the
experimental results is found to be non-linear.

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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: math
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph