Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Front Propagation at the Isotropic Nematic Transition Temperature   We study the gradient flow model for the Landau-de Gennes energy functional
for nematic liquid crystals at the nematic-isotropic transition temperature on
prototype geometries. We study the dynamic model on a three-dimensional droplet
and on a disc with Dirichlet boundary conditions and different types of initial
conditions. In the case of a droplet with radial boundary conditions, a large
class of physically relevant initial conditions generate dynamic solutions with
a well-defined isotropic-nematic interface which propagates according to mean
curvature for small times. On a disc, we make a distinction between "planar"
and "non-planar" initial conditions and "minimal" and "non-minimal" Dirichlet
boundary conditions. Planar initial conditions generate solutions with an
isotropic core for all times whereas non-planar initial conditions generate
solutions which escape into the third dimension. Non-minimal boundary
conditions generate solutions with boundary layers and these solutions can
either have a largely ordered interior profile or an almost entirely disordered
isotropic interior profile. Our examples suggest that whilst critical points of
the Landau-de Gennes energy typically have highly localized disordered-ordered
interfaces, the transient dynamics exhibit observable isotropic-nematic
interfaces of potential experimental relevance.

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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn