Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nematic-Isotropic phase transition in Liquid crystals: a variational
  derivation of effective geometric motions   In this work, we study the nematic-isotropic phase transition based on the
dynamics of the Landau--De Gennes theory of liquid crystals. At the critical
temperature, the Landau--De Gennes bulk potential favors the isotropic phase
and nematic phase equally. When the elastic coefficient is much smaller than
that of the bulk potential, a scaling limit can be derived by formal asymptotic
expansions: the solution gradient concentrates on a closed surface evolving by
mean curvature flow. Moreover, on one side of the surface the solution tends to
the nematic phase which is governed by the harmonic map heat flow into the
sphere while on the other side, it tends to the isotropic phase. To rigorously
justify such a scaling limit, we prove a convergence result by combining weak
convergence methods and the modulated energy method. Our proof applies as long
as the limiting mean curvature flow remains smooth.

9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph