Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of hexagonal solidification patterns   We investigate the dynamics of cellular solidification patterns using
three-dimensional phase-field simulations. The cells can organize into stable
hexagonal patterns or exhibit unsteady evolutions. We identify the relevant
secondary instabilities of regular hexagonal arrays and find that the stability
boundaries depend significantly on the strength of crystalline anisotropy. We
also find multiplet states that can be reached by applying well-defined
perturbations to a pre-existing hexagonal array.

2
The categories of this paper are: math
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th