Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decorated vertices with 3-edged cells in 2D foams: exact solutions and
  properties   The energy, area and excess energy of a decorated vertex in a 2D foam are
calculated. The general shape of the vertex and its decoration are described
analytically by a reference pattern mapped by a parametric Moebius
transformation. A single parameter of control allows to describe, in a common
framework, different types of decorations, by liquid triangles or 3-sided
bubbles, and other non-conventional cells. A solution is proposed to explain
the stability threshold in the flower problem.

22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess