Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistics of cross sections of Voronoi tessellations   In this paper we investigate relationships between the volumes of cells of
three-dimensional Voronoi tessellations and the lengths and areas of sections
obtained by intersecting the tessellation with a randomly oriented plane. Here,
in order to obtain analytical results, Voronoi cells are approximated to
spheres. First, the probability density function for the lengths of the radii
of the sections is derived and it is shown that it is related to the Meijer
$G$-function; its properties are discussed and comparisons are made with the
numerical results. Next the probability density function for the areas of cross
sections is computed and compared with the results of numerical simulations.

35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph