Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Fractal Dimension of Ionization Cascades in the Glow Discharge   The glow discharge's main ionization breakdown processes have been understood
for about one hundred years. The glow discharge, however, still remains an area
of active research in relation to pattern formation and far-from-equilibrium
systems. The primary and secondary ionization processes can be mathematically
modelled as general branching processes. Not only is the Townsend breakdown
criterion obtained but the ionization avalanche can be characterized as a
branching set with a unique Hausdorff fractal dimension. These fractal
dimensions can be utilized in applications using similarity principles and
Paschen's Law.

31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs