Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Open canals flow with fluvial to torrential phase transitions on
  networks   Network flows and specifically open canal flows can be modeled by systems of
balance laws defined on topological graphs. The shallow water or Saint-Venant
system of balance laws is one of the most used model and present two phases:
fluvial or sub-critical and torrential or super critical. Phase transitions may
occur within the same canal but transitions related to networks are less
investigated. In this paper we provide a complete characterization of possible
phase transitions for a simple network with two canals and one junction. Our
analysis allows the study of more complicate scenarios. Moreover, we provide
some numerical simulations to show the theory at work.

5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci