Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A `liquid-solid' phase transition in a simple model for swarming, based
  on the `no flat-spots' theorem for subharmonic functions   We consider a non-local shape optimization problem, which is motivated by a
simple model for swarming and other self-assembly/aggregation models, and prove
the existence of different phases. A technical key ingredient, which we
establish, is that a strictly subharmonic function cannot be constant on a set
of positive measure.

19
The categories of this paper are: eess
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn