Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Virial theorem and dynamical evolution of self-gravitating Brownian
  particles and bacterial populations in an unbounded domain   We derive the Virial theorem appropriate to the generalized
Smoluchowski-Poisson system describing self-gravitating Brownian particles and
bacterial populations (chemotaxis). We extend previous works by considering the
case of an unbounded domain and an arbitrary equation of state. We use the
Virial theorem to study the diffusion (evaporation) of an isothermal Brownian
gas above the critical temperature T_c in dimension d=2 and show how the
effective diffusion coefficient and the Einstein relation are modified by
self-gravity or chemotactic attraction. We also study the collapse at T=T_c and
show that the central density increases logarithmically with time instead of
exponentially in a bounded domain. Finally, for d>2, we show that the
evaporation of the system is essentially a pure diffusion slightly slowed-down
by self-gravity. We also study the linear dynamical stability of stationary
solutions of the generalized Smoluchowski-Poisson system representing isolated
clusters of particles and investigate the influence of the equation of state
and of the dimension of space on the dynamical stability of the system.
Finally, we propose a general kinetic and hydrodynamic description of
self-gravitating Brownian particles and biological populations and recover
known models in some particular limits.

26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ