Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Application of Bogolyubov's approach to the derivation of kinetic
  equations for dissipative systems   The main goal of the present article is to extend the Bogolyubov method for
deriving kinetic equations to dissipative many-body systems. The basic
conjecture underlying the Bogolyubov approach is the functional hypothesis,
according to which, the many-particle distribution functions are assumed to be
functionals of the one-particle distribution function on kinetic time scales.
Another ingredient in the Bogolyubov approach is the principle of the spatial
weakening of correlations, which reflects statistical independence of physical
values at distant spatial points. One can consider it as a reasonable mixing
property of many-particle distribution functions. The motivation behind the
generalization of Bogolyubov's approach to (classical) many-body dissipative
systems is the wish to describe the dynamics of granular systems, in particular
granular fluids. To this end we first define a general dissipative fluid
through a dissipation function, thereby generalizing the commonly employed
models for granular fluids. Using the Bogolyubov functional hypothesis we show
how a reduction of the pertinent BBGKY hierarchy can be achieved. The method is
then employed to cases which can be treated perturbatively, such as those in
which the interactions are weak or the dissipation is small or the particle
density is small. Kinetic descriptions are obtained in all of these limiting
cases. As a test case, we show that the Bogolyubov method begets the now
standard inelastic Boltzmann equation for dilute monodisperse collections of
spheres whose collisions are characterized by a fixed coefficient of normal
restitution. Possible further applications and implications are discussed.

18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg