Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Advection of a passive scalar field by turbulent compressible fluid:
  renormalization group analysis near $d = 4$   The field theoretic renormalization group (RG) and the operator product
expansion (OPE) are applied to the model of a density field advected by a
random turbulent velocity field. The latter is governed by the stochastic
Navier-Stokes equation for a compressible fluid. The model is considered near
the special space dimension $d = 4$. It is shown that various correlation
functions of the scalar field exhibit anomalous scaling behaviour in the
inertial-convective range. The scaling properties in the RG+OPE approach are
related to fixed points of the renormalization group equations. In comparison
with physically interesting case $d = 3$, at $d = 4$ additional Green function
has divergences which affect the existence and stability of fixed points. From
calculations it follows that a new regime arises there and then by continuity
moves into $d = 3$. The corresponding anomalous exponents are identified with
scaling dimensions of certain composite fields and can be systematically
calculated as series in $y$ (the exponent, connected with random force) and
$\epsilon=4-d$. All calculations are performed in the leading one-loop
approximation.

1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
2
The categories of this paper are: math
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph