Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anomalous scaling of a passive scalar advected by the synthetic
  compressible flow   The field theoretic renormalization group and operator product expansion are
applied to the problem of a passive scalar advected by the Gaussian
nonsolenoidal velocity field with finite correlation time, in the presence of
large-scale anisotropy. The energy spectrum of the velocity in the inertial
range has the form $E(k)\propto k^{1-\epsilon}$, and the correlation time at
the wavenumber $k$ scales as $k^{-2+\eta}$. It is shown that, depending on the
values of the exponents $\epsilon$ and $\eta$, the model exhibits various types
of inertial-range scaling regimes with nontrivial anomalous exponents. Explicit
asymptotic expressions for the structure functions and other correlation
functions are obtained; they are represented by superpositions of power laws
with nonuniversal amplitudes and universal (independent of the anisotropy)
anomalous exponents, calculated to the first order in $\epsilon$ and $\eta$ in
any space dimension. These anomalous exponents are determined by the critical
dimensions of tensor composite operators built of the scalar gradients, and
exhibit a kind of hierarchy related to the degree of anisotropy: the less is
the rank, the less is the dimension and, consequently, the more important is
the contribution to the inertial-range behavior. The leading terms of the even
(odd) structure functions are given by the scalar (vector) operators. The
anomalous exponents depend explicitly on the degree of compressibility.

10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph