Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistics of the relative velocity of particles in turbulent flows :
  monodisperse particles   We use direct numerical simulations to calculate the joint probability
density function of the relative distance $R$ and relative radial velocity
component $V_R$ for a pair of heavy inertial particles suspended in homogeneous
and isotropic turbulent flows. At small scales the distribution is scale
invariant, with a scaling exponent that is related to the particle-particle
correlation dimension in phase space, $D_2$. It was argued [1, 2] that the
scale invariant part of the distribution has two asymptotic regimes: (1) $|V_R|
\ll R$ where the distribution depends solely on $R$; and (2) $|V_R| \gg R$
where the distribution is a function of $|V_R|$ alone. The probability
distributions in these two regimes are matched along a straight line $|V_R| =
z^\ast R$. Our simulations confirm that this is indeed correct. We further
obtain $D_2$ and $z^\ast$ as a function of the Stokes number, ${\rm St}$. The
former depends non-monotonically on ${\rm St}$ with a minimum at about ${\rm
St} \approx 0.7$ and the latter has only a weak dependence on ${\rm St}$.

0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph