Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase Diagram for Turbulent Transport: Sampling Drift, Eddy Diffusivity
  and Variational Principles   We study the long-time, large scale transport in a three-parameter family of
isotropic, incompressible velocity fields with power-law spectra. Scaling law
for transport is characterized by the scaling exponent $q$ and the Hurst
exponent $H$, as functions of the parameters. The parameter space is divided
into regimes of scaling laws of different {\em functional forms} of the scaling
exponent and the Hurst exponent. We present the full three-dimensional phase
diagram.
  The limiting process is one of three kinds: Brownian motion ($H=1/2$),
persistent fractional Brownian motions ($1/2<H<1$) and regular (or smooth)
motion (H=1).
  We discover that a critical wave number divides the infrared cutoffs into
three categories, critical, subcritical and supercritical; they give rise to
different scaling laws and phase diagrams. We introduce the notions of sampling
drift and eddy diffusivity, and formulate variational principles to estimate
the eddy diffusivity. We show that fractional Brownian motions result from a
dominant sampling drift.

30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat