Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimizing the Source Distribution in Fluid Mixing   A passive scalar is advected by a velocity field, with a nonuniform spatial
source that maintains concentration inhomogeneities. For example, the scalar
could be temperature with a source consisting of hot and cold spots, such that
the mean temperature is constant. Which source distributions are best mixed by
this velocity field? This question has a straightforward yet rich answer that
is relevant to real mixing problems. We use a multiscale measure of
steady-state enhancement to mixing and optimize it by a variational approach.
We then solve the resulting Euler--Lagrange equation for a perturbed uniform
flow and for simple cellular flows. The optimal source distributions have many
broad features that are as expected: they avoid stagnation points, favor
regions of fast flow, and their contours are aligned such that the flow blows
hot spots onto cold and vice versa. However, the detailed structure varies
widely with diffusivity and other problem parameters. Though these are model
problems, the optimization procedure is simple enough to be adapted to more
complex situations.

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The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ