Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Macroscopic behaviour in a two-species exclusion process via the method
  of matched asymptotics   We consider a two-species simple exclusion process on a periodic lattice. We
use the method of matched asymptotics to derive evolution equations for the two
population densities in the dilute regime, namely a cross-diffusion system of
partial differential equations for the two species densities. First, our result
captures non-trivial interaction terms neglected in the mean-field approach,
including a non-diagonal mobility matrix with explicit density dependence.
Second, it generalises the rigorous hydrodynamic limit of Quastel [Commun. Pure
Appl. Math. 45(6), 623--679 (1992)], valid for species with equal jump rates
and given in terms of a non-explicit self-diffusion coefficient, to the case of
unequal rates in the dilute regime. In the equal-rates case, by combining
matched asymptotic approximations in the low- and high-density limits, we
obtain a cubic polynomial approximation of the self-diffusion coefficient that
is numerically accurate for all densities. This cubic approximation agrees
extremely well with numerical simulations. It also coincides with the Taylor
expansion up to the second-order in the density of the self-diffusion
coefficient obtained using a rigorous recursive method.

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The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys