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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Macroscopic behaviour in a two-species exclusion p
rocess via the method of matched asymptotics - Jam
es Mason (University of Cambridge)
DTSTART;TZID=Europe/London:20220315T145000
DTEND;TZID=Europe/London:20220315T153500
UID:TALK171530AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/171530
DESCRIPTION:We consider a two-species simple exclusion process
on a periodic lattice. We use the method of match
ed asymptotics to derive evolution equations for t
he two population densities in the dilute regime\,
namely a cross-diffusion system of partial differ
ential equations for the two species densities. Fi
rst\, our result captures non-trivial interaction
terms neglected in the mean-field approach\, inclu
ding a non-diagonal mobility matrix with explicit
density dependence. Second\, it generalises the ri
gorous hydrodynamic limit of Quastel [Commun. Pure
Appl. Math. 45(6)\, 623--679 (1992)]\, valid for
species with equal jump rates and given in terms o
f a non-explicit self-diffusion coefficient\, to t
he case of unequal rates in the dilute regime. In
the equal-rates case\, by combining matched asympt
otic approximations in the low- and high-density l
imits\, we obtain a cubic polynomial approximation
of the self-diffusion coefficient that is numeric
ally accurate for all densities. This cubic approx
imation agrees extremely well with numerical simul
ations. It also coincides with the Taylor expansio
n up to the second-order in the density of the sel
f-diffusion coefficient obtained using a rigorous
recursive method.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:
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