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SUMMARY:Macroscopic behaviour in a two-species exclusion process via the m
 ethod of matched asymptotics - James Mason (University of Cambridge)
DTSTART:20220315T145000Z
DTEND:20220315T153500Z
UID:TALK171530@talks.cam.ac.uk
DESCRIPTION:We consider a two-species simple exclusion process on a period
 ic lattice. We use the method of matched asymptotics to derive evolution e
 quations for the two population densities in the dilute regime\, namely a 
 cross-diffusion system of partial differential equations for the two speci
 es densities. First\, our result captures non-trivial interaction terms ne
 glected in the mean-field approach\, including a non-diagonal mobility mat
 rix 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 asymptot
 ic approximations in the low- and high-density limits\, we obtain a cubic 
 polynomial approximation of the self-diffusion coefficient that is numeric
 ally accurate for all densities. This cubic approximation agrees extremely
  well with numerical simulations. It also coincides with the Taylor expans
 ion up to the second-order in the density of the self-diffusion coefficien
 t obtained using a rigorous recursive method.
LOCATION:Seminar Room 2\, Newton Institute
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