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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Macroscopic behaviour in a two-species exclusion process via the method of matched asymptotics

## Macroscopic behaviour in a two-species exclusion process via the method of matched asymptoticsAdd to your list(s) Download to your calendar using vCal - James Mason (University of Cambridge)
- Tuesday 15 March 2022, 14:50-15:35
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact nobody. FKT - Frontiers in kinetic theory: connecting microscopic to macroscopic scales - KineCon 2022 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. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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