This week's seminars
Applied Mathematics Seminars: Chemical front propagation in cellular vortex flows: the role of large deviations
18 May 2018 14:00 in CM219
We discuss the propagation of chemical fronts arising in Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) type models in the presence of a steady cellular flow. In the long-time limit, a pulsating front is established. Its speed, on which we focus, can be obtained by solving an eigenvalue problem closely related to large-deviation theory. We employ asymptotic methods to solve this eigenvalue problem in the limit of small molecular diffusivity (large Peclet number, Pe) and arbitrary reaction rate (arbitrary Damkohler number, Da). We identify three regimes corresponding to the distinguished limits Da = O(1/Pe), Da = O (1/logPe) and Da = O(Pe) and, in each regime, obtain the front speed in terms of a different non-trivial function of the relevant combination of Pe and Da, determined by solving a (Pe-independent) one-dimensional problem: An ordinary differential equation in Regime I, an integral eigenvalue problem in Regime II, and an optimization problem in Regime III. Our results are contrasted against front speed values obtained from the so-called G equation: a level-set approximation that is commonly used when the front interface is sharp.
Joint work with J Vanneste (U. Edinburgh)
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