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arXiv · 2201.05487

Applications of Grassmannian flows to coagulation systems

Anastasia Doikou·Simon J. A. Malham·Ioannis Stylianidis·Anke Wiese
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Abstract

We demonstrate how many classes of Smoluchowski-type coagulation models can be realised as multiplicative Grassmannian flows and are therefore linearisable, and thus integrable in this sense. First, we prove that a general Smoluchowski-type equation with a constant frequency kernel, that encompasses a large class of such models, is realisable as a multiplicative Grassmannian flow. Second, we establish that several other related constant kernel models can also be realised as such. These include: the Gallay--Mielke coarsening model; the Derrida--Retaux depinning transition model and a general mutliple merger coagulation model. Third, we show how the additive and multiplicative frequency kernel cases can be realised as rank-one analytic Grassmannian flows.

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Anastasia Doikou, Simon J. A. Malham, Ioannis Stylianidis, Anke Wiese. 2022-01-14. Applications of Grassmannian flows to coagulation systems. https://doi.org/10.1016/j.physd.2023.133771

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