Applications of Grassmannian flows to coagulation systems
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.
Keywords
Cite
@article{arxiv.2201.05487,
title = {Applications of Grassmannian flows to coagulation systems},
author = {Anastasia Doikou and Simon J. A. Malham and Ioannis Stylianidis and Anke Wiese},
journal= {arXiv preprint arXiv:2201.05487},
year = {2023}
}
Comments
16 pages. This is now a shorter, more focused, version of the previous manuscript. Some new material has been added in the final main section. arXiv admin note: substantial text overlap with arXiv:1905.05035