Applications of Grassmannian flows to coagulation equations

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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.
Original languageEnglish
Article number133771
JournalPhysica D: Nonlinear Phenomena
Volume451
Early online date1 May 2023
DOIs
Publication statusPublished - Sept 2023

Keywords

  • Faà di Bruno algebra
  • Grassmannian flows
  • Smoluchowski coagulation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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