Abstract
The multicomponent coagulation equation is a generalization of the Smoluchowski coagulation equation, where the size of a particle is described by a vector. Similar to the original Smoluchowski equation, the multicomponent coagulation equation exhibits gelation behavior when supplied with a multiplicative kernel. Additionally, a new type of behaviour called localization is observed due to the multivariate nature of the particle size distribution. Here we extend the branching process representation technique, which we introduced to study differential equations in our previous work, and apply it to find a concise probabilistic solution of the multicomponent coagulation equation supplied with monodisperse initial conditions. We also provide short proofs for the gelation time and characterisation the localization phenomenon.
| Original language | English |
|---|---|
| Article number | 91 |
| Number of pages | 15 |
| Journal | Journal of Statistical Physics |
| Volume | 191 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - 23 Jul 2024 |
Bibliographical note
Publisher Copyright:© The Author(s) 2024.
Funding
This publication is part of the project \u201CRandom graph representation of nonlinear evolution problems\u201D of the research programme Mathematics Cluster/NDNS+ which is financed by the Dutch Research Council (NWO). The authors thank Mike de Vries for his help with the proof of the Corollary . We also would like to thank the reviewers for their valuable comments, which improved the paper.
| Funders | Funder number |
|---|---|
| Nederlandse Organisatie voor Wetenschappelijk Onderzoek | |
| Dutch Research Council |
Keywords
- 60J80
- 82C05
- Branching processes
- Gelation
- Localization
- Multicomponent coagulation
- Multiplicative coalescence
- Smoluchowski coagulation equation