Stability condition of the steady oscillations in aggregation models with shattering process and self-fragmentation. - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Stability condition of the steady oscillations in aggregation models with shattering process and self-fragmentation.

Résumé

We consider a system of clusters of various sizes or masses, subject to aggregation and fragmentation by collision with monomers or by self-disintegration. The aggregation rate for the cluster of size (or mass) k is given by a kernel proportional to k a with a ≥ 0. The collision rate and the disintegration rate are given by λk b and µk b , respectively, with 0 ≤ a, b ≤ 1 and positive factors λ and µ. We study the emergence of oscillations in the phase diagram (λ, µ) for two models: (a, b) = (1, 0) and (1, 1). It is shown that the monomer population satisfies a class of integral equations possessing oscillatory solutions in a finite domain in the plane (λ, µ). We evaluate analytically this domain in a precise way and give an estimate of the oscillation frequency. In particular, these oscillations are found to occur generally for small but nonzero values of the parameter µ, far smaller than λ.
Fichier principal
Vignette du fichier
preprint_bis.pdf (3.36 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Licence : Domaine public

Dates et versions

hal-04084416 , version 1 (28-04-2023)
hal-04084416 , version 2 (01-05-2023)
hal-04084416 , version 3 (31-08-2023)

Licence

Domaine public

Identifiants

  • HAL Id : hal-04084416 , version 1

Citer

Jean-Yves Fortin, MooYoung Choi. Stability condition of the steady oscillations in aggregation models with shattering process and self-fragmentation.. 2023. ⟨hal-04084416v1⟩
40 Consultations
9 Téléchargements

Partager

Gmail Facebook X LinkedIn More