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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 $k^{a}$, whereas the collision and disintegration kernels are given by $\lambda k^{b}$ and $\mu k^{b}$, respectively, with $0\le a,b\le 1$ and positive factors $\lambda$ and $\mu$. We study the emergence of oscillations in the phase diagram $(\lambda,\mu)$ 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 $(\lambda,\mu)$. We evaluate analytically this domain 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 $\mu$, far smaller than $\lambda$.
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Dates et versions

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

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Domaine public

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  • HAL Id : hal-04084416 , version 2

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Jean-Yves Fortin, MooYoung Choi. Stability condition of the steady oscillations in aggregation models with shattering process and self-fragmentation.. 2023. ⟨hal-04084416v2⟩
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