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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2023

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

MooYoung Choi
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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 $\mu k^{a}$, 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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Paternité - Pas d'utilisation commerciale

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Jean-Yves Fortin, MooYoung Choi. Stability condition of the steady oscillations in aggregation models with shattering process and self-fragmentation.. Journal of Physics A: Mathematical and Theoretical, 2023, 56, pp.385004. ⟨10.1088/1751-8121/acf3b9⟩. ⟨hal-04084416v3⟩
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