Exact asymptotic solution of an aggregation model with a bell-shaped distribution

Leyvraz, F.

doi:10.1103/physreve.103.022123

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2021

2022

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Cited by 4 publications

(2 citation statements)

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“…Specifically, the kernel solved in [6], K(k, l) = 1/k + 1/l has, as can be shown exactly, see [15], the following large time behaviour lim t→∞…”

Section: Summary Of Resultsmentioning

confidence: 70%

Remarks on a combinatorial solution of a stochastic aggregation model

Leyvraz¹

2022

Preprint

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“…Specifically, the kernel solved in [6], K(k, l) = 1/k + 1/l has, as can be shown exactly, see [15], the following large time behaviour lim t→∞…”

Section: Summary Of Resultsmentioning

confidence: 70%

Remarks on a combinatorial solution of a stochastic aggregation model

Leyvraz¹

2022

Preprint

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“…Further comment on that issue can be found in [26]. Nevertheless, classic approach is widely used and researched [18,19,21,22].…”

Section: Introductionmentioning

confidence: 99%

How initial condition impacts aggregation -- a systematic numerical study

Łepek¹

2021

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In a process of aggregation, a finite number of particles merge irreversibly to create growing clusters. In this work, impact of particular initial conditions: monodisperse, power-law, exponential, and inspired by condensation nuclei was tested against several aggregation processes: constant, additive, product, electrorheological, anti-social, Berry's, Brownian, shear, and gravitational kernels. Coagulating systems consisting of a thousand monomers were observed in the late time of the evolution, for the moment when only fifty clusters were left in the system. In this way, the impact of particular initial condition was revealed in relation to other initial conditions. Several similarities between different kernels were observed, among others, strong correspondence between the constant and the Brownian kernel was confirmed. In case of the product kernel, unexpected behaviour related to the condensation nuclei initial conditions was revealed and explained. According to the results, it is doubtful that a phase transition can be triggered by appropriate setting of initial condition.

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