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J Math Biol. 2017 Jan;74(1-2):259-287. doi: 10.1007/s00285-016-1026-0. Epub 2016 May 25.

A numerical scheme for the early steps of nucleation-aggregation models.

Author information

1
Center for Research in Scientific Computation (CRSC), North Carolina State University, Raleigh, NC, USA.
2
Sorbonne Universit├ęs, Inria, UPMC Univ Paris 06, Lab. J.L. Lions UMR CNRS, 75005, Paris, France. marie.doumic@inria.fr.
3
Sorbonne Universit├ęs, Inria, UPMC Univ Paris 06, Lab. J.L. Lions UMR CNRS, 75005, Paris, France.

Abstract

In the formation of large clusters out of small particles, the initializing step is called the nucleation, and consists in the spontaneous reaction of agents which aggregate into small and stable polymers called nuclei. After this early step, the polymers are involved in a number of reactions such as polymerization, fragmentation and coalescence. Since there may be several orders of magnitude between the size of a particle and the size of an aggregate, building efficient numerical schemes to capture accurately the kinetics of the reaction is a delicate step of key importance. In this article, we propose a conservative scheme, based on finite volume methods on an adaptive grid, which is capable of simulating well the early steps of the reaction as well as the later chain reactions.

KEYWORDS:

Adaptive grid; Aggregation-fragmentation models; Finite volume schemes; Polymerization

PMID:
27225430
DOI:
10.1007/s00285-016-1026-0
[Indexed for MEDLINE]

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