Journal of Mathematical Biology

, Volume 74, Issue 1–2, pp 259–287 | Cite as

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

  • Harvey Thomas Banks
  • Marie DoumicEmail author
  • Carola Kruse


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.


Polymerization Aggregation-fragmentation models Finite volume schemes Adaptive grid 

Mathematics Subject Classification

65N08 35L02 35Q92 34K28 34E05 



This research was supported in part by the Air Force Office of Scientific Research under Grant Number AFOSR FA9550-12-1-0188.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Harvey Thomas Banks
    • 1
  • Marie Doumic
    • 2
    Email author
  • Carola Kruse
    • 2
  1. 1.Center for Research in Scientific Computation (CRSC)North Carolina State UniversityRaleighUSA
  2. 2.Sorbonne Universités, Inria, UPMC Univ Paris 06, Lab. J.L. Lions UMR CNRSParisFrance

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