Post-gelation behavior of a spatial coagulation model
Wolfgang Wagner, Weierstrass Institute for Applied Analysis and Stochastics
Abstract
A coagulation model on a finite spatial grid is considered.
Particles of discrete masses jump randomly between sites
and, while located at the same site,
stick together according to some
coagulation kernel. The asymptotic behavior (for increasing
particle numbers) of this model is studied in the situation
when the coagulation kernel grows sufficiently fast so that the
phenomenon of gelation is observed.
Weak accumulation points of an appropriate sequence
of measure-valued processes
are characterized in terms of solutions of a nonlinear equation.
A natural description of the behavior of the gel is obtained
by using the one-point compactification of the size space.
Two aspects of the limiting equation are of special interest.
First, for a certain class of coagulation kernels,
this equation differs from a naive extension of
Smoluchowski's coagulation equation.
Second, due to spatial
inhomogeneity, an equation for the time evolution
of the gel mass density has to be added.
The jump rates are assumed to vanish with increasing particle
masses so that the gel is immobile. Two different
gel growth mechanisms (active and passive gel)
are found depending on the type of the coagulation kernel.
Full text: PDF | PostScript
Copyright for articles published in this journal is retained by the authors, with first publication rights granted to the journal. By virtue of their appearance in this open access journal, articles are free to use, with proper attribution, in educational and other non-commercial settings.
The authors of papers published in EJP/ECP retain the copyright. We ask for the permission to use the material in any form. We also require that the initial publication in EJP or ECP is acknowledged in any future publication of the same article.
Before a paper is published in the Electronic Journal of Probability or Electronic Communications in Probability we must receive a hard-copy of the copyright form. Please mail it to
Philippe Carmona
Laboratoire Jean Leray UMR 6629
Universite de Nantes,
2, Rue de la Houssinière BP 92208
F-44322 Nantes Cédex 03
France
You can also send it by FAX: (33|0) 2 51 12 59 12 to the attention of Philippe Carmona. You can even send a scanned jpeg or pdf of this copyright form to the managing editor ejpecpme@math.univ-nantes.fr. as an attached file.
If a paper has several authors, the corresponding author signs the copyright form on behalf of all the authors.