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Post-gelation behavior of a spatial coagulation model


 
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1. Title Title of document Post-gelation behavior of a spatial coagulation model
 
2. Creator Author's name, affiliation, country Wolfgang Wagner; Weierstrass Institute for Applied Analysis and Stochastics
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Spatial coagulation model; post-gelation behavior; stochastic particle systems
 
3. Subject Subject classification 60K40
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2006-10-18
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/359
 
10. Identifier Digital Object Identifier 10.1214/EJP.v11-359
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 11
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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