Post-gelation behavior of a spatial coagulation model
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 1128 | |
dc.contributor.author | Wagner, Wolfgang | |
dc.date.accessioned | 2016-12-03T02:45:30Z | |
dc.date.available | 2019-06-28T08:20:09Z | |
dc.date.issued | 2006 | |
dc.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, the formal extension of Smoluchowski's coagulation equation to the spatially inhomogeneous case has to be modified for a certain class of coagulation kernels. 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. | |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 0946-8633 | |
dc.identifier.uri | https://doi.org/10.34657/3009 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/3241 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.subject.ddc | 510 | |
dc.subject.other | Spatial coagulation model | eng |
dc.subject.other | post-gelation behavior | eng |
dc.subject.other | stochastic particle systems | eng |
dc.title | Post-gelation behavior of a spatial coagulation model | |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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