Exchange Driven Growth

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dc.creatorBen-Naim, E.
dc.creatorKrapivsky, P. L.
dc.date2003-05-08
dc.date.accessioned2026-07-07T02:51:14Z
dc.date.available2026-07-07T02:51:14Z
dc.descriptionWe study a class of growth processes in which clusters evolve via exchange of particles. We show that depending on the rate of exchange there are three possibilities: I) Growth: Clusters grow indefinitely; II) Gelation: All mass is transformed into an infinite gel in a finite time; and III) Instant Gelation. In regimes I and II, the cluster size distribution attains a self-similar form. The large size tail of the scaling distribution is Phi(x) ~ exp(-x^{2-ν}), where nu is a homogeneity degree of the rate of exchange. At the borderline case nu=2, the distribution exhibits a generic algebraic tail, Phi(x)\sim x^{-5}. In regime III, the gel nucleates immediately and consumes the entire system. For finite systems, the gelation time vanishes logarithmically, T\sim [\ln N]^{-(ν-2)}, in the large system size limit N\to\infty. The theory is applied to coarsening in the infinite range Ising-Kawasaki model and in electrostatically driven granular layers.
dc.description8 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0305154
dc.identifierhttp://arxiv.org/abs/cond-mat/0305154
dc.identifierPhys. Rev. E 68, 031104 (2003)
dc.identifierdoi:10.1103/PhysRevE.68.031104
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/21376
dc.subjectStatistical Mechanics
dc.subjectSoft Condensed Matter
dc.titleExchange Driven Growth
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