title: Exchange-driven growth.
abstract: We 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) approximately exp(-x(2-nu)), 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) approximately x(-5). In regime III, the gel nucleates immediately and consumes the entire system. For finite systems, the gelation time vanishes logarithmically, T approximately [lnN](-(nu-2)), in the large system size limit N--> infinity. The theory is applied to coarsening in the infinite range Ising-Kawasaki model and in electrostatically driven granular layers.
authors.affiliation: Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. ebn@lanl.gov
authors.forename: E
authors.initials: E
authors.lastname: Ben-Naim
authors.forename: P L
authors.initials: PL
authors.lastname: Krapivsky