Exchange-driven growth.

نویسندگان

  • E Ben-Naim
  • P L Krapivsky
چکیده

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.

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عنوان ژورنال:
  • Physical review. E, Statistical, nonlinear, and soft matter physics

دوره 68 3 Pt 1  شماره 

صفحات  -

تاریخ انتشار 2003