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) ~ 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.

8 pages, 3 figures

References in corpus (6)

• Theory of Phase Ordering Kinetics
• Wealth Distributions in Models of Capital Exchange
• Electrostatically-Driven Granular Media: Phase Transitions and Coarsening
• Coarsening in the q-State Potts Model and the Ising Model with Globally Conserved Magnetization
• Scaling Theory for Migration-Driven Aggregate Growth
• Stochastic Coagulation and the Timescale for Runaway Growth

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