title: Genuine non-self-averaging and ultraslow convergence in gelation.
abstract: In irreversible aggregation processes droplets or polymers of microscopic size successively coalesce until a large cluster of macroscopic scale forms. This gelation transition is widely believed to be self-averaging, meaning that the order parameter (the relative size of the largest connected cluster) attains well-defined values upon ensemble averaging with no sample-to-sample fluctuations in the thermodynamic limit. Here, we report on anomalous gelation transition types. Depending on the growth rate of the largest clusters, the gelation transition can show very diverse patterns as a function of the control parameter, which includes multiple stochastic discontinuous transitions, genuine non-self-averaging and ultraslow convergence of the transition point. Our framework may be helpful in understanding and controlling gelation.
authors.affiliation: Center for Complex Systems Studies and CTP, Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.
authors.forename: Y S
authors.initials: YS
authors.lastname: Cho
authors.affiliation: Max Planck Institute for Dynamics and Self-Organization (MPI DS) Göttingen, Am Faßberg 17, 37077 Germany.
authors.forename: M G
authors.initials: MG
authors.lastname: Mazza
authors.affiliation: Center for Complex Systems Studies and CTP, Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.
authors.forename: B
authors.initials: B
authors.lastname: Kahng
authors.affiliation: Center for Complex Systems Studies and CTP, Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.|Max Planck Institute for Dynamics and Self-Organization (MPI DS) Göttingen, Am Faßberg 17, 37077 Germany.|Computational Physics, IfB, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland.
authors.forename: J
authors.initials: J
authors.lastname: Nagler