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We analyze systems of clusters and interacting upon colliding---a collisionbetween two clusters may lead to merging or fragmentation---and we alsoinvestigate the influence of additional spontaneous fragmentation events. Weconsider both closed systems in which the total mass remains constant and opensystems driven by a source of small-mass clusters. In closed systems, the sizedistribution of aggregates approaches a steady state. For these systems therelaxation time and the steady state distribution are determined mostly byspontaneous fragmentation while collisional fragmentation plays a minor role.For open systems, in contrast, the collisional fragmentation dominates. In thiscase, the system relaxes to a quasi-stationary state where cluster densitieslinearly grow with time, while the functional form of the cluster sizedistribution persists and coincides with the steady state size distribution ofa system which has the same aggregation and fragmentation rates and onlycollisional fragmentation.

Kinetic regimes in aggregating systems with spontaneous and collisional fragmentation