Absorbing phase transitions and temporal intermittency in collisional aggregation-fragmentation models.

In aggregation, masses coalesce irreversibly to form a cluster, and in frag-

mentation, clusters break up into smaller ones. These processes occur in a

wide range of phenomena varying from tissue development in cell biology

to the formation of planetary rings. Our work is motivated by astro-

physical applications, in particular Saturn rings. A model describing such

systems considers binary collision reactions between masses, and upon

collision, the two clusters can either aggregate or fragment completely

(shatter) into the smallest constituent masses. At the mean-field level,

the time evolution of the cluster sizes is described by the deterministic

Smoluchowski equation.

We have studied the effects of stochasticity and finite total mass in these

models. In such a setting, the Smoluchowski equation does not give the

correct answer for the mass distribution. We therefore use Monte Carlo

simulation to study the system. The key question that we address is

whether such a system shows a phase transition, and if so, what is the

nature of the phases? There is indeed an active-absorbing phase transition

in the system; in the absorbed phase, all masses aggregate into a single

cluster. The active phase, depending upon the locality of the reaction

Kernel shows temporal intermittency. Details of these aspects will be

given during the talk.