#### Alladi Ramakrishnan Hall

#### Effects of Stochasticity and non-locality on a model of aggregation-fragmentation for Saturn rings

#### Bijoy Daga

##### IMSc

*Saturn rings are composed of water-ice particles and traces of rocky materials whose sizes may vary from micro meters to a few meters. A model that describes the observed size distribution considers aggregation and*

fragmentation of ring particles upon collision and the distribution can be calculated analytically by solving the steady state Smoluchowski equation. In writing down the deterministic Smoluchowski equation, it is assumed that the total mass is infinite. We try to understand the behavior of the system when the total mass is finite and the effects of Stochasticity becomes important. Further, it has been observed that the steady state in these systems becomes unstable and shows oscillations for non-local reaction Kernels. We will also discuss the role of non-locality for the case of finite total mass when Stochasticity becomes relevant and see whether oscillations would survive or not.

Done