Alladi Ramakrishnan Hall

Modelling aggregation and fragmentation phenomena using the Smoluchowski equation

Arghya Dutta

Institute of Mathematical Sciences

In nature, there are a number of physical phenomena whose dynamics are dominated by transport, aggregation and fragmentation. Examples include formation of rain drops, polymerization and the formation of the planetary rings. In this talk, I will present results from an analysis of a model with collision dependent fragmentation, based on the Smoluchowski equation. For a general class of collision kernels, I will derive the
scaling limits of the mass distribution using moment and singularity analysis of the generating functions, and exact solutions for special cases. We will identify a new regime (relevant for ballistic collision) where the exponents depend
non-trivially on the kernel. The results will be compared with the data obtained from the mass distribution of the particles constituting the Saturn rings.