Random multiple-fragmentation and flow of particles on a surface

We investigate stochastic fragmentation processes for particles with spatial position. The mathematical problem models the time evolution of a system of particles which move on an Euclidean surface driven by a given force (e.g., gravitational, fluid interaction, repulsion/attraction), and split in fragments with smaller masses and velocities. We establish a multiple-fragmentation process and we solve the corresponding stochastic integro-differential equation. Finally, we present several numerical simulations of such processes.