A mathematical stochastic model for the particles diffusion in atmosphere

A mathematical model for the analysis of the random diffusion and dispersion of solid particles with arbitrary shape in a steady state flow defined is here proposed. In particular a mathematical model for the drag coefficient C_D is defined including a scalar random parameter suitable to describe the fluctuations of the physical conditions of the gas surface system. The equation of the dynamics of the particles, which is, in the proposed model, a random non-linear differential equation is qualitatively discussed and some quasi-analytical solutions are obtained with the perturbations techniques. Some numerical experiments visualize the gap between the results obtained by the proposed model and the ones obtained by the corresponding deterministic model.