The silo discharge process is studied by molecular dynamics simulations. The development of the
velocity profile and the probability density function for the displacements in the horizontal and vertical
axis are obtained. The PDFs obtained at the beginning of the discharge reveal non-Gaussian statistics
and superdiffusive behaviors. When the stationary flow is developed, the PDFs at shorter temporal scales
are non-Gaussian too. For big orifices a well-defined transition between ballistic and diffusive regime is
observed. In the case of a small outlet orifice, no well-defined transition is observed. We use a nonlinear
diffusion equation introduced in the framework of non-extensive thermodynamics in order to describe the
movements of the grains. The solution of this equation gives a well-defined relationship (
= 2/(3 − q))
between the anomalous diffusion exponent
and the entropic parameter q introduced by the non-extensive
formalism to fit the PDF of the fluctuations
