Diffusion in agitated frictional granular matter near the jamming transition

We study agitated frictional disks in two dimensions with the aim of developing a scaling theory for their diffusion over time. As a function of the area fraction ϕ and mean-square velocity fluctuations ⟨v2⟩ the mean-square displacement of the disks ⟨d2⟩ spans four to five orders of magnitude. The motion evolves from a subdiffusive form to a complex diffusive behavior at long times. The statistics of ⟨dn⟩ at all times are multiscaling, since the probability distribution function (PDF) of displacements has very broad wings. Even where a diffusion constant can be identified it is a complex function of ϕ and ⟨v2⟩. By identifying the relevant length and time scales and their interdependence one can rescale the data for the mean-square displacement and the PDF of displacements into collapsed scaling functions for all ϕ and ⟨v2⟩. These scaling functions provide a predictive tool, allowing one to infer from one set of measurements (at a given ϕ and ⟨v2⟩) what are the expected results at any value of ϕ and ⟨v2⟩ within the scaling range.