Fractional diffusion model for force distribution in static granular media

We present the results of a numerical and an experimental investigation of the probability distribution of normal contact forces in static packs of particles with two different hardnesses. Force distributions are computed and compared with existing models and experimental data. It is found that the probability distribution function of normal contact forces P(f) is well described by a semiempirical model derived from a fractional diffusion equation. This model reproduces most of the features common to force distributions observed in experimental and numerical studies including the finite value for P(f) as the forces tend to zero. The results indicate that the fractional model fits well both the numerical and experimental data over a wide range of particle deformations in contrast to the existing models. These results provide an insight into the physics of granular media and complement previous findings.