RESUMO
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.
RESUMO
Advection of tracers is studied numerically in time-dependent, two-dimensional cellular flows and a time-independent, three-dimensional cellular flow field. Tracers in these flows follow trajectories that are either periodic or chaotic and mimic correlated Lévy flights. The probability density function of displacements for particles in the ordered regions of the flow follows a classical Gaussian dispersion process. The particle trajectories in the chaotic regions of the flow exhibit anomalous diffusion and the probability density function of displacements is well modeled by a time-fractional diffusion equation of order alpha. The overall process of particle dispersion is found to be controlled mainly by the chaotic regions within the flow field. From the perspective of Lagrangian dynamics our results indicate that the advection of particles in flow fields prone to exhibit chaotic advection is a combination of both classical, i.e., Gaussian, behavior and anomalous, i.e., non-Gaussian, diffusion.
