Fractional Brownian motion and anomalous diffusion in vibrated granular materials

We propose a new approach to the study of diffusion dynamics in vibrated granular systems. The dynamic of a granular material is mainly defined by dry friction interactions. This type of interaction is difficult to model for a large quantity of particles. In this work, we study a granular system by analyzing the angular position time series of an immersed torsion oscillator and of an identical, torsionally unconstrained probe. In order to interpret the behavior of our mechanical system, the experiments are compared to simulations. We generate simulated time series using a simple model of a confined random walk. The global properties of the recorded signals, both experimental and simulated, are extracted by applying fractal signal processing analysis. We show that the Hurst exponent of the time series can be employed to discriminate the dynamics of the system. We conclude that the immersed probe behaves as a Brownian particle that can switch between three distinct dynamical regimes, depending on the strength of the torsional constraint applied to it. If the probe is strongly constrained, its trail can be described with a fractal Brownian motion showing anomalous diffusion (subdiffusive behavior). As the strength of the constraint is reduced, the system 'unjams' in a ordinary Brownian motion (normal diffusion). Finally, as the constraints are further reduced, we observe the onset of convection phenomena, which in turn induce a superdiffusive behavior.