In this Letter, we address the relationship between the statistical fluctuations of grain displacements for a full quasistatic plane shear experiment, and the corresponding anomalous diffusion exponent $\alpha$. We experimentally validate a particular case of the Tsallis-Bukman scaling law, $\alpha =2/(3-q)$, where $q$ is obtained by fitting the probability density function (PDF) of the displacement fluctuations with a $q$-Gaussian distribution, and the diffusion exponent is measured independently during the experiment. Applying an original technique, we are able to evince a transition from an anomalous diffusion regime to a Brownian behavior as a function of the length of the strain window used to calculate the displacements of the grains. The outstanding conformity of fitting curves to a massive amount of experimental data shows a clear broadening of the fluctuation PDFs as the length of the strain window decreases, and an increment in the value of the diffusion exponent—anomalous diffusion. Regardless of the size of the strain window considered in the measurements, we show that the Tsallis-Bukman scaling law remains valid, which is the first experimental verification of this relationship for a classical system at different diffusion regimes. We also note that the spatial correlations show marked similarities to the turbulence in fluids, a promising indication that this type of analysis can be used to explore the origins of the macroscopic friction in confined granular materials.

It is demonstrated, by numerical simulations of a 2D assembly of polydisperse disks, that there exists a range (plateau) of coarse-graining scales for which the stress tensor field in a granular solid is nearly resolution independent, thereby enabling an “objective” definition of this field. Expectedly, it is not the mere size of the system but the (related) magnitudes of the gradients that determine the widths of the plateaus. Ensemble averaging (even over “small” ensembles) extends the widths of the plateaus to subparticle scales. The fluctuations within the ensemble are studied as well. Both the response to homogeneous forcing and to an external compressive localized load (and gravity) are studied. Implications to small solid systems and constitutive relations are briefly discussed.

COVID-19 pandemic is an immediate major public health concern. The search for the understanding of the disease spreading made scientists around the world turn their attention to epidemiological studies. An interesting approach in epidemiological modeling nowadays is to use agent-based models, which allow to consider a heterogeneous population and to evaluate the role of superspreaders in this population. In this work, we implemented an agent-based model using probabilistic cellular automata to simulate SIR (Susceptible-Infected-Recovered) dynamics using COVID-19 infection parameters. Differently to the usual studies, we did not define the superspreaders individuals a priori, we only left the agents to execute a random walk along the sites. When two or more agents share the same site, there is a probability to spread the infection if one of them is infected. To evaluate the spreading, we built the transmission network and measured the degree distribution, betweenness, and closeness centrality. The results displayed for different levels of mobility restriction show that the degree reduces as the mobility reduces, but there is an increase of betweenness and closeness for some network nodes. We identified the superspreaders at the end of the simulation, showing the emerging behavior of the model since these individuals were not initially defined. Simulations also showed that the superspreaders are responsible for most of the infection propagation and the impact of personal protective equipment in the spreading of the infection. We believe that this study can bring important insights for the analysis of the disease dynamics and the role of superspreaders, contributing to the understanding of how to manage mobility during a highly infectious pandemic as COVID-19.