title: Experimental Validation of a Nonextensive Scaling Law in Confined Granular Media.
abstract: 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 α. We experimentally validate a particular case of the Tsallis-Bukman scaling law, α=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.
authors.affiliation: Université Grenoble Alpes, 3SR, F-38000 Grenoble, France and CNRS, 3SR, F-38000 Grenoble, France.
authors.forename: Gaël
authors.initials: G
authors.lastname: Combe
authors.affiliation: Université Grenoble Alpes, 3SR, F-38000 Grenoble, France and CNRS, 3SR, F-38000 Grenoble, France.
authors.forename: Vincent
authors.initials: V
authors.lastname: Richefeu
authors.affiliation: Université Grenoble Alpes, 3SR, F-38000 Grenoble, France and CNRS, 3SR, F-38000 Grenoble, France.
authors.forename: Marta
authors.initials: M
authors.lastname: Stasiak
authors.affiliation: Departamento de Física e Matemática, National Institute of Science and Technology for Complex Systems, Centro Federal de Educação Tecnológica de Minas Gerais - CEFET-MG, Avenida Amazonas 7675, 30510-000 Belo Horizonte-MG, Brazil.
authors.forename: Allbens P F
authors.initials: AP
authors.lastname: Atman