Combe Gaël, Richefeu Vincent, Stasiak Marta, Atman Allbens P F
Université Grenoble Alpes, 3SR, F-38000 Grenoble, France and CNRS, 3SR, F-38000 Grenoble, France.
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.
Phys Rev Lett. 2015 Dec 4;115(23):238301. doi: 10.1103/PhysRevLett.115.238301. Epub 2015 Dec 1.
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.
在本信函中，我们探讨了全准静态平面剪切实验中颗粒位移的统计涨落与相应的反常扩散指数α之间的关系。我们通过实验验证了Tsallis-Bukman标度律的一个特殊情况，即α = 2/(3 - q)，其中q是通过用q-高斯分布拟合位移涨落的概率密度函数（PDF）得到的，并且扩散指数是在实验过程中独立测量的。应用一种原创技术，我们能够揭示出随着用于计算颗粒位移的应变窗口长度的变化，从反常扩散 regime 到布朗行为的转变。拟合曲线与大量实验数据的出色吻合表明，随着应变窗口长度的减小，涨落PDF明显变宽，并且扩散指数的值增加——反常扩散。无论测量中考虑的应变窗口大小如何，我们都表明Tsallis-Bukman标度律仍然有效，这是该关系在不同扩散 regime 下对于经典系统的首次实验验证。我们还注意到空间相关性与流体中的湍流有显著相似之处，这是一个有希望的迹象，表明这种类型的分析可用于探索受限颗粒材料中宏观摩擦的起源。
