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arXiv 0806.4022cond-mat.stat-mechcond-mat.mtrl-sci
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颗粒堆积中的结构转变:统计力学和统计几何学研究

Structural transitions in granular packs: statistical mechanics and statistical geometry investigations

T. Aste, T. Di Matteo

摘要:

我们调查平等的球体包装从几个实验和大量不同的数值模拟产生。这些无序包装的结构组织的共同邻居的网络方面进行了研究。该几何分析揭示了在对应于所谓的随机松散堆积极限(RLP,$ρ\sim 0.555$)和随机紧密堆积极限(RCP,$ρ\sim 0.645$)的堆积分数(相对于总体积,由球体占据的体积分数,$ρ$)处发生的网络聚类的急剧变化。在这些包装分数,我们也观察到突然的变化,在波动的自由体积的一部分,每个球周围。我们分析了这种波动的统计力学的方法,我们表明,这些异常与急剧变化的广义natural变量,这是类似于这些非热系统的比热在热系统。

英文摘要:

We investigate equal spheres packings generated from several experiments and from a large number of different numerical simulations. The structural organization of these disordered packings is studied in terms of the network of common neighbours. This geometrical analysis reveals sharp changes in the network's clustering occurring at the packing fractions (fraction of volume occupied by the spheres respect to the total volume, $ρ$) corresponding to the so called Random Loose Packing limit (RLP, $ρ\sim 0.555$) and Random Close Packing limit (RCP, $ρ\sim 0.645$). At these packing fractions we also observe abrupt changes in the fluctuations of the portion of free volume around each sphere. We analyze such fluctuations by means of a statistical mechanics approach and we show that these anomalies are associated to sharp variations in a generalized thermodynamical variable which is the analogous for these a-thermal systems to the specific heat in thermal systems.

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