Data from: Measuring the configurational temperature of a binary disc packing

Jammed packings of granular materials differ from systems normally described by statistical mechanics in that they are athermal. In recent years a statistical mechanics of static granular media has emerged where the thermodynamic temperature is replaced by a configurational temperature X which describes how the number of mechanically stable configurations depends on the volume. Four different methods have been suggested to measure X. Three of them are computed from properties of the Voronoi volume distribution, the fourth takes into account the contact number and the global volume fraction. This paper answers two questions using experimental binary disc packings: First we test if the four methods to measure compactivity provide identical results when applied to the same dataset. We find that only two of the methods agree quantitatively. This implies that at least two of the four methods are wrong. Secondly, we test if X is indeed an intensive variable; this becomes true only for samples larger than roughly 200 particles. This result is shown to be due to recently measured correlations between the particle volumes [Zhao et al., Europhys. Lett., 2012, 97, 34004].

颗粒材料的堵塞堆积体与统计力学通常描述的体系存在本质区别，这类体系属于无热（athermal）体系。近年来，静态颗粒介质的统计力学研究逐渐兴起，其中热力学温度被构型温度（configurational temperature）X取代——该参数用于描述力学稳定构型的数量随体积的变化规律。目前已提出四种不同的X值测量方案：其中三种基于沃罗诺伊（Voronoi）体积分布的特征计算得到，第四种则综合考虑了接触数（contact number）与全局体积分数（global volume fraction）。本文基于二元圆盘堆积的实验数据解答了两个核心问题：其一，我们验证了四种测量紧度参数（compactivity）的方法在同一数据集上是否能得到一致结果。研究发现仅两种方法可实现定量吻合，这表明四种方案中至少存在两种错误的测量方法。其二，我们验证了构型温度X是否为强度量（intensive variable）；结果显示，仅当样品包含至少约200个颗粒时，X才满足强度量的定义。该现象源于近期被观测到的颗粒体积间的关联效应[Zhao et al., Europhys. Lett., 2012, 97, 34004]。