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...颗粒材料的堵塞堆积体系与统计力学常规描述的体系存在本质差异：前者属于无热（athermal）体系。近年来，静态颗粒介质的统计力学框架逐步发展成熟，该框架将热力学温度替换为构型温度X（configurational temperature X），用于表征力学稳定构型的数量随体积的变化规律。目前已有四种用于测量该堆积活性（compactivity）的方法被提出：其中三种方法通过沃罗诺伊体积分布（Voronoi volume distribution）的相关特性计算得到，第四种方法则同时考虑了接触数（contact number）与整体体积分数（global volume fraction）。本文基于实验获取的二元圆盘堆积体（binary disc packings）数据集解答了两个核心问题：其一，我们验证了四种测量堆积活性（compactivity）的方法在应用于同一数据集时能否得到一致的结果；研究结果显示仅两种方法的定量结果相符，这表明四种方法中至少有两种存在谬误。其二，我们验证了构型温度X是否确为强度量（intensive variable）；该结论仅在样本……