Interdependence of the volume and stress ensembles and equipartition in statistical mechanics of granular systems.
Interdependence of the volume and stress ensembles and equipartition in statistical mechanics of granular systems.
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DOI：
10.1103/physrevlett.109.238001
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发表时间：
2012-04
影响因子：
8.6
通讯作者：
R. Blumenfeld;Joe F. Jordan;S. Edwards
中科院分区：
文献类型：
--
作者：
R. Blumenfeld;Joe F. Jordan;S. Edwards
我们讨论了颗粒物质的统计力学，并得出了几个有意义的结果。首先，我们证明，与通常的看法相反，音量和应力集合是相互依赖的，这就需要两者都使用。我们使用组合系综来显式计算二维系统的结构量和应力相关量的期望值。我们由此证明，结构性质可能取决于角度张量，而基于应力的量可能取决于压实度。这对以前对静态颗粒系统的统计力学分析和期望值的相关推导提出了质疑。其次，我们建立了一个耐人寻味的均分原理--总体积在结构自由度和与应力相关的自由度之间平均分配。第三，我们推导出了一个紧凑性的表达式，它使得从宏观测量中量化它成为可能。
We discuss the statistical mechanics of granular matter and derive several significant results. First, we show that, contrary to common belief, the volume and stress ensembles are interdependent, necessitating the use of both. We use the combined ensemble to calculate explicitly expectation values of structural and stress-related quantities for two-dimensional systems. We thence demonstrate that structural properties may depend on the angoricity tensor and that stress-based quantities may depend on the compactivity. This calls into question previous statistical mechanical analyses of static granular systems and related derivations of expectation values. Second, we establish the existence of an intriguing equipartition principle-the total volume is shared equally amongst both structural and stress-related degrees of freedom. Third, we derive an expression for the compactivity that makes it possible to quantify it from macroscopic measurements.