Abstract

A general theory is developed for the evolution of the cell order (CO) distribution in planar granular systems. Dynamic equations are constructed and solved in closed form for several examples: systems under compression; dilation of very dense systems; and the general approach to steady state. We find that all the steady states are stable and that they satisfy a detailed balance-like condition when the CO\(\,\le 6\). Illustrative numerical solutions of the evolution are shown. Our theoretical results are validated against an extensive simulation of a sheared system. The formalism can be readily extended to other structural characteristics, paving the way to a general theory of structural organisation of granular systems.

Graphic abstract

中文翻译：

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颗粒系统的结构演化：理论

摘要

针对平面颗粒系统中细胞序（CO）分布的演化，发展了一个通用理论。对于几个示例，以封闭形式构造和求解动力学方程：压缩系统 非常密集的系统的扩张；以及达到稳态的一般方法。我们发现，当CO \（\，\ le 6 \）时，所有稳态都是稳定的，并且满足详细的类似平衡的条件。显示了演化的说明性数值解。我们的理论结果通过对剪切系统的广泛仿真得到了验证。形式主义可以很容易地扩展到其他结构特征，从而为粒状系统的结构组织的一般理论铺平了道路。

图形摘要