The percolation model is an effective tool to solve the problem of fluid flow in the pores; the situation of outsiders crossing the crowd is similar. This paper verifies the obvious percolation phenomenon in the randomly distributed crowd by [Formula: see text] simulation and reveals several characteristics and laws of the crowd percolation phenomena. Studies have shown that sites with different spatial dimensions have different densities of crowd percolation: when the actual density of the crowd is greater than the critical density of the crowd percolation, the outsider is difficult to pass through the crowd; otherwise, the outsider can pass through the crowd easily. Therefore, the critical density of crowd percolation can be one of the indicators of crowd management in public areas, which will provide important guidance for the design of public areas, site selection of public activities and crowd management.

中文翻译：

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公共场所人群渗流临界密度研究

渗流模型是解决孔隙中流体流动问题的有效工具；外人穿越人群的情况也类似。本文通过[公式：见正文]仿真验证了随机分布人群中明显的渗流现象，揭示了人群渗流现象的几个特征和规律。研究表明，不同空间维度的场地，人群渗透密度不同：当实际人群密度大于人群渗透临界密度时，外来者难以通过人群；否则，外人很容易穿过人群。因此，人群渗透临界密度可以作为公共区域人群管理的指标之一，