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摘要翻译：
随机介质的整体物理性质在渗流阈值处发生质的变化，孤立的团簇合并形成一个无限连通的组分。因此，对渗流阈值的准确了解是至关重要的。对于二维格子图，我们利用团簇尺寸分布的普遍标度形式，导出了临界逾渗模式的平均欧拉特性与阈值密度P_c$之间的关系。从这个关系中，我们推导出一个简单的规则来估计$P_c$，它是非常准确的。我们给出了一些证据，证明连续介质渗流和高维渗流的类似关系可能成立。
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英文标题：
《Topological estimation of percolation thresholds》
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作者：
Richard A. Neher, Klaus Mecke, and Herbert Wagner
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最新提交年份：
2008
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount importance. For two dimensional lattice graphs, we use the universal scaling form of the cluster size distributions to derive a relation between the mean Euler characteristic of the critical percolation patterns and the threshold density $p_c$. From this relation, we deduce a simple rule to estimate $p_c$, which is remarkably accurate. We present some evidence that similar relations might hold for continuum percolation and percolation in higher dimensions.
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PDF链接：
https://arxiv.org/pdf/708.325
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