泊松几何的尺寸效应和渗流性质
Finite-size effects and percolation properties of Poisson geometries
摘要：
空间的随机镶嵌代表了一类异质介质的原型模型，这在物理学、工程学和生命科学中的几个应用中是核心。本文利用蒙特卡罗模拟研究了$d$维各向同性Poisson几何的统计性质，特别是对$d=3$维Poisson几何的统计性质进行了研究。我们首先分析这些随机几何形状的关键特征的行为作为维度$d$和域的线性大小$L$的函数。然后，我们考虑泊松二元混合物的情况下，多面体被分配两个“标签”与互补的概率。对于这后一类的随机几何形状，我们数值表征的逾渗阈值，集群的强度和平均集群大小。
英文摘要：
Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering and life sciences. In this work, we investigate the statistical properties of $d$-dimensional isotropic Poisson geometries by resorting to Monte Carlo simulation, with special emphasis on the case $d=3$. We first analyse the behaviour of the key features of these stochastic geometries as a function of the dimension $d$ and the linear size $L$ of the domain. Then, we consider the case of Poisson binary mixtures, where the polyhedra are assigned two `labels' with complementary probabilities. For this latter class of random geometries, we numerically characterize the percolation threshold, the strength of the percolating cluster and the average cluster size.
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