Ferraro M, Zaninetti L
Dipartimento di Fisica Sperimentale and CNISM, via P. Giuria 1, I-10125 Turin, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Oct;84(4 Pt 1):041107. doi: 10.1103/PhysRevE.84.041107. Epub 2011 Oct 7.
In this paper, we investigate relationships between the volumes of cells of three-dimensional Voronoi tessellations and the lengths and areas of sections obtained by intersecting the tessellation with a randomly oriented plane. Here, in order to obtain analytical results, Voronoi cells are approximated to spheres. First, the probability density function for the lengths of the radii of the sections is derived and it is shown that it is related to the Meijer G function; its properties are discussed and comparisons are made with the numerical results. Next, the probability density function for the areas of cross sections is computed and compared with the results of numerical simulations.
在本文中，我们研究了三维Voronoi镶嵌的细胞体积与通过将镶嵌与随机定向平面相交而获得的截面长度和面积之间的关系。在这里，为了获得解析结果，将Voronoi细胞近似为球体。首先，推导了截面半径长度的概率密度函数，并表明它与梅杰G函数有关；讨论了其性质，并与数值结果进行了比较。接下来，计算了横截面面积的概率密度函数，并与数值模拟结果进行了比较。
