Random packing and random tessellation in relation to the dimension of space
Random packing and random tessellation in relation to the dimension of space
复制标题
与空间维度相关的随机堆积和随机镶嵌
DOI：
10.1111/j.1365-2818.1988.tb04685.x
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发表时间：
1988
影响因子：
2
通讯作者：
M. Tanemura
中科院分区：
文献类型：
--
作者：
M. Tanemura
讨论了非重叠物体的随机填充和物体对空间的随机镶嵌问题，并讨论了它们与空间维数的关系。本文讨论的随机填充是随机“顺序”填充，随机镶嵌定义为泊松点过程的Voronoi镶嵌。利用已有的四维数据检验了Palásti关于立方体齐次填充的猜想；从二维和三维空间的蒙特卡罗模拟的结果也检验了球体的广义Palásti猜想。对于随机镶嵌，使用二维和三维空间的数据检验了jiang的猜想。研究结果表明，所有的猜想都是错误的。详细介绍了仿真方法。
The random packing of non‐overlapping objects and the random tessellation of space by objects are discussed with relation to the dimension of space. The random packing discussed here is random ‘sequential’ packing and random tessellation is defined in this paper as the Voronoi tessellation of Poisson point processes. The conjecture by Palásti is examined for homothetic packing of cubes by using the existing data up to four dimensions; the generalized Palásti conjecture for spheres is also examined from the results of Monte Carlo simulations for two‐ and three‐dimensional space. As for the random tessellation, Kiang's conjecture is examined using the data for two‐ and three‐dimensional space. The results of the study indicate that all of the conjectures are false. Some details are given of the simulation methods.