Simulation of spatial random dense structure and stereology

在生物组织或冶金介质中，实现了颗粒的随机和致密结构的状态。为了建立一种新的体视学，这类粒子的空间结构模型是必不可少的。基本上很难在一个理论框架内处理这些模型。但这个困难可以通过计算机模拟来克服。为此，有必要发展模拟方法，从上述观点出发，本研究项目主要发展了粒子空间随机和密度结构的模拟方法，1993年开发了新的计算机程序，实现了具有任意半径分布的粒子系统的三维随机密度结构。在同一时期，计算机模拟的随机堆积的非球形颗粒，如椭圆形或矩形。在西班牙举行的国际研讨会上发表了部分成果。1994年，旨在为更现实的粒子系统构建新的体视学。然后，本文主要对非球形颗粒的空间致密结构进行了研究。首先，研究了从非球形物体的空间方向图估计方向相互作用的一种实用方法。这是在加拿大举行的国际会议上提出的。同时，从理论上研究了椭圆的密排堆积的规则结构，即胞元P3堆积。研究结果已准备在国际期刊上发表。最后，开发了一个计算机程序，用于椭圆和矩形系统的马尔可夫链蒙特卡罗模拟。这对于真实粒子数据的空间统计非常有用。

In the biological tissues or in the metallurgical mediums, a state of random and dense structure of particles is realized. In order to construct a new stereology, it is indispensable for the models of spatial structure of such particles. It is basically difficult to treat such models in a theoretical framework. But the difficulty could be overcome by the use of computer simulation. For that purpose, it is necessary to develop simulation methods.From the above point of view, in this research project, the investigation has mainly developed simulation methods of spatially random and dence structure of particles.In the year 1993, new computer programs were developed for realizing three-dimentional random dense structure of a system of particles having an aritrary distribution of radius. At the same period, computer simulations of random packing by non-spherical particles such as ellipses or rectangles were done. A part of the results was spoken at the International workshop which was held in Spain.In the year 1994, the construction of a new stereology for a system of more realistic particles was aimed. Then, the invesigations were concentrated mainly for the spatial dense structure of non-spherical particles. At first, a statisical procedure for estimating a directional interaction from a spatial pattern of orientations of non-spherical ojects was investigated. This was presented at the International Conference held in Canada. At the same time, the regular structure of densest packing of ellipses, celled p3 packing, was investigated theoretically. Its result was prepared for publication in the international journal. Finally, a computer program was developed for a Markov chain Monte Carlo simulation of systems of ellipses and rectangles. This is useful for the spatial statistics of realistic particle data.