Simulation of spatial random dense structure and stereology

在生物组织或冶金介质中，实现了颗粒的随机致密结构状态。为了构建一种新的体视学，这些粒子的空间结构模型是必不可少的。基本上很难用理论框架来看待这类模型。但这一困难可以通过使用计算机模拟来克服。为此，有必要开发模拟方法。从以上角度来看，本研究项目主要发展了粒子的空间随机和随机结构的模拟方法。1993年，开发了新的计算机程序，以实现具有任意半径分布的粒子系统的三维随机密集结构。同时，对椭圆形或矩形等非球形颗粒的随机堆积进行了计算机模拟。在西班牙举行的国际研讨会上发表了部分结果。1994年，目标是为更逼真的粒子系统建立新的体视学。其次，主要针对非球形颗粒的空间致密结构进行了研究。首先，研究了一种从非球形物体取向的空间模式估计方向相互作用的统计方法。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最密集堆积的规律性结构--单胞p3堆积。研究结果准备发表在《国际期刊》上。最后，编制了椭圆和矩形系统的马尔可夫链蒙特卡罗模拟的计算机程序。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.