Abstract A theory is formulated that relates the rates of the three topological events to the evolution of the face distribution function. Implementation of the theory requires introduction of the concept of participation probabilities which reflect the face distribution of those grains that are incident upon the events. The prediction of the evolving face distribution is tested with a 3-D Monte Carlo simulation of the grain growth process that permits evaluation of the topological event rates by face class and the participation probabilities. The theory also develops a relation between the average number of faces per grain and the topological rates as well as the asymptotic distribution function; these results are also tested using the simulation. The transient period prior to normal grain growth is explained in terms of the evolution of the event rates that control the creation of small grains and evolve the face distribution to its final shape.

中文翻译：

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拓扑事件率和晶粒生长过程中晶粒面分布的演变

摘要 提出了一种理论，该理论将三种拓扑事件的速率与人脸分布函数的演化联系起来。该理论的实施需要引入参与概率的概念，该概念反映了事件中发生的那些颗粒的面分布。不断变化的人脸分布的预测通过晶粒生长过程的 3-D 蒙特卡罗模拟进行测试，该模拟允许按人脸类别和参与概率评估拓扑事件率。该理论还建立了每个晶粒的平均面数与拓扑率以及渐近分布函数之间的关系；这些结果也使用模拟进行了测试。