有限线段的两个Lilypond系
Two lilypond systems of finite line-segments
摘要：
本文讨论了两个模型的非重叠有限线段通过lilypond协议，在这里操作的一个给定的数组中的点的平面上，与相关的方向。在时间0，每个线段开始在给定方向上围绕其中心以单位速率增长;在模型1下，每个线段在其一端撞击另一条线时停止增长，而在模型2下，当其一端撞击另一条线时，它的增长停止，或者当它被其他线的增长端撞击时。该文件表明，这些程序是定义良好的，并给出建设性的算法来计算段的长度。此外，它指定的假设下，随机版本，即基于点过程的模型，存在。之后，它涉及的问题，是否有渗流模型1。文件最后一节载有若干说明和最后评论。
英文摘要：
The paper discusses two models for non-overlapping finite line-segments constructed via the lilypond protocol, operating here on a given array of points in the plane with which are associated directions. At time 0, each line-segment starts growing at unit rate around its center in the given direction; each line-segment, under Model 1, ceases growth when one of its ends hits another line, while under Model 2, its growth ceases either when one of its ends hits another line, or when it is hit by the growing end of some other line. The paper shows that these procedures are well-defined and gives constructive algorithms to compute the lengths of the segments. Moreover it specifies assumptions under which stochastic versions, i.e. models based on point processes, exist. Afterwards it deals with the question as to whether there is percolation in Model 1. The paper concludes with a section containing several conjectures and final remarks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
