标题： 两个有限线段的lilypond系统 显示英文标题

标题： Two lilypond systems of finite line-segments

摘要： 本文讨论了两种通过百合花协议构建的非重叠有限线段模型，在平面上给定的点阵上进行操作，这些点与方向相关联。 在时间 0，每条线段以单位速率在其中心沿给定方向增长；在模型 1 中，当其一端碰到另一条线段时，线段的增长停止；而在模型 2 中，当其一端碰到另一条线段，或者被其他线段的生长端碰到时，线段的增长停止。 本文证明了这些过程是定义良好的，并给出了计算线段长度的构造性算法。 此外，它指定了存在随机版本（即基于点过程的模型）的假设。 随后，它处理了模型 1 中是否存在渗透的问题。 本文最后包含一个包含多个猜想和最终备注的章节。 显示英文摘要

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.