针叶生长中的几何选择
Geometrical selection in growing needles
摘要：
我们研究从一个平面基板的针的生长。我们关注的情况是，针突然开始从随机分布在线上的种子中生长出来。针的宽度被忽略，我们还假设（i）所有针的生长速率相同;（ii）每个针的生长方向是从相同的分布中随机选择的;（iii）每当针尖碰到另一根针的主体时，前一根针冻结，而后者继续生长。我们阐明了大的时间行为，采用精确的分析和玻尔兹曼方程的方法。我们还分析了当种子位于半线上时，在有限的间隔上的演化。还检查了从二维衬底生长的针。
英文摘要：
We investigate the growth of needles from a flat substrate. We focus on the situation when needles suddenly begin to grow from the seeds randomly distributed on the line. The width of needles is ignored and we additionally assume that (i) the growth rate is the same for all needles; (ii) the direction of the growth of each needle is randomly chosen from the same distribution; (iii) whenever the tip of a needle hits the body of another needle, the former needle freezes, while the latter continues to grow. We elucidate the large time behavior by employing an exact analysis and the Boltzmann equation approach. We also analyze the evolution when seeds are located on a half-line, on a finite interval. Needles growing from the two-dimensional substrate are also examined.
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。
