Geometrical selection in growing needles

• Main Authors: Krapivsky, P. L, Nazarov, L. I, Tamm, M. V
• Format: Journal Article
• Language: English
• Published: 16-04-2019
• Subjects: Physics - Statistical Mechanics
• DOI: 10.48550/arxiv.1902.01964

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.