ИСТИНА

I will describe a toy model describing growth of needle crystals from a flat substrate, starting simultaneously from the seeds randomly distributed on a line/plane. 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. Large time behavior of the system will be discussed by employing an exact analysis and the Boltzmann equation approach for the cases of needles distributed on a line, half-line, finite interval, and a plane.