Distribution of extension rates of growth fronts along Rosiwal's line in the growing two-dimensional cell model

A growing two-dimensional cell model is defined as follows. In an area there are Poisson-distributed nuclei. Arising from these nuclei, grains start to grow simultaneously. All grains grow circularly with the same constant radial growth rate . During the process of growth no new nuclei are formed. If two grains touch each other, growth is stopped there by formation of a straight grain boundary. We arbitrarily put a straight line, called Rosiwal's line, into the area. While grains are growing many straight grain boundaries and circular growth fronts cross Rosiwal's line. At a fixed fraction transformed, F(=crystallized area/total area), we consider the different extension rates of growth fronts (growing borders) along Rosiwal's line, v( v<), in the left (or right) direction. The number of grains that have a growth front along Rosiwal's line into the left (or right) direction depends on F. Although the number changes with variation of F, we obtained theoretically the surprising result that the distribution density of reduced extension rates V = v/ , w(V), does not depend on F, and is always V ^–2(V ²–1)^–1/2. In order to verify this result we found an experimental possibility to realize the growing two-dimensional cell model.