DISTRIBUTION OF EXTENSION RATES OF GROWTH FRONTS ALONG ROSIWALS LINE IN THE GROWING 2-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, grai ns start to grow simultaneously. All grains grow circularly with the s ame constant radial growth rate R. 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 cros s Rosiwal's line. At a fixed fraction transformed, F( = crystallized a rea/total area), we consider the different extension rates of growth f ronts (growing borders) along Rosiwal's line, v(R less-than-or-equal-t o v < infinity), in the left (or right) direction. The number of grain s that have a growth front along Rosiwal's line into the left (or righ t) direction depends on F Although the number changes with variation o f F, we obtained theoretically the surprising result that the distribu tion density of reduced extension rates V = v/R, w(V), does not depend on F, and is always V-2(V2 - 1)-1/2. In order to verify this result w e found an experimental possibility to realize the growing two-dimensi onal cell model.