Numerical simulation of a coarsening two-dimensional network

Abstract

Topological correlations in a coarsening two-dimensional soap froth or polycrystalline network are studied by computer simulation. With use of a continuum model, grain growth in very large systems of over ${10}^5$ grains can be simulated. The correlations found between the size or the number of vertices of adjacent grains are in accordance with semiempirical rules of metallurgy. The average grain size grows in proportion to the square root of time, as predicted by mean-field theory. This result, that correlation effects do not modify the growth exponent, is consistent with dynamical scaling and agrees with simulations done on a lattice.