First results on 3-D simulation grain growth using Laguerre diagrams

Laguerre diagrams are used as a geometric idealization of 3-dimensional polycrystals. These cell structures are entirely defined by a set of weighted sites. Each site is given an additional weight which affects the size of the associated cell. Models of growth can be constructed for this idealized polycrystal geometry by writing the motion equation in terms of the weighted sites alone. In computer simulation, the solution of non-linear differential system is approximated by piecewise linear motions. During a small interval of time §t, every site Si is moved to Si+§Si and the topological transformations induced by all these simultaneous linear motions are determined and performed in an appropiate manner. Primary simulation results are presented.