VORONOI FOAMS

The Voronoi partition is generalized introducing a site-dependent mult iplicative constant in the definition of distance. This allows the des cription of foams because the inter-faces are now circle arcs (in two dimensions) instead of straight lines as in usual Voronoi partitions. A property of this construction is that the centers of the three circl e arcs converging to a vertex are aligned. We show that this property is also satisfied in an equilibrated foam. The equilibrium conditions (under the fast dynamics) fix the values of the a(i)'s in terms of the distances among points. We find that not all equilibrated foams can b e described with this construction, but only a subset of them.