odellirlg of disordered cellular s
Tomaso Aste, N. Rivier · 1997
We model the structure of space-filling disordered cellular systems. These systems are cellular networks with minimum incidence numbers {D+ 1 edges incident on a vertex in D-dimension). In the literature such systems are known as froths since the soap froth is the archetype of these structures. We present a method where the structure of froths is analyzed as organized in concentric layers of cells around a given, arbitrary, central cell. A simple map gives, by recursion, the number of cells in each layer. The map has one parameter, gi’ven as a function of the average topological properties of the cells in the neighbouring layers. From the behuvzour of the nunaber of cells per layer with the topological distance, one obtaans the curvature of the space tiled by the froth. By using the map it is therefore possible to characterise the shape of the manifold tiled by thx froth in term of the topological arrangements of its tiles. In two dimensions, we propose a method to deduce the Gaussian curvature of surfaces from a set of sampled points. In three dimensions, we use the map to investigate the freedom in constructing disordered Euclidean cellular structures. Among the closed packed stvxtures, we find the average shape of the cells that maximize this freedom in filling space.