STATISTICAL PROPERTIES AND SHELL ANALYSIS IN RANDOM CELLULAR STRUCTURES

We investigate the statistical properties of two-dimensional random ce llular systems (froths) in terms of their shell structure. The froth i s analyzed as a system of concentric layers of cells around a given ce ntral cell. We derive exact analytical relations for the topological p roperties of the sets of cells belonging to these layers. Experimental observations of the shell structure of two-dimensional soap froth are made and compared with the results on two kinds of Voronoi constructi ons. It is found that there art specific differences between soap frot hs and purely geometrical constructions. In particular these systems d iffer in the topological charge of clusters as a function of shell num ber. In the asymptotic values of defect concentrations. and in the num ber of cells in a given layer. We derive approximate expressions with no free parameters which correctly explain these different behaviors.