  We investigate the statistical properties of two dimensional random cellular
systems (froths) in term of their shell structure. The froth is analyzed as a
system of concentric layers of cells around a given central cell. We derive
exact analytical relations for the topological properties 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 constructions. It is found that there are specific differences
between soap froths and purely geometrical constructions. In particular these
systems differ in the topological charge of clusters as a function of shell
number, in the asymptotic values of defect concentrations, and in the number of
cells in a given layer. We derive approximate expressions with no free
parameters which correctly explain these different behaviors.

Disordered Systems and Neural Networks