 
Summary: Statistical properties and shell analysis in random cellular structures
T. Aste,* K. Y. Szeto, and W. Y. Tam
Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Received 24 April 1996
We investigate the statistical properties of twodimensional random cellular systems froths in terms 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 twodimensional 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. S1063651X 96 131111
PACS number s : 82.70. y, 68.90. g
I. INTRODUCTION
Materials consisting of cellular structures such as metal
grains and biological tissues are common in nature 1,2 .
Among these systems, soap froth is considered to be the
paradigm for the study of trivalent twodimensional cellular
structures. The structural analysis of twodimensional cellu
