CORRELATIONS IN TOPOLOGICAL MODELS OF 2D-RANDOM CELLULAR STRUCTURES

General relations and constraints which must be satisfied by the topol ogical correlations in 2D space-filling random cellular structures are discussed and a topological short-range order coefficient is defined. Topological models of 2D structures are associated with planar tessel lations with topologically unstable sites which belong to z > 3 polygo ns. The stable configurations, called states, are obtained by replacin g every vertex by z - 3 added sides. The topological properties of the latter models are calculated exactly for a distribution of independen t and equiprobable states on the various sites and for any value of z. The case of the structures associated with tilings by triangles is th oroughly considered. The calculated correlations are compared with the correlations in alumina cuts and in random Voronoi froths. The variab ility of the topological properties of 2D random cellular structures i s discussed.