Effective Conductivity of Densely Packed Disks and Energy of Graphs

Abstract

The theory of structural approximations is extended to two-dimensional double periodic structures and applied to determination of the effective conductivity of densely packed disks. Statistical simulations of non-overlapping disks with the different degrees of clusterization are considered. The obtained results shows that the distribution of inclusions in a composite, as an amount of geometrical information, remains in the discrete corresponding Voronoi tessellation, hence, precisely determines the effective conductivity for random composites.

Keywords

• random composite
• effective conductivity
• non-overlapping disks
• structural approximation
• discrete network
• voronoi tessellation