Effective Conductivity of Densely Packed Disks and Energy of Graphs

Wojciech Nawalaniec, Katarzyna Necka and Vladimir Mityushev
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Wojciech Nawalaniec: Faculty of Exact and Natural Sciences, Pedagogical University of Krakow, 30-084 Krakow, Poland
Katarzyna Necka: Faculty of Exact and Natural Sciences, Pedagogical University of Krakow, 30-084 Krakow, Poland
Vladimir Mityushev: Faculty of Exact and Natural Sciences, Pedagogical University of Krakow, 30-084 Krakow, Poland

Mathematics, 2020, vol. 8, issue 12, 1-12

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; energy of graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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