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Effective Conductivity of Densely Packed Disks and Energy of Graphs

Author

Listed:
  • 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)

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.

Suggested Citation

  • Wojciech Nawalaniec & Katarzyna Necka & Vladimir Mityushev, 2020. "Effective Conductivity of Densely Packed Disks and Energy of Graphs," Mathematics, MDPI, vol. 8(12), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2161-:d:456759
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