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Effective Conductivity and Critical Properties of a Hexagonal Array of Superconducting Cylinders

In: Contributions in Mathematics and Engineering

Author

Listed:
  • Simon Gluzman

    (Ekayna Vihara
    Ryukoku University)

  • Vladimir Mityushev

    (Pedagogical University, Department of Computer Sciences and Computer Methods)

  • Wojciech Nawalaniec

    (Pedagogical University, Department of Computer Sciences and Computer Methods)

  • Galina Starushenko

    (Dnipropetrovs’k Regional Institute of State Management of National Academy of State Management at the President of Ukraine Gogolya 29)

Abstract

Effective conductivity of a 2D composite corresponding to the regular hexagonal arrangement of superconducting disks is expressed in the form of a long series in the volume fraction of ideally conducting disks. According to our calculations based on various resummation techniques, both the threshold and critical index are obtained in good agreement with expected values. The critical amplitude is in the interval (5. 14, 5. 24) that is close to the theoretical estimation 5. 18. The next-order (constant) term in the high-concentration regime is calculated for the first time, and the best estimate is equal to − 6. 229. The final formula is derived for the effective conductivity for arbitrary volume fraction.

Suggested Citation

  • Simon Gluzman & Vladimir Mityushev & Wojciech Nawalaniec & Galina Starushenko, 2016. "Effective Conductivity and Critical Properties of a Hexagonal Array of Superconducting Cylinders," Springer Books, in: Panos M. Pardalos & Themistocles M. Rassias (ed.), Contributions in Mathematics and Engineering, pages 255-297, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-31317-7_13
    DOI: 10.1007/978-3-319-31317-7_13
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