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

Simon Gluzman; Vladimir Mityushev; Wojciech Nawalaniec; Galina Starushenko

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

Statistical Mechanics 2015-08-21 v1

Authors: Simon Gluzman , Vladimir Mityushev , Wojciech Nawalaniec , Galina Starushenko

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 re-summation 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 $(-6.229)$ . Final formula is derived for the effective conductivity for arbitrary volume fraction.

Keywords

effective conductivity superconducting cylinders hexagonal array critical properties volume fraction

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@article{arxiv.1508.05068,
  title  = {Effective Conductivity and Critical Properties of a Hexagonal Array of Superconducting Cylinders},
  author = {Simon Gluzman and Vladimir Mityushev and Wojciech Nawalaniec and Galina Starushenko},
  journal= {arXiv preprint arXiv:1508.05068},
  year   = {2015}
}

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

Abstract

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