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

Simon Gluzman (), Vladimir Mityushev (), Wojciech Nawalaniec () and Galina Starushenko ()
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Simon Gluzman: Ekayna Vihara
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

A chapter in Contributions in Mathematics and Engineering, 2016, pp 255-297 from Springer

Abstract: 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.

Keywords: Hexagonal Lattice; Moment Problem; Effective Conductivity; Original Series; Critical Index (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-31317-7_13

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DOI: 10.1007/978-3-319-31317-7_13

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