2015/08/19 by S. Gluzman, Gluzman, Simon, Vladimir Mityushev +5
Computer Science · Engineering · Physics and Astronomy · #74Q15 #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Superconducting Materials and Applications #Superconductivity in MgB2 and Alloys
paper · pdf · doi:10.48550/arxiv.1508.05068
openalex publication_date 2015/08/19 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
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.