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

الأصل · EN

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.