Series, Index and Threshold for Random 2D Composite

TL;DR

This paper develops a series expansion approach to analyze the effective conductivity of 2D random composites, enabling accurate reconstruction of the critical index for superconductivity and providing comprehensive analytical expressions across all concentrations.

Contribution

It introduces a method to directly reconstruct the critical index for superconductivity from series expansions of effective conductivity.

Findings

Successfully reconstructs the critical index with high accuracy.

Derives general analytical expressions valid for all concentrations.

Compares new models with existing ones, showing improved accuracy.

Abstract

Effective conductivity of a 2D random composite is expressed in the form of long series in the volume fraction of ideally conducting disks. The problem of a {\it direct} reconstruction of the critical index for superconductivity from the series is solved with good accuracy, for the first time. General analytical expressions for conductivity in the whole range of concentrations are derived and compared with the regular composite and existing models.