Effective conductivity of the infinite checkerboard and its higher-dimension analogs

TL;DR

This paper derives an algebraic expression for the effective conductivity of infinite checkerboard and higher-dimensional checkered structures by leveraging their symmetries.

Contribution

It introduces a novel algebraic approach to compute effective conductivity in complex, symmetric, checkered structures.

Findings

Derived algebraic expression for 2D checkerboard conductivity

Extended the method to higher-dimensional analogs

Utilized symmetry properties to simplify calculations

Abstract

The effective conductivity of the infinite checkerboard (chessboard) and analogous higher-dimensional checkered structures, are considered. An algebraic expression is derived by accounting for the symmetries of the structures.