The checkerboard is one of the few microstructures which yield an explicit formula for its effective conductivity. The famous formula for the effective conductivity λ_(eff) = (λ_gλ_w)~(1/2) for a standard checkerboard of conductivities λ_g and λ_w, were proved about 30 years ago by Dykhne [4]. The explicit solution of the corresponding temperature-field was later found by Berdichevskii [1]. In particular he found that the heat-flux is infinitely high in the corners of the squares.
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