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To compute the overall conductivity of this periodic composite, the bcc unit cell, containing two sand grains, was digitized into a 3-D array of pixels, typically 1283 in size. A macroscopic electric field was applied in one of the principal cubic directions. Each pixel is then treated as a tri-linear finite element, which results in a set of 1283 linear equations that are solved with a conjugate gradient algorithm [19]. A resolution of 643 was also used, with only very small changes in overall results so the 1283 resolution was judged to be adequate to represent both the sand grain, and more importantly, the thin interfacial zone volume. We have also carried out finite difference calculations on identical 3-D grids. Generally, the finite element calculations lead to conductivities that are between 2 and 8% higher than the corresponding finite difference results. Physically this difference is associated with the fact that the finite element calculations map onto a resistor network with second and third neighbor coupling, while the finite difference calculations map onto a resistor network with nearest neighbor coupling only. A brief comparison of these two methods is presented in the Appendix.