Periodic structures separated by highly conductive thin layers
Résumé
We derive a model for the conduction in an $\veps$-periodic structure containing highly conductive thin layers. The case of plane thin layers is first considered. It is shown that the resulting model displays an increased conductivity along the directions of the layers planes. The more involved case of tubular layers yields a similar result with an increase of the conductivity along the direction of the tubes, while the presence of highly conductive thin layers confined between spheres of $\veps$-order radii does not increase the macroscopic conductivity in any direction. It seems that the presence of $\veps$-periodic highly conductive thin layers determines an increase of the macroscopic conductivity in a certain direction only if these layers cover entirely segment lines of unity order having this direction.
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