We prove that the effective conductivity of a three-dimensional medium with a periodic chessboard structure does not exceed\Lambda\sqrt{\alpha\beta}, where \alpha and \beta are the values of the conductivity in the cells of the chessboard, and \Lambda is a positive constant; then we show how the corresponding "random" structure behaves in a quite different way, according to recent results in percolation theory.
Some Bounds on the Bulk Conductivity of a two-phase Medium: a Comparison between Periodic and Random Structure / Gavioli, Andrea. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - STAMPA. - 2-3:(1992), pp. 283-294.
Some Bounds on the Bulk Conductivity of a two-phase Medium: a Comparison between Periodic and Random Structure
GAVIOLI, Andrea
1992
Abstract
We prove that the effective conductivity of a three-dimensional medium with a periodic chessboard structure does not exceed\Lambda\sqrt{\alpha\beta}, where \alpha and \beta are the values of the conductivity in the cells of the chessboard, and \Lambda is a positive constant; then we show how the corresponding "random" structure behaves in a quite different way, according to recent results in percolation theory.
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