Effective conductivity of composite materials with random positions of cylindrical inclusions: finite number inclusions in the cell

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Abstract:

The effective conductivity of composite materials with random position n 2 , n ∈ N , and the cylindrical identical inclusions inside periodic cells is considered. We compare the results for symmetric and nonsymmetric cases of location of the inclusions in the cells and find that a symmetric structure provides a minimum for the effective conductivity among all the structures having n 2 inclusions of such conductivity and sizes.
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