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Perturbation analysis of the effective conductivity of a periodic composite

  • * Corresponding author: Paolo Musolino

    * Corresponding author: Paolo Musolino
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  • We consider the effective conductivity $ \lambda^{\mathrm{eff}} $ of a periodic two-phase composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material. Then we study the behavior of $ \lambda^{\mathrm{eff}} $ upon perturbation of the shape of the inclusions, of the periodicity structure, and of the conductivity of each material.

    Mathematics Subject Classification: Primary: 74E30, 74G10, 31B10; Secondary: 35J25, 35J05, 45A05, 74M15.


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  • Figure 1.  The sets $ \mathbb{S}_{q}[q\mathbb{I}[\phi]]^- $, $ \mathbb{S}_{q}[q\mathbb{I}[\phi]] $, and $ q\phi(\partial\Omega) $ in case $ n = 2 $

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