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Bloch Wave Homogenization Relative to a Microstructure

In this work, we study the aspect of Bloch wave homogenization of the new notion of convergence of microstructures represented by matrices $B^ε$ related to the classical $H$-convergence of $A^ε$ introduced in \cite{TG-MV-1}. The new macro quantity $B^{#}$ appears to incorporate the interaction between the two microstructures $A^ε,B^ε$. Here we present its Bloch spectral representation along with the homogenization result.