Dispersion tensor and its unique minimizer in Hashin-Shtrikman micro-structures

In this paper, we introduce the macroscopic quantity, namely the dispersion tensor or the $\mathit{\text{Burnett}}\mathit{\text{coefficient}}$s in the class of generalized Hashin-Shtrikman micro-structures \cite[page no. 281]{T}. In the case of two-phase materials associated with the periodic Hashin-Shtrikman structures, we settle the issue that the dispersion tensor has an unique minimizer, which is so called Apollonian-Hashin-Shtrikman micro-structure.