Modelling of dielectric materials with cubic inclusion shapes

The objective of this research is to calculate the polarizability of a cubical scatterer as accurately as possible and to develop an approximate formula for the polarizability. The problem of a dielectric cube in a uniform static electric field is solved numerically with a surface-integral-equation approach. The resulting dipole moment for this kind of scatterer is dependent on the dielectric contrast between the internal and external regions. The results give an improvement compared to earlier literature and also present a way to predict the effective properties of mixtures where cube-shaped inclusions are embedded in dielectric environment which type of mixtures strongly generalize the effective-medium theories of the present literature. Similar calculations are to be made also for other polyhedra.