Dilute spherical-inclusion conductivity
= Dilute spherical-inclusion conductivity
{title2=$a^*=a_0I+p\beta I+o(p)$}
Well-separated shrinking spheres respond independently at leading order, so their polarization contributions add according to volume fraction. Clusters kept at fixed relative internal separation can have a different leading response; the dilute limit alone does not guarantee independent-sphere polarizability.