Polarization field of a conductivity inclusion
= Polarization field of a conductivity inclusion
{title2=$P=(a-a_0I)\nabla u$}
= Conductivity polarization field
{synonym}
Relative to a uniform reference conductivity $a_0$, this polarization is the excess positive conductivity flux. The equation becomes $a_0\Delta u+\nabla\cdot P=0$. For a prescribed mean gradient $E$, averaging gives $a^*E=a_0E+\langle P\rangle$. This sign convention differs from the physical heat-flux sign.