  The Bruggeman formalism provides an estimate $\eps^{Br}_{hcm}$ of the
relative permittivity of a homogenized composite material (HCM), arising from
two component materials with relative permittivities $\eps_a$ and $\eps_b$. It
can be inverted to provide an estimate of $\eps_a$, from a knowledge of
$\eps^{Br}_{hcm}$ and $\eps_b$. Numerical studies show that the inverse
Bruggeman estimate $\eps_a$ can be physically implausible when (i)
$Re\{\eps^{Br}_{hcm}\}/Re\{\eps_b\} > 0 $ and the degree of HCM dissipation is
moderate or greater; or (ii) $Re\{\eps^{Br}_{hcm}\}/Re\{\eps_b\} < 0 $
regardless of the degree of HCM dissipation. Furthermore, even when the inverse
Bruggeman estimate is not obviously implausible, huge discrepancies can exist
between this estimate and the corresponding estimate provided by the inverse
Maxwell Garnett formalism.
