  We present numerical simulations of the periodic polarimetric variations
produced by a binary star placed at the center of an empty spherical cavity
inside a circumbinary ellipsoidal and optically thin envelope made of dust
grains. Mie single-scattering is considered along with pre- and post-scattering
extinction factors which produce a time-varying optical depth and affect the
morphology of the periodic variations. We are interested in the effects that
various parameters will have on the average polarization, the amplitude of the
polarimetric variations, and the morphology of the variability. We show that
the absolute amplitudes of the variations are smaller for Mie scattering than
for Thomson scattering. Among the four grain types that we have studied, the
highest polarizations are produced by grains with sizes in the range 0.1-0.2
micron. In general, the variations are seen twice per orbit. In some cases,
because spherical dust grains have an asymmetric scattering function, the
polarimetric curves produced also show variations seen once per orbit.
Circumstellar disks produce polarimetric variations of greater amplitude than
circumbinary envelopes.
  Another goal of these simulations is to see if the 1978 BME (Brown, McLean, &
Emslie, ApJ, 68, 415) formalism, which uses a Fourier analysis of the
polarimetric variations to find the orbital inclination for Thomson-scattering
envelopes, can still be used for Mie scattering. We find that this is the case,
if the amplitude of the variations is sufficient and the true inclinations is
i_true > 45 deg. For eccentric orbits, the first-order coefficients of the
Fourier fit, instead of second-order ones, can be used to find almost all
inclinations.
