  The usual treatments of the neutrino flavor-evolution, beyond a surface above
the last scattering, assume identical angular distributions at this distance
for the different initial (unmixed) flavors, and for particles and
antiparticles. Taking into account differences in these distributions that must
be present, as a result of the species-dependent scattering cross-sections
lower down in the star, leads to a new set of non-linear equations. These
equations are unstable, even at the initial surface, with respect to
perturbations that have both tiny mixing from neutrino oscillations and that
break all-over spherical-symmetry. There could be important consequences for:
1) the dynamics of the explosion, 2) R-process-nucleosynthesis, and 3) some
future observable neutrino pulse.
