  For physically reasonable bulk and surface properties, quark matter has
recently been found to coexist with nuclear matter inside neutron stars in a
uniform background of electrons. The microstructure of this mixed phase starts
out with a few quark matter droplets embedded in the nuclear matter but as the
density of droplets increase towards the center of the neutron star they merge
into rods, plates and other structures. The topology, size as well as Coulomb
and surface energies of these structures depend sensitively on the
quark/nuclear matter interface tension. A major fraction of the interior of
neutron stars could consist of matter in this new phase, which would provide
new mechanisms for glitches, cooling and supernovae.
