  We present the first magnetohydrodynamic simulation in which a circumbinary
disk around a relativistic binary black hole feeds mass to individual accretion
disks ("mini-disks") around each black hole. Mass flow through the accretion
streams linking the circumbinary disk to the mini-disks is modulated
quasi-periodically by the streams' interaction with a nonlinear $m=1$ density
feature, or "lump", at the inner edge of the circumbinary disk: the stream
supplying each mini-disk comes into phase with the lump at a frequency $0.74$
times the binary orbital frequency. Because the binary is relativistic, the
tidal truncation radii of the mini-disks are not much larger than their
innermost stable circular orbits; consequently, the mini-disks' inflow times
are shorter than the conventional estimate and are comparable to the stream
modulation period. As a result, the mini-disks are always in inflow
disequilibrium, with their masses and spiral density wave structures responding
to the stream's quasi-periodic modulation. The fluctuations in each mini-disk's
mass are so large that as much as $75\%$ of the total mini-disk mass can be
contained within a single mini-disk. Such quasi-periodic modulation of the
mini-disk structure may introduce distinctive time-dependent features in the
binary's electromagnetic emission.
