  We study the behavior of large dust grains in turbulent molecular clouds
(MCs). In primarily neutral regions, dust grains move as aerodynamic particles,
not necessarily with the gas. We therefore directly simulate, for the first
time, the behavior of aerodynamic grains in highly supersonic,
magnetohydrodynamic turbulence typical of MCs. We show that, under these
conditions, grains with sizes a >0.01 micron exhibit dramatic (exceeding factor
~1000) fluctuations in the local dust-to-gas ratio (implying large small-scale
variations in abundances, dust cooling rates, and dynamics). The dust can form
highly filamentary structures (which would be observed in both dust emission
and extinction), which can be much thinner than the characteristic width of gas
filaments. Sometimes, the dust and gas filaments are not even in the same
location. The 'clumping factor' of the dust (critical for dust
growth/coagulation/shattering) can reach ~100, for grains in the ideal size
range. The dust clustering is maximized around scales ~0.2pc*(a/micron)*(100
cm^-3/n_gas), and is 'averaged out' on larger scales. However, because the
density varies widely in supersonic turbulence, the dynamic range of scales
(and interesting grain sizes) for these fluctuations is much broader than in
the subsonic case. Our results are applicable to MCs of essentially all sizes
and densities, but we note how Lorentz forces and other physics (neglected
here) may change them in some regimes. We discuss the potentially dramatic
consequences for star formation, dust growth and destruction, and dust-based
observations of MCs.
