  We present a series of simulations of turbulent stratified protostellar discs
with the goal of characterizing the settling of dust throughout a minimum-mass
solar nebula. We compare the evolution of both compact spherical grains, as
well as highly fractal grains. Our simulations use a shearing-box formulation
to study the evolution of dust grains locally within the disc, and collectively
our simulations span the entire extent of a typical accretion disc. The dust is
stirred by gas that undergoes MRI-driven turbulence. This establishes a steady
state scale height for the dust that is different for dust of different sizes.
This sedimentation of dust is an important first step in planet formation and
we predict that ALMA should be able to observationally verify its existence.
When significant sedimentation occurs, the dust will participate in a streaming
instability that significantly enhances the dust density. We show that the
streaming instability is pervasive in the outer disc. We characterize the scale
heights of dust whose size ranges from a few microns to a few centimeters. We
find that for spherical grains, a power-law relationship develops for the scale
height with grain size, with a slope that is slightly steeper than -1/2. The
sedimentation is strongest in the outer disc and increases for large grains.
The results presented here show that direct measurements of grain settling can
be made by ALMA and we present favorable conditions for observability. The
streaming instability should also be directly observable and we provide
conditions for directly observing it. We calculate collision rates and growth
rates for the dust grains in our simulations of various sizes colliding with
other grains, and find that these rates are significantly enhanced through the
density enhancement arising from the streaming instability.
