  We use vertically-resolved numerical hydrodynamic simulations to study star
formation and the interstellar medium (ISM) in galactic disks. We focus on
outer disk regions where diffuse HI dominates, with gas surface densities
Sigma_SFR=3-20 Msun/kpc^2/yr and star-plus-dark matter volume densities
rho_sd=0.003-0.5 Msun/pc^3. Star formation occurs in very dense, cold,
self-gravitating clouds. Turbulence, driven by momentum feedback from supernova
events, destroys bound clouds and puffs up the disk vertically. Time-dependent
radiative heating (FUV) offsets gas cooling. We use our simulations to test a
new theory for self-regulated star formation. Consistent with this theory, the
disks evolve to a state of vertical dynamical equilibrium and thermal
equilibrium with both warm and cold phases. The range of star formation surface
densities and midplane thermal pressures is Sigma_SFR ~ 0.0001 - 0.01
Msun/kpc^2/yr and P_th/k_B ~ 100 -10000 cm^-3 K. In agreement with
observations, turbulent velocity dispersions are ~7 km/s and the ratio of the
total (effective) to thermal pressure is P_tot/P_th~4-5, across this whole
range. We show that Sigma_SFR is not well correlated with Sigma alone, but
rather with Sigma*(rho_sd)^1/2, because the vertical gravity from stars and
dark matter dominates in outer disks. We also find that Sigma_SFR has a strong,
nearly linear correlation with P_tot, which itself is within ~13% of the
dynamical-equilibrium estimate P_tot,DE. The quantitative relationships we find
between Sigma_SFR and the turbulent and thermal pressures show that star
formation is highly efficient for energy and momentum production, in contrast
to the low efficiency of mass consumption. Star formation rates adjust until
the ISM's energy and momentum losses are replenished by feedback within a
dynamical time.
