  The structure and dynamics of diffuse gas in the Milky Way and other disk
galaxies may be strongly influenced by thermal and magnetorotational
instabilities (TI and MRI) on scales of about 1-100 pc. We initiate a study of
these processes, using two-dimensional numerical hydrodynamic and
magnetohydrodynamic (MHD) simulations with conditions appropriate for the
atomic interstellar medium (ISM). We demonstrate, consistent with previous
work, that nonlinear development of ``pure TI'' produces a network of filaments
that condense into cold clouds at their intersections, yielding a distinct
two-phase warm/cold medium within about 20 Myr. TI-driven turbulent motions of
the clouds saturate at subsonic amplitudes for uniform initial P/k=2000 K
cm^-3. MRI has previously been studied in near-uniform media; our simulations
include both TI+MRI models, which begin from uniform-density conditions, and
cloud+MRI models, which begin with a two-phase cloudy medium. Both the TI+MRI
and cloud+MRI models show that MRI develops within a few galactic orbital
times, just as for a uniform medium. The mean separation between clouds can
affect which MRI mode dominates the evolution. Provided intercloud separations
do not exceed half the MRI wavelength, we find the MRI growth rates are similar
to those for the corresponding uniform medium. This opens the possibility, if
low cloud volume filling factors increase MRI dissipation times compared to
those in a uniform medium, that MRI-driven motions in the ISM could reach
amplitudes comparable to observed HI turbulent linewidths.
