We use ZEUS-MP to perform high-resolution, three-dimensional, super-Alfvenic turbulent simulations in order to investigate the role of magnetic fields in self-gravitating core formation within turbulent molecular clouds. Statistical properties of our super-Alfvenic model without gravity agree with previous similar studies. Including self-gravity, our models give the following results. They are consistent with the turbulent fragmentation prediction of the core mass distribution of Padoan & Nordlund. They also confirm that local gravitational collapse is not prevented by magnetohydrodynamic waves driven by turbulent flows, even when the turbulent Jeans mass exceeds the mass in the simulation volume. Comparison of results between 256~3 and 512~3 zone simulations reveals convergence in the collapse rate. Analysis of self-gravitating cores formed in the simulation shows the following: (1) All cores formed are magnetically supercritical by at least an order of magnitude. (2) A power-law relation between central magnetic field strength and density B_c ∝ ρ_c~(1/2) is observed despite the cores being strongly supercritical. (3) Specific angular momentum j ∝ R~(3/2) for cores with radius R. (4) Most cores are prolate and triaxial in shape, in agreement with the results of Gammie and coworkers. We find a weak correlation between the minor axis of the core and the local magnetic field in our simulation at late times, different from the uncorrelated results reported by Gammie and coworkers. The core shape analysis and the power-law relationship between core mass and radius M ∝ R~(2.75) suggest the formation of some highly flattened cores. We identified 12 cloud cores with disklike appearance at a later stage of our high-resolution simulation. Instead of being tidally truncated or disrupted, the core disks survive and flourish while undergoing strong interactions. We discuss the physical properties of these disklike cores under the constraints of resolution limits.
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