9320068 Lovelace There are important fundamental unsolved problems in astrophysics such as supernova explosions, formation and propagation of stellar and extragalactic jets, formation of stars and compact objects where rotation and magnetic fields are significant. A rigorous understanding of these rotating magnetized systems can be obtained only as a result of systematic development of one, two, and three dimensional magneto-hydrodynamical models and corresponding computer simulation codes. In this proposal the Principal Investigators plan to treat a number of astrophysical problems based partly on advanced 2D computer codes created at the M.V. Keldysh Institute of Applied Mathematics at Moscow University, and on codes developed at Cornell University. The collaboration of scientists at the Space Research Institute (IKI) in Moscow and Cornell began more than two years ago, and several joint papers have been published. They have now involved applied mathematicians in the project, and several computer codes have been created and successfully tested on small, personal computers in Russia and the U.S. However, to obtain the physically interesting results, much longer calculations on the larger computers and supercomputers are needed. This research will enhance the interactions between scientists in the U.S. and Russia and will lead to advances in our understanding of magneto- rotational phenomena in astrophysics which may have practical laboratory applications.