Research at the MPA is devoted to a broad range of topics in theoretical astrophysics. Major concentrations of interest lie in the areas of stellar evolution, stellar atmospheres and accretion phenomena, nuclear and particle astrophysics, supernova physics, astrophysical fluid dynamics, high-energy astrophysics, radiative processes, the structure, formation and evolution of galaxies, gravitational lensing, the large-scale structure of the Universe and physical cosmology. Because of the overlapping and interdependence of these different fields, the MPA is not formally separated into distinct divisions. Projects in national and international collaboration are an important part of the research activities at the MPA.

The MPA has traditionally been strong in numerical simulation of astrophysical processes. Current activity concentrates on hydrodynamical phenomena such as accretion flows, stellar collisions, supernova explosions, protostellar and radio jets, as well as on N-body and hydrodynamical treatments of the formation and evolution of galaxies, galaxy clusters and larger structures. Much of the latter work is carried out as part of the Virgo Consortium, an Anglo-German-Canadian collaboration aimed at effective scientific exploitation of the largest available parallel supercomputers. Supercomputing methods used at MPA can sometimes also be applied to problems in other fields. For example, the propagation of burning fronts in stars is similar to that in certain industrial processes. Work in high-energy astrophysics focuses on the interpretation of X-ray and gamma-ray observations and the theoretical modeling of the relevant emission processes to obtain information about neutron stars and black holes

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