2-D models of layered protoplanetary discs: I. The ring instability
  In this work we use the radiation hydrodynamic code TRAMP to perform a two-dimensional axially symmetric model of the layered disc. Using this model we follow the accumulation of mass in the dead zone due to the radially varying accretion rate. We found a new type of instability which causes the dead zone to split into rings. This "ring instability" works due to the positive feedback between the thickness of the dead zone and the mass accumulation rate.   We give an analytical description of this instability, taking into account non-zero thickness of the dead zone and deviations from the Keplerian rotational velocity. The analytical model agrees reasonably well with results of numerical simulations. Finally, we speculate about the possible role of the ring instability in protoplanetary discs and in the formation of planets. 
R. Wunsch, H. Klahr, M. Rozyczka