"The main goal of this proposal to the ERC Starting Grant scheme is to make ground-breaking progress in our understanding of the dynamical processes that shape the structure of protoplanetary disks. This will be achieved by performing state-of-the-art high resolution numerical simulations of protoplanetary disks, using novel computing techniques and taking advantage of the future European petascale supercomputers. The project will address the following fundamental questions in accretion disks theory:- What are the properties of MHD turbulence in protoplanetary disks?- What are the effects of radiative processes on protoplanetary disks structure?- What are the consequences of dead zones for protoplanetary disk structure?In addition, the project will look for potential observational signatures of these processes that might be detected by ALMA. Since planetary systems like our own are believed to emerge from protoplanetary disks, the project will make decisive contributions in describing the structure of the environment in which planetary systems form, the interest of which extends to the entire planet formation community."