Columnar defects provide effective pinning centers for magnetic flux lines in high-temperature superconductors. Previous work addressing the Bose glass phase at low fields has shown that the long-range intervortex repulsion produces a soft "Coulomb" gap in the distribution of pinning energies, and drastically reduces vortex transport. By extending these Monte-Carlo simulations to higher filling fractions near 1, allowing the flux lines to occupy both defect and interstitial sites, the transition into the conjectured Mott insulator phase can be investigated, as well as structural and transport properties which may be directly compared to experiments.
A field-theoretical model for branching and annihilating random walks and the corresponding reaction-diffusion system is to be studied. Simulations have revealed that the cases of even and odd offspring numbers belong to different universality classes. The goal is to understand this remarkable behaviour and deduce the power laws at low dimensions within the framework of dynamical renormalization group theory.