The pasta structure in the hadron-quark phase transition and the effects on magnetized compact stars
We report the effects of quark-hadron phase transition on the structures of general relativistic stars with purely toroidal magnetic field. For the mixed phase, we take into account of the finite-size effects, which lead to non-uniform"Pasta"structures. Our study is based on axisymetric and stationary formalism including purely toroidal magnetic field. For hybrid stars, we find the characteristic distribution of magnetic field, which has a discontinuity originated in the quark-hadron mixed phase. These distributions of magnetic field will change astrophysical phenomena, such as cooling processes.
Certain structural aspects of two-dimensional Penrose tilings are studied using de Bruijn's pentagrid picture. The authors discuss the statistics of hexagons, decagons and 'worms' (sequences of adjacent hexagons bounded by two decagons). They show that within the discrete framework considered here, phason modes and structural transformation modes are located along particular 'worms' and they derive the spatial distribution of the latter.