In this work the low density regions of nuclear and neutron star matter are studied. The search for the existence of pasta phases in this region is performed within the context of the quark-meson coupling (QMC) model, which incorporates quark degrees of freedom. Fixed proton fractions are considered, as well as nuclear matter in beta equilibrium at zero temperature. We discuss the recent attempts to better understand the surface energy in the coexistence phases regime and we present results that show the existence of the pasta phases subject to some choices of the surface energy coefficient. We also analyze the influence of the nuclear pasta on some neutron star properties. The equation of state containing the pasta phase will be part of a complete grid for future use in supernova simulations.
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