Construction of the nuclear equation of state with the variational method at finite temperatures and its applications to supernova simulations

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Starting from the realistic nuclear forces, we constructed the equation of state of uniform nuclear matter that is applicable to core-collapse supernova numerical simulations, using the variational method. With use of the equation of state, we calculated structures of hot proto-neutron stars, and performed supernova simulations. Furthermore, we calculated the equation of state of non-uniform nuclear matter, and then, at typical temperatures, we obtained the phase diagrams of nuclear matter including τ particles, covering a wide range of the density and proton fraction.