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This book is dedicated to the theory of supernovae, focusing on new computational methods and simulations. It contains three parts: basic principles, numerical methods, and applications. The first part contains a non-formal introduction into the basics of supernovae, Boltzmann kinetic equations -- with details of two particles reaction rate calculations -- and the transformation of Boltzmann kinetic equations into hydrodynamic elements of statistical physics. It also contains the equation of state for matter of high energy density, with details of calculations for thermodynamic parameters, weak interactions, reaction rate details, and thermonuclear burning. The second part introduces elements of computational physics.The book closes with a presentation of original thought regarding the regime of burning in degenerate carbon-oxygen cores, a neutrino transport in Type II supernovae, a simulation of general relativity (GR) coalescence of neutron stars, aspherical nucleosynthesis in a core-collapse supernova, and thermalization in a pair of plasma winds from a compact strange star.This book brings together generally accepted simulations methods as well as original material written by two respected members of Russian research groups: the Keldysh Institute of Applied Mathematics and Institute of Theoretical and Experimental Physics. It contains the necessary information for a person to start independent research in this fast-developing field, and is therefore an important read for new researchers in this subject.
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