Transport Description of Heavy Ion Collisions and Dynamic Fragmentation

In this lecture we review the theoretical investigation of heavy ion collisions in order to obtain information on the nuclear equation-of-state (EOS). We discuss the present knowledge of the EOS, and stress, in particular, the large uncertainty about the density dependence of the symmetry energy. We develop the treatment of heavy ion collisions with transport theory and non-equilibrium effects. We then discuss investigations both of the high density EOS with intermediate energy collisions and of the low density EOS in the Fermi energy regime. At the high density we make connections with neutron stars. At low density we discuss the fragmentation process and, in particular, the role and treatment of fluctuations and the dynamical fragment formation.