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In this review article, we first briefly introduce the transport theory and quantum molecular dynamics model applied in the study of the heavy ion collisions from low to intermediate energies. The developments of improved quantum molecular dynamics model (ImQMD) and ultra-relativistic quantum molecular dynamics model (UrQMD), are reviewed. The reaction mechanism and phenomena related to the fusion, multinucleon transfer, fragmentation, collective flow and particle production are reviewed and discussed within the framework of the two models. The constraints on the isospin asymmetric nuclear equation of state and in-medium nucleon-nucleon cross sections by comparing the heavy ion collision data with transport models calculations in last decades are also discussed, and the uncertainties of these constraints are analyzed as well. Finally, we discuss the future direction of the development of the transport models for improving the understanding of the reaction mechanism, the descriptions of various observables, the constraint on the nuclear equation of state, as well as for the constraint on in-medium nucleon-nucleon cross sections.
A variety of phenomena connected with the formation of a dinuclear complex is observed in the heavy ion collisions at low energies. The dinuclear system model allows us to analyze the experimental data and to interpret them by comparison of the parti
Deblurring procedure is proposed for accessing three-dimensional (3D) differential distributions relative to the reaction plane in energetic high-multiplicity heavy-ion collisions. Because reaction plane direction can be only coarsely estimated in me
A systematic analysis of correlations between different orders of $p_T$-differential flow is presented, including mode coupling effects in flow vectors, correlations between flow angles (a.k.a. event-plane correlations), and correlations between flow
The longitudinal asymmetry arises in relativistic heavy ion collisions due to fluctuation in the number of participating nucleons. This asymmetry causes a shift in the center of mass rapidity of the participant zone. The rapidity shift as well as the
A QCD phase transition may reflect in a inhomogeneous decoupling surface of hadrons produced in relativistic heavy-ion collisions. We show that due to the non-linear dependence of the particle densities on the temperature and baryon-chemical potentia