We study effects of eccentricity fluctuations on the elliptic flow coefficient $v_2$ at midrapidity in both $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Cu}+\mathrm{Cu}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV by using a hybrid model that combines ideal hydrodynamics for space-time evolution of the quark gluon plasma phase and a hadronic transport model for the hadronic matter. For initial conditions in hydrodynamic simulations, both the Glauber model and the color glass condensate model are employed to demonstrate the effect of initial eccentricity fluctuations originating from the nucleon position inside a colliding nucleus. The effect of eccentricity fluctuations is modest in semicentral $\mathrm{Au}+\mathrm{Au}$ collisions, but significantly enhances $v_2$ in $\mathrm{Cu}+\mathrm{Cu}$ collisions.

We study the effects of hadronic rescattering on hadron distributions in high-energy nuclear collisions by using an integrated dynamical approach. This approach is based on a hybrid model combining (3 + 1)-dimensional ideal hydrodynamics for the quark gluon plasma (QGP) and a transport model for the hadron resonance gas. Since the hadron distributions are the result of the entire expansion history of the system, understanding the QGP properties requires investigating how rescattering during the hadronic stage affects the final distributions of hadrons. We include multistrange hadrons in our study and quantify the effects of hadronic rescattering on their mean transverse momenta and elliptic flow. We find that multistrange hadrons scatter less during the hadronic stage than nonstrange particles, and thus their distributions reflect the properties of the system in an earlier stage than the distributions of nonstrange particles.

We predict the elliptic flow parameter v2 in U+U collisions at sNN=200 GeV and in Pb+Pb collisions at sNN=2.76 TeV using a hybrid model in which the evolution of the quark gluon plasma is described by ideal hydrodynamics with a state-of-the-art lattice QCD equation of state and the subsequent hadronic stage is described by a hadron cascade model.

Relativistic quantum molecular dynamics based on the relativistic mean field theory (RQMD.RMF) is extended by including momentum-dependent potential. The equation of state (EoS) dependence of the directed and the elliptic flow of protons in the beam energy range of $2.3<\sqrt{s_{NN}}<20$ GeV is examined. It is found that the directed flow depends strongly on the optical potential at high energies, $\sqrt{s_{NN}}>3$ GeV, where no information is available experimentally. The correlation between effective mass at saturation density and the optical potential is found: smaller values of effective mass require smaller strengths of the optical potential to describe the directed flow data. This correlation can also be seen in the beam energy dependence of the elliptic flow at $\sqrt{s_{NN}}>3$ GeV, although its effect is rather weak. On the other hand, stiff EoS is required to describe the elliptic flow at lower energies. Experimental constraints on the optical potential from $pA$ collisions will provide important information on the EoS at high energies. The proton directed and the elliptic flow are well described in the RQMD.RMF model from $\sqrt{s_{NN}}=2.3$ to 8.8 GeV. In contrast, to reproduce the collapse of the directed flow above 10 GeV, pressure has to be reduced, which indicates a softening of the EoS around $\sqrt{s_{NN}}=10$ GeV.

The beam energy dependence of the directed flow is a sensitive probe for the properties of strongly interacting matter. Hybrid models that simulate dense (core) and dilute (corona) parts of the system by combining the fluid dynamics and hadronic cascade model describe well the bulk observables, strangeness productions, and radial and elliptic flows in high-energy heavy-ion collisions in the high baryon density region. However, the beam energy dependence of the directed flow cannot be described in existing hybrid models. We focus on improving the corona part, i.e., the nonequilibrium evolution part of the system, by introducing the mean-field potentials into a hadronic cascade model. For this purpose, we consider different implementations of momentum-dependent hadronic mean fields in the relativistic quantum molecular dynamics (RQMD) framework. First, Lorentz scalar implementation of a Skyrme type potential is examined. Then, full implementation of the Skyrme type potential as a Lorentz vector in the RQMD approach is proposed. We find that scalar implementation of the Skyrme force is too weak to generate repulsion explaining observed data of sideward flows at $\sqrt{s_{NN}}<10$ GeV, while vector implementation gives collective flows compatible with the data for a wide range of beam energies $2.7<\sqrt{s_{NN}}<20$ GeV. We show that our approach reproduces the negative proton directed flow at $\sqrt{s_{NN}}>10$ GeV discovered by experiments. We discuss the dynamical generation mechanisms of the directed flow within a conventional hadronic mean field. A positive slope of proton directed flow is generated predominantly during compression stages of heavy-ion collisions by the strong repulsive interaction due to high baryon densities. In contrast, at the expansion stages of the collision, the negative directed flow is generated more strongly than the positive one by the tilted expansion and shadowing by the spectator matter. At lower collision energies $\sqrt{s_{NN}}<10$ GeV, the positive flow wins against the negative flow because of a long compression time. On the other hand, at higher energies $\sqrt{s_{NN}}>10$ GeV, negative flow wins because of shorter compression time and longer expansion time. A transition beam energy from positive to negative flow is highly sensitive to the strength of the interaction.

We study the sensitivities of the directed flow in Au+Au collisions on the equation of state (EoS), employing the transport theoretical model JAM. The EoS is modified by introducing a new collision term in order to control the pressure of a system by appropriately selecting an azimuthal angle in two-body collisions according to a given EoS. It is shown that this approach is an efficient method to modify the EoS in a transport model. The beam energy dependence of the directed flow of protons is examined with two different EoS, a first-order phase transition and crossover. It is found that our approach yields quite similar results as hydrodynamical predictions on the beam energy dependence of the directed flow; Transport theory predicts a minimum in the excitation function of the slope of proton directed flow and does indeed yield negative directed flow, if the EoS with a first-order phase transition is employed. Our result strongly suggests that the highest sensitivity for the critical point can be seen in the beam energy range of $4.7\leq\srtNN\leq11.5$ GeV.Comment: 7 pages, 5 figure