Using a hydrodynamic model, we predict the transverse momentum dependence of the spectra and the elliptic flow for different hadrons in Au+Au collisions at √ s = 130 A GeV. The dependence of the differential and pt-integrated elliptic flow on the hadron mass, equation of state and freeze-out temperature is studied both numerically and analytically.

We compare the trace anomaly, strangeness and baryon number fluctuations calculated in lattice QCD with expectations based on hadron resonance gas model. We find that there is a significant discrepancy between the hadron resonance gas and the lattice data. This discrepancy is largely reduced if the hadron spectrum is modified to take into account the larger values of the quark mass used in lattice calculations as well as the finite lattice spacing errors. We also give a simple parametrization of QCD equation of state, which combines hadron resonance gas at low temperatures with lattice QCD at high temperatures. We compare this parametrization with other parametrizations of the equation of state used in hydrodynamical models and discuss differences in hydrodynamic flow for different equations of state.

Anisotropic transverse flow is studied in Pb+Pb and Au+Au collisions at SPS and RHIC energies. The centrality and transverse momentum dependence at midrapidity of the elliptic flow coefficient v2 is calculated in the hydrodynamic and low density limits. Hydrodynamics is found to agree well with the RHIC data for semicentral collisions up to transverse momenta of 1-1.5 GeV/c, but it considerably overestimates the measured elliptic flow at SPS energies. The low density limit LDL is inconsistent with the measured magnitude of v2 at RHIC energies and with the shape of its pt-dependence at both RHIC and SPS energies. The success of the hydrodynamic model points to very rapid thermalization in Au+Au collisions at RHIC and provides a serious challenge for kinetic approaches based on classical scattering of on-shell particles. Cascade calculations based on the incoherent scattering of classical on-shell particles and the low density limit of classical kinetic theory are expected to work best for peripheral collisions where the density of produced particles is sufficiently low and only a few rescatterings occur. Central collisions produce higher particle densities where the hydrodynamic limit may be more suitable. One of the most interesting questions in the kinetic theory of relativistic heavy ion collisions is where and how the transition between the dilute and dense limits happens.In this paper we present detailed calculations of the impact parameter and transverse momentum dependence of elliptic flow in a hydrodynamic model [7,8] and in the low density limit (LDL) of Ref.[11], and we compare the results to recent SPS and RHIC data [3][4][5]. We test the

Application of hydrodynamics for modeling of heavy-ion collisions is reviewed. We consider several physical observables that can be calculated in this approach and compare them to the experimental measurements.Comment: 42 pages, 15 figures, An invited review for Nov. 2006 edition of Annual Review of Nuclear and Particle Physic