Hydrodynamic Description of Heavy Ion Collisions

We give a short review of hydrodynamic models at heavy ion collisions from the point of view of initial conditions, an equation of states (EoS) and freezeout process. Then we show our latest results of a combined fully three-dimensional macroscopic/microscopic transport approach. In this model for the early, dense, deconfined stage relativistic 3D-hydrodynamics of the reaction and a microscopic non-equilibrium model for the later hadronic stage where the equilibrium assumptions are not valid anymore are employed. Within this approach we study the dynamics of hot, bulk QCD matter, which is being created in ultra-relativistic heavy ion collisions at RHIC.Comment: 8 pages, 9 figures, latex, plenary presentation at the 19th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions (QM2006), Shanghai, China Nov. 14-20, 200

A new relativistic viscous hydrodynamics code and its application to the Kelvin-Helmholtz instability in high-energy heavy-ion collisions

We construct a new relativistic viscous hydrodynamics code optimized in the Milne coordinates. We split the conservation equations into an ideal part and a viscous part, using the Strang spitting method. In the code a Riemann solver based on the two-shock approximation is utilized for the ideal part and the Piecewise Exact Solution (PES) method is applied for the viscous part. We check the validity of our numerical calculations by comparing analytical solutions, the viscous Bjorken's flow and the Israel-Stewart theory in Gubser flow regime. Using the code, we discuss possible development of the Kelvin-Helmholtz instability in high-energy heavy-ion collisions.Comment: 14 pages, 9 figure

Masses of vector bosons in two-color dense QCD based on the hidden local symmetry

We construct a low energy effective Lagrangian for the two-color QCD including the "vector" bosons (mesons with J^P=1^- and diquark baryons with J^P=1^+) in addition to the pseudo Nambu-Goldstone bosons with a degenerate mass M_\pi (mesons with J^P=0^- and baryons with J^P=0^+) based on the chiral symmetry breaking pattern of SU(2N_f) \to Sp(2N_f) in the framework of the hidden local symmetry. We investigate the dependence of the "vector" boson masses on the baryon number density \mu_B. We show that the \mu_B-dependence signals the phase transition of U(1)_B breaking. We find that it gives information about mixing among "vector" bosons: e.g. the mass difference between \rho and \omega mesons is proportional to the mixing strength between the diquark baryon with J^P=1^+ and the anti-baryon. We discuss the comparison with lattice data for two-color QCD at finite density.Comment: 24 pages, 5 figure

(3+1)-dimensional relativistic hydrodynamical expansion of hot and dense matter in ultra-relativistic nuclear collision

A full (3+1)-dimensional calculation using the Lagrangian hydrodynamics is proposed for relativistic nuclear collisions. The calculation enables us to evaluate anisotropic flow of hadronic matter which appears in non-central and/or asymmetrical relativistic nuclear collisions. Applying hydrodynamical calculations to the deformed uranium collisions at AGS energy region, we discuss the nature of space-time structure and particle distributions in detail.Comment: 24 pages, 25 eps figures, LaTeX 2 epsilo

A new relativistic hydrodynamics code for high-energy heavy-ion collisions

We construct a new Godunov type relativistic hydrodynamics code in Milne coordinates, using a Riemann solver based on the two-shock approximation which is stable under the existence of large shock waves. We check the correctness of the numerical algorithm by comparing numerical calculations and analytical solutions in various problems, such as shock tubes, expansion of matter into the vacuum, the Landau-Khalatnikov solution, and propagation of fluctuations around Bjorken flow and Gubser flow. We investigate the energy and momentum conservation property of our code in a test problem of longitudinal hydrodynamic expansion with an initial condition for high-energy heavy-ion collisions. We also discuss numerical viscosity in the test problems of expansion of matter into the vacuum and conservation properties. Furthermore, we discuss how the numerical stability is affected by the source terms of relativistic numerical hydrodynamics in Milne coordinates.Comment: 20 pages, 16 figure