Скачать презентацию WPCF Krakow Sept 11 2008 Comparisons between hydrodynamics Скачать презентацию WPCF Krakow Sept 11 2008 Comparisons between hydrodynamics

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WPCF, Krakow, Sept. 11, 2008 Comparisons between hydrodynamics and transport calculations Zhe Xu WPCF, Krakow, Sept. 11, 2008 Comparisons between hydrodynamics and transport calculations Zhe Xu

Motivation • How small is the h/s ? • Are there Mach cone shock Motivation • How small is the h/s ? • Are there Mach cone shock waves at RHIC ? Zhe Xu

Outline • Transport model • Transport vs. viscous and ideal Hydro 1. elliptic flow Outline • Transport model • Transport vs. viscous and ideal Hydro 1. elliptic flow 2. anisotropy, energy density, temperature 3. shock waves • Conclusion Zhe Xu

Transport Model BAMPS: Boltzmann Approach of Multi. Parton Scatterings A transport algorithm solving the Transport Model BAMPS: Boltzmann Approach of Multi. Parton Scatterings A transport algorithm solving the Boltzmann-Equations for on-shell partons with p. QCD interactions (Z)MPC, VNI/BMS, AMPT, PACIAE new development ggg gg Elastic scatterings are ineffective in thermalization ! Inelastic interactions are needed ! Zhe Xu

Stochastic algorithm P. Danielewicz, G. F. Bertsch, Nucl. Phys. A 533, 712(1991) A. Lang Stochastic algorithm P. Danielewicz, G. F. Bertsch, Nucl. Phys. A 533, 712(1991) A. Lang et al. , J. Comp. Phys. 106, 391(1993) Space has to be divided into small cells ! D 3 x collision rate per unit phase space for incoming particles p 1 and p 2 with D 3 p 1 and D 3 p 2: collision probability (Monte Carlo) Zhe Xu

Interaction Probability ZX and C. Greiner, PRC 71, 064901 (2005) Zhe Xu Interaction Probability ZX and C. Greiner, PRC 71, 064901 (2005) Zhe Xu

screened partonic interactions in leading order p. QCD J. F. Gunion, G. F. Bertsch, screened partonic interactions in leading order p. QCD J. F. Gunion, G. F. Bertsch, PRD 25, 746(1982) T. S. Biro at el. , PRC 48, 1275 (1993) S. M. Wong, NPA 607, 442 (1996) screening mass: LPM suppression: the formation time Lg: mean free path Gluons freeze out at local energy density = 1 Ge. V/fm 3. Zhe Xu

3+1 dim. expansion of gluon matter in Au+Au at RHIC Rapidity dependence of total 3+1 dim. expansion of gluon matter in Au+Au at RHIC Rapidity dependence of total transverse energy ZX, Greiner, Stöcker, PRL 101, 082302, 2008 Zhe Xu

Elliptic Flow and Shear Viscosity in Au+Au at RHIC viscous hydro. 2 -3 Parton Elliptic Flow and Shear Viscosity in Au+Au at RHIC viscous hydro. 2 -3 Parton cascade BAMPS ZX, Greiner, Stöcker, PRL 101, 082302, 2008 Romatschke, PRL 99, 172301, 2007 h/s at RHIC > 0. 08 ZX and C. Greiner, PRL 100, 2008 Zhe Xu

Longitudinal expansion with boost invariance (1+1 dim. ) Israel-Stewart hydrodynamics Zhe Xu Longitudinal expansion with boost invariance (1+1 dim. ) Israel-Stewart hydrodynamics Zhe Xu

P. Huovinen and D. Molnar, ar. Xiv: 0808. 0953 [nucl-th] for isotropic 2 -2 P. Huovinen and D. Molnar, ar. Xiv: 0808. 0953 [nucl-th] for isotropic 2 -2 cross sections Zhe Xu

A. El for p. QCD 2 -2 and 2 -3 Zhe Xu A. El for p. QCD 2 -2 and 2 -3 Zhe Xu

A. El Zhe Xu A. El Zhe Xu

Shock waves in 1+1 dim. Riemann porblem isotropic 2 -2 cross sections I. Bouras Shock waves in 1+1 dim. Riemann porblem isotropic 2 -2 cross sections I. Bouras Shocks at RHIC ? Zhe Xu

viscous effect Zhe Xu viscous effect Zhe Xu

Comparison to Israel-Stewart I. Bouras and E. Molnar Viscous hydro falls to describe the Comparison to Israel-Stewart I. Bouras and E. Molnar Viscous hydro falls to describe the viscous effect in the shock front. Zhe Xu

Conclusion • 3+1 Dim. expansion at RHIC: p. QCD 23 + 32 explain large Conclusion • 3+1 Dim. expansion at RHIC: p. QCD 23 + 32 explain large collective flow and small shear viscosity of QCD matter. Initial conditions, hadronization and afterburning are important . • 1+1 Dim. with boost invariance: good agreement between parton cascade and IS-hydro in momentum anisotropy, energy density. large difference in fugacity • 1+1 Dim. Riemann problem: Parton casacde can describe shock waves, hydro not. Zhe Xu

2 -3 Parton cascade BAMPS viscous hydro. Romatschke, PRL 99, 172301, 2007 Hadronization is 2 -3 Parton cascade BAMPS viscous hydro. Romatschke, PRL 99, 172301, 2007 Hadronization is imporatant ! Zhe Xu