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 waves at RHIC ? Zhe Xu
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 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 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
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 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 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
![P. Huovinen and D. Molnar, ar. Xiv: 0808. 0953 [nucl-th] for isotropic 2 -2](https://present5.com/presentation/491d488fb0368041fdb24cc5cb968cbf/image-11.jpg "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 Zhe Xu
Shock waves in 1+1 dim. Riemann porblem isotropic 2 -2 cross sections I. Bouras Shocks at RHIC ? Zhe Xu
viscous effect Zhe Xu
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 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 imporatant ! Zhe Xu
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