| Single particle spectrum, elliptic flow and two-particle Hanbury-Brown-Twiss (HBT) correlations are three crucial final-state observables in high energy heavy-ion collisions. They reflect the source characters from different aspects at the different stages, therefore a com-bined investigation of these observables can provide very strong constraints for the phenom-enal models of the final particle-emitting source. So far, much progress has been made in understanding the results of the heavy ion collisions at the BNL RHIC by comparing the experimental data with model calculations. Recently, the experimental data of several TeV heavy ion collisions at the CERN LHC have been published. It is an ambitious goal for the models to explain the data of the heavy ion collisions at the RHIC and LHC systematically and consistently.In order to explain the RHIC HBT puzzle, people proposed and developed a granular source model of quark-gluon plasma droplets. In this work, we further systematically inves-tigate the pion transverse momentum spectrum, elliptic flow and HBT interferometry for the granular particle-emitting sources for the heavy ion collisions at the RHIC and LHC with different centralities. Our results indicate that the granular source model can reproduce the experimental data of the pion transverse momentum spectra, elliptic flow and HBT radii of the Au-Au collisions with 0-5%,10-20% and 30-50% centralities at (?)= 200 GeV at the RHIC, and the Pb-Pb collisions with 10-20% and 40-50% centralities at (?)= 2.76 TeV at the LHC. The parameters in the granular source model exhibit certain regularities for the col-lision centralities and energies. They are helpful for people to understand the evolution and the dynamical behaviours of the pion-emitting sources in the collisions. On these bases, we further change the initial energy density distributions for the droplets in the granular source, and investigate the initial condition effects on the model parameters through reproducing the experimental data.In the year of 2015, the PHENIX collaboration measured the kaon HBT correlations in the Au+Au collisions at (?)= 200 GeV in different centrality regions and provided the pion HBT radii in a larger transverse mass region compared to the previous measurements. Therefore, explaining the new interferometry data of pion and kaon in the granular source model will be of interest. Considering that the kaons emit early from the source, they are more possible to meet other droplets with higher temperatures and be absorbed when propagating inward in the granular source. Therefore, we perform a simple consideration for the absorption effect and investigate this absorption on the HBT radii of the pion and kaon. In our analyses, the considered absorption effect is important in the kaon interferometry analyses. After considering the absorption, the granular source can better reproduce the HBT experimental data of pion and kaon.Recently, viscous hydrodynamics has been developed significantly in the high energy heavy-ion collisions. We generalize the granular source model with ideal hydrodynamical evolution to the one with viscous hydrodynamics through considering the viscous hydrody-namical evolution in the droplets. We investigate the viscous effects on the model results of pion transverse momentum spectrum, elliptic flow and the HBT radii, and analyse the difference and variation between the model parameters of the ideal and the viscous granu-lar source. It indicates that the shear viscosity of the QGP droplet speeds up the droplet evolution, but the bulk viscous influence is negligible. The pion transverse-momentum spec-trum and elliptic flow change little for the granular sources with and without viscosity The crucial effect of droplet viscosity is on the HBT radius Rout. It has a significant decrease for the viscous granular source compared to that for the granular source without viscosity. The viscosity of droplet leads to the increase of the initial droplet-radius parameter and the decreases of the source-shell parameter and the initial droplet velocity in the granular source model.In high energy heavy-ion collisions, the created extreme hot and dense matter are not uniform in the space. There are event-by-event fluctuations of the system initial quanti-ties in size, shape and magnitude, due to the fluctuating positions of the nucleons inside the colliding nuclei and the quantum fluctuations of the quark and gluon fields inside those nucleons. With the following dynamical evolutions, these initial geometry fluctuations will gradually transform into the anisotropies in the final momentum distributions of the emitted particles. At the end of this thesis, we use Monte Carlo Glauber (MC-Glauber) model as the initial condition and combine with (2+1) dimensional viscous hydrodynamics to investigate the transformation from the initial space fluctuations to the final momentum anisotropies of Pb+Pb collisions at (?)=2.76 TeV at LHC. It is shown that, due to the correlations between the different order initial eccentricities which are caused by the initial fluctuations, the transformation from the initial eccentricity ?n to the corresponding order final trans-verse momentum flow coefficient ?n is not one-to-one, and the final angles of the different order event-plane are also correlated. The initial correlations between the different order participant-planes will bring interactions during the evolution process, therefore produce the final anisotropic flow. |
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