Fluctuations Of The Pion HBT Correlation And Collective Flow Forthe Evolving SPH Source

In this paper, we study the evolution of model, which is named smoothed particle hydrodynamic evolution of relativistic heavy ion collsions(SP H), at different collsion-energy as RHIC(Relativistic Heavy Ion Collider) 200 NNs = Ge V Au+Au and LHC(Large Hadron Collider) 2.76 NNs = Te V Pb+Pb. The distribution of the nuclear collision are inhomogeneous even at the later stage of the evolutions because of the inhomogeneous shape of the initial sources. So it is different when we calculate the observables for the hydrodynamic sources with the fluctuating initial conditions or the hydrodynamic sources with the smoothed initial conditions.At first, we introduce the basic theory of the SPH, derive the basic equation and the equation of state of the evolution of the hydrodynamic sources. Then we study the evolution of hydrodynamic sources with different initial energy, different impacting parameter to find the difference between the fluctuating initial conditions and the smoothed initial conditions. And we calculate the results of the elliptic flows, the triangular flows, the transverse spectrums, and the two-pion correlation functions according to the information of the final state particles with FIC and SIC. Above all, we study the fluctuation of the two-pion correlation functions, according to the expanded width of a special parameter f with different initial conditions. The results show that the width of f increase with the collision energy and the impact parameter, and for the SIC, the two-pion correlation functions do not change significantly. At last we calculate the collective flows of the SPH with two ways, find out the correlation of fluctuation for the elliptic flows, the triangular flows with the impact parameter and the collision energy. We also study the relationship between the distribution of the fuctuations of elliptic flow and triangular flow for different sub-events collections and the whole events carefully. And we find the elliptic flows and the triangular flows change to be obvious with the increase of the transverse momentum only when we take a large numbers of statistics events.