In view of the upcoming ALICE experiment, a dedicated detector to study ultra-relativistic heavy ion collisions at the Large Hadron Collider (LHC) at CERN, the present thesis has been devoted to the study of Elliptic Flow, i.e. the azimuthal anisotropy in the momenta distribution of the final state particles produced in the collision. The anisotropic flow is a key observable to study the thermodynamic properties and the Equation of State of the system created in the collision: the final momenta anisotropy can be connected to the spatial anisotropy of the initial state only by assuming that the system's constituents are strongly coupled and the system behaves as a relativistic fluid. The expected values of elliptic flow and charged multiplicity have been extrapolated to LHC energy (for lead-lead collision at 5.5 TeV per nucleon) in two independent ways; in the Low Density Limit approximation and with the Relativistic Hydro-Dynamic model, producing different impact parameter dependences of the elliptic flow. These predictions have been used as an input for events simulations in the AliRoot framework, to develop and test a flow analysis package for the ALICE environment. The analysis code is based on the event plane method, which has been already successfully used for flow study in other heavy ion experiments at lower energy, such as the Relativistic Heavy Ion Collider (RHIC) in Brookhaven, and the NA experiments at the Super Proton Synchrotron (SPS) at CERN. One of the biggest experimental uncertainties in measuring flow at LHC is the magnitude of non-flow effects, i.e. azimuthal correlations between collision products not due to collective flow, and therefore not correlated with the reaction plane. Depending on the analysis method, non-flow effects can introduce a systematic error in the flow measurement. Non-flow effects have been simulated using the Hijing event generator, which implements all known physics effects from a superposition of proton-proton collisions. Comparison between the expected magnitude of elliptic flow and the estimated magnitude of non-flow contributions defines the applicability of the Event Plane analysis. The study also showed that non-flow effects are less important when the genuine flow or the multiplicity are large, leading to the conclusion that only peripheral reactions are heavily affected by non-flow, while the best sensitivity is achieved in semi-central collisions. It has also been observed that non-flow contributions change significantly for different particle selections and for different definitions of sub-events. Therefore, with different analysis settings, it is possible to minimize them
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