The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory provides experiments with the most energetic nucleus-nucleus collisions ever achieved in a laboratory. These have been used to investigate the phase diagram of nuclear matter at very high temperature and low baryon chemical potential. Under such conditions, quantum chromodynamics predicts a deconfinement of quarks from their hadronic boundaries, and this is believed to result in a phase transition to a quark gluon plasma (QGP).

The characterization of the substance in a microscopic collision system is difficult because the matter undergoes significant changes as it rapidly inflates and cools. The collective expansion of the medium perpendicular to the collision axis is a revealing feature that can be related to the early stages of the system evolution. Arising as a consequence of the natural spatial asymmetry in non-head-on collisions, the back-to-back "elliptic flow" is a particularly informative mode of the expansion.

The collective movement is characterized in terms of the relaxation of a compressed liquid. The magnitude of the elliptic flow constrains the parameters of various hydrodynamics-based models, and these suggest that the matter behaves as an ultra low-viscosity liquid, achieving local thermal equilibrium very early in the collision evolution.

This thesis presents measurements of the elliptic flow anisotropy parameter, v₂, for Au+Au and Cu+Cu collisions at center-of-mass energies of 200 GeV and 62 GeV per nucleon pair. The data was taken at the PHOBOS experiment at RHIC using the spectrometer in conjunction with the ring and octagon multiplicity detectors.

A Monte Carlo Glauber model is used to establish the eccentricity of the overlap region in non-head-on collisions. When this geometry is taken into account, the elliptic flow is shown to evolve smoothly between collision systems. This behavior is evident, not only in the elliptic flow as a function of reaction centrality, but also as a function of the transverse momentum. The agreement lends support to the prevailing theory of a smooth progression with increasing system size and collision energy towards a hydrodynamic limit.