The Relativistic Heavy Ion Collider (RHIC) has provided its experiments with the most energetic nucleus-nucleus collisions ever achieved in a laboratory. These collisions allow for the study of the properties of nuclear matter at very high temperature and energy density, and may uncover new forms of matter created under such conditions. This thesis presents measurements of the elliptic flow amplitude, v2, in Au+Au collisions at RHIC's top center of mass energy of 200 GeV per nucleon pair. Elliptic flow is interesting as a probe of the dynamical evolution of the system formed in the collision. The elliptic flow dependences on transverse momentum, centrality, and pseudorapidity were measured using data collected by the PHOBOS detector during the 2001 RHIC run. The reaction plane of the collision was determined using the multiplicity detector, and the azimuthal angles of tracks reconstructed in the spectrometer were then correlated with the found reaction plane. The v2 values grow almost linearly with transverse momentum, up to P[sub]T of approximately 1.5 GeV, saturating at about 14%. As a function of centrality, v2 is minimum for central events, as expected from geometry, and increases up to near 7% (for 0

Measurements of collective flow and two-particle correlations have proven to be effective tools for understanding the properties of the system produced in ultrarelativistic nucleus-nucleus collisions at the Relativistic Heavy Ion Collider (RHIC). Accurate modeling of the initial conditions of a heavy ion collision is crucial in the interpretation of these results. The anisotropic shape of the initial geometry of heavy ion collisions with finite impact parameter leads to an anisotropic particle production in the azimuthal direction through collective flow of the produced medium. In "head-on" collisions of Copper nuclei at ultrarelativistic energies, the magnitude of this "elliptic flow" has been observed to be significantly large. This is understood to be due to fluctuations in the initial geometry which leads to a significant anisotropy even for most central Cu+Cu collisions. This thesis presents a phenomenological study of the effect of initial geometry fluctuations on two-particle correlations and an experimental measurement of the magnitude of elliptic flow fluctuations which is predicted to be large if initial geometry fluctuations are present. Two-particle correlation measurements in Au+Au collisions at the top RHIC energies have shown that after correction for contributions from elliptic flow, strong azimuthal correlation signals are present at A0 = 0 and A0 ~ 120. These correlation structures may be understood in terms of event-by-event fluctuations which result in a triangular anisotropy in the initial collision geometry of heavy ion collisions, which in turn leads to a triangular anisotropy in particle production. It is observed that similar correlation structures are observed in A Multi-Phase Transport (AMPT) model and are, indeed, found to be driven by the triangular anisotropy in the initial collision geometry. Therefore "triangular flow" may be the appropriate description of these correlation structures in data. The measurement of elliptic flow fluctuations is complicated by the contributions of statistical fluctuations and other two-particle correlations (non-flow correlations) to the observed fluctuations in azimuthal particle anisotropy. New experimental techniques, which crucially rely on the uniquely large coverage of the PHOBOS detector at RHIC, are developed to quantify and correct for these contributions. Relative elliptic flow fluctuations of approximately 30-40% are observed in 6-45% most central Au+Au collisions at s NN= 200 GeV. These results are consistent with the predicted initial geometry fluctuations.

We present measurements of elliptic flow and event-by-event fluctuations established by the PHOBOS experiment. Elliptic flow scaled by participant eccentricity is found to be similar for both systems when collisions with the same number of participants or the same particle area density are compared. The agreement of elliptic flow between Au+Au and Cu+Cu collisions provides evidence that the matter is created in the initial stage of relativistic heavy ion collisions with transverse granularity similar to that of the participant nucleons. The event-by-event fluctuation results reveal that the initial collision geometry is translated into the final state azimuthal particle distribution, leading to an event-by-event proportionality between the observed elliptic flow and initial eccentricity.

"Ultrareletivistic nuclear collisions at the Relativistic Heavy-Ion Collider have produced a high temperature, high energy density medium consisting of a strongly interacting plasma of quarks and gluons. This extreme state of matter provides a testing ground for quantum chromodynamics. Previous studies of gold-gold collisions over a wide range of beam energies revealed many properties of the produced medium. However, these studies were restricted to relatively large colliding systems which resulted in large collision volumes; it is therefore important to investigate what role the size of the collision volume plays in the evolution of the source, particularly as the source volume becomes vanishingly small. This can be achieved with symmetric copper-copper collisions, which offer access to a range of system sizes from [approximately] 10 participating nucleons up through volumes comparable to those created in gold-gold collisions. Collective behaviors of the produced particles in heavy-ion collisions can provide useful probes into the state of the medium produced, including its degree of thermalization and its properties. The elliptic flow, an anisotropy in the azimuthal distribution of the produced particles that is strongly correlated to the initial transverse geometry of the colliding nuclei, is one such collective motion that has proven to be a very useful observable for studying heavy-ion collisions. This is because it exhibits fairly large magnitudes in the systems being studied and is sensitive to the strength of the partonic interactions in-medium. The PHOBOS experiment, which can measure the positions of produced charged particles with high precision over nearly the full solid angle, is well-suited to study the elliptic flow and its evolution over an extended range along the beam direction. The elliptic flow from copper-copper collisions at center-of-mass energies of 22.4, 62.4, and 200GeV per nucleon pair are presented as a function of pseudorapidity and system size. The appearance of unexpected behaviors in the smaller system prompted a re-examination of the role of the collision geometry on the production of elliptic flow. Studies using Monte-Carlo Glauber simulations found that the fluctuating spatial configurations of the component nucleons in the colliding nuclei could result in significant variation of the shape of the nuclear overlap on an event-by-event basis, and that these fluctuations become important for small systems. The eccentricity, a quantity that characterizes the ellipticity of the nuclear overlap in the transverse plane, is redefined to account for these fluctuations as the participant eccentricity. It is found that the event-by-event fluctuations of the participant eccentricity are able to fully account for the observed elliptic flow in the smaller system. The participant eccentricity is used to normalize the measured elliptic flow across different colliding systems to a common initial geometry so that a direct comparison of the properties of the produced medium can be made. It is found that the produced medium evolves smoothly from systems of [approximately] 10 participant nucleons to systems involving more than 350 nucleons and for collision energies from 19.6 to 200GeV per nucleon pair. This smooth evolution of the elliptic flow is also observed as a function of pseudorapidity in all the systems studied. After accounting for the initial geometry, no indication of the identity of the original colliding system is observed"--Page vi-vii.