ATLAS measurements of the azimuthal anisotropy in lead-lead collisions at $\sqrt{s_{NN}}=2.76$ TeV are shown using a dataset of approximately 7 $\mu$b$^{-1}$ collected at the LHC in 2010. The measurements are performed for charged particles with transverse momenta $0.5<p_T<20$ GeV and in the pseudorapidity range $|\eta|<2.5$. The anisotropy is characterized by the Fourier coefficients, $v_n$, of the charged-particle azimuthal angle distribution for n = 2-4. The Fourier coefficients are evaluated using multi-particle cumulants calculated with the generating function method. Results on the transverse momentum, pseudorapidity and centrality dependence of the $v_n$ coefficients are presented. The elliptic flow, $v_2$, is obtained from the two-, four-, six- and eight-particle cumulants while higher-order coefficients, $v_3$ and $v_4$, are determined with two- and four-particle cumulants. Flow harmonics $v_n$ measured with four-particle cumulants are significantly reduced compared to the measurement involving two-particle cumulants. A comparison to $v_n$ measurements obtained using different analysis methods and previously reported by the LHC experiments is also shown. Results of measurements of flow fluctuations evaluated with multi-particle cumulants are shown as a function of transverse momentum and the collision centrality. Models of the initial spatial geometry and its fluctuations fail to describe the flow fluctuations measurements.

Measurements of the azimuthal anisotropy in lead-lead collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV are presented using a data sample corresponding to 0.49 $\mathrm{nb}^{-1}$ integrated luminosity collected by the ATLAS experiment at the LHC in 2015. The recorded minimum-bias sample is enhanced by triggers for "ultra-central" collisions, providing an opportunity to perform detailed study of flow harmonics in the regime where the initial state is dominated by fluctuations. The anisotropy of the charged-particle azimuthal angle distributions is characterized by the Fourier coefficients, $v_{2}-v_{7}$, which are measured using the two-particle correlation, scalar-product and event-plane methods. The goal of the paper is to provide measurements of the differential as well as integrated flow harmonics $v_{n}$ over wide ranges of the transverse momentum, 0.5 $

Measurements of two-particle correlation functions and the first five azimuthal harmonics, $v_1$ to $v_5$, are presented, using 28 $\mathrm{nb}^{-1}$ of $p$+Pb collisions at a nucleon-nucleon center-of-mass energy of $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV measured with the ATLAS detector at the LHC. Significant long-range "ridge-like" correlations are observed for pairs with small relative azimuthal angle ($|\Delta\phi|<\pi/3$) and back-to-back pairs ($|\Delta\phi| > 2\pi/3$) over the transverse momentum range $0.4 < p_{\rm T} < 12$ GeV and in different intervals of event activity. The event activity is defined by either the number of reconstructed tracks or the total transverse energy on the Pb-fragmentation side. The azimuthal structure of such long-range correlations is Fourier decomposed to obtain the harmonics $v_n$ as a function of $p_{\rm T}$ and event activity. The extracted $v_n$ values for $n=2$ to 5 decrease with $n$. The $v_2$ and $v_3$ values are found to be positive in the measured $p_{\rm T}$ range. The $v_1$ is also measured as a function of $p_{\rm T}$ and is observed to change sign around $p_{\rm T}\approx 1.5$-2.0 GeV and then increase to about 0.1 for $p_{\rm T}>4$ GeV. The $v_2(p_{\rm T})$, $v_3(p_{\rm T})$ and $v_4(p_{\rm T})$ are compared to the $v_n$ coefficients in Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}} =2.76$ TeV with similar event multiplicities. Reasonable agreement is observed after accounting for the difference in the average $p_{\rm T}$ of particles produced in the two collision systems.

Correlations between the elliptic or triangular flow coefficients $v_m$ ($m$=2 or 3) and other flow harmonics $v_n$ ($n$=2 to 5) are measured using $\sqrt{s_{NN}}=2.76$ TeV Pb+Pb collision data collected in 2010 by the ATLAS experiment at the LHC, corresponding to an integrated lumonisity of 7 $\mu$b$^{-1}$. The $v_m$-$v_n$ correlations are measured in midrapidity as a function of centrality, and, for events within the same centrality interval, as a function of event ellipticity or triangularity defined in a forward rapidity region. For events within the same centrality interval, $v_3$ is found to be anticorrelated with $v_2$ and this anticorrelation is consistent with similar anticorrelations between the corresponding eccentricities $\epsilon_2$ and $\epsilon_3$. On the other hand, it is observed that $v_4$ increases strongly with $v_2$, and $v_5$ increases strongly with both $v_2$ and $v_3$. The trend and strength of the $v_m$-$v_n$ correlations for $n$=4 and 5 are found to disagree with $\epsilon_m$-$\epsilon_n$ correlations predicted by initial-geometry models. Instead, these correlations are found to be consistent with the combined effects of a linear contribution to $v_n$ and a nonlinear term that is a function of $v_2^2$ or of $v_2v_3$, as predicted by hydrodynamic models. A simple two-component fit is used to separate these two contributions. The extracted linear and nonlinear contributions to $v_4$ and $v_5$ are found to be consistent with previously measured event-plane correlations.

The integrated elliptic flow of charged particles produced in Pb+Pb collisions at sqrt(s_NN)=2.76 TeV has been measured with the ATLAS detector using data collected at the Large Hadron Collider. The anisotropy parameter, v_2, was measured in the pseudorapidity range |eta| <= 2.5 with the event-plane method. In order to include tracks with very low transverse momentum pT, thus reducing the uncertainty in v_2 integrated over pT, a 1 mu b-1 data sample without a magnetic field in the tracking detectors is used. The centrality dependence of the integrated v_2 is compared to other measurements obtained with higher pT thresholds. A weak pseudorapidity dependence of the integrated elliptic flow is observed for central collisions, and a small decrease when moving away from mid-rapidity is observed only in peripheral collisions. The integrated v2 transformed to the rest frame of one of the colliding nuclei is compared to the lower-energy RHIC data.

The distributions of event-by-event harmonic flow coefficients v_n for n=2-4 are measured in sqrt(s_NN)=2.76 TeV Pb+Pb collisions using the ATLAS detector at the LHC. The measurements are performed using charged particles with transverse momentum pT> 0.5 GeV and in the pseudorapidity range |eta|<2.5 in a dataset of approximately 7 ub^-1 recorded in 2010. The shapes of the v_n distributions are described by a two-dimensional Gaussian function for the underlying flow vector in central collisions for v_2 and over most of the measured centrality range for v_3 and v_4. Significant deviations from this function are observed for v_2 in mid-central and peripheral collisions, and a small deviation is observed for v_3 in mid-central collisions. It is shown that the commonly used multi-particle cumulants are insensitive to the deviations for v_2. The v_n distributions are also measured independently for charged particles with 0.5<pT<1 GeV and pT>1 GeV. When these distributions are rescaled to the same mean values, the adjusted shapes are found to be nearly the same for these two pT ranges. The v_n distributions are compared with the eccentricity distributions from two models for the initial collision geometry: a Glauber model and a model that includes corrections to the initial geometry due to gluon saturation effects. Both models fail to describe the experimental data consistently over most of the measured centrality range.

We report systematic measurements of bulk properties of the system created in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 14.5 GeV recorded by the STAR detector at the Relativistic Heavy Ion Collider (RHIC).The transverse momentum spectra of $\pi^{\pm}$, $K^{\pm}$ and $p(\bar{p})$ are studied at mid-rapidity ($|y| < 0.1$) for nine centrality intervals. The centrality, transverse momentum ($p_T$),and pseudorapidity ($\eta$) dependence of inclusive charged particle elliptic flow ($v_2$), and rapidity-odd charged particles directed flow ($v_{1}$) results near mid-rapidity are also presented. These measurements are compared with the published results from Au+Au collisions at other energies, and from Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV. The results at $\sqrt{s_{\mathrm{NN}}}$ = 14.5 GeV show similar behavior as established at other energies and fit well in the energy dependence trend. These results are important as the 14.5 GeV energy fills the gap in $\mu_B$, which is of the order of 100 MeV,between $\sqrt{s_{\mathrm{NN}}}$ =11.5 and 19.6 GeV. Comparisons of the data with UrQMD and AMPT models show poor agreement in general.

Collisions between prolate uranium nuclei are used to study how particle production and azimuthal anisotropies depend on initial geometry in heavy-ion collisions. We report the two- and four-particle cumulants, $v_2\{2\}$ and $v_2\{4\}$, for charged hadrons from U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV and Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV. Nearly fully overlapping collisions are selected based on the amount of energy deposited by spectators in the STAR Zero Degree Calorimeters (ZDCs). Within this sample, the observed dependence of $v_2\{2\}$ on multiplicity demonstrates that ZDC information combined with multiplicity can preferentially select different overlap configurations in U+U collisions. An initial-state model with gluon saturation describes the slope of $v_2\{2\}$ as a function of multiplicity in central collisions better than one based on Glauber with a two-component multiplicity model.

In high-energy heavy-ion collisions, partonic collectivity is evidenced by the constituent quark number scaling of elliptic flow anisotropy for identified hadrons. A breaking of this scaling and dominance of baryonic interactions is found for identified hadron collective flow measurements in $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. In this paper, we report measurements of the first- and second-order azimuthal anisotropic parameters, $v_1$ and $v_2$, of light nuclei ($d$, $t$, $^{3}$He, $^{4}$He) produced in $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions at the STAR experiment. An atomic mass number scaling is found in the measured $v_1$ slopes of light nuclei at mid-rapidity. For the measured $v_2$ magnitude, a strong rapidity dependence is observed. Unlike $v_2$ at higher collision energies, the $v_2$ values at mid-rapidity for all light nuclei are negative and no scaling is observed with the atomic mass number. Calculations by the Jet AA Microscopic Transport Model (JAM), with baryonic mean-field plus nucleon coalescence, are in good agreement with our observations, implying baryonic interactions dominate the collective dynamics in 3 GeV Au+Au collisions at RHIC.

Dihadron angular correlations in $d$+Au collisions at $\sqrt{s_{\rm NN}}=200$ GeV are reported as a function of the measured zero-degree calorimeter neutral energy and the forward charged hadron multiplicity in the Au-beam direction. A finite correlated yield is observed at large relative pseudorapidity ($\Delta\eta$) on the near side (i.e. relative azimuth $\Delta\phi\sim0$). This correlated yield as a function of $\Delta\eta$ appears to scale with the dominant, primarily jet-related, away-side ($\Delta\phi\sim\pi$) yield. The Fourier coefficients of the $\Delta\phi$ correlation, $V_{n}=\langle\cos n\Delta\phi\rangle$, have a strong $\Delta\eta$ dependence. In addition, it is found that $V_{1}$ is approximately inversely proportional to the mid-rapidity event multiplicity, while $V_{2}$ is independent of it with similar magnitude in the forward ($d$-going) and backward (Au-going) directions.