Measurements of multi-particle azimuthal correlations (cumulants) for charged particles in p-Pb and Pb-Pb collisions are presented. They help address the question of whether there is evidence for global, flow-like, azimuthal correlations in the p-Pb system. Comparisons are made to measurements from the larger Pb-Pb system, where such evidence is established. In particular, the second harmonic two-particle cumulants are found to decrease with multiplicity, characteristic of a dominance of few-particle correlations in p-Pb collisions. However, when a $|\Delta \eta|$ gap is placed to suppress such correlations, the two-particle cumulants begin to rise at high-multiplicity, indicating the presence of global azimuthal correlations. The Pb-Pb values are higher than the p-Pb values at similar multiplicities. In both systems, the second harmonic four-particle cumulants exhibit a transition from positive to negative values when the multiplicity increases. The negative values allow for a measurement of $v_{2}\{4\}$ to be made, which is found to be higher in Pb-Pb collisions at similar multiplicities. The second harmonic six-particle cumulants are also found to be higher in Pb-Pb collisions. In Pb-Pb collisions, we generally find $v_{2}\{4\} \simeq v_{2}\{6\}\neq 0$ which is indicative of a Bessel-Gaussian function for the $v_{2}$ distribution. For very high-multiplicity Pb-Pb collisions, we observe that the four- and six-particle cumulants become consistent with 0. Finally, third harmonic two-particle cumulants in p-Pb and Pb-Pb are measured. These are found to be similar for overlapping multiplicities, when a $|\Delta\eta| > 1.4$ gap is placed.

The elliptic flow coefficient ($v_{2}$) of identified particles in Pb-Pb collisions at $\sqrt{s_\mathrm{{NN}}} = 2.76$ TeV was measured with the ALICE detector at the LHC. The results were obtained with the Scalar Product method, a two-particle correlation technique, using a pseudo-rapidity gap of $|\Delta\eta| > 0.9$ between the identified hadron under study and the reference particles. The $v_2$ is reported for $\pi^{\pm}$, $\mathrm{K}^{\pm}$, $\mathrm{K}^0_\mathrm{S}$, p+$\overline{\mathrm{p}}$, $\mathrm{\phi}$, $\Lambda$+$\overline{\mathrm{\Lambda}}$, $\Xi^-$+$\overline{\Xi}^+$ and $\Omega^-$+$\overline{\Omega}^+$ in several collision centralities. In the low transverse momentum ($p_{\mathrm{T}}$) region, $p_{\mathrm{T}} < 2 $GeV/$c$, $v_2(p_\mathrm{T})$ exhibits a particle mass dependence consistent with elliptic flow accompanied by the transverse radial expansion of the system with a common velocity field. The experimental data for $\pi^{\pm}$ and $\mathrm{K}$ are described fairly well by hydrodynamical calculations coupled to a hadronic cascade model (VISHNU) for central collisions. However, the same calculations fail to reproduce the $v_2(p_\mathrm{T})$ for p+$\overline{\mathrm{p}}$, $\mathrm{\phi}$, $\Lambda$+$\overline{\mathrm{\Lambda}}$ and $\Xi^-$+$\overline{\Xi}^+$. For transverse momentum values larger than about 3 GeV/$c$, particles tend to group according to their type, i.e. mesons and baryons. However, the experimental data at the LHC exhibit deviations from the number of constituent quark (NCQ) scaling at the level of $\pm$20$\%$ for $p_{\mathrm{T}} > 3 $GeV/$c$.

The production of the prompt charmed mesons $D^0$, $D^+$ and $D^{*+}$ relative to the reaction plane was measured in Pb-Pb collisions at a centre-of-mass energy per nucleon-nucleon collision of $\sqrt{s_{\rm NN}} = 2.76$ TeV with the ALICE detector at the LHC. D mesons were reconstructed via their hadronic decays at central rapidity in the transverse momentum ($p_{\rm T}$) interval of 2-16 GeV/$c$. The azimuthal anisotropy is quantified in terms of the second coefficient $v_2$ in a Fourier expansion of the D meson azimuthal distribution, and in terms of the nuclear modification factor $R_{\rm AA}$, measured in the direction of the reaction plane and orthogonal to it. The $v_2$ coefficient was measured with three different methods and in three centrality classes in the interval 0-50%. A positive $v_2$ is observed in mid-central collisions (30-50% centrality class), with an mean value of $0.204_{-0.036}^{+0.099}$ (tot.unc.) in the interval $2 < p_{\rm T} < 6$ GeV/$c$, which decreases towards more central collisions (10-30% and 0-10% classes). The positive $v_2$ is also reflected in the nuclear modification factor, which shows a stronger suppression in the direction orthogonal to the reaction plane for mid-central collisions. The measurements are compared to theoretical calculations of charm quark transport and energy loss in high-density strongly-interacting matter at high temperature. The models that include substantial elastic interactions with an expanding medium provide a good description of the observed anisotropy. However, they are challenged to simultaneously describe the strong suppression of high-$p_{\rm T}$ yield of D mesons in central collisions and their azimuthal anisotropy in non-central collisions.

We report on the first measurement of inclusive J/$\psi$ elliptic flow, $v_2$, in heavy-ion collisions at the LHC. The measurement is performed with the ALICE detector in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV in the rapidity range $2.5 < y < 4.0$. The dependence of the J/$\psi$ $v_2$ on the collision centrality and on the J/$\psi$ transverse momentum is studied in the range $0 < p_{\rm T} < 10$ GeV/$c$. For semi-central Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV, an indication of non-zero $v_2$ is observed with a maximum value of $v_2 = 0.116 \pm 0.046 {\rm (stat.)} \pm 0.029 {\rm (syst.)}$ for J/$\psi$ in the transverse momentum range $2 < p_{\rm T} < 4$ GeV/$c$. The elliptic flow measurement complements the previously reported ALICE results on the inclusive J/$\psi$ nuclear modification factor and favors the scenario of a significant fraction of J/$\psi$ production from charm quarks in a deconfined partonic phase.

The azimuthal anisotropy coefficient $v_2$ of prompt D$^0$, D$^+$, D$^{*+}$ and D$_s^+$ mesons was measured in mid-central (30-50% centrality class) Pb-Pb collisions at a centre-of-mass energy per nucleon pair $\sqrt{s_{\rm NN}} = 5.02$ TeV, with the ALICE detector at the LHC. The D mesons were reconstructed via their hadronic decays at mid-rapidity, $|y|<0.8$, in the transverse momentum interval $1<p_{\rm T}<24$ GeV/$c$. The measured D-meson $v_2$ has similar values as that of charged pions. The D$_s^+$ $v_2$, measured for the first time, is found to be compatible with that of non-strange D mesons. The measurements are compared with theoretical calculations of charm-quark transport in a hydrodynamically expanding medium and have the potential to constrain medium parameters.

Azimuthally anisotropic distributions of D$^0$, D$^+$ and D$^{*+}$ mesons were studied in the central rapidity region ($|y|<0.8$) in Pb-Pb collisions at a centre-of-mass energy $\sqrt{s_{\rm NN}} = 2.76$ TeV per nucleon-nucleon collision, with the ALICE detector at the LHC. The second Fourier coefficient $v_2$ (commonly denoted elliptic flow) was measured in the centrality class 30-50% as a function of the D meson transverse momentum $p_{\rm T}$, in the range 2-16 GeV/$c$. The measured $v_2$ of D mesons is comparable in magnitude to that of light-flavour hadrons. It is positive in the range $2 < p_{\rm T} < 6$ GeV/$c$ with $5.7\sigma$ significance, based on the combination of statistical and systematic uncertainties.

The inclusive J/$\psi$ elliptic ($v_2$) and triangular ($v_3$) flow coefficients measured at forward rapidity (2.5 $<y<$ 4) and the $v_2$ measured at midrapidity ($|y|<$ 0.9) in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV using the ALICE detector at the LHC are reported. The entire Pb-Pb data sample collected during Run 2 is employed, amounting to an integrated luminosity of 750 $\mu$b$^{-1}$ at forward rapidity and 93 $\mu$b$^{-1}$ at midrapidity. The results are obtained using the scalar product method and are reported as a function of transverse momentum $p_{\rm T}$ and collision centrality. At midrapidity, the J/$\psi$ $v_2$ is in agreement with the forward rapidity measurement. The centrality averaged results indicate a positive J/$\psi$ $v_3$ with a significance of more than 5$\sigma$ at forward rapidity in the $p_{\rm T}$ range $2<p_{\rm T}<5$ GeV/$c$. The forward rapidity $v_2$, $v_3$, and $v_3$/$v_2$ results at low and intermediate $p_{\rm T}$ ($p_{\rm T} \lesssim 8$ GeV/$c$) exhibit a mass hierarchy when compared to pions and D mesons, while converging into a species-independent curve at higher $p_{\rm T}$. At low and intermediate $p_{\rm T}$, the results could be interpreted in terms of a later thermalization of charm quarks compared to light quarks, while at high $p_{\rm T}$, path-length dependent effects seem to dominate. The J/$\psi$ $v_2$ measurements are further compared to a microscopic transport model calculation. Using a simplified extension of the quark scaling approach involving both light and charm quark flow components, it is shown that the D-meson $v_{\rm n}$ measurements can be described based on those for charged pions and J/$\psi$ flow.

We report the first measurement of charged particle elliptic flow in Pb-Pb collisions at 2.76 TeV with the ALICE detector at the CERN Large Hadron Collider. The measurement is performed in the central pseudorapidity region (|$\eta$|<0.8) and transverse momentum range 0.2< $p_{\rm T}$< 5.0 GeV/$c$. The elliptic flow signal v$_2$, measured using the 4-particle correlation method, averaged over transverse momentum and pseudorapidity is 0.087 $\pm$ 0.002 (stat) $\pm$ 0.004 (syst) in the 40-50% centrality class. The differential elliptic flow v$_2(p_{\rm T})$ reaches a maximum of 0.2 near $p_{\rm T}$ = 3 GeV/$c$. Compared to RHIC Au-Au collisions at 200 GeV, the elliptic flow increases by about 30%. Some hydrodynamic model predictions which include viscous corrections are in agreement with the observed increase.

Measurements of the elliptic flow coefficient relative to the collision plane defined by the spectator neutrons $v_2${$\Psi_{\rm SP}$} in collisions of Pb ions at center-of-mass energy per nucleon-nucleon pair $\sqrt{s_{\rm NN}}$=2.76 TeV and Xe ions at $\sqrt{s_{\rm NN}}$=5.44 TeV are reported. The results are presented for charged particles produced at midrapidity as a function of centrality and transverse momentum. The ratio between $v_2${$\Psi_{\rm SP}$} and the elliptic flow coefficient relative to the participant plane $v_2$4, estimated using four-particle correlations, deviates by up to 20% from unity depending on centrality. This observation differs strongly from the magnitude of the corresponding eccentricity ratios predicted by the TRENTo and the elliptic power models of initial state fluctuations that are tuned to describe the participant plane anisotropies. The differences can be interpreted as a decorrelation of the neutron spectator plane and the reaction plane because of fragmentation of the remnants from the colliding nuclei, which points to an incompleteness of current models of initial state fluctuations. A significant transverse momentum dependence of the ratio $v_2${$\Psi_{\rm SP}$}/$v_2${4} is observed in all but the most central collisions, which may help to understand whether momentum anisotropies at low and intermediate transverse momentum have a common origin in initial state fluctuations. The ratios of $v_2${$\Psi_{\rm SP}$} and $v_2${4} to the corresponding initial state eccentricities for Xe-Xe and Pb-Pb collisions at similar initial entropy density show a difference of $(7.0 \pm 0.9)$% with an additional variation of +1.8% when including RHIC data in the TRENTo parameter extraction. These observations provide new experimental constraints for viscous effects in the hydrodynamic modeling of the expanding quark-gluon plasma.

The elliptic and triangular flow coefficients $v_2$ and $v_3$ of prompt D$^{0}$, D$^{+}$, and D$^{*+}$ mesons were measured at midrapidity ($|y|<0.8$) in Pb-Pb collisions at the centre-of-mass energy per nucleon pair of $\sqrt{s_{NN}} = 5.02$ TeV with the ALICE detector at the LHC. The D mesons were reconstructed via their hadronic decays in the transverse momentum interval $1< p_{\rm T}<36$ GeV/$c$ in central (0-10%) and semi-central (30-50%) collisions. Compared to pions, protons, and J/$\psi$ mesons, the average D-meson $v_{n}$ harmonics are compatible within uncertainties with a mass hierarchy for $p_{\rm T} \lesssim 3$ GeV/$c$, and are similar to those of charged pions for higher $p_{\rm T}$. The coupling of the charm quark to the light quarks in the underlying medium is further investigated with the application of the event-shape engineering (ESE) technique to the D-meson $v_2$ and $p_{\rm T}$-differential yields. The D-meson $v_2$ is correlated with average bulk elliptic flow in both central and semi-central collisions. Within the current precision, the ratios of per-event D-meson yields in the ESE-selected and unbiased samples are found to be compatible with unity. All the measurements are found to be reasonably well described by theoretical calculations including the effects of charm-quark transport and the recombination of charm quarks with light quarks in a hydrodynamically expanding medium.