Denes Molnar, Pasi Huovinen
In an earlier work (arXiv:0808.0953) we established that causal Israel-Stewart viscous hydrodynamics is only accurate in RHIC applications at very low shear viscosities 4 pi eta_s / s < ~ 1.5-2. We show here that the region of applicability is significantly reduced if bulk viscosity plays a role in the dynamics.
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In this proceeding, we briefly describe the viscous hydrodynamics + hadron cascade hybrid model VISHNU for relativistic heavy ion collisions and report the current status on extracting the QGP viscosity from elliptic flow data.
We report recent progress on causal viscous hydrodynamics for relativistic heavy ion collisions. For fixed specific shear viscosity eta/s, uncertainties in the elliptic flow arising from initial conditions, equation of state, bulk viscosity and numerical viscosity, and the treatment of the highly viscous hadronic stage and freeze-out procedure are analysed. A comparison of current viscous hydrodynamic results with experimental data yields a robust upper limit eta/s < 5/(4pi).
Using the (2+1)-dimensional ultrarelativistic viscous hydrodynamics+hadron cascade, VISHNU, hybrid model, we study the $p_{\rm T}$-spectra and elliptic flow of $Λ$, $Ξ$, and $Ω$ in Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV and in Pb+Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV. Comparing our model results with the data measurements, we find that the VISHNU model gives general descriptions of the measurements of these strange and multi-strange hadrons at several centrality classes at RHIC and LHC. Mass ordering of elliptic flow $v_{2}$ among $π$, $K$, $p$, $Λ$, $Ξ$, and $Ω$ are further investiga…
Using ideal and viscous hydrodynamics, the ratio of azimuthal moments v4/(v2)^2 is calculated for pions, protons, and kaons in sqrt{s}=200 A*GeV Au+Au collisions. For any value of viscosity here is little dependence on particle species. Ideal hydrodynamics and data show a flat curve as a function of pt. Adding viscosity in the standard way destroys this flatness. However, it can be restored by replacing the standard quadratic ansatz for delta f (the viscous correction to the distribution function at freeze-out) with a weaker momentum dependence.
We have studied the space-time evolution of minimally viscous ($\fracη{s}$=0.08) QGP fluid, undergoing boost-invariant longitudinal motion and arbitrary transverse expansion. Relaxation equations for the shear stress tensor components, derived from the phenomenological Israel-Stewart's theory of dissipative relativistic fluid, are solved simultaneously with the energy-momentum conservation equations. Comparison of evolution of ideal and viscous fluid, both initialized under the similar conditions, e.g. same equilibration time, energy density and velocity profile, indicate that in viscous fluid…
The charged-particle's final state spectrum is derived from an analytic perturbative solution for the relativistic viscous hydrodynamics. By taking into account the longitudinal acceleration effect in relativistic viscous hydrodynamics, the pseudorapidity spectrum describes well the nucleus-nucleus colliding systems at RHIC and LHC. Based on both the extracted longitudinal acceleration parameters $λ^{*}$ and a phenomenological description of the $λ^{*}$, the charged-particle's pseudorapidity distributions for $\sqrt{s_{NN}}$ = 5.44 TeV Xe+Xe collisions are computed from the final state express…
Hydrodynamic behavior and the associated discussions of viscosity at RHIC has inspired a r enaissance in modeling viscous hydrodynamics. An explanation of Israel-Stewart hydrodynamics is presented here, with an emphasis on the tangible benefits compared to Navier Stokes.
Charged hadron spectra and anisotropic flow from the AMPT model with shear viscous transport dynamics simulations at RHIC
该研究利用AMPT模型模拟RHIC能区金核碰撞的部分子剪切粘滞输运，验证了模拟结果与实验数据的吻合性，并揭示了相变温度对粒子产额及各向异性流的调控规律。
Polarized $ϕ$ meson rates with viscous corrections at RHIC
该研究分析超相对论重离子碰撞中极化$ϕ$介子的发射，推导了强子相下领头阶与次领头阶的发射率修正，探讨了其对重离子碰撞中$ϕ$介子排列的意义。
We investigate the form of the viscous correction to the equilibrium distribution function in the context of a Cooper-Frye freeze out prescription for viscous hydrodynamic simulations of relativistic heavy ion collisions. The standard quadratic ansatz used by all groups for the case of shear viscosity is found to be disfavored by experimental data for v4/(v2)^2 at the Relativistic Heavy Ion Collider, and is unlikely to be correct for the hadron resonance gas present at freeze out. Instead, data for v2(pt) along with v4/(v2)^2 favor a momentum dependence between linear and quadratic.
We compute v4/(v2)^2 in ideal and viscous hydrodynamics. We investigate its sensitivity to details of the hydrodynamic model and compare the results to experimental data from RHIC. Whereas v2 has a significant sensitivity only to initial eccentricity and viscosity while being insensitive to freeze out temperature, we find that v4/(v2)^2 is quite insensitive to initial eccentricity. On the other hand, it can still be sensitive to shear viscosity in addition to freeze out temperature, although viscous effects do not universally increase v4/(v2)^2 as originally predicted. Consistent with data, we…
In this dissertation I introduce relativistic heavy ion collisions and describe theoretical approaches to understanding them--in particular, viscous hydrodynamic simulations and investigations of final state interactions. The successful ideal hydrodynamic models of the collisions at the Relativistic Heavy Ion Collider (RHIC) were extended by performing viscous hydrodynamic simulations. This was done by making use of the recently derived full conformally invariant second order relativistic viscous hydrodynamic equations. Results for multiplicity, radial flow and elliptic flow in sqrt{s_NN}=200 …
A variety of physical phenomena can lead to viscous effects. In this talk we review several sources of shear and bulk viscosity with an emphasis on the bulk viscosity associated with chiral restoration. We show that in the limit of a second order phase transition, the viscosity peaks in a singularity at the critical point.
A variety of physical phenomena can lead to viscous effects. Several sources of shear and bulk viscosity are reviewed with an emphasis on the bulk viscosity associated with chiral restoration and with chemical non-equilibrium. We show that in a mean-field treatment of the limiting case of a second order phase transition, the bulk viscosity peaks in a singularity at the critical point.
A state-of-the-art 3+1 dimensional cascade + viscous hydro + cascade model vHLLE+UrQMD has been applied to heavy ion collisions in RHIC Beam Energy Scan range $\sqrt{s_{\rm NN}}=7.7\dots 200$ GeV. Based on comparison to available experimental data it was estimated that an effective value of shear viscosity over entropy density ratio $η/s$ in hydrodynamic stage has to decrease from $η/s=0.2$ to $0.08$ as collision energy increases from $\sqrt{s_{\rm NN}} = 7.7$ to $39$ GeV, and to stay at $η/s=0.08$ for $39\le\sqrt{s_{\rm NN}}\le200$ GeV. In this work we show how an equation of state with first…
A new set of equations for relativistic viscous hydrodynamics that captures both weak-coupling and strong-coupling physics to second order in gradients has been developed recently. We apply this framework to bulk physics at RHIC, both for standard (Glauber-type) as well as for Color-Glass-Condensate initial conditions and show that the results do not depend strongly on the values for the second-order transport coefficients. Results for multiplicity, radial flow and elliptic flow are presented and we quote the ratio of viscosity over entropy density for which our hydrodynamic model is consisten…
In the RHIC Beam Energy Scan program, gold nuclei are collided with different collision energies in the range from few to 62.4 GeV. The goals of the program are to explore the onset of QGP creation, locate the critical point of QCD and study dense baryon matter. We report on the first application of Monte Carlo Glauber (GLISSANDO2) and T$_{\rm R}$ENTo $p=0$ initial states extended to 3D for event-by-event viscous fluid dynamic (vHLLE) with hadronic cascade modelling of Au+Au collisions at $\sqrt{s_{_{\rm NN}}}=27$ and 62.4 GeV, which is the upper region of RHIC BES energies. The initial states…
We compare 2->2 covariant transport theory and causal Israel-Stewart hydrodynamics in 2+1D longitudinally boost invariant geometry with RHIC-like initial conditions and a conformal e = 3p equation of state. The pressure evolution in the center of the collision zone and the final differential elliptic flow v2(pT) from the two theories agree remarkably well for a small shear viscosity to entropy density ratio eta/s ~ 1/(4 pi), and also for a large cross section sigma ~ 50 mb. A key to this agreement is keeping ALL terms in the Israel-Stewart equations of motion. Our results indicate promising pr…
The viscosity of the QGP is a presently hotly debated subject. Since its computation from first principles is difficult, it is desirable to try to extract it from experimental data. Viscous hydrodynamics provides a tool that can attack this problem and which may work in regions where ideal hydrodynamics begins to fail. This thesis focuses on viscous hydrodynamics for relativistic heavy ion collisions. We first review the 2nd order viscous equations obtained from different approaches, and then report on the work of the Ohio State University group on setting up the equations for causal viscous h…
The matter created in relativistic heavy ion collisions is fairly well described by ideal hydrodynamics, and somewhat better described by viscous hydrodynamics. To this point, most viscous calculations have been two-dimensional, based on an assumption of Bjorken boost invariance along the beam axis. Here, first results are presented for a fully three-dimensional viscous model. The model is described and tests of the numerical accuracy of the code are presented. Two- and three-dimensional runs are compared, and modest changes are observed for mid-rapidity observables at the highest RHIC (Relati…
We present a systematic hydrodynamic study of the evolution of hadron spectra and their azimuthal anisotropy from the lowest collision energy studied at the Relativistic Heavy Ion Collider (RHIC), sqrt(s) = 7.7 A GeV, to the highest energy reachable at the Large Hadron Collider (LHC), sqrt(s) = 5500 A GeV. The energy dependence of the flow observables are quantitatively studied for both the Monte-Carlo Glauber and Monte-Carlo Kharzeev-Levin-Nardi (MC-KLN) models. For MC-Glauber model initial conditions with η/s = 0.08, the differential charged hadron elliptic flow v_2^{ch}(p_T, sqrt(s)) is fou…
Relativistic heavy ion collisions have reached energies that enable the creation of a novel state of matter termed the quark-gluon plasma. Many observables point to a picture of the medium as rapidly equilibrating and expanding as a nearly inviscid fluid. In this article, we explore the evolution of experimental flow observables as a function of collision energy and attempt to reconcile the observed similarities across a broad energy regime in terms of the initial conditions and viscous hydrodynamics. If the initial spatial anisotropies are very similar for all collision energies from 39 GeV t…
We present event-by-event viscous hydrodynamic calculations of the anisotropic flow coefficients v_2 to v_5 for heavy-ion collisions at the Relativistic Heavy-Ion Collider (RHIC). We study the dependence of different flow harmonics on shear viscosity and the morphology of the initial state. v_3 and higher flow harmonics exhibit a particularly strong dependence on both the initial granularity and shear viscosity. We argue that a combined analysis of all available flow harmonics will allow to determine eta/s of the quark gluon plasma precisely. Presented results strongly hint at a value (eta/s)_…
Extended applicability domain of viscous anisotropic hydrodynamics in (2+1)-D Bjorken flow with transverse expansion
本文通过(2+1)维模拟展示黏性各向异性流体动力学在宽范围不透明度下的优越描述能力，扩展了流体动力学建模的应用范围，为小系统集体流描述提供新方法。
We present a first calculation of the dilepton yield and elliptic flow done with 3+1D viscous hydrodynamical simulations of relativistic heavy ion collisions at the top RHIC energy. A comparison with recent experimental data from the STAR collaboration is made.
The particle spectra and Hanbury-Brown Twiss (HBT) radius of Au+Au collisions at RHIC energy are investigated by a hydrodynamical expanding source with both shear and bulk viscosities ($ζ$). With a large width of the ratio of $ζ$ to entropy density $s$, both the particle transverse momentum spectra and the ratio $R_{out}/R_{side}$ of HBT radii in the direction of the total transverse momentum of detected two particles ($R_{out}$) and perpendicular to both this direction and the beam direction ($R_{side}$) become a little steeper.
Identified particle observables from viscous hydrodynamics are sensitive to the fluid-to-particle conversion. Instead of the commonly assumed "democratic" Grad ansatz for phase space corrections $δf$, we utilize corrections calculated from linearized covariant transport theory. Estimates based on a pion-proton system with binary collisions indicate that protons are much closer to equilibrium than pions, significantly affecting the dissipative reduction of differential elliptic flow in Au+Au at RHIC. In addition, we test linear response against fully nonlinear transport for a two-component mass…
Following the experimental program at BNL RHIC, we perform a similar "energy scan" using 3+1D viscous hydrodynamics coupled to the UrQMD hadron cascade, and study the collision energy dependence of pion and kaon rapidity distributions and $m_T$-spectra, as well as charged hadron elliptic flow. To this aim the equation of state for finite baryon density from a Chiral model coupled to the Polyakov loop is employed for hydrodynamic stage. 3D initial conditions from UrQMD are used to study gradual deviation from boost-invariant scaling flow. We find that the inclusion of shear viscosity in the hyd…
The invariant mass spectrum and the elliptic flow of lepton pairs produced in relativistic heavy-ion collisions at RHIC are studied with viscous hydrodynamics. The effects of viscous corrections on dilepton observables are explored. The lepton pairs originating from charm quarks evolving in the viscous background are seen to be a good probe of quark energy loss and gain, as quantified by the dilepton spectrum and by the dilepton elliptic flow.
We present the first calculation of longitudinal decorrelation of anisotropic flow at RHIC Beam Energy Scan (BES) energies using event-by-event viscous hydrodynamic model (vHLLE), with two different initial states (GLISSANDO2 and UrQMD) and hadronic cascade. We investigate the origin of the observed decorrelation by checking separately flow angle and flow magnitude decorrelation and by calculating decorrelation in the initial state eccentricity.
We investigate the collision energy dependence of $η/s$ in a transport + viscous hydrodynamics hybrid model. A Bayesian analysis is performed on RHIC beam energy scan data for $Au+Au$ collisions at $\sqrt{s_{NN}}=19.6,39,$ and $62.4$ GeV. The resulting posterior probability distributions for the model parameters show a preference for a larger value of $η/s$ at $19.6$ GeV compared to $62.4$ GeV, indicating dependence on baryon chemical potential $μ_B$.
Hydrodynamic model simulations of Au-Au collisions at RHIC have indicated recently, that with improved simulations in the coming years, it may be feasible to quantify the viscosity of the matter produced in heavy ion collisions. To this end, a consistent fluid dynamic description of viscous effects is clearly needed. In this note, we observe that a recently used, approximate form of the 2nd order Israel-Stewart viscous hydrodynamic equations of motion cannot account consistently for the transverse flow fields, which are expected to develop in heavy ion collisions. We identify the appropriate e…
We present state-of-the-art calculations of viscous photon emission from nuclear collisions at RHIC and LHC. Fluctuating initial density profiles are evolved with event-by-event viscous hydrodynamics. Momentum spectra of thermal photons radiated by these explosively expanding fireballs and their $p_T$-differential anisotropic flow coefficients $v_n(p_T)$ are computed, both with and without accounting for viscous corrections to the standard thermal emission rates. Viscous corrections to the rates are found to have a larger effect on the $v_n$ coefficients than the viscous suppression of hydrody…
Simulations of the viscous hydrodynamic model for relativistic heavy-ion collisions at RHIC and LHC energies are presented. Results for spectra, femtoscopy radii, and transverse momentum fluctuations are favorably compared to the experimental data. Effects of the local charge conservation on correlation observables are also studied.
Using a (2+1)-d viscous hydrodynamical model, we study the dependence of flow observables on the collision energy ranging from sqrt(s)=7.7 A GeV at the Relativistic Heavy Ion Collider (RHIC) to sqrt(s)=2760 A GeV at the Large Hadron Collider (LHC). With a realistic equation of state, Glauber model initial conditions and a small specific shear viscosity eta/s = 0.08, the differential charged hadron elliptic flow v_2^{ch}(p_T,sqrt(s)) is found to exhibit a very broad maximum as a function of sqrt(s) around top RHIC energy, rendering it almost independent of collision energy for 39 < sqrt(s) < 27…
Hydrodynamic simulations are used to make predictions for the integrated elliptic flow coefficient v_2 in sqrt(s)=5.5 TeV lead-lead and sqrt(s)=14 TeV proton-proton collisions at the LHC. We predict a 10% increase in v_2 from RHIC to Pb+Pb at LHC, and v_2 ~ 0 in p+p collisions unless eta/s < 0.08.
Relativistic viscous hydrodynamic fits to RHIC data on the centrality dependence of multiplicity, transverse and elliptic flow for sqrt{s}=200 GeV Au+Au collisions are presented. For Glauber-type initial conditions, while data on integrated v_2 is consistent with a ratio of viscosity over entropy density up to eta/s=0.16, data on minimum bias v_2 seems to favor a much smaller viscosity over entropy ratio, below the bound from the AdS/CFT conjecture. Some caveats on this result are discussed.
We review the results from the event-by-event next-to-leading order perturbative QCD + saturation + viscous hydrodynamics (EbyE NLO EKRT) model. With a simultaneous analysis of LHC and RHIC bulk observables we systematically constrain the QCD matter shear viscosity-to-entropy ratio eta/s(T), and test the initial state computation. In particular, we study the centrality dependences of hadronic multiplicities, pT spectra, flow coefficients, relative elliptic flow fluctuations, and various flow-correlations in 2.76 and 5.02 TeV Pb+Pb collisions at the LHC and 200 GeV Au+Au collisions at RHIC. Ove…
To study the bulk properties of the quark-gluon-plasma (QGP) produced at the beam energy scan (BES) energies at the Relativistic Heavy Ion Collider (RHIC), we extend the (3+1)-dimensional viscous hydrodynamics CLVisc to include net baryon number conservation and Israel-Stewart-like equation for baryon diffusion with the NEOS-BQS equation of state, fluctuating initial conditions from Monte-Carlo Glauber model, and the afterburner SMASH. This integrated framework is shown to provide a good description of identified particle spectra, mean transverse momenta and anisotropic flows for different cen…
Relativistic Viscous Hydrodynamics in the Density Frame: Numerical Tests and Comparisons
本文对密度框架下的一维相对论粘性流体动力学进行数值研究，验证其与QCD动理学理论模拟的一致性及边界稳健性，并与BDNK理论和MUSIC程序进行比较。
We explore the effects of shear viscosity on the hydrodynamic evolution and final hadron spectra of Cu+Cu collisions at ultrarelativistic collision energies, using the newly developed (2+1)-dimensional viscous hydrodynamic code VISH2+1. Based on the causal Israel-Stewart formalism, this code describes the transverse evolution of longitudinally boost-invariant systems without azimuthal symmetry around the beam direction. Shear viscosity is shown to decelerate the longitudinal and accelerate the transverse hydrodynamic expansion. For fixed initial conditions, this leads to a longer quark-gluon p…
In this work we simulate a viscous hydrodynamical model of non-central Au-Au collisions in 2+1 dimensions, assuming longitudinal boost invariance. The model fluid equations were proposed by Öttinger and Grmela \cite{OG}. Freezeout is signaled when the viscous corrections become large relative to the ideal terms. Then viscous corrections to the transverse momentum and differential elliptic flow spectra are calculated. When viscous corrections to the thermal distribution function are not included, the effects of viscosity on elliptic flow are modest. However, when these corrections are included,…
I compare the first viscous hydrodynamic prediction for integrated elliptic flow in Pb-Pb collisions at the LHC with the first data released by the ALICE collaboration. These new data are found to be consistent with hydrodynamic extrapolations of RHIC data with no change in medium parameters (e.g., average viscosity). I also discuss how, in general, a precise comparison of data to theoretical calculations requires an understanding of some subtleties of the measurement -- most notably the cut on transverse momentum of the particles used and the differing sensitivities to flow fluctuations and n…
The quantitative extraction of quark-gluon plasma (QGP) properties from heavy-ion data, such as its specific shear viscosity $η/s$, typically requires comparison to viscous hydrodynamic or "hybrid" hydrodynamics+transport simulations. In either case, one has to convert the fluid to hadrons, yet without additional theory input the conversion is ambiguous for dissipative fluids. Here, shear viscous phase-space corrections calculated using linearized transport theory are applied in Cooper-Frye freezeout to quantify the effects on anisotropic flow coefficients $v_n(p_T)$ at both RHIC and LHC energ…
Attractor for 1+1D viscous hydrodynamics with general rapidity distribution
本文基于MIS理论，研究了具有一般快度分布的1+1维粘性流体动力学，发现吸引子行为，并指出流体速度的快速膨胀对早期吸引子的形成至关重要。
Recent analyses of small collision systems, namely $p+p$ and $p+$Pb at the LHC and $p+$Au, $d+$Au and $^{3}$He+Au at RHIC, have revealed azimuthal momentum anisotropies commonly associated with collective flow in larger systems. Viscous hydrodynamics and parton cascade calculations have proved successful at describing some flow-like observables in these systems. These two classes of calculations also confirm these observables to be directly related to the initial geometry of the created medium. However, the question of whether equilibrium dynamics is the dominant driver of the signal remains o…
We study to what extent the measured elliptic flow at RHIC constrains viscous deviations from ideal hydrodynamics. We solve a toy model where only transverse momenta are thermalized while the system undergoes longitudinal free-streaming. We show that RHIC data exclude such a model and thus require fast 3-dimensional thermalization.
We apply a 3+1D viscous hydrodynamic + cascade model to the heavy ion collision reactions with $\sqrt{s_{NN}}=6.3\dots39$ GeV. To accommodate the model for a given collision energy range, the initial conditions for hydrodynamic phase are taken from UrQMD, and the equation of state at finite baryon density is based on Chiral model coupled to the Polyakov loop. We study the collision energy dependence of pion and kaon rapidity distributions and $m_T$-spectra, as well as charged hadron elliptic flow and how shear viscosity affects them. The model calculations are compared to the data for Pb-Pb co…
We extend our hybrid model HydHSD by taking into account shear viscosity within the Israel-Stewart hydrodynamics. The influence of different forms of $π^{μν}$ constraints on observables is analyzed. We show that the form of the corresponding condition plays an important role for the sensitivity of viscous hydrodynamics to the ratio of shear viscosity to the entropy density, $η/s$. It is shown that the constraint used in the vHLLE model, results in most sensitivity of rapidity distributions and transverse momentum spectra to a change of the $η/s$ ratio; however, their applicability for large va…
Using the newly developed hybrid model VISHNU which connects viscous hydrodynamics with a hadron cascade model, we study the differential and integrated elliptic flow v_2 at different centrality bins for 200 A GeV Au+Au collisions and 2.76 A TeV Pb+Pb collisions. We find that the average Quark Gluon Plasma (QGP) specific shear viscosity eta/s slightly increases from Relativistic Heavy Ion Collider (RHIC) to Large Hadron Collider (LHC) energies. However, a further study assuming different temperature dependencies for (eta/s)_QGP shows that one cannot uniquely constrain the form of (eta/s)_QGP(T…
We analyze event-by-event fluctuations of the transverse momentum in relativistic heavy-ion collisions at RHIC in the framework based on the fluctuating Glauber-model initial conditions, event-by-event (3+1)-dimensional viscous hydrodynamics, and statistical hadronization. We use the scaled fluctuation measure < Delta p_Ti Delta p_Tj > / << p_T >>. The identified "geometric" mechanism of generating the transverse-momentum fluctuations from the initial size fluctuations, transmitted to the final statistical-hadronization phase with hydrodynamics, is capable of easily reproducing the magnitude o…
Comparison of hydrodynamic and "hybrid" hydrodynamics+transport calculations to heavy-ion data inevitably requires the conversion of the fluid to particles. For dissipative fluids the conversion is ambiguous without additional theory input complementing hydrodynamics. We obtain self-consistent shear viscous phase space corrections from linearized Boltzmann transport theory for a gas of hadrons. These corrections depend on the particle species, and incorporating them in Cooper-Frye freezeout affects identified particle observables. For example, with additive quark model cross sections,proton el…
Finding the existence and the location of the QCD critical point is one of the main goals of the RHIC beam energy scan program. To make theoretical predictions and corroborate with the experimental data requires modeling the space-time evolution of the matter created in heavy-ion collisions by dynamical models such as the relativistic hydrodynamics with an appropriate Equation of State (EoS). In the present exploratory study, we use a viscous 2+1 dimensional event-by-event (e-by-e) hydrodynamic code at finite baryon densities with two different EoSs (i) Lattice QCD + HRG with a crossover trans…
We calculate the spectra of produced thermal photons in Au+Au collisions taking into account the nonequilibrium contribution to photon production due to finite shear viscosity. The evolution of the fireball is modeled by second-order as well as by divergence-type 2+1 dissipative hydrodynamics, both with an ideal equation of state and with one based on Lattice QCD that includes an analytical crossover. The spectrum calculated in the divergence-type theory is considerably enhanced with respect to the one calculated in the second-order theory, the difference being entirely due to differences in t…
We present a combined analysis of elliptic and triangular flow data from LHC and RHIC using viscous relativistic hydrodynamics. Elliptic flow $v_2$ in hydrodynamics is proportional to the participant eccentricity $\varepsilon_2$ and triangular flow is proportional to the participant triangularity $\varepsilon_3$, which means $v_n=C_n\varepsilon_n$, where $C_n$ is the linear response coefficient in harmonic n. Experimental data for $v_2$ and $v_3$ combined with hydrodynamic calculations of $C_n$ thus provide us with the rms values of initial anisotropies $\varepsilon_2$ and $\varepsilon_3$. By …
Anisotropic flow coefficients v_1-v_5 in heavy ion collisions are computed by combining a classical Yang-Mills description of the early time glasma flow with the subsequent relativistic viscous hydrodynamic evolution of matter through the quark-gluon plasma and hadron gas phases. The glasma dynamics, as realized in the IP-Glasma model, takes into account event-by-event geometric fluctuations in nucleon positions and intrinsic sub-nucleon scale color charge fluctuations; the pre-equilibrium flow of matter is then matched to the MUSIC algorithm describing viscous hydrodynamic flow and particle p…
In this proceedings contribution I review recent progress in our understanding of the bulk dynamics of relativistic systems that possess potentially large local rest frame momentum-space anisotropies. In order to deal with these momentum-space anisotropies, a reorganization of relativistic viscous hydrodynamics can been made around an anisotropic background, and the resulting dynamical framework has been dubbed "anisotropic hydrodynamics." I also discuss expectations for the degree of momentum-space anisotropy of the quark gluon plasma generated in relativistic heavy ion collisions at RHIC and…
We generalize the Gubser solution of viscous hydrodynamics by including the finite density effect and analytically compute the flow harmonics $v_n$. We explicitly show how $v_n$ and their viscous corrections depend on the chemical potential. The difference in $v_n$ between particles and antiparticles is also analytically computed and shown to be proportional to various chemical potentials and the viscosity. Excellent agreement is obtained between the results and the available experimental data from the SPS, RHIC and the LHC.
Correlation femtoscopy allows one to measure the space-time characteristics of particle production in relativistic heavy-ion collisions due to the effects of quantum statistics (QS) and final state interactions (FSI). The main features of the femtoscopy measurements at top RHIC and LHC energies are considered as a manifestation of strong collective flow and are well interpreted within hydrodynamic models employing equation of state (EoS) with a crossover type transition between Quark-Gluon Plasma (QGP) and hadron gas phases. The femtoscopy at lower energies was intensively studied at AGS and S…
This work reports on investigations of the effects on the evolution of viscous hydrodynamics and on the flow coefficients of thermal dileptons, originating from a temperature-dependent specific shear viscosity $η/s (T)$ at temperatures beyond 180 MeV formed at the Relativistic Heavy-Ion Collider (RHIC). We show that the elliptic flow of thermal dileptons can resolve the magnitude of $η/s$ at the high temperatures, where partonic degrees of freedom become relevant, whereas discriminating between different specific functional forms will likely not be possible at RHIC using this observable.
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