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High-energy nuclear collisions produce a nonequilibrium plasma of quarks and gluons which thermalizes and exhibits hydrodynamic flow. There are currently no practical frameworks to connect the early particle production in classical field…
We develop a far-from-equilibrium hydrodynamic model to evolve ultrarelativistic heavy-ion collisions in event-by-event simulations. Anisotropic hydrodynamics is designed to better handle the strong and highly anisotropic expansion during…
Multistage models based on relativistic viscous hydrodynamics have proven successful in describing hadron measurements from relativistic nuclear collisions. These measurements are sensitive to the shear and the bulk viscosities of QCD and…
We discuss recent theoretical developments in understanding the early pre-equilibrium dynamics and onset of hydrodynamic behavior in high-energy heavy-ion collisions. We highlight possible experimental signatures of the pre-equilibrium…
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…
We develop a combined hydro-kinetic approach which incorporates a hydrodynamical expansion of the systems formed in \textit{A}+\textit{A} collisions and their dynamical decoupling described by escape probabilities. The method corresponds to…
Recent theory progresses in (3+1)D dynamical descriptions of relativistic nuclear collisions at finite baryon density are reviewed. Heavy-ion collisions at different collision energies produce strongly coupled nuclear matter to probe the…
To assess the degree of equilibration of the matter created in heavy-ion reactions at low to intermediate beam energies, a hadronic transport approach (SMASH) is employed. By using a coarse-graining method, we compute the energy momentum…
Theoretical studies on the early-time dynamics in the ultra-relativistic heavy-ion collisions are reviewed including pedagogical introductions on the initial condition with small-x gluons treated as a color glass condensate, the bottom-up…
We present algorithms to solve relativistic hydrodynamics in 3+1--dimensional situations without apparent symmetry to simplify the solution. In simulations of heavy--ion collisions, these numerical schemes have to deal with the physical…
We evaluate the full opacity dependence of collective flow in high-energy heavy-ion collisions within a microscopic kinetic description based on the Boltzmann equation in the conformal relaxation time approximation. By comparing kinetic…
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…
In ultrarelativistic heavy-ion collisions, a plasma of deconfined quarks and gluons is formed within $1$ fm/c of the nuclei's impact. The complex dynamics of the collision before $\approx 1$ fm/c is often described with parametric models,…
The fluidity of the hot and dense QCD matter is a key characteristic of the medium created in high-energy heavy-ion collisions. We extend the framework of the relativistic hydrodynamic model to incorporate non-thermal momentum distributions…
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…
We describe some of the recent progress in the calculation of thermodynamic quantities in QCD at high temperatures and densities by weak-coupling techniques and extrapolation to realistic coupling strength. We argue that a (mostly) weakly…
Heavy-ion collisions at $\sqrt{s_\mathrm{NN}} \sim 10$ GeV probe the QCD phase diagram at large baryon densities. Because the longitudinal Lorentz contraction is small at these collision energies, understanding the dynamics during the early…
The fluid-dynamical modeling of a nuclear collision at high energy usually starts shortly after the collision. A major source of uncertainty comes from the detailed modeling of the initial state. While the collision itself likely involves…
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…
Relativistic hydrodynamics has been quite successful in explaining the collective behaviour of the QCD matter produced in high energy heavy-ion collisions at RHIC and LHC. We briefly review the latest developments in the hydrodynamical…