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We review progress in the hydrodynamic description of heavy-ion collisions, focusing on recent developments in modeling the fluctuating initial state and event-by-event viscous hydrodynamic simulations. We discuss how hydrodynamics can be used to extract information on fundamental properties of quantum-chromo-dynamics from experimental data, and review successes and challenges of the hydrodynamic framework.

The density distributions of large nuclei are typically modeled with a Woods-Saxon distribution characterized by a radius $R_{0}$ and skin depth $a$. Deformation parameters $\beta$ are then introduced to describe non-spherical nuclei using an expansion in spherical harmonics $R_{0}(1+\beta_2Y^0_2+\beta_4Y^0_4)$. But when a nucleus is non-spherical, the $R_{0}$ and $a$ inferred from electron scattering experiments that integrate over all nuclear orientations cannot be used directly as the parameters in the Woods-Saxon distribution. In addition, the $\beta_2$ values typically derived from the reduced electric quadrupole transition probability B(E2)$\uparrow$ are not directly related to the $\beta_2$ values used in the spherical harmonic expansion. B(E2)$\uparrow$ is more accurately related to the intrinsic quadrupole moment $Q_{0}$ than to $\beta_2$. One can however calculate $Q_0$ for a given $\beta_2$ and then derive B(E2)$\uparrow$ from $Q_0$. In this paper we calculate and tabulate the $R_0$, $a$, and $\beta_2$ values that when used in a Woods-Saxon distribution, will give results consistent with electron scattering data. We then present calculations of the eccentricity $\varepsilon_2$ and $\varepsilon_3$ with the new and old parameters. We demonstrate that $\varepsilon_3$ is particularly sensitive to $a$ and argue that using the incorrect value of $a$ has important implications for the extraction of $\eta/s$ from the QGP created in Heavy Ion collisions.

We present theoretical approaches to high energy nuclear collisions in detail putting a special emphasis on technical aspects of numerical simulations. Models include relativistic hydrodynamics, Monte-Carlo implementation of k_T-factorization formula, jet quenching in expanding fluids, a hadronic transport model and the Vlasov equation for colored particles.

The (3+1)-dimensional ideal hydrodynamics is used to simulate collisions of gold nuclei with bombarding energies from 1 to 160 GeV per nucleon. The initial state is represented by two cold Lorentz-boosted nuclei. Two equations of state: with and without the deconfinement phase transition are used. We have investigated dynamical trajectories of compressed baryon-rich matter as functions of various thermodynamical variables. The parameters of collective flow and hadronic spectra are calculated. It is shown that presence of the deconfinement phase transition leads to increase of the elliptic flow and to flattening of proton rapidity distributions.

We describe here a model for inelastic collisions for electronic excitation and deexcitation processes in a general, multifluid plasma. The model is derived from kinetic theory, and applicable to any mixture and mass ratio. The principle of detailed balance is strictly enforced, and the model is consistent with all asymptotic limits. The results are verified with direct Monte Carlo calculations, and various numerical tests are conducted for the case of an electron-hydrogen two-fluid system, using a generic, semiclassical model of collision cross sections. We find that in some cases, the contribution of inelastic collisions to the momentum and thermal resistance coefficients is not negligible, in contrast to the assumptions of current multifluid models. This fundamental model is also applied to ionization and recombination processes, the studies on which are currently underway.

A two dimensional hydrocode based on 2-D SALE was modified to include strength effects and fragmentation equations for fracture resulting from tensile stress in one dimension. Output from this code includes a complete fragmentation summary for each cell of the modeled object: fragment size (mass) distribution, vector velocities of particles, peak values of pressure and tensile stress, and peak strain rates associated with fragmentation. Contour plots showing pressure and temperature at given times within the object are also produced. By invoking axial symmetry, three dimensional events can be modeled such as zero impact parameter collisions between asteroids. The code was tested against the one dimensional model and the analytical solution for a linearly increasing tensile stress under constant strain rate.

Understanding the detailed production and hadronization mechanisms for heavy quarkonia and their modification in a nuclear environment presents one of the major challenges in QCD. Calculations including nuclear-modified parton distribution functions (nPDFs) and fitting of break-up cross sections (sigma_breakup) as parameters have been successful at describing many features of J/psi modification in proton(deuteron)-nucleus collisions. In this paper, we extend these calculations to explore different geometric dependencies of the modification and confront them with new experimental results from the PHENIX experiment. We find that no combination of nPDFs and sigma_breakup, regardless of the nPDF parameter set and the assumed geometric dependence, can simultaneously describe the entire rapidity and centrality dependence of J/psi modifications in d+Au collisions at sqrt(s_NN) = 200 GeV. We also compare the data with coherence calculations and find them unable to describe the full rapidity and centrality dependence as well. We discuss how these calculations might be extended and further tested, in addition to discussing other physics mechanisms including initial-state parton energy loss.

We present a new "collisional grooming" algorithm that enables us to model images of debris disks where the collision time is less than the Poynting Robertson time for the dominant grain size. Our algorithm uses the output of a collisionless disk simulation to iteratively solve the mass flux equation for the density distribution of a collisional disk containing planets in 3 dimensions. The algorithm can be run on a single processor in ~1 hour. Our preliminary models of disks with resonant ring structures caused by terrestrial mass planets show that the collision rate for background particles in a ring structure is enhanced by a factor of a few compared to the rest of the disk, and that dust grains in or near resonance have even higher collision rates. We show how collisions can alter the morphology of a resonant ring structure by reducing the sharpness of a resonant ring's inner edge and by smearing out azimuthal structure. We implement a simple prescription for particle fragmentation and show how Poynting-Robertson drag and fragmentation sort particles by size, producing smaller dust grains at smaller circumstellar distances. This mechanism could cause a disk to look different at different wavelengths, and may explain the warm component of dust interior to Fomalhaut's outer dust ring seen in the resolved 24 micron Spitzer image of this system.

Glauber models based on nucleon--nucleon interactions are commonly used to characterize the initial state in high-energy nuclear collisions, and the dependence of its properties on impact parameter or number of participating nucleons. In this paper, an extension to the Glauber model is presented, which accounts for an arbitrary number of effective sub-nucleon degrees of freedom, or active constituents, in the nucleons. Properties of the initial state, such as the number of constituent participants and collisions, as well as eccentricity and triangularity, are calculated and systematically compared for different assumptions of how to distribute the sub-nuclear degrees of freedom and for various collision systems. It is demonstrated that at high collision energy the number of produced particles scales with an average number of sub-nucleon degrees of freedom of between $3$ and $5$. The source codes for the constituent Monte Carlo Glauber extension, as well as for the calculation of the overlap area and participant density in a standard Glauber model, are made publicly available.

This contribution presents a theoretical overview of hydrodynamic modelling of heavy-ion collisions, with highlights on some recent developments. In particular, the formulation of anisotropic hydrodynamics, the role of hydrodynamic fluctuations, and the non-linear coupling of flow coefficients will be discussed.

We describe here a model for inelastic collisions for electronic excitation and deexcitation processes in a general, multifluid plasma. The model is derived from kinetic theory, and applicable to any mixture and mass ratio. The principle of detailed balance is strictly enforced, and the model is consistent with all asymptotic limits. The results are verified with direct Monte Carlo calculations, and various numerical tests are conducted for the case of an electron-hydrogen two-fluid system, using a generic, semi-classical model of collision cross sections. We find that in some cases, the contribution of inelastic collisions to the momentum and thermal resistance coefficients is not negligible, in contrast to the assumptions of current multifluid models. This fundamental model is also applied to ionization and recombination processes, the studies on which are currently underway.

We use (3+1) dimensional ideal hydrodynamics to describe the space-time evolution of strongly interacting matter created in Au+Au and Pb+Pb collisions. The model is applied for the domain of bombarding energies 1-160 AGeV which includes future NICA and FAIR experiments. Two equations of state are used: the first one corresponding to resonance hadron gas and the second one including the deconfinement phase transition. The initial state is represented by two Lorentz-boosted nuclei. Dynamical trajectories of matter in the central box of the system are analyzed. They can be well represented by a fast shock-wave compression followed by a relatively slow isentropic expansion. The parameters of collective flows and hadronic spectra are calculated under assumption of the isochronous freeze-out. It is shown that the deconfinement phase transition leads to broadening of proton rapidity distributions, increase of elliptic flows and formation of the directed antiflow in the central rapidity region. These effects are most pronounced at bombarding energies around 10 AGeV, when the system spends the longest time in the mixed phase. From the comparison with three-fluid calculations we conclude that the transparency effects are not so important in central collisions at NICA-FAIR energies (below 30 AGeV).

We present the Superparticle Model/Algorithm for Collisions in Kuiper belts and debris disks (SMACK), a new method for simultaneously modeling, in 3-D, the collisional and dynamical evolution of planetesimals in a debris disk with planets. SMACK can simulate azimuthal asymmetries and how these asymmetries evolve over time. We show that SMACK is stable to numerical viscosity and numerical heating over 10(exp 7) yr, and that it can reproduce analytic models of disk evolution. We use SMACK to model the evolution of a debris ring containing a planet on an eccentric orbit. Differential precession creates a spiral structure as the ring evolves, but collisions subsequently break up the spiral, leaving a narrower eccentric ring.

We study the nuclear modification of angular and momentum correlations between heavy quark pairs in ultrarelativistic heavy-ion collisions. The evolution of heavy quarks inside the thermalized medium is described via a modified Langevin approach that incorporates both elastic and inelastic interactions with the medium constituents. The spacetime evolution of the fireball is obtained from a (2+1)-dimensional viscous hydrodynamics simulation. The hadronization of heavy quarks is performed utilizing a hybrid model of fragmentation and coalescence. Our results show that the nuclear modification of the transverse momentum imbalance of D\bar{D} pairs reflects the total energy loss experienced by the heavy quarks and may help us probe specific regions of the medium. The angular correlation of heavy flavor pairs, especially in the low to intermediate transverse momentum regime, is sensitive to the detailed energy loss mechanism of heavy quarks inside the QGP.

Partonic matter produced in the early stage of ultrarelativistic nucleus-nucleus collisions is assumed to be composed mainly of gluons, and quarks and antiquarks are produced at later times. The comparable hydrodynamic simulations of heavy-ion collisions for (2+1)-flavor and Yang-Mills equations of state performed by using three different hydrodynamic codes are presented. Assuming slow chemical equilibration of quarks, the spectra and elliptic flows of thermal dileptons and photons are calculated for central Pb+Pb collisions at the LHC energy of $\sqrt{s_{_{\rm NN}}} = 2.76$ TeV. It is shown that a suppression of quarks at early times leads to a significant reduction of the yield of the thermal dileptons, but only to a rather modest suppression of the $p_T$-distribution of direct photons. It is demonstrated that an enhancement of photon and dilepton elliptic flows might serve as a promising signature of the pure-glue initial state. Calculations based on Bjorken hydrodynamics suggest that collisions of small systems at intermediate energies available at RHIC or future FAIR facilities may show stronger effects associated with initial pure gluodynamic evolution.

We analyze correlations between the event-plane angles in different intervals of pseudorapidity within the 3+1-dimensional viscous hydrodynamics with the Glauber-model initial conditions. As predicted earlier, the fluctuations in the particle production mechanism in the earliest stage, together with asymmetry of the emission profiles in pseudorapidity from the forward- and backward going wounded nucleons, lead to the torque effect, namely, decorrelation of the event-plane angles in distant pseudorapidity bins. We use two- or three-bin measures of correlation functions to quantify the effect, with the latter compared to the recent data from the CMS collaboration. We find a sizable torque effect, with magnitude larger at RHIC than at the LHC.

We describe here a model for inelastic collisions for electronic excitation and deexcitation processes in a general, multifluid plasma. The model is derived from kinetic theory, and applicable to any mixture and mass ratio. The principle of detailed balance is strictly enforced, and the model is consistent with all asymptotic limits. The results are verified with direct Monte Carlo calculations, and various numerical tests are conducted for the case of an electron-hydrogen two-fluid system, using a generic, semi-classical model of collision cross sections. We find that in some cases, the contribution of inelastic collisions to the momentum and thermal resistance coefficients is not negligible, in contrast to the assumptions of current multifluid models. This fundamental model is also applied to ionization and recombination processes, the studies on which are currently underway.

Collective flow and femtoscopy in ultrarelativistic 3He-Au collisions are investigated within the 3+1-dimensional (3+1D) viscous event-by-event hydrodynamics. We evaluate elliptic and triangular flow coefficients as functions of the transverse momentum. We find the typical long-range ridge structures in the two-particle correlations in the relative azimuth and pseudorapidity, in the pseudorapidity directions of both Au and 3He. We also make predictions for the pionic interferometric radii, which decrease with the transverse momentum of the pion pair. All features found hint on collectivity of the dynamics of the system formed in 3He-Au collisions, with hydrodynamics leading to quantitative agreement with the up-to-now released data.

A model for ionization and recombination collisions in a multifluid plasma is formulated using the framework introduced in previous work [{Phys. Plasmas} \textbf{22}, 093512 (2015)]. The exchange source terms for density, momentum and energy are detailed for the case of electron induced ionization and three body recombination collisions with isotropic scattering. The principle of detailed balance is enforced at the microscopic level. We describe how to incorporate the standard collisional-radiative model into the multifluid equations using the current formulation. Numerical solutions of the collisional-radiative rate equations for atomic hydrogen are presented to highlight the impact of the multifluid effect on the kinetics.

For a complete understanding of the QCD phase diagram it is important to connect first-principle thermodynamic calculations to experimental data from the RHIC Beam Energy Scan and the future experimental facilities FAIR, GSI, and NICA, Dubna. This can only be achieved by a realistic modeling of the dynamical evolution of critical fluctuations in heavy-ion collisions at the QCD phase transition. In this note I will summarize the current status of these dynamical models and highlight some of the important issues, which need to be addressed in the future.

Collisions play an important role in many aspects of the physics of musical instruments. The striking action of a hammer or mallet in keyboard and percussion instruments is perhaps the most important example, but others include reed-beating effects in wind instruments, the string/neck interaction in fretted instruments such as the guitar as well as in the sitar and the wire/membrane interaction in the snare drum. From a simulation perspective, whether the eventual goal is the validation of musical instrument models or sound synthesis, such highly nonlinear problems pose various difficulties, not the least of which is the risk of numerical instability. In this article, a novel finite difference time domain simulation framework for such collision problems is developed, where numerical stability follows from strict numerical energy conservation or dissipation, and where a a power law formulation for collisions is employed, as a potential function within a Hamiltonian formulation. The power law serves both as a model of deformable collision, and as a mathematical penalty under perfectly rigid, non-deformable collision. This formulation solves a major problem underlying previous work, where a Hamiltonian framework was not employed for collisions, and thus stability was not ensured. Various numerical examples, illustrating the unifying features of such methods across a wide variety of systems in musical acoustics are presented, including numerical stability and energy conservation/dissipation, bounds on spurious penetration in the case of rigid collisions, as well as various aspects of musical instrument physics.

The Final Technical Report covering the period from 15 Aug. 1989 to 14 Aug. 1991 is presented. Areas of research included Infrared Astronomy Satellite (IRAS) high resolution studies and modeling of closely interacting galaxies; galaxy collisions: infrared observations and analysis of numerical models; and UV spectroscopy of massive young stellar populations in interacting galaxies. Both observational studies and theoretical modelling of interacting galaxies are covered. As a consequence the report is divided into two parts, one on each aspect of the overall project.