Elliptic flow at SPS and RHIC: from kinetic transport to hydrodynamics

Anisotropic transverse flow is studied in Pb+Pb and Au+Au collisions at SPS and RHIC energies. The centrality and transverse momentum dependence at midrapidity of the elliptic flow coefficient v₂ is calculated in the hydrodynamic and low density limits. Hydrodynamics is found to agree well with the RHIC data for semicentral collisions up to transverse momenta of 1–1.5 GeV/c, but it considerably overestimates the measured elliptic flow at SPS energies. The low density limit LDL is inconsistent with the measured magnitude of v₂ at RHIC energies and with the shape of its p_t-dependence at both RHIC and SPS energies. The success of the hydrodynamic model points to very rapid thermalization in Au+Au collisions at RHIC and provides a serious challenge for kinetic approaches based on classical scattering of on-shell particles.     

Elliptic flow in an integrated (3+1)d microscopic + macroscopic approach with fluctuating initial conditions

The elliptic flow excitation function calculated in a Boltzmann approach with an intermediate hydrodynamic stage for heavy-ion reactions from GSI-SIS to the highest CERN-SPS energies is discussed in the context of the experimental data. The specific setup with initial conditions and freeze-out from a non-equilibrium transport model allows for a direct comparison between ideal fluid dynamics and hadronic transport simulations. At higher SPS energies, where the pure transport calculation cannot account for the high elliptic flow values, the smaller mean free path in the hydrodynamic evolution leads to higher elliptic flow values. The lower mean free path leads to higher pressure gradients in the early stage and as a consequence to higher elliptic flow values even without a phase transition. Special emphasis is put on the influence of the initial conditions on the results of the hybrid model calculation. Event-by-event fluctuations are directly taken into account via event-wise non-equilibrium initial conditions generated by the primary collisions and string fragmentations in the microscopic UrQMD model. This leads to non-trivial velocity and energy density distributions for the hydrodynamical initial conditions. Due to the more realistic initial conditions and the incorporated hadronic rescattering the results are in line with the experimental data almost over the whole energy range from E _lab=2–160A GeV.     

Elliptic flow of identified hadrons in Au+Au collisions at sqrt sNN =200 GeV

The anisotropy parameter (v(2)), the second harmonic of the azimuthal particle distribution, has been measured with the PHENIX detector in Au+Au collisions at sqrt[s(NN)]=200 GeV for identified and inclusive charged particle production at central rapidities (|eta|<0.35) with respect to the reaction plane defined at high rapidities (|eta|=3-4 ). We observe that the v(2) of mesons falls below that of (anti)baryons for p(T)>2 GeV/c, in marked contrast to the predictions of a hydrodynamical model. A quark-coalescence model is also investigated.     

Stability of 3D flow of viscous liquid streamlined by the turbulent gas flow

Stability of the combined flow of liquid film and turbulent gas is studied theoretically for an arbitrary angle between the directions of gas flow and gravity force. The three-dimensional wave flow of the film is described on the basis of integral approach and quasilaminar model of the turbulent gas flow. Increment and phase velocity of waves are calculated for the case of a vertical film and horizontal gas flow depending on the direction of their propagation. According to calculations, the cross gas flow increases the instability area significantly as well as the range of directions for propagation of the fast growing perturbations on the film surface.     

Observables from a solution of (1+3)-dimensional relativistic hydrodynamics

In this paper we analyze a (1+3)-dimensional solution of relativistic hydrodynamics. We calculate momentum distribution and other observables from the solution and compare them to measurements from the Relativistic Heavy-Ion Collider (RHIC). We find that the solution we analyze is compatible with the data. In the last several years many numerical models were tested, but it is the first time that an exact, parametric, (1+3)-dimensional relativistic solution is compared to data.     

Fully implicit 1D radiation hydrodynamics: Validation and verification

A fully implicit finite difference scheme has been developed to solve the hydrodynamic equations coupled with radiation transport. Solution of the time-dependent radiation transport equation is obtained using the discrete ordinates method and the energy flow into the Lagrangian meshes as a result of radiation interaction is fully accounted for. A tridiagonal matrix system is solved at each time step to determine the hydrodynamic variables implicitly. The results obtained from this fully implicit radiation hydrodynamics code in the planar geometry agrees well with the scaling law for radiation driven strong shock propagation in aluminium. For the point explosion problem the self similar solutions are compared with results for pure hydrodynamic case in spherical geometry. Results obtained when radiation interaction is also accounted agree with those of point explosion with heat conduction for lower input energies. Having, thus, benchmarked the code, self convergence of the method w.r.t. time step is studied in detail for both the planar and spherical problems. Spatial as well as temporal convergence rates are ?1 as expected from the difference forms of mass, momentum and energy conservation equations. This shows that the asymptotic convergence rate of the code is realized properly.     

Simulation of surface tension in 2D and 3D with smoothed particle hydrodynamics method

The methods for simulating surface tension with smoothed particle hydrodynamics (SPH) method in two dimensions and three dimensions are developed. In 2D surface tension model, the SPH particle on the boundary in 2D is detected dynamically according to the algorithm developed by Dilts [G.A. Dilts, Moving least-squares particle hydrodynamics II: conservation and boundaries, International Journal for Numerical Methods in Engineering 48 (2000) 1503–1524]. The boundary curve in 2D is reconstructed locally with Lagrangian interpolation polynomial. In 3D surface tension model, the SPH particle on the boundary in 3D is detected dynamically according to the algorithm developed by Haque and Dilts [A. Haque, G.A. Dilts, Three-dimensional boundary detection for particle methods, Journal of Computational Physics 226 (2007) 1710–1730]. The boundary surface in 3D is reconstructed locally with moving least squares (MLS) method. By transforming the coordinate system, it is guaranteed that the interface function is one-valued in the local coordinate system. The normal vector and curvature of the boundary surface are calculated according to the reconstructed boundary surface and then surface tension force can be calculated. Surface tension force acts only on the boundary particle. Density correction is applied to the boundary particle in order to remove the boundary inconsistency. The surface tension models in 2D and 3D have been applied to benchmark tests for surface tension. The ability of the current method applying to the simulation of surface tension in 2D and 3D is proved.     

A scaling law in the hydrodynamics of anisotropic viscous liquids

Summary We show that 1) the stationary flow of an isotropic liquid in a given viscosimeter is described by the same equations valid for a wellaligned nematic liquid crystal, having suitable values of the five viscosity coefficients, flowing in a viscosimeter like the previous one, but whose dimensions along the average molecular directionň are contracted; 2) a similar equivalence exists for a nematic flowing in a suitably chosen viscosimeter in two experiments which differ only for the direction ofň. This equivalence allows us to exactly compensate boundary effects in the measurement of the ratio between two of the Miesowicz viscosity coefficients. Furtherly a new particularly simple derivation of the Rayleigh dissipation function for nematics is given. To speed up publication, the author of this paper has agreed to not receive the proofs for correction.     

Elliptic flow for phi mesons and (anti)deuterons in Au+Au collisions at square root of sNN=200 GeV

Differential elliptic flow (v(2)) for phi mesons and (anti)deuterons (d)d is measured for Au+Au collisions at square root of sNN=200 GeV. The v(2) for phi mesons follows the trend of lighter pi+/- and K+/- mesons, suggesting that ordinary hadrons interacting with standard hadronic cross sections are not the primary driver for elliptic flow development. The v(2) values for (d)d suggest that elliptic flow is additive for composite particles. This further validation of the universal scaling of v(2) per constituent quark for baryons and mesons suggests that partonic collectivity dominates the transverse expansion dynamics.     

Examining the necessity to include event-by-event fluctuations in experimental evaluations of elliptical flow

Elliptic flow at BNL RHIC is computed event by event with NeXSPheRIO. We show that when symmetry of the particle distribution in relation to the reaction plane is assumed, as usually done in the experimental extraction of elliptic flow, there is a disagreement between the true and reconstructed elliptic flows (15%-30% for eta=0, 30% for p perpendicular=0.5 GeV). We suggest a possible way to take into account the asymmetry and get good agreement between these elliptic flows.     

Spin dynamics of the S = 5/2 2D triangular antiferromagnet Ba3NbFe3Si2O14

We report pulse-field magnetization, ac susceptibility, and 100 GHz electron spin resonance (ESR) measurements on the S = 5/2 two-dimensional triangular compound Ba3NbFe3Si2O14 with the Néel temperature T(N) = 26 K. The magnetization curve shows an almost linear increase up to 60 T with no indication of a one-third magnetization plateau. An unusually large frequency dependence of the ac susceptibility in the temperature range of T = 20-100 K reveals a spin-glass behavior or superparamagnetism, signaling the presence of frustration-related slow magnetic fluctuations. The temperature dependence of the ESR linewidth exhibits two distinct critical regimes; (i) ΔH(pp)(T) is proportional to (T-T(N))(-p) with the exponent p = 0.2(1)-0.2(3) for temperatures above 27 K, and (ii) ΔH(pp)(T) is proportional to (T-T*)(-p) with T* = 12 K and p = 0.8(1)-0.8(4) for temperatures between 12 and 27 K. This is interpreted as indicating a dimensional crossover of magnetic interactions and the persistence of short-range correlations with a helically ordered state.     

3D numerical analysis on mechanisms of flow and heat transfer in a square channel with right triangular wavy surfaces

Numerical investigations on thermo-hydraulic performance and mechanisms of flow and heat transfer in a square channel heat exchanger inserted with right triangular wavy surfaces are examined. The influence of the flow attack angles (30°, 45° and 60°) is investigated for laminar flow (Re = 100–2000). The configurations of the right triangular wavy surfaces are varied as inclined and V-shaped wavy surfaces (the pointing of V-tip with downstream and upstream called “V-downstream” and “V-upstream”, respectively). The insertions of the wavy surfaces in the channel heat exchanger are divided into two types: middle and diagonal insertions. The computational results reveal that the maximum thermal enhancement factor, TEF, is around 2.31 for the 30° V-downstream wavy surface with diagonal insertion at Re = 2000.     

(1 + 1) dimensional hydrodynamics for high-energy heavy-ion collisions

A (1 + 1)-dimensional hydrodynamical model in the light-cone coordinates is used to describe central heavy-ion collisions at ultrarelativistic bombarding energies. Deviations from Bjorken scaling are taken into account by choosing finite-size profiles for the initial energy density. The sensitivity of fluid-dynamical evolution to the equation of state and the parameters of initial state are investigated. Experimental constraints on the total energy of produced particles are used to reduce the number of model parameters. Spectra of secondary particles are calculated under the assumption that the transition from the hydrodynamical stage to the collisionless expansion of matter occurs at a certain freeze-out temperature. An important role of resonances in the formation of observed hadronic spectra is demonstrated. The calculated rapidity distributions of pions, kaons, and antiprotons in central Au + Au collisions at √^s NN = 200 GeV are compared with experimental data of the BRAHMS Collaboration. Parameters of the initial state are reconstructed for different choices of the equation of state. The best fit of these data is obtained for a soft equation of state and Gaussian-like initial profiles of the energy density, intermediate between the Landau and Bjorken limits. The text was submitted by the authors in English.     

D3+D6 solution and D4+D6 solution

We make the supergravity solutions describing the branes (D3 branes and D4 branes) localized within the D6 branes in the near core region of D6 brane. From the D=11 solutions (M3 branes and M4 branes with the Z_N identifications in the transverse space) we obtain the D=10 supergravity solutions of D3 branes localized within D6 branes and D4 branes localized within D6 branes by reducing the dimension down to D=10 along a circular direction of S³ part of the transverse space. M3 brane solution leads to D=10 background representing D3 branes localized on D6 branes in the region close to the D6 branes core. M4 branes lead to the D4 branes localized on D6 branes in the region close to the D6 brane core.     

Integro-differential equation method in the hydrodynamics of an incompressible viscous fluid

An integro-differential equation method is proposed to describe the motion of an incompressible viscous fluid. The method uses an analogy between the hydrodynamic equations for an incompressible viscous fluid and the magnetostatic equations. An analysis is made of the flow of an incompressible viscous fluid round an object as a specific application. The solution automatically satisfies the boundary conditions at the surface of the object and at infinity. Zh. éksp. Teor. Fiz. 112, 1332–1339 (October 1997)     

Correlations in charged fermion–boson mixture in dimensionalities D=2 and D=3

We numerically study the correlation effects in a two-component charged fermion–boson mixture at zero temperature investigating the role played by the statistical effects and Coulomb correlations in a model with different fermion and boson mass ratios in two and three dimensions. The local-field factors describing the correlation effects and collective excitation modes are determined through the self-consistent scheme. We find that the effects of correlations and statistics are more pronounced in two-dimensional mixtures.     

Spin liquid state in the S = 1/2 triangular lattice Ba3CuSb2O9

The synthesis and characterization of Ba3CuSb2O9, which has a layered array of Cu2+ spins in a triangular lattice, are reported. The magnetic susceptibility and neutron scattering experiments of this material show no magnetic ordering down to 0.2 K with a θ(CW) = -55 K. The magnetic specific heat reveals a T-linear dependence with a γ = 43.4 mJ K(-2) mol(-1) below 1.4 K. These observations suggest that Ba3CuSb2O9 is a new quantum spin liquid candidate with a S = 1/2 triangular lattice.