GLOBAL WEAK SOLUTIONS TO ONE-DIMENSIONAL COMPRESSIBLE VISCOUS HYDRODYNAMIC EQUATIONS

In this article, we are concerned with the global weak solutions to the 1D com- pressible viscous hydrodynamic equations with dispersion correction δ2ρ（（φ（ρ））xxφ′（ρ））x with φ（ρ） = ρα. The model consists of viscous stabilizations because of quantum Fokker-Planck operator in the Wigner equation and is supplemented with periodic boundary and initial con- ditions. The diffusion term εuxx in the momentum equation may be interpreted as a classical conservative friction term because of particle interactions. We extend the existence result in [1] （α=1/2） to 0 〈 α ≤ 1. In addition, we perform the limit ε→0 with respect to 0 〈 α ≤1/2.

Two-pion interferometry for viscous hydrodynamic sources

The space-time evolution of the （1＋1）-dimensional viscous hydrodynamics with an initial quarkgluon plasma （QGP） produced in ultrarelativistic heavy ion collisions is studied numerically. The particleemitting sources undergo a crossover transition from the QGP to hadronic gas. We take into account a usual shear viscosity for the strongly coupled QGP as well as the bulk viscosity which increases significantly in the crossover region. The two-pion Hanbury-Brown-Twiss （HBT） interferometry for the viscous hydrodynamic sources is performed. The HBT analyses indicate that the viscosity effect on the two-pion HBT results is small if only the shear viscosity is taken into consideration in the calculations. The bulk viscosity leads to a larger transverse freeze-out configuration of the pion-emitting sources, and thus increases the transverse HBT radii. The results of the longitudinal HBT radius for the source with Bjorken longitudinal scaling are consistent with the experimental data.

Pseudo-rapidity distribution from a perturbative solution of viscous hydrodynamics for heavy ion collisions at RHIC and LHC

The charged-particle final state spectrum is derived from an analytic perturbative solution for relativistic viscous hydrodynamics. By taking into account the longitudinal acceleration effect in relativistic viscous hydrody namics, the pseudorapidity spectrum describes the nucleus-nucleus colliding systems at RHIC and the LHC well. Based on both the extracted longitudinal acceleration parameter λ^＊ and a phenomenological description of λ^＊, the charged-particle pseudorapidity distributions for √SNN= 5.44 TeV Xe＋Xe collisions are computed from the final state expression in a limited space-time rapidity ~/8 region.

Perturbation solutions of relativistic viscous hydrodynamics for longitudinally expanding fireballs

The solutions of the relativistic viscous hydrodynamics for longitudinally expanding fireballs are investig-ated with the Navier-Stokes theory and Israel-Stewart theory.The energy and the Euler conservation equations for the viscous fluid are derived in Rindler coordinates,by assuming that the longitudinal expansion effect is small.Under the perturbation assumption,an analytical perturbation solution for the Navier-Stokes approximation and numerical solutions for the Israel-Stewart approximation are presented.The temperature evolution with both shear viscous ef-fect and longitudinal acceleration effect in the longitudinal expanding framework are presented.The specific temper-ature profile shows symmetric Gaussian shape in the Rindler coordinates.Further,we compare the results from the Israel-Stewart approximation with the results from the Bjorken and the Navier-Stokes approximations,in the pres-ence of the longitudinal acceleration expansion effect.We found that the Israel-Stewart approximation gives a good description of the early stage evolutions than the Navier-Stokes theory.

VARIATIONAL PRINCIPLES AND GENERALIZED VARIATIONAL PRINCIPLES IN HYDRODYNAMICS OF VISCOUS FLUIDS

In this paper, the variational principles of hydrodynamic problems for the incompressible and compressible viscous fluids are established. These principles are principles of maximum power losses. Their generalized variational principles are also discussed on the basis of Lagrangian multiplier methods.

EXPONENTIAL DECAY FOR THE VISCOUS BIPOLAR QUANTUM HYDRODYNAMIC MODEL

In this paper, we pay attention to the time-decay rate of the viscous bipolar quantum hydrodynamic （QHD） models for semiconductors. By applying the entropy method, we prove that the solution of the viscous bipolar QHD models tends to the equilibrium state at an exponential decay rate for the multi-dimensional cases. The arguments is based on a series of a priori estimates.

Induced magnetic field stagnation point flow of nanofluid past convectively heated stretching sheet with Buoyancy effects

This paper presents the buoyancy effects on the magneto-hydrodynamics stagnation point flow of an incompressible,viscous,and electrically conducting nanofluid over a vertically stretching sheet.The impacts of an induced magnetic field and viscous dissipation are taken into account.Both assisting and opposing flows are considered.The overseeing nonlinear partial differential equations with the associated boundary conditions are reduced to an arrangement of coupled nonlinear ordinary differential equations utilizing similarity transformations and are then illuminated analytically by using the optimal homotopy investigation strategy（OHAM）.Graphs are introduced and examined for different parameters of the velocity,temperature,and concentration profile.Additionally,numerical estimations of the skin friction,local Nusselt number,and local Sherwood number are explored using numerical values.

Pion transverse-momentum spectrum, elliptic flow, and Hanbury-Brown-Twiss interferometry in a viscous granular source model

We examine the evolution of quark-gluon plasma（QGP） droplets with viscous hydrodynamics and analyze the pion transverse-momentum spectrum, elliptic flow, and Hanbury-Brown-Twiss（HBT） interferometry in a granular source model consisting of viscous QGP droplets. The shear viscosity of the QGP droplet speeds up and slows down the droplet evolution in the central and peripheral regions of the droplet, respectively. The effect of the bulk viscosity on the evolution is negligible. Although there are viscous effects on the droplet evolution, the pion momentum spectrum and elliptic flow change little for granular sources with and without viscosity. On the other hand,the influence of viscosity on HBT radius Rout is considerable. It makes Rout decrease in the granular source model.We determine the model parameters of granular sources using the experimental data of pion transverse-momentum spectrum, elliptic flow, and HBT radii together, and investigate the effects of viscosity on the model parameters. The results indicate that the granular source model may reproduce the experimental data of pion transverse-momentum spectrum, elliptic flow, and HBT radii in heavy-ion collisions of Au-Au at√s（NN）=200 GeV and Pb-Pb at√s（NN） =2.76 Te V in different centrality intervals. The viscosity of the droplet leads to an increase in the initial droplet radius and a decrease of the source shell parameter in the granular source model.

Numerical study of roll motion of a 2-D floating structure in viscous flow

In the present study,an open source CFD tool,Open FOAM has been extended and applied to investigate roll motion of a 2-D rectangular barge induced by nonlinear regular waves in viscous flow.Comparisons of the present Open FOAM results with published potential-flow solutions and experimental data have indicated that the newly extended Open FOAM model is very capable of accurate modelling of wave interaction with freely rolling structures.The wave-induced roll motions,hydrodynamic forces on the barge,velocities and vorticity fields in the vicinity of the structure in the presence of waves have been investigated to reveal the real physics involved in the wave induced roll motion of a 2-D floating structure.Parametric analysis has been carried out to examine the effect of structure dimension and body draft on the roll motion.

Electropolishing of titanium alloy under hydrodynamic mode

Titanium(Ti) alloys are widely used in aerospace industry due to the low density and high corrosion resistance. However, machining and polishing remain great challenges because of the hardness and chemical stability. With a home-made electrochemical machining workstation, cyclic voltammetry is performed at a wide potential range of [0 V, 20 V] to record the details of passivation and depassivation processes under a hydrodynamic mode. The results show that the thickness of viscous layer formed on the alloy surface plays a crucial effect on the electropolishing quality. The technical parameters, including the mechanical motion rate, polishing time and electrode gap, are optimized to achieve a surface roughness less than 1.9 nm, which shows a prospective application in the electrochemical machining of Ti and it alloys.