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Flow simulation with a particle dynamics method is studied. The fluid is made of hard particles which obey the Newtonian equations of motion and the collisions between particles are elastic, that is, energy and momentum are conserved. The viscosity appears autonomously together with the local equilibrium state. When a particle collides with a nonslip boundary, a new velocity is given randomly from the thermal distribution if the wall is isothermal, or a random reflection angle is selected if the wall is adiabatic. Shear viscosity is estimated from simulations of plane Poiseuille flow together with the confirmation that the system obeys the Navier–Stokes equation. Flows past a cylinder are also simulated. Depending on the Reynolds number up to 106, flow patterns are properly reproduced, and Kármán vortex shedding is observed. The estimated values of drag coefficient show quantitative agreement with experiments.

We compute the spectrum of thermal photons created in Au+Au collisions at , taking into account dissipative corrections in production processes corresponding to the quark–gluon plasma and hadronic phases. To describe the evolution of the fireball, we use a viscous fluid dynamic model with different parametrizations for the temperature-dependence of η/s. We find that the spectrum significantly depends on the values of η/s in the QGP phase, and is almost insensitive to the values in the hadronic phase. We also compare the influence of the temperature-dependence of η/s on the spectrum of thermal photons to that of using different equations of state in the fluid dynamic simulations, finding that both effects are of the same order of magnitude.

We study the effect of magnetic field on the transport properties like shear and bulk viscosities of hot and dense hadronic matter within hadron resonance gas model. We estimate the bulk viscosity using low energy theorems for bilocal correlators of the energy–momentum tensor generalized to finite temperature, density and magnetic field. We use Gaussian ansatz for the spectral function at low frequency. We estimate shear viscosity coefficient using molecular kinetic theory. We find that vacuum contribution due to finite magnetic field dominates the bulk viscosity (ζ) for the temperatures up to 0.1 GeV and increases with magnetic field while ratio ζ/s decreases with magnetic field. We also find that shear viscosity coefficient of hadronic matter decreases with magnetic field.

In this paper, we introduced the black brane solution in Rastall theory and in the context of massive gravity. The ratio of shear viscosity to entropy density is calculated for this solution. Our result shows that the KSS bound violates this theory.

In this paper, the Einstein AdS black brane solution in the presence of a string cloud in the context of d-dimensional massive gravity is introduced. The ratio of shear viscosity to entropy density for this solution violates the KSS bound by applying the Dirichlet boundary and regularity on the horizon conditions. Our result shows that this value is independent of string cloud in any arbitrary dimensions.

In this paper, the Einstein AdS black brane solution in the presence of quintessence in context of massive gravity is introduced. The ratio of shear viscosity to entropy density for this solution violates the KSS bound by applying the Dirichlet boundary and regularity conditions on the horizon for $c_i<0$. Our result shows that this value is independent of quintessence in any arbitrary dimensions.

In this paper, we introduce the black brane solutions in anti-de Sitter (AdS) space in four-dimensional (4D) Einstein–Gauss–Bonnet–Yang–Mills theory in the presence of string cloud and quintessence. Shear viscosity to entropy density ratio is computed via fluid–gravity duality, as a transport coefficient for this model.

A real-time thermal field theoretical calculation of shear viscosity has been described in the Kubo formalism for bosonic and fermionic medium. The two-point function of viscous-stress tensor in the lowest order provides one-loop skeleton diagram of boson or fermion field for bosonic or fermionic matter. According to the traditional diagrammatic technique of transport coefficients, the finite thermal width of boson or fermion is introduced in their internal lines during the evaluation of boson–boson or fermion–fermion loop diagram. These thermal widths of ϕ boson and ψ fermion are respectively obtained from the imaginary part of self-energy for ϕΦ and ψΦ loops, where interactions of higher mass Φ boson with ϕ and ψ are governed by the simple ϕϕΦ and interaction Lagrangian densities. A two-loop diagram, having same power of coupling constant as in the one-loop diagram, is deduced and its contribution appears much lower than the one-loop values of shear viscosity. Therefore, the one-loop results of Kubo-type shear viscosity may be considered as leading order results for this simple ϕϕΦ and interactions. This approximation is valid for any values of coupling constant and at the temperatures greater than the mass of constituent particles of the medium.

Based on the first principle calculation, a Lagrangian for the system describing quarks, gluons, and their interactions, is constructed. Ascribed to the existence of dissipative behavior as a consequence of strong interaction within quark–gluon plasma (QGP) matter, auxiliary terms describing viscosities are constituted into the Lagrangian. Through a "kind" of phase transition, gluon field is redefined as a scalar field with four-vector velocity inherently attached. Then, the Lagrangian is elaborated further to produce the energy–momentum tensor of dissipative fluid-like system and the equation of motion (EOM). By imposing the law of energy and momentum conservation, the values of shear and bulk viscosities are analytically calculated. Our result shows that, at the energy level close to hadronization, the bulk viscosity is bigger than shear viscosity. By making use of the conjectured values η/s~1/4π and ζ/s~1, the ratio of bulk to shear viscosity is found to be ζ/η>4π.

This paper reviews experimental and modeling efforts aimed at the determination of the shear viscosity of strongly-coupled Yukawa liquids. After briefly reviewing prior work on three-dimensional (3D) systems, recent experimental and computer simulation studies of two-dimensional (2D) settings are presented in detail. In the experiments two counterpropagating laser beams were used to perturb a dusty plasma monolayer and monitoring of the velocity field reconstructed from particle trajectories allowed the determination of the shear viscosity with the aid of an analytical model. Subsequent computer simulations based on the molecular dynamics approach resulted in velocity profiles which are in very good agreement with the experimental ones. Further simulation studies of idealized 2D Yukawa liquids (in which gas friction is neglected) gave results for the shear viscosity over a wide range of system parameters and demonstrated the existence of the shear thinning effect (non-Newtonian behavior) of the liquid at high shear rates.

A model of a collapsing radiating star consisting of a fluid with shear viscosity and bulk viscosity undergoing radial heat flow with outgoing radiation is studied. This kind of fluid is the most general viscous fluid we can have. The pressure of the star, at the beginning of the collapse, is isotropic but, due to the presence of the shear viscosity and the bulk viscosity, the pressure becomes more and more anisotropic. The radial and temporal behaviors of the density, pressure, mass, luminosity, the effective adiabatic index and the Kretschmann scalar are analyzed. The collapsing time, density, mass, luminosity and Kretschmann scalar of the star do not depend on the viscosity of the fluid (nor the shear viscosity and neither the bulk viscosity).

A direct relation between the time-dependent Milne geometry and the Rindler spacetime is shown. Milne's metric corresponds to the region beyond Rindler's event horizon (in the wedge t ≻ |x|). We point out that inside a Schwarzschild black hole and near its horizon, the metric may be Milne's flat metric.

It was found that the shear tensor associated to a congruence of fluid particles of the RHIC expanding fireball has the same structure as that corresponding to the anisotropic fluid from the black hole interior, even though the latter geometry is curved.

The effects of viscosity on the space-time evolution of quark gluon plasma produced in nuclear collisions at relativistic heavy ion collider energies have been studied. The entropy generated due to the viscous motion of the fluid has been taken into account in constraining the initial temperature by the final multiplicity (measured at the freeze-out point). The viscous effects on the photon spectra has been introduced consistently through the evolution dynamics and phase space factors of all the participating partons/hadrons in the production process. In contrast to some of the recent calculations the present work includes the contribution from the hadronic phase. A small change in the transverse momentum (p_T) distribution of photons is observed due to viscous effects.

The Large Hadron Collider (LHC) at CERN has a plan to have Oxygen–Oxygen (O+O) collisions at $\sqrt{s_{\mathrm{\text{NN}}}}=7$TeV collision energy in the forthcoming run. As the system size of $\mathrm{\text{O+O}}$ collisions has the final state multiplicity overlap with those produced in PbPb, p+Pb, and pp collisions, it becomes exciting to study thermodynamic quantities using the Color String Percolation Model (CSPM). The thermodynamic quantities like temperature, shear viscosity to entropy density ratio, and trace anomaly are obtained from the soft region of the transverse momentum spectra of O+O collisions at $\sqrt{s_{\mathrm{\text{NN}}}}=7$TeV. The percolation approach within CSPM can be successfully used to describe the initial stages in high-energy heavy ion collisions in the soft region in high-energy heavy ion collisions. The obtained results for O+O collisions are compared with the published results from pp and AA collisions using ALICE data.

To evaluate shear viscosity of ethylene glycol oligomers (EGO)/water binary mixture by means of coarse-grained molecular dynamics (CG-MD) simulations, we proposed the self-diffusion-coefficient-based parameterization of non-bonded interactions among CG particles. Our parameterization procedure consists of three steps: (1) determination of bonded potentials, (2) scaling for time and solvent diffusivity and (3) optimization of Lennard-Jones parameters to reproduce experimental self-diffusion coefficient and density data. With the determined parameters and the scaling relations, we evaluated shear viscosities of aqueous solutions of EGOs with various molecular weights and concentrations. Our simulation results are in close agreement with the experimental data. The largest simulation in this article corresponds to a 1.2 μs atomistic simulation for 100,000 atoms. Our CG model with the parameterization scheme for CG particles may be useful to study the dynamic properties of a liquid which contains relatively low molecular weight polymers or oligomers.

With the dielectric function derived from the chromohydrodynamic approach, we investigate wakes in induced charge density and wake potential induced by a fast parton traveling through the viscous quark-gluon plasma (QGP). When the fast parton moves with a speed v = 0.55c which is less than the phase velocity of plasmon v_p in QGP, the equicharge lines show a sign flip in the backward-forward spaces. While for v = 0.99c which is larger than v_p, the equicharge lines show an oscillatory behavior. A Lennard-Jones potential and an oscillatory wake potential are found in the backward direction for v = 0.55c and v = 0.99c respectively. In addition, the viscous effect on wakes is also speed-dependent. When v = 0.55c, shear viscosity has a trivial impact on the wakes. While for v = 0.99c, shear viscosity modifies the strength and structure of the wakes significantly.

We summarize recent results regarding the equilibrium and non-equilibrium behavior of cold dilute atomic gases in the limit in which the two body scattering length a goes to infinity. In this limit the system is described by a Galilean invariant (non-relativistic) conformal field theory. We discuss the low energy effective lagrangian appropriate to the limit a → ∞, and compute low energy coefficients using an ϵ-expansion. We also show how to combine the effective lagrangian with kinetic theory in order to compute the shear viscosity, and compare the kinetic theory predictions to experimental results extracted from the damping of collective modes in trapped Fermi gases.

We review the progress in the holographic calculation of shear viscosity for strongly coupled field theories. We focus on the calculation of shear viscosity from the effective coupling of transverse gravitons and present some explicit examples.