Ratio Of Shear Viscosity Research Articles

Study of shear viscosity of SU(2)-gluodynamics within lattice simulation

This paper is devoted to the study of two-point correlation function of the energy-momentum tensor T_{12}T_{12} for SU(2)-gluodynamics within lattice simulation of QCD. Using multilevel algorithm we carried out the measurement of the correlation function at the temperature T/T_c = 1.2. It is shown that lattice data can be described by spectral functions which interpolate between hydrodynamics at low frequencies and asymptotic freedom at high frequencies. The results of the study of spectral functions allowed us to estimate the ratio of shear viscosity to the entropy density {\eta}/s = 0.134 +- 0.057.

Equation of state and viscosities from a gravity dual of the gluon plasma

Employing new precision data of the equation of state of the SU(3) Yang–Mills theory (gluon plasma) the dilaton potential of a gravity-dual model is adjusted in the temperature range (1–10)Tc within a bottom-up approach. The ratio of bulk viscosity to shear viscosity follows then as ζ/η≈πΔvs2 for Δvs2<0.2 and achieves a maximum value of 0.94 at Δvs2≈0.3, where Δvs2≡1/3−vs2 is the non-conformality measure and vs2 is the velocity of sound squared, while the ratio of shear viscosity to entropy density is known as (4π)−1 for the considered set-up with Hilbert action on the gravity side.

Backreaction effects due to matter coupled higher derivative gravity

AdS-hydrodynamics has proven to be a useful tool for obtaining transport coefficients observed in the collective flow of strongly coupled fluids like quark gluon plasma (QGP). Particularly, the ratio of shear viscosity to entropy density η/s obtained from elliptic flow measurements can be matched with the computation done in the dual gravity theory. The experimentally observed temperature dependence of η/s requires the study of scalar matter coupled AdS gravity including higher derivative curvature corrections. We obtain the backreaction to the metric for such a matter coupled AdS gravity in D-dimensional spacetime due to the higher derivative curvature corrections. Then, we present the backreaction corrections to shear viscosity η and entropy density s.

Nearly perfect fluidity in a high-temperature superconductor

Perfect fluids are characterized as having the smallest ratio of shear viscosity to entropy density, {\eta}/s, consistent with quantum uncertainty and causality. So far, nearly perfect fluids have only been observed in the Quark-Gluon Plasma (QGP) and in unitary atomic Fermi gases (UFG), exotic systems that are amongst the hottest and coldest objects in the known universe, respectively. We use Angle Resolve Photoemission Spectroscopy (ARPES) to measure the temperature dependence of an electronic analogue of {\eta}/s in an optimally doped cuprate high temperature superconductor, finding it too is a nearly perfect fluid around, and above, its superconducting transition temperature Tc.

Hydrodynamic Interaction of Elastic Capsules in Bounded Shear Flow

AbstractThis paper presents a modified Loop’s subdivision algorithm for studying the deformation of a single capsule, the hydrodynamic interaction between two capsules and the hydrodynamic diffusion of a suspension of capsules in bounded shear flow. A subdivision thin-shell model is employed to compute the forces generated on the surface of the elastic capsule during deformation. The capsule surface is approximated using the modified Loop’s subdivision scheme which guarantees bounded curvature and C1 continuity everywhere on the limit surface. The present numerical technique has been validated by studying the deformation of a spherical capsule in shear flow. Computations are also performed for a biconcave capsule over a wide range of shear rates and viscosity ratios to investigate its dynamics. In addition, the hydrodynamic interaction between two elastic capsules in bounded shear flow is studied. Depending on the wall separation distance, the trajectory-bifurcation points that separate reversing and crossing motions for both spherical and biconcave capsules can be found. Compared to the spherical capsules, the biconcave capsules exhibit additional types of interaction such as rotation and head-on collision. The head-on collision results in a large trajectory shift which contribute to the hydrodynamic diffusion of a suspension. A suspension of a large number of biconcave capsules in shear flow is also simulated to show the ability of the modified scheme in running a large-scale simulation over a long period of time.

Transport coefficients of bulk viscous pressure in the 14-moment approximation

We compute the transport coefficients that appear in the fluid-dynamical equations for the bulk viscous pressure and shear-stress tensor using the 14-moment approximation in the limit of small, but finite, masses. In this limit, we are able to express all these coefficients in terms of known thermodynamic quantities, such as the thermodynamic pressure, energy density, and the velocity of sound. We explicitly demonstrate that the ratio of bulk viscosity to bulk relaxation time behaves very differently, as a function of temperature, than the ratio of shear viscosity to shear relaxation time. We further explicitly compute, for the first time, the transport coefficients that couple the bulk viscous pressure to the shear-stress tensor and vice versa. The coefficient that couples bulk viscous pressure to shear-stress tensor is found to be orders of magnitude larger than the bulk viscosity itself, suggesting that bulk viscous pressure production owes more to this coupling than to the expansion rate of the system.

Mach cones in viscous heavy-ion collisions

The formation of Mach cones is studied in a full $(3+1)$-dimensional setup of ultrarelativistic heavy-ion collisions, considering a transverse and longitudinal expanding medium at Relativistic Heavy-Ion Collider energies. For smooth initial conditions and central collisions the jet-medium interaction is investigated using high-energy jets and various values of the ratio of shear viscosity over entropy density, $\ensuremath{\eta}/s$. For small viscosities, the formation of Mach cones is proven, whereas for larger viscosities the characteristic structures smear out and vanish eventually. The formation of a double-peak structure both in a single- and in a multiple-jet event is discussed.

A Note on Black Holes in Asymptotically Lifshitz Spacetime

We investigate several aspects of exact black hole solutions in asymptotically Lifshitz spacetime. Firstly, we calculate the tidal forces and find that in the near horizon region of such black hole backgrounds, the tidal forces diverge in the near extremal limit. Secondly, we evaluate the Wilson loops in both extremal and finite temperature cases. Finally, we obtain the corresponding shear viscosity and square of the sound speed and find that the ratio of shear viscosity to entropy density takes the universal value 1/4π in arbitrary dimensions while the square of the speed of sound saturates the conjectured bound 1/3 in five dimensions.

Charmonium spectral functions and transport properties of quark-gluon plasma

We study vacuum masses of charmonia and the charm-quark diffusion coefficient in the quark-gluon plasma based on the spectral representation for meson correlators. To calculate the correlators, we solve the quark gap equation and the inhomogeneous Bethe–Salpeter equation in the rainbow-ladder approximation. It is found that the ground-state masses of charmonia in the pseudoscalar, scalar, and vector channels can be well described. For 1.5Tc<T<3.0Tc, the value of the diffusion coefficient D is comparable with that obtained by lattice QCD and experiments: 3.4<2πTD<5.9. Relating the diffusion coefficient with the ratio of shear viscosity to entropy density η/s of the quark-gluon plasma, we obtain values in the range 0.09<η/s<0.16.

Effect of flow type, channel height, and viscosity on drop production from micro-pores

The formation and detachment of drops from micron-sized pores into shear flow fields is investigated using numerical simulations. The open source software OpenFOAM is used for the simulations. The numerical algorithm employs the finite volume method for solving the mass and momentum conservation equations with a volume-of-fluid approach for capturing the fluid–fluid interface. In addition, a contact model accounts for the interaction between the fluids and the walls of the channel and pore. After validating the numerical models and methods by comparison to experimental data, a parameter study is performed to investigate the effect of various geometrical, flow and fluid parameters on the characteristics of drop production, in particular, drop size. The effect of the type of imposed channel shear flow (pressure-driven or plane Couette), channel height and fluid viscosity is considered. It is found that, in one range of Reynolds and capillary numbers, the channel wall shear rate is a good indicator of drop sizes, regardless of imposed shear flow type, channel height or viscosity ratio. In this flow regime, a master drop size curve is produced for each viscosity ratio considered, with the curve being shifted lower for the higher viscous disperse phase. In another flow regime, when Reynolds numbers are very large relative to capillary numbers, the average shear rate in the channel was a better drop size indicator, although a different master curve was produced for each channel height.

Hydrodynamics in a black brane with hyperscaling violation metric background

In this paper we consider a metric with hyperscaling violation on a black brane background. In this background we calculate the ratio of shear viscosity to entropy density with hydrodynamics information. The calculation of this quantity leads us to a constraint on θ as 3 ≤ θ &lt; 4, and θ ≤ 0. In that case we show that the quantity η/s is not dependent on hyperscaling violation parameter θ. Our results about ratio of shear viscosity to entropy density from the QCD point of view agree with other works in the literature as 1/4π.

A simple thixotropic–viscoelastic constitutive model produces unique signatures in large-amplitude oscillatory shear (LAOS)

Here we demonstrate that a simple thixotropic constitutive model produces unique signatures in large-amplitude oscillatory shear (LAOS) distinct from other nonlinear mechanisms and separate from viscoelastic time dependence. Our approach is to define the simplest model that produces the essential features of both thixotropy and viscoelasticity, a structure-parameter evolution equation coupled to a three-element fluid (Jeffreys model). In strain-controlled LAOS, the response of the model depends on four dimensionless parameters: two deformation parameters (Deborah and Weissenberg) and two material parameters (the ratio of viscoelastic to thixotropic timescales and the ratio of infinite shear viscosity to aggregate viscosity). We present numerical results for the full nonlinearities across this four-dimensional parameter space. The dimensionality is reduced by considering the asymptotically-nonlinear regime (Weissenberg number expansion). We present the first analytical solution for a thixotropic model in this asymptotically-nonlinear LAOS regime, which produces distinct power function scaling not predicted by other known solutions to nonlinear viscoelastic models. With this separation of thixotropic from viscoelastic timescales, this canonical model predicts that short thixotropic timescales can be experimentally observed with nonlinear oscillatory deformation. This is relevant to recent suggestions in distinguishing thixotropic versus “simple” yield stress fluids with no experimentally observable thixotropy.

Holographic parity-violating charged fluid dual to Chern-Simons modified gravity

We discuss the ($2+1$)-dimensional parity-violating charged fluid on a finite cutoff surface ${\mathrm{\ensuremath{\Sigma}}}_{c}$, dual to the nondynamical and dynamical Chern-Simons (CS) modified gravities. Using the nonrelativistic long-wavelength expansion method, the field equations are solved up to $\mathcal{O}({\ensuremath{\epsilon}}^{2})$ in the nondynamical model. It is shown that there exists nonvortical dual fluid with shear viscosity $\ensuremath{\eta}$ and Hall viscosity ${\ensuremath{\eta}}_{A}$ on the cutoff surface ${\mathrm{\ensuremath{\Sigma}}}_{c}$. The ratio of shear viscosity over entropy density $\ensuremath{\eta}/s$ of the fluid takes the universal value $1/4\ensuremath{\pi}$, while the ratio of Hall viscosity over entropy density ${\ensuremath{\eta}}_{A}/s$ depends on the ${\mathrm{\ensuremath{\Sigma}}}_{c}$ and black brane charge $q$. Moreover, the nonvortical dual fluid obeys the magnetohydrodynamic (MHD) equation. However, these kinematic viscosities $\ensuremath{\nu}$ and ${\ensuremath{\nu}}_{A}$ related to $\ensuremath{\eta}$ and ${\ensuremath{\eta}}_{A}$ do not appear in this MHD equation due to the constraint condition ${\stackrel{\texttildelow{}}{\ensuremath{\partial}}}^{2}{\ensuremath{\beta}}_{j}=0$ for the ($2+1$)-dimensional dual fluid. Then, we extend our discussion to the dynamical CS modified gravity and show that the dual vortical fluid possesses another so-called Curl viscosity ${\ensuremath{\zeta}}_{A}$, whose ratio to entropy density ${\ensuremath{\zeta}}_{A}/s$ also depends on the ${\mathrm{\ensuremath{\Sigma}}}_{c}$ and $q$. Moreover, the value of $\ensuremath{\eta}/s$ still equals $1/4\ensuremath{\pi}$ and the result of ${\ensuremath{\eta}}_{A}/s$ agrees with the previous result under the probe limit of the pseudoscalar field at the infinite boundary in the charged black brane background for the dynamical CS modified gravity. This vortical dual fluid corresponds to the MHD turbulence equation in plasma physics.

The shear viscosity of a chemically equilibrating quark-gluon plasma at finite baryon density

Taking account of elastic and bremsstrahlung processes, as well as quark elastic scattering, we calculated the shear viscous coefficient of a chemically equilibrating quark-gluon plasma at finite baryon density. We found that the inelastic bremsstrahlung processes make the shear viscosity remarkably lower, and the ratio of shear viscosity to entropy density increases with increasing initial quark chemical potential. Considering the effect of shear viscosity the evolution of the QGP system was investigated. We found that the evolution of the system becomes slower owing to viscosity compared to the one in the ideal case, and the inelastic bremsstrahlung processes make the slower rate of the system not as much as in our previous calculations.

Shear viscosity to entropy density ratio of nuclear matter by transport model

The ratio of shear viscosity to entropy density for an equilibrated nuclear system is investigated at intermediate energy heavy-ion collisions within the framework of the Boltzmann-Uehling-Uhlenbeck (BUU) model. After the collision system almost reaching a local equilibration, the temperature, pressure and energy density are obtained from the phase-space information and shear viscosity is calculated using the Green-Kubo method. The results show that shear viscosity to entropy density ratio decreases with the increase of incident energy and tends toward a constant value around 0.5, which is close the BNL Relativistic Heavy Ion Collider results.

Analytical solution of two-fluid electro-osmotic flows of viscoelastic fluids

This paper presents an analytical model that describes a two-fluid electro-osmotic flow of stratified fluids with Newtonian or viscoelastic rheological behavior. This is the principle of operation of an electro-osmotic two-fluid pump as proposed by Brask et al. [Tech. Proc. Nanotech., 1, 190–193, 2003], in which an electrically non-conducting fluid is transported by the interfacial dragging viscous force of a conducting fluid that is driven by electro-osmosis. The electric potential in the conducting fluid and the analytical steady flow solution of the two-fluid electro-osmotic stratified flow in a planar microchannel are presented by assuming a planar interface between the two immiscible fluids with Newtonian or viscoelastic rheological behavior. The effects of fluid rheology, shear viscosity ratio, holdup and interfacial zeta potential are analyzed to show the viability of this technique, where an enhancement of the flow rate is observed as the shear-thinning effects are increased.

Towards a holographic realization of Homes’ law

Gauge/gravity duality has proved to be a very successful tool for describing strongly coupled systems in particle physics and heavy ion physics. The application of the gauge/gravity duality to quantum matter is a promising candidate to explain questions concerning non-zero temperature dynamics and transport coefficients. To a large extent, the success of applications of gauge/gravity duality to the quark-gluon plasma is founded on the derivation of a universal result, the famous ratio of shear viscosity and entropy density. As a base for applications to condensed matter physics, it is highly desirable to have a similar universal relation in this context as well. A candidate for such a universal law is given by Homes' law: High Tc superconductors, as well as some conventional superconductors, exhibit a universal scaling relation between the superfluid density at zero temperature and the conductivity at the critical temperature times the critical temperature itself. In this work we describe progress in employing the models of holographic superconductors to realize Homes' law and to find a universal relation governing strongly correlated quantum matter. We calculate diffusive processes, including the backreaction of the gravitational matter fields on the geometry. We consider both holographic s-wave and p-wave superconductors. We show that a particular form of Homes' law holds in the absence of backreaction. Moreover, we suggest further steps to be taken for holographically realizing Homes' law more generally in the presence of backreaction.

The Effect of Higher Derivative Correction on η/s and Conductivities in STU Model

In this paper we study the ratio of shear viscosity to entropy, electrical and thermal conductivities for the R-charged black hole in STU model. We generalize previous works to the case of a black hole with three different charges. Actually we use diffusion constant to obtain ratio of shear viscosity to entropy. By applying the thermodynamical stability we recover previous results. Also we investigate the effect of higher derivative corrections.

Analytic approaches to anisotropic holographic superfluids

We construct an analytic solution of the Einstein-SU(2)-Yang-Mills system as the holographic dual of an anisotropic superfluid near its critical point, up to leading corrections in both the inverse Yang-Mills coupling and a symmetry breaking order parameter. We have also calculated the ratio of shear viscosity to entropy density in this background, and shown that the universality of this ratio is lost in the broken symmetry direction. The ratio displays a scaling behavior near the critical point with critical exponent $\beta=1$, at the leading order in the double expansion.

Ratio of shear viscosity to entropy density in multifragmentation of Au + Au

The ratio of the shear viscosity (η) to entropy density (s) for the intermediate energy heavy-ion collisions has been calculated by using the Green-Kubo method in the framework of the quantum molecular dynamics model. The theoretical curve of η/s as a function of the incident energy for the head-on Au + Au collisions displays that a minimum region of η/s has been approached at higher incident energies, where the minimum η/s value is about 7 times Kovtun-Son-Starinets (KSS) bound (1/4π). We argue that the onset of minimum η/s region at higher incident energies corresponds to the nuclear liquid gas phase transition in nuclear multifragmentation.