Bulk viscosity of interacting magnetized strange quark matter

The bulk viscosity of interacting strange quark matter in a strong external magnetic field B m with a real equation of state is investigated.It is found that interquark interactions can significantly increase the bulk viscosity,and the magnetic field B_(m) can cause irregular oscillations in both components of the bulk viscosity,ξ||(parallel to B_(m))and ξ⊥(perpendicular to B_(m)).A comparison with non-interacting strange quark matter reveals that when B_(m) is sufficiently large,ξ⊥is more affected by interactions than ξ||.Additionally,the quasi-oscillation of the bulk viscosity with changes in density may facilitate the for-mation of magnetic domains.Moreover,the resulting r-mode instability windows are in good agreement with observational data for compact stars in low-mass X-ray binaries.Specifically,the r-mode instability window for interacting strange quark matter in high magnetic fields has a minimum rotation frequency exceeding 1050 Hz,which may explain the observed very high spin frequency of a pulsar with V=1122 Hz.

CORRELATION OF ION-CLUSTER STRUCTURE WITH BULK VISCOSITY AND DENSITY OF TiO_2-BEARING MOLTEN SLAG

An approach was made to correlate the proposed model of ion-cluster structure and structural parameter of TiO_2-bearing pentan system of molten slag with properties.Re- sults showed that an increase of ions with 4-coordination number in molten slag makes the increase of bulk viscosity and the decrease of density,while ions with 6-coordination number are the contrary.The structural parameter proposed is so fairly interrelated to the properties of slag,that it may be available for the prediction about properties.In comparison with ions of 4-coordination number.Ti is more effective than Al and Si.

Effects of bulk viscosity on hadron spectra and the Hanbury-Brown Twiss radius by causal viscous hydrodynamics

The particle spectra and Hanbury-Brown Twiss （HBT） radius of Au＋Au collisions at RHIC energy are investigated by a hydrodynamical expanding source with both shear and bulk viscosities （ζ）. With a large width of the ratio of ζ to entropy density s, both the particle transverse momentum spectra and the ratio Rout/Raide Of HBT radii in the direction of the total transverse momentum of detected two particles （Rout） and perpendicular to both this direction and the beam direction （Rside） become a little steeper.

Cosmic acceleration with bulk viscosity in an anisotropic f(R, Lm) background

In this article,we investigate the observed cosmic acceleration in the framework of a cosmological f(R,Lm)model dominated by bulk viscous matter in an anisotropic background.We consider the locally rotationally symmetric Bianchi type I metric and derive the Friedmann equations that drive the gravitational interactions in f((R,Lm)gravity.Further,we assume the functional form f(R,Lm)=R/2+Lαm,where a is a free model parameter,and then find the exact solutions of field equations corresponding to our viscous matter dominated model.We incorporate the updated H(z)data and the Pantheon data to acquire the best-fit values of parameters of our model by utilizing theχ2 minimization technique along with the Markov Chain Monte Carlo random sampling method.Further,we present the behavior of physical parameters that describe the Universe’s evolution phase,such as density,effective pressure and EoS parameters,skewness parameter,and the statefinder diagnostic parameters.We find that the energy density indicates expected positive behavior,whereas the negative behavior of bulk viscous pressure contributes to the Universe’s expansion.The effective EoS parameter favors the accelerating phase of the Universe’s expansion.Moreover,the skewness parameter shows the anisotropic nature of spacetime during the entire evolution phase of the Universe.Finally,from the statefinder diagnostic test,we found that our cosmological f(R,Lm)model lies in the quintessence region,and it behaves like a de-Sitter universe in the far future.We analyze different energy conditions in order to test the consistency of the obtained solution.We find that all energy conditions except strong energy condition(SEC)show positive behavior,while the violation of SEC favors the recently observed acceleration with the transition from decelerated to an accelerated epoch of the Universe’s expansion in the recent past.

Determination of bulk viscosity of liquid water via pulse duration measurements in stimulated Brillouin scattering

We present a method by which to determine the bulk viscosity of water from pulse duration measurements of stimulated Brillouin scattering （SBS）. Beginning from a common model of Brillouin scattering, the bulk viscosity is shown to play an important role in Brillouin linewidth determination. Pulse durations of SBS back-reflected optical pulses are measured over the temperature range of 5-40℃. SBS linewidths are de- termined via Fourier transformation of the time-domain results, and the bulk viscosity of water is measured and derived from the obtained values. Our results show that the proposed method for measurement of pulse durations is an effective approach for determining bulk viscosity. The method can be easily extended to determine bulk viscosities of other Newtonian liquids.

Bulk viscosity for interacting strange quark matter and r-mode instability windows for strange stars

We investigate the bulk viscosity of strange quark matter in the framework of the equivparticle model,where analytical formulae are obtained for certain temperature ranges,which can be readily applied to those with various quark mass scalings.In the case of adopting a quark mass scaling with both linear confinement and perturbative interactions,the obtained bulk viscosity increases by 1-2 orders of magnitude compared with those in bag model scenarios.Such an enhancement is mainly due to the large quark equivalent masses adopted in the equivparticle model,which are essentially attributed to the strong interquark interactions and are related to the dynamical chiral symmetry breaki ng.Due to the high bulk viscosity,the predicted damping time of oscillatio ns for a can on ical 1.4 M⊙ strange star is less than one millisecond,which is shorter than previous findings.Consequently,the obtained r-mode instability window for the canonical strange stars well accommodates the observational frequencies and temperatures for pulsars in low-mass X-ray binaries(LMXBs).

Shear and bulk viscosity of high-temperature gluon plasma

We calculate the shear viscosity（η） and bulk viscosity（ζ） to entropy density（s） ratios η/s and ζ/s of a gluon plasma system in kinetic theory, including both the elastic gg←→gg forward scattering and the inelastic soft gluon bremsstrahlung gg←→ggg processes. Due to the suppressed contribution to η and ζ in the gg←→gg forward scattering and the effective g←→gg gluon splitting, Arnold, Moore and Yaffe（AMY） and Arnold, Dogan and Moore（ADM） have got the leading order computations for η and ζ in high-temperature QCD matter. In this paper, we calculate the correction to η and ζ in the soft gluon bremsstrahlung gg←→ggg process with an analytic method.We find that the contribution of the collision term from the gg←→ggg soft gluon bremsstrahlung process is just a small perturbation to the gg←→gg scattering process and that the correction is at～ 5% level. Then, we obtain the bulk viscosity of the gluon plasma for the number-changing process. Furthermore, our leading-order result for bulk viscosity is the formula ζ∝（αs^2 T^3）/（lnαs^-1） in high-temperature gluon plasma.

Bulk viscosity of hot dense Quark matter in the PNJL model

Starting from the Kubo formula and the QCD low energy theorem, we study the the bulk viscosity of hot dense quark matter in the PNJL model from the equation of state. We show that the bulk viscosity has a sharp peak near the chiral phase transition, and that the ratio of bulk viscosity over entropy rises dramatically in the vicinity of the phase transition. These results agree with those from the lattice and other model calculations. In addition, we show that the increase of chemical potential raises the bulk viscosity.

Shear Viscosity to Non-Equilibrium Entropy Density Ratio of Hot Quark-Gluon Plasma at Finite Chemical Potential

In the framework of irreversible thermodynamics, we study the transport properties of hot quark-gluon plasmas. The viscous entropy production at finite chemical potential as well as the shear viscosity to non-equilibrium entropy density ratio is investigated in weakly coupled limit by using kinetic theory. The results show that the chemical potential contributes positively to their ratio compared to the pure temperature case. The ratio exhibits two boundaries in the coupling strength in which a minimum value of 0.42 is found at αs=0.6.

Bianchi type V universe with bulk viscous matter and time varying gravitational and cosmological constants

We consider spatially homogeneous and anisotropic Bianchi type V space- time with a bulk viscous fluid source, and time varying gravitational constant G and cosmological term A. The coefficient of bulk viscosity ζ is assumed to be a simple linear function of the Hubble parameter H （i.e. ζ = ζ0 ＋ ζ1H, where ζ0 and ζ1 are constants）. The Einstein field equations are solved explicitly by using a law of varia- tion for the Hubble parameter, which yields a constant value of the deceleration pa- rameter. Physical and kinematical parameters of the models are discussed. The models are found to be compatible with the results of astronomical observations.

Bianchi-Type VI_(0) Bulk Viscous Fluid Models with Variable Gravitational and Cosmological Constants

This paper deals with Bianchi type VI0 anisotropic cosmological models filled with a bulk viscous cosmic fluid in the presence of time-varying gravitational and cosmological constant. Physically realistic solutions of Einstein's field equations are obtained by assuming the conditions 1) the expansion scalar is proportional to shear scalar 2) the coefficient of the bulk viscosity is a power function of the energy density and 3) the cosmic fluid obeys the barotropic equation of state. We observe that the corresponding models retain the well established features of the standard cosmology and in addition, are in accordance with recent type Ia supernovae observations. Physical behaviours of the cosmological models are also discussed.

Bianchi Type-I Anisotropic Universe with Metric Potential in Saez-Ballester Theory of Gravitation

Bianchi Type-I cosmological model in the presence of Saez-Ballester theory gravitation is studied. An exact solution of the field equation is given by considering the cosmological model yield a metric potential included with a real number. The relation between the deceleration parameter and Hubble parameter and average scale factor is used in that cosmological model. The effect of the viscosity on the entropy of the universe is utilized by energy momentum tensor with bulk viscous terms in a conservative manner. We obtained a formula for calculating the entropy of the universe in terms of viscosity and used it to compare to the study. Also, various physical and kinematical properties have been discussed.

FRICTION IN GEAR TEETH UNDER EXTREME PRESSURE LUBRICATION

The data measured by using the two-disc tester show that the concentration of EP addi- tives and the viscosity temperature characteristic of lubricant have a cooperation effect on the fric- tion coefficient in boundary lubrication.

Inverse design of mesoscopic models for compressible flow using the Chapman-Enskog analysis

In this paper,based on simplified Boltzmann equation,we explore the inverse-design of mesoscopic models for compressible flow using the Chapman-Enskog analysis.Starting from the single-relaxation-time Boltzmann equation with an additional source term,two model Boltzmann equations for two reduced distribution functions are obtained,each then also having an additional undetermined source term.Under this general framework and using Navier-Stokes-Fourier(NSF)equations as constraints,the structures of the distribution functions are obtained by the leading-order Chapman-Enskog analysis.Next,five basic constraints for the design of the two source terms are obtained in order to recover the NSF system in the continuum limit.These constraints allow for adjustable bulk-to-shear viscosity ratio,Prandtl number as well as a thermal energy source.The specific forms of the two source terms can be determined through proper physical considerations and numerical implementation requirements.By employing the truncated Hermite expansion,one design for the two source terms is proposed.Moreover,three well-known mesoscopic models in the literature are shown to be compatible with these five constraints.In addition,the consistent implementation of boundary conditions is also explored by using the Chapman-Enskog expansion at the NSF order.Finally,based on the higher-order Chapman-Enskog expansion of the distribution functions,we derive the complete analytical expressions for the viscous stress tensor and the heat flux.Some underlying physics can be further explored using the DNS simulation data based on the proposed model.

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.

Viscosities in chiral symmetry breaking phase

In the chiral symmetry breaking phase described by the NJL model at quark level,along with the chiral symmetry restoration the ratio of shear viscosity to entropy density η/s drops down monotonously and reaches the minimum at the critical point,while the ratio of bulk viscosity to entropy density ζ/s behaves oppositely.

Continuum Formulation for Non-Equilibrium Shock Structure Calculation

Are extensions to continuum formulations for solving fluid dynamic problems in the transition-to-rarefied regimes viable alternatives to particle methods?It is well known that for increasingly rarefied flow fields,the predictions from continuum formulation,such as the Navier-Stokes equations lose accuracy.These inaccuracies are attributed primarily to the linear approximations of the stress and heat flux terms in the Navier-Stokes equations.The inclusion of higher-order terms,such as Burnett or highorder moment equations,could improve the predictive capabilities of such continuum formulations,but there has been limited success in the shock structure calculations,especially for the high Mach number case.Here,after reformulating the viscosity and heat conduction coefficients appropriate for the rarefied flow regime,we will show that the Navier-Stokes-type continuum formulation may still be properly used.The equations with generalization of the dissipative coefficients based on the closed solution of the Bhatnagar-Gross-Krook(BGK)model of the Boltzmann equation,are solved using the gas-kinetic numerical scheme.This paper concentrates on the non-equilibrium shock structure calculations for both monatomic and diatomic gases.The Landau-Teller-Jeans relaxation model for the rotational energy is used to evaluate the quantitative difference between the translational and rotational temperatures inside the shock layer.Variations of shear stress,heat flux,temperatures,and densities in the internal structure of the shock waves are compared with,(a)existing theoretical solutions of the Boltzmann solution,(b)existing numerical predictions of the direct simulation Monte Carlo(DSMC)method,and(c)available experimental measurements.The present continuum formulation for calculating the shock structures for monatomic and diatomic gases in the Mach number range of 1.2 to 12.9 is found to be satisfactory.