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In this work it is shown how the entropy scaling paradigm introduced by Rosenfeld (Phys Rev A 15:2545–2549, 1977, https://doi.org/10.1103/PhysRevA.15.2545 ) can be extended to calculate the viscosities of branched alkanes by group contribution methods (GCM), making the technique more predictive. Two equations of state (EoS) requiring only a few adjustable parameters (Lee–Kesler–Plöcker and PC-SAFT) were used to calculate the thermodynamic properties of linear and branched alkanes. These EOS models were combined with first-order and second-order group contribution methods to obtain the fluid-specific scaling factor allowing the scaled viscosity values to be mapped onto the generalized correlation developed by Yang et al. (J Chem Eng Data 66:1385–1398, 2021, https://doi.org/10.1021/acs.jced.0c01009 ) The second-order scheme offers a more accurate estimation of the fluid-specific scaling factor, and overall the method yields an AARD of 10 % versus 8.8 % when the fluid-specific scaling factor is fit directly to the experimental data. More accurate results are obtained when using the PC-SAFT EoS, and the GCM generally out-performs other estimation schemes proposed in the literature for the fluid-specific scaling factor.

Two sets of shock compression tests (i.e. conventional and reverse impact) were conducted to determine the shock response of two rock materials using a plate impact facility. Embedded manganin stress gauges were used for the measurements of longitudinal stress and shock velocity. Photon Doppler velocimetry was used to capture the free surface velocity of the target. Experimental data were obtained on a fine-grained marble and a coarse-grained gabbro over a shock pressure range of approximately 1.5-12 GPa. Gabbro exhibited a linear Hugoniot equation of state (EOS) in the pressure-particle velocity (P-up) plane, while for marble a nonlinear response was observed. The EOS relations between shock velocity (US) and particle velocity (up) are linearly fitted as US = 2.62 + 3.319up and US = 5.4 85 + 1.038up for marble and gabbro, respectively. This article is part of the themed issue ‘Experimental testing and modelling of brittle materials at high strain rates’.

In this White Paper we present the potential of the Enhanced X-ray Timing and Polarimetry (eXTP) mission for determining the nature of dense matter; neutron star cores host an extreme density regime which cannot be replicated in a terrestrial laboratory. The tightest statistical constraints on the dense matter equation of state will come from pulse profile modelling of accretion-powered pulsars, burst oscillation sources, and rotation-powered pulsars. Additional constraints will derive from spin measurements, burst spectra, and properties of the accretion flows in the vicinity of the neutron star. Under development by an international Consortium led by the Institute of High Energy Physics of the Chinese Academy of Science, the eXTP mission is expected to be launched in the mid 2020s.

A new equation of state for argon was developed with the view of extending the range of validity of the equation of state previously proposed by Tegeler et al. and obtaining a better physical description of the experimental thermodynamic data for the whole fluid region (single-phase, metastable, and saturation states). As proposed by Tegeler et al., this equation is also based on a functional form of the residual part of the reduced Helmholtz free energy. However, in this work, the fundamental equation for Helmholtz free energy was derived from the measured quantities CV(ρ, T) and P(ρ, T). The empirical description of the isochoric heat capacity CV(ρ, T) was based on an original empirical description explicitly containing the metastable states. The thermodynamic properties (internal energy, entropy, and free energy) were then obtained by combining the integration of CV(ρ, T). The arbitrary functions introduced by the integration process were deduced from a comparison between calculated and experimental pressure P(ρ, T) data. The new formulation is valid for the whole fluid region from the melting line to 2300 K and for pressures up to 50 GPa. It also predicts the existence of a maximum of the isochoric heat capacity CV along isochors, as experimentally observed in several other fluids. For many applications, an approximate form of the equation of state for the liquid phase may be sufficient. A Tait–Tammann equation is therefore proposed between the triple-point temperature and 148 K.

Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual approach to this problem consists mainly in the numerical investigation of the Tolman-Oppenheimer-Volkoff and of the mass continuity equations, which describes the hydrostatic stability of the dense stars. In the present paper we introduce an alternative approach for the study of the relativistic fluid sphere, based on the relativistic mass equation, obtained by eliminating the energy density in the Tolman-Oppenheimer-Volkoff equation. Despite its apparent complexity, the relativistic mass equation can be solved exactly by using a power series representation for the mass, and the Cauchy convolution for infinite power series. We obtain exact series solutions for general relativistic dense astrophysical objects described by the linear barotropic and the polytropic equations of state, respectively. For the polytropic case we obtain the exact power series solution corresponding to arbitrary values of the polytropic index  n . The explicit form of the solution is presented for the polytropic index n = 1 , and for the indexes n = 1 / 2 and n = 1 / 5 , respectively. The case of n = 3 is also considered. In each case the exact power series solution is compared with the exact numerical solutions, which are reproduced by the power series solutions truncated to seven terms only. The power series representations of the geometric and physical properties of the linear barotropic and polytropic stars are also obtained.

Hanbury-Brown-Twiss (HBT) correlations for charged pions in central Au+Au collisions at s NN = 2.4 − 7.7 GeV (corresponding to beam kinetic energies in the fixed target frame from E lab = 1.23 to 30 GeV/nucleon) are calculated using the ultra-relativistic quantum molecular dynamics model with different equations of state (EoSs). The effects of a phase transition at high baryon densities are clearly observed in the explored HBT parameters. The results show that the available data on the HBT radii, R O / R S and R O 2 − R S 2 , in the investigated energy region favor a relatively stiff EoS at low beam energies, which then turns into a soft EoS at high collision energies consistent with astrophysical constraints on the high-density EoS of quantum chromodynamics (QCD). The specific effects of two different phase transition scenarios on R O / R S and R O 2 − R S 2 are investigated. A phase transition with a significant softening of the EoS below four times the nuclear saturation density can be excluded using HBT data. Our results highlight that the pion’s R O /R S and R O 2 − R S 2 are sensitive to the stiffness of the EoS and can be used to constrain and understand the QCD EoS in a high baryon density region.

Carbon has been proposed as a major component in the Martian core alongside sulfur for its siderophile behavior during core‐mantle segregation. However, the core C content remains poorly constrained, due to uncertainties in both seismically observed core properties and the equation of state of C‐bearing Fe‐rich liquids. Here we conducted first‐principles molecular dynamics simulations to investigate the equation of state and sound velocity of Fe–S–C liquids under pressures of 10–55 GPa and temperatures of 1,700–3,200 K, conditions relevant to the Martian core. Our results show that the presence of C increases the sound velocity of Fe–S liquids, in contrast to what is observed for other light elements such as S, O, and H. Regardless of the particular seismic model used for the Martian core, we find that about 4.3 ± 1.5 wt% C is required to reproduce the velocity of the core, confirming its role as a major light element.

We trap individual 1D Bose gases and obtain the associated equation of state by combining calibrated confining potentials with in situ density profiles. Our observations agree well with the exact Yang-Yang 1D thermodynamic solutions under the local density approximation. We find that our final 1D system undergoes inefficient evaporative cooling that decreases the absolute temperature, but monotonically reduces a degeneracy parameter.

In order to determine an accurate and reliable high‐pressure and high‐temperature equation of state (EOS) of MgO, unified analyses were carried out for various pressure‐scale‐free experimental data sets measured at 1 atm to 196 GPa and 300–3700 K, which are zero‐pressure thermal expansion data, zero‐pressure and high‐temperature adiabatic bulk modulus (KS) data, room temperature and high‐pressure KS data, and shock compression data. After testing several EOS models based on the Mie‐Grüneisen‐Debye description for the thermal pressures with the Vinet and the third‐order Birch‐Murnaghan equations for the 300‐K isothermal compression, we determined the K′T0 and γ(V) using a new functional form γ = γ0{1 + a[(V/V0)b − 1]} to express the volume dependence of the Grüneisen parameter. Through least squares analyses with prerequisite zero‐pressure and room temperature properties of V0, KS0, α0, and CP0, we simultaneously optimized a set of parameters of K′T0, γ0, a, and b required to represent the P‐V‐T EOS. Determined new EOS models of MgO successfully reproduced all the analyzed P‐V‐T‐KS data up to 196 GPa and 3700 K within the uncertainties, and the total residuals between calculated and observed pressures were found to be 0.8 GPa in root mean squares. These EOS models, even though very simple, are able to reproduce available data quite accurately in the wide pressure‐temperature range and completely independent from other pressure scales. We propose these models for primary pressure calibration standards applicable to quantitative high‐pressure and high‐temperature experiments.

The process of the gravitational collapse might lead not only to a black hole but also to naked singularity formation. In this paper, we consider the generalized Vaidya spacetime with polytropic and generalized polytropic equations of state. We solve the Einstein and Einstein–Maxwell equations to obtain the explicit form of a mass function. We consider the limiting cases of solutions and find out, that generalized Vaidya spacetime might behave like Vaidya–de Sitter and Bonnor–Vaidya–de sitter solutions. Moreover, we explicitly show, that the part of solution, which depends on the polytropic index, is similar to cosmological fields surrounding both Vaidya and Bonnor–Vaidya black holes. The process of the gravitational collapse has been then considered. We have found out that the conditions of the naked singularity formation don’t depend on the polytropic index.