Single Equation Of State Research Articles

Magnetic, magnetocaloric and critical exponent properties of Eu3(PO4)2 prepared by sol gel method

The Eu3(PO4)2 compound was prepared by the sol gel chemical route and its magnetic, magnetocaloric, and critical exponent properties have been investigated. Combining different models, a detailed analysis of the magnetic phase transitions in the Eu3(PO4)2 compound has been actually performed. At 5.9 K, the phase transition from the AFM (Antiferromagnetic) state to the PM (Paramagnetic) state is 2nd order. A phenomenological model is now used to comprehend the MCE (magnetocaloric effect) behavior of this sample. The CEs (Critical Exponents) are clearly obtained employing MAPs (Modified-Arrott-Plots), CIA (Critical Isotherm Analysis) and also WSR (Windom Scaling Relation) techniques based upon the data of magnetic measurements registered around the TN (Néel temperature). Besides, an analysis of critical performance on the basis of the MCE is also provided. These exponents are β (beta), γ (gamma), and δ (delta) were properly revealed to be nearby those of the MFM (Mean-Field-Model) values. This simply reflects the existence of an AFM long-range order in our sample. A single equation of state also can be used to scale the magnetization below and above TN. Nevertheless, it should be noted that the scaling relations are respected, which indicates a renormalization of the interactions nearby the TN. The forecasting of the J(r) (exchange interaction) validated the long-range AFM order in this sample.

Equationsof state in multiphase lattice Boltzmann method revisited.

The single-component multiphase fluids can be described by a single equationof state (EOS), and various EOSs have been employed in the multiphase lattice Boltzmann (LB) method. In this work, we revisit five commonly used EOSs, including the van der Waals EOS, the Redlich-Kwong EOS, the Redlich-Kwong-Soave EOS, the Peng-Robinson EOS, and the Carnahan-Starling EOS. The recent multiphase LB model with self-tuning EOS is employed because of its thermodynamic consistency in a strict sense and clear physical picture at the microscopic level. First, the way to incorporate these multiphase EOSs is proposed. Two scaling factors are introduced to independently adjust the surface tension and interface thickness, and the lattice sound speed is EOS-dependent to ensure the numerical stability. Then, numerical tests are conducted to validate the incorporations of these EOSs and compare their numerical performances. The surface tension and interface thickness are set to the same values for different EOSs in the comparisons. The liquid and gas densities, surface tension, and interface thickness by the LB simulation agree well with the thermodynamic results. The maximum density ratios achieved with different EOSs are at the same level and could be very close to each other when the interface thickness is relatively small. The effects of multiphase EOS, density ratio, and dimensionless relaxation time on the spurious current are discussed in detail. It is interesting to find the van der Waals EOS shows the best numerical performance in reducing the spurious current.

Publisher's Note: “A new single equation of state to describe the dynamic viscosity and self-diffusion coefficient for all fluid phases of water from 200 to 1800 K based on a new original microscopic model” [Phys. Fluids 33, 117112 (2021)

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A new single equation of state to describe the dynamic viscosity and self-diffusion coefficient for all fluid phases of water from 200 to 1800 K based on a new original microscopic model

A microscopic model, which is able to simultaneously describe the dynamic viscosity and the self-diffusion coefficient of fluids, is presented. This model is shown to emerge from the introduction of fractional calculus in a usual model of condensed matter physics based on an elastic energy functional. The main feature of the model is that all measurable quantities are predicted, depending on external parameters in a non-trivial way (e.g., the experimental set-up geometry, in particular the sample size). On the basis of an unprecedented comparative analysis of a collection of published experimental data, the modeling is applied to the case of water in all its fluid phases, in particular in the supercooled phase. It is shown that the discrepancies in the literature data are only apparent and can be quantitatively explained by different experimental configurations (e.g., geometry, calibration). This approach makes it possible to reproduce the water viscosity with a better accuracy than the 2008 International Association for the Properties of Water and Steam (IAPWS) formulation and also with a more physically satisfying modeling of the isochors. Moreover, it also allows the modeling within experimental accuracy of the translational self-diffusion data available in the literature in all water fluid phases. Finally, the formalism of the model makes it possible to understand the “anomalies” observed on the dynamic viscosity and self-diffusion coefficient and their possible links.

Numerical inside view of hypermassive remnant models for GW170817

The first multimessenger observation attributed to a merging neutron star binary provided an enormous amount of observational data. Unlocking the full potential of this data requires a better understanding of the merger process and the early post-merger phase, which are crucial for the later evolution that eventually leads to observable counterparts. In this work, we perform standard hydrodynamical numerical simulations of a system compatible with GW170817. We focus on a single equation of state (EOS) and two mass ratios, while neglecting magnetic fields and neutrino radiation. We then apply newly developed postprocessing and visualization techniques to the results obtained for this basic setting. The focus lies on understanding the three-dimensional structure of the remnant, most notably the fluid flow pattern, and its evolution until collapse. We investigate the evolution of mass and angular momentum distribution up to collapse, as well as the differential rotation along and perpendicular to the equatorial plane. For the cases that we studied, the remnant cannot be adequately modeled as a differentially rotating axisymetric NS. Further, the dominant aspect leading to collapse is the GW radiation and not internal redistribution of angular momentum. We relate features of the gravitational wave signal to the evolution of the merger remnant, and make the waveforms publicly available. Finally, we find that the three-dimensional vorticity field inside the disk is dominated by medium-scale perturbances and not the orbital velocity, with potential consequences for magnetic field amplification effects.

Surface of rapidly-rotating neutron stars: Implications to neutron star parameter estimation

The Neutron star Interior Composition Explorer (NICER) is currently observing the x-ray pulse profiles emitted by hot spots on the surface of rotating neutron stars allowing for an inference of their radii with unprecedented precision. A critical ingredient in the pulse profile model is an analytical formula for the oblate shape of the star. These formulas require a fitting over a large ensemble of neutron star solutions, which cover a wide set of equations of state, stellar compactnesses and rotational frequencies. However, this procedure introduces a source of systematic error, as (i) the fits do not describe perfectly the surface of all stars in the ensemble and (ii) neutron stars are described by a single equation of state, whose influence on the surface shape is averaged out during the fitting procedure. Here we perform a first study of this systematic error, finding evidence that it is subdominant relative to the statistical error in the radius inference by NICER. We also find evidence that the formula currently used by NICER can be used in the inference of the radii of rapidly rotating stars, outside of the formula's domain of validity. Moreover, we employ an accurate enthalpy-based method to locate the surface of numerical solutions of rapidly rotating neutron stars and a new highly accurate formula to describe their surfaces. These results can be used in applications that require an accurate description of oblate surfaces of rapidly rotating neutron stars.

Temperature dependence of η/s of strongly interacting matter: Effects of the equation of state and the parametric form of (η/s)(T)

We investigate the temperature dependence of the shear viscosity to entropy density ratio $\eta/s$ using a piecewise linear parametrization. To determine the optimal values of the parameters and the associated uncertainties, we perform a global Bayesian model-to-data comparison on Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV and Pb+Pb collisions at $2.76$ TeV and $5.02$ TeV, using a 2+1D hydrodynamical model with the EKRT initial state. We provide three new parametrizations of the equation of state (EoS) based on contemporary lattice results and hadron resonance gas, and use them and the widely used $s95p$ parametrization to explore the uncertainty in the analysis due to the choice of the equation of state. We found that $\eta/s$ is most constrained in the temperature range $T\approx 150$--$220$ MeV, where, for all EoSs, $0.08 < \eta/s < 0.23$ when taking into account the 90% credible intervals. In this temperature range the EoS parametrization has only a small $\approx 10\%$ effect on the favored $\eta/s$ value, which is less than the $\approx 30\%$ uncertainty of the analysis using a single EoS parametrization. Our parametrization of $(\eta/s)(T)$ leads to a slightly larger minimum value of $\eta/s$ than the previously used parametrizations. When we constrain our parametrization to mimic the previously used parametrizations, our favored value is reduced, and the difference becomes statistically insignificant.

Classical optimal designs on annulus and numerical approximations

We consider optimal design problems for stationary diffusion equation, seeking for the arrangement of two isotropic materials, with prescribed amounts, which maximizes the energy functional. The aim is to present some classes of problems on an annulus with classical solutions.The first class is a single state equation problem with a constant right-hand side and homogenous Dirichlet boundary condition. By analyzing the optimality conditions, we are able to show that there exists a unique (classical) solution. We prove that, depending on the amounts of given materials, only two optimal configurations in both two- and three-dimensional case are possible.The second class of problems deals with a two-state optimal design problem. A numerical method based on shape derivative is presented, showing good results when applied to described problems with classical solutions on annulus.

Thermodynamically Consistent Equations of State

The equation of state for gaseous plasma is well described bу the Saha model. In this work, accounting for the finite ion core volume is included in this model. This improvement allows the expansion of the Saha model to superhigh densities and moderate temperatures, where plasma can be considered as a liquid. In this domain, the thermodynamics of the Saha model is quite close to that of the Thomas–Fermi model with corrections (TFC), which is conventionally used for condensed matter. This improved the agreement of the theory with experimental data. Using a special interpolation, the Saha model and the TFC model are united in a single equation of state, in which the strict thermodynamic consistency of all quantities is provided. The latter is very important for the application of the equation of state in gasdynamic calculations.

Evaluation of Thermodynamic Models for Predicting Phase Equilibria of $$\hbox {CO}_{2}$$ CO 2 + Impurity Binary Mixture

For the design and operation of $$\hbox {CO}_{2}$$ capture and storage (CCS) processes, equation of state (EoS) models are used for phase equilibrium calculations. Reliability of an EoS model plays a crucial role, and many variations of EoS models have been reported and continue to be published. The prediction of phase equilibria for $$\hbox {CO}_{2}$$ mixtures containing $$\hbox {SO}_{2}$$ , $$\hbox {N}_{2}$$ , NO, $$\hbox {H}_{2}$$ , $$\hbox {O}_{2}$$ , $$\hbox {CH}_{4}$$ , $$\hbox {H}_{2}\mathrm{S}$$ , Ar, and $$\hbox {H}_{2}\mathrm{O}$$ is important for $$\hbox {CO}_{2}$$ transportation because the captured gas normally contains small amounts of impurities even though it is purified in advance. For the design of pipelines in deep sea or arctic conditions, flow assurance and safety are considered priority issues, and highly reliable calculations are required. In this work, predictive Soave–Redlich–Kwong, cubic plus association, Groupe Europeen de Recherches Gazieres (GERG-2008), perturbed-chain statistical associating fluid theory, and non-random lattice fluids hydrogen bond EoS models were compared regarding performance in calculating phase equilibria of $$\hbox {CO}_{2}$$ -impurity binary mixtures and with the collected literature data. No single EoS could cover the entire range of systems considered in this study. Weaknesses and strong points of each EoS model were analyzed, and recommendations are given as guidelines for safe design and operation of CCS processes.

Analysis based on scaling relations of critical behaviour at PM-FM phase transition and universal curve of magnetocaloric effect in selected Ag-doped manganites.

The critical behaviour of Pr0.5Sr0.5−xAgxMnO3 (0 ≤ x ≤ 0.2) samples around the paramagnetic–ferromagnetic phase transition is studied based on isothermal magnetization measurements. The assessments based on Banerjee's criteria reveal the samples undergoing a second-order magnetic phase transition. Various techniques such as modified Arrott plot, Kouvel–Fisher method, and critical isotherm analysis were used to determine the values of the ferromagnetic transition temperature TC, as well as the critical exponents of β, γ and δ. The values of critical exponents, derived from the magnetization data using the Kouvel–Fisher method, are found to be (β = 0.43 ± 0.002, 0.363 ± 0.068 and 0.328 ± 0.012), (γ = 1.296 ± 0.007, 1.33 ± 0.0054 and 1.236 ± 0.012) for x = 0.0, 0.1 and 0.2, respectively. This implies that the Pr0.5Sr0.5−xAgxMnO3 with 0 ≤ x ≤ 0.2 systems does not belong to a single universality class and indicates that the presence of magnetic disorder in the system must be taken into account to fully describe the microscopic interaction of these manganites. With these values, magnetic-field dependences of magnetization at temperatures around TC can be well described following a single equation of state for our samples. From magnetic entropy change (ΔSM), it was possible to evaluate the critical exponents of the magnetic phase transitions. Their values are in good agreement with those obtained from the critical exponents using a modified Arrott plot (MAP). We used the scaling hypotheses to scale the magnetic entropy change and heat capacity changes to a universal curve respectively for Pr0.5Sr0.5−xAgxMnO3 samples.

Two Coexisting Families of Compact Stars: Observational Implications for Millisecond Pulsars

Abstract It is usually thought that a single equation of state (EoS) model “correctly” represents cores of all compact stars. Here we emphasize that two families of compact stars, viz., neutron stars and strange stars, can coexist in nature, and that neutron stars can get converted to strange stars through the nucleation process of quark matter in the stellar center. From our fully general relativistic numerical computations of the structures of fast-spinning compact stars, known as millisecond pulsars, we find that such a stellar conversion causes a simultaneous spin-up and decrease in gravitational mass of these stars. This is a new type of millisecond pulsar evolution through a new mechanism, which gives rise to relatively lower mass compact stars with higher spin rates. This could have an implication for the observed mass and spin distributions of millisecond pulsars. Such a stellar conversion can also rescue some massive, spin-supported millisecond pulsars from collapsing into black holes. Besides, we extend the concept of critical mass for the neutron star sequence to the case of fast-spinning neutron stars, and point out that neutron star EoS models cannot be ruled out by the stellar mass measurement alone. Finally, we emphasize the additional complexity for constraining EoS models, for example, by stellar radius measurements using X-ray observations, if two families of compact stars coexist.

Method of construction in a variable pressure and temperature single equation of state satisfying the scaling hypothesis

Method of construction in a variable pressure and temperature single equation of state satisfying the scaling hypothesis

A Cosmological Model Describing the Early Inflation, the Intermediate Decelerating Expansion, and the Late Accelerating Expansion of the Universe by a Quadratic Equation of State

We develop a cosmological model based on a quadratic equation of state \(p/c^2=-(\alpha+1){\rho^2}/{\rho_P}+\alpha\rho-(\alpha+1)\rho_ {\Lambda}\), where \(\rho_P\) is the Planck density and \(\rho_{\Lambda}\) the cosmological density, ``unifying'' vacuum energy and dark energy in the spirit of a generalized Chaplygin gas model. For \(\rho\rightarrow \rho_P\), it reduces to \(p=-\rho_P c^2\) leading to a phase of early accelerating expansion (early inflation) with a constant density equal to the Planck density \(\rho_P=5.16 \times 10^{99}\, {\rm g}/{\rm m}^3\) (vacuum energy). For \(\rho_{\Lambda}\ll\rho\ll \rho_P\), we recover the standard linear equation of state \(p=\alpha \rho c^2\) describing radiation (\(\alpha=1/3\)) or pressureless matter (\(\alpha=0\)) and leading to an intermediate phase of decelerating expansion. For \(\rho\rightarrow \rho_{\Lambda}\), we get \(p=-\rho_{\Lambda} c^2\) leading to a phase of late accelerating expansion (late inflation) with a constant density equal to the cosmological density \(\rho_{\Lambda}=7.02\times 10^{-24}\, {\rm g}/{\rm m}^3\) (dark energy). The pressure is successively negative (vacuum energy), positive (radiation and matter), and negative again (dark energy). We show a nice ``symmetry'' between the early universe (vacuum energy \(+\) \(\alpha\)-fluid) and the late universe (\(\alpha\)-fluid \(+\) dark energy). In our model, they are described by two polytropic equations of state with index \(n=+1\) and \(n=-1\) respectively. Furthermore, the Planck density \(\rho_P\) in the early universe plays a role similar to the cosmological density \(\rho_{\Lambda}\) in the late universe. They represent fundamental upper and lower density bounds differing by \(122\) orders of magnitude. The cosmological constant ``problem'' may be a false problem. We study the evolution of the scale factor, density, and pressure. Interestingly, our quadratic equation of state leads to a fully analytical model describing the evolution of the universe from the early inflation (Planck era) to the late accelerating expansion (de Sitter era). These two phases are bridged by a decelerating algebraic expansion (\(\alpha\)-era). Our model does not present any singularity at \(t=0\) and exists eternally in the past (although it may be incorrect to extrapolate the solution to the infinite past). On the other hand, it admits a scalar field interpretation based on an inflaton, quintessence, or tachyonic field. Our model generalizes the standard \(\Lambda\)CDM model by incorporating naturally a phase of early inflation that avoids the primordial singularity. Furthermore, it describes the early inflation, the intermediate decelerating expansion, and the late accelerating expansion of the universe simultaneously in terms of a single equation of state. We determine the corresponding scalar field potential that unifies the inflaton and quintessence potentials.

Limitations on silicon in the outer core: Ultrasonic measurements at high temperatures and high dK/dP values of Fe‐Ni‐Si liquids at high pressures

AbstractThe sound velocities of four iron‐nickel‐silicon liquids (Fe‐5 wt %Ni‐6 wt %Si, Fe‐5 wt %Ni‐10 wt %Si, Fe‐5 wt %Ni‐14 wt %Si, and Fe‐5 wt %Ni‐20 wt %Si) are measured between 1460 and 1925 K at ambient pressures using ultrasonic interferometry. The results constrain both the dependence on Si content of the bulk modulus of these liquids and the temperature dependence of their elasticity. These elastic data are utilized to assess both relatively low pressure (to 12 GPa) compressional data on Fe‐Si liquids and to extrapolate to higher‐pressure and higher‐temperature conditions. If a single equation of state for Fe‐Ni‐Si liquids of a given composition applies from low pressure to near core conditions, then our results imply that the isothermal pressure derivative of the bulk modulus of these liquids is high: likely 8 and above at high temperatures. This high value of the pressure derivative of the bulk modulus at low pressures in Fe‐Si liquids causes marked stiffening at higher pressures, leading to notable incompressibility and apparent low values of the pressure derivative of the bulk modulus at core conditions. These results reinforce the conclusion that silicon is not a major alloying component of Earth's core.

From holography towards real-world nuclear matter

Quantum chromodynamics is notoriously difficult to solve at nonzero baryon density, and most models or effective theories of dense quark or nuclear matter are restricted to a particular density regime and/or a particular form of matter. Here we study dense (and mostly cold) matter within the holographic Sakai-Sugimoto model, aiming at a strong-coupling framework in the wide density range between nuclear saturation density and ultra-high quark matter densities. The model contains only three parameters, and we ask whether it fulfills two basic requirements of real-world cold and dense matter, a first-order onset of nuclear matter and a chiral phase transition at high density to quark matter. Such a model would be extremely useful for astrophysical applications because it would provide a single equation of state for all densities relevant in a compact star. Our calculations are based on two approximations for baryonic matter, firstly an instanton gas and secondly a homogeneous ansatz for the non-abelian gauge fields on the flavor branes of the model. While the instanton gas shows chiral restoration at high densities but an unrealistic second-order baryon onset, the homogeneous ansatz behaves exactly the other way around. Our study thus provides all ingredients that are necessary for a more realistic model and allows for systematic improvements of the applied approximations.

3D-Ising ferromagnetic characteristics and magnetocaloric study in Pr0.4Eu0.2Sr0.4MnO3 manganite

The structure, critical exponents and magnetocaloric effect (MCE) of Pr0.4Eu0.2Sr0.4MnO3 were investigated in detail. A solid state reaction method was used in the preparation phase. Phase purity, structure, size, and crystallinity were investigated using XRD and SEM. The Reitveld refinement of XRD pattern shows that the sample adopts an orthorhombic structure with Pnma space group. Analyzing temperature and field dependences of magnetization around the ferromagnetic–paramagnetic transition reveals the sample undergoing the second-order magnetic phase transition with the critical parameters TC∼238K, β=0.310(3), γ=1.264(1) and δ=4.761(9).The exponents are close to 3D-Ising values. This reflects an existence of ferromagnetic short-range order in our sample. With these values one can scale the magnetization below and above TC following a single equation of state. However, it is noteworthy that the scaling relations are obeyed indicating renormalization of interactions around the TC. Temperature variation in effective exponents βeff and γeff resemble with those for disordered ferromagnet. In the vicinity of TC, the magnetic entropy change ΔS reached maximum values of 2.80 and 5.32J/kgK under magnetic field variations of 2 and 5T, respectively. The field dependence of the magnetic entropy changes are also analyzed, which show power law dependence ΔSMmax≈aμ0Hn at transition temperature. The critical exponent analysis related to magnetocaloric effect is described. Moreover, the temperature dependence of the exponent n for a different magnetic field is also studied. The values of n obey to the Curie Weiss law above the transition temperature. In particularly, n can be related to the critical exponents β, γ and δ at the magnetic transition. We used the scaling hypotheses to scale the magnetic entropy change and heat capacity changes to a single universal curve respectively for Pr0.4Eu0.2Sr0.4MnO3 sample.

Simulation of Acoustic Behavior of Bubbly Liquids with Hybrid Lattice Boltzmann and Homogeneous Equilibrium Models

AbstractHomogeneous equilibrium model (HEM) has been widely used in cavitating flow simulations. The major feature of this model is that a single equation of state (EOS) is proposed to describe the thermal behavior of bubbly liquid, where both kinematic and thermal equilibrium is assumed between two phases. In this paper, the HEM was coupled with multi-relaxation-time lattice Boltzmann model (MRT-LBM) and the acoustic behavior was simulated. Two approaches were applied alternatively: adjusting speed of sound (Buick, J. Phys. A, 2006, 39:13807-13815) and setting real gas EOS. Both approaches result in high accuracy in acoustic speed predictions for different void (gas) volume of fractions. It is demonstrated that LBM could be successfully applied as a Navier-Stokes equation solver for industrial applications. However, further dissipation and dispersion analysis shows that Shan-Chen type approaches of LBM are deficient, especially in large wave-number region.

A new model for the density of saturated solutions of CO2–H2O–NaCl in saline aquifers

A new model is proposed to find the density of saturated ternary solutions of H2O–CO2–NaCl in the temperature range of 50–100°C and pressures up to 600bar. The model calculates the partial molar volume of dissolved CO2 from the density of saturated binary, H2O–CO2, solution and the corresponding mole fraction of dissolved CO2. The density of the saturated binary solution is determined as a function of temperature and pressure from a regression of experimental data. The mole fraction of dissolved CO2 is obtained from the Redlich–Kwong equation of state. The partial molar volume of CO2 obtained in his manner is then made to coincide with one solution branch of the Redlich–Kwong equation while retaining the other solution branch associated with the molar volume of the gas phase. This allows the simultaneous calculation of both the gas and the liquid molar volume with a single equation of state. The density of the saturated ternary solution predicted by the new model is found to be in good agreement with experimental data. The new model is then used to characterize the effects of temperature, pressure and salinity on the onset of buoyancy driven convection during CO2 sequestration.

A new limiting procedure for discontinuous Galerkin methods applied to compressible multiphase flows with shocks and interfaces

Although the Discontinuous Galerkin (dg) method has seen widespread use for compressible flow problems in a single fluid with constant material properties, it has yet to be implemented in a consistent fashion for compressible multiphase flows with shocks and interfaces. Specifically, it is challenging to design a scheme that meets the following requirements: conservation, high-order accuracy in smooth regions and non-oscillatory behavior at discontinuities (in particular, material interfaces). Following the interface-capturing approach of Abgrall [1], we model flows of multiple fluid components or phases using a single equation of state with variable material properties; discontinuities in these properties correspond to interfaces. To represent compressible phenomena in solids, liquids, and gases, we present our analysis for equations of state belonging to the Mie–Grüneisen family. Within the dg framework, we propose a conservative, high-order accurate, and non-oscillatory limiting procedure, verified with simple multifluid and multiphase problems. We show analytically that two key elements are required to prevent spurious pressure oscillations at interfaces and maintain conservation: (i) the transport equation(s) describing the material properties must be solved in a non-conservative weak form, and (ii) the suitable variables must be limited (density, momentum, pressure, and appropriate properties entering the equation of state), coupled with a consistent reconstruction of the energy. Further, we introduce a physics-based discontinuity sensor to apply limiting in a solution-adaptive fashion. We verify this approach with one- and two-dimensional problems with shocks and interfaces, including high pressure and density ratios, for fluids obeying different equations of state to illustrate the robustness and versatility of the method. The algorithm is implemented on parallel graphics processing units (gpu) to achieve high speedup.