Different Equations Of State Research Articles

Phase behavior modeling for gas condensate fluids with PC-SAFT and an improved binary interaction coefficient model

The accurate reservoir fluid phase behavior prediction in the gas condensate samples is still a challenging problem. The binary interaction coefficients are among the effective parameters in the phase behavior calculations. The binary interaction coefficients (BICs) are different for different equations of state. This work provides a solution to this problem with a modified version of Hudson-McCoubrey (HM) equation to determine the BICs of PC-SAFT, over a number of real gas condensate samples.The modeling procedure in this work includes two separate steps; in the first step, the proposed binary interaction estimation models parameters are regressed and in the second step, the prepared models are used, to evaluate the performance under phase behavior prediction feedback with different binary mixtures and real gas condensate samples. The modeling results are presented for PC-SAFT with the new BICs models and original HM in comparison to the experimental data and Peng-Robinson equation of state (with a common interaction coefficients set). The experimental data for the liquid dropouts and dew point pressures for different real gas condensate fluids are used from published data in the literature.The average absolute deviations percent (AAD%) for the dew point pressure prediction over the evaluation samples data, by PR is 20.8, by PC-SAFT with HM BICs, AAD% is 18.0 and for PC-SAFT with the proposed BICs model, AAD% is 9.6. All of these results are taken over the same samples when the EOS are used in prediction mode (after BIC model development). Beside this, the predictions of the liquid dropout are relatively improved in the case of PC-SAFT respect to Peng Robinson with the proposed set of binary interaction coefficients.

Constant entropy hybrid stars: a first approximation of cooling evolution

We aim to study the possibility of a hadron-quark phase transition in the interior of neutron stars, taking into account different schematic evolutionary stages at finite temperature. We also discuss the strange quark matter stability in the quark matter phase. Furthermore, we aim to analyze the astrophysical properties of hot and cold hybrid stars, considering the constraint on maximum mass given by the pulsars J1614-2230 and J0348+0432. We have developed a computational code to construct semi-analytical hybrid equations of state at fixed entropy per baryon and to obtain different families of hybrid stars. An analytical approximation of the Field Correlator Method is developed for the quark matter equation of state. For the hadronic equation of state we use a table based on the relativistic mean field theory, without hyperons. We solved the relativistic structure equations of hydrostatic equilibrium and mass conservation for hybrid star configurations. For the different equations of state obtained, we calculated the stability window for the strange quark matter, lepton abundances, temperature profiles and contours profiles for the maximum mass star depending on the parameters of the Field Correlator Method. We also computed the mass-radius and gravitational mass-baryonic mass relationships for different hybrid star families. We have analyzed different stages of hot hybrid stars as a first approximation of the cooling evolution of neutron stars with quark matter cores. We obtain cold hybrid stars with maximum masses $\geq 2 M_\odot$ for different combinations of the Field Correlator Method parameters. In addition, our study based on the gravitational mass - baryonic mass plane shows a late phase transition between hadronic and quark matter during the proto-hybrid star evolution, in contrast with previous studies of proto-neutron stars.

Stochastic gravitational wave background from newly born massive magnetars: The role of a dense matter equation of state

Newly born massive magnetars are generally considered to be produced by binary neutron star (NS) mergers, which could give rise to short gamma-ray bursts (SGRBs). The strong magnetic fields and fast rotation of these magnetars make them promising sources for gravitational wave (GW) detection using ground based GW interferometers. Based on the observed masses of Galactic NS-NS binaries, by assuming different equations of state (EOSs) of dense matter, we investigate the stochastic gravitational wave background (SGWB) produced by an ensemble of newly born massive magnetars. The massive magnetar formation rate is estimated through: (i) the SGRB formation rate (hereafter entitled as MFR1); (ii) the NS-NS merger rate (hereafter entitled as MFR2). We find that for massive magnetars with masses $M_{\rm mg}=2.4743 M_\odot$, if EOS CDDM2 is assumed, the resultant SGWBs may be detected by the future Einstein Telescope (ET) even for MFR1 with minimal local formation rate, and for MFR2 with a local merger rate $\dot{\rho}_{\rm c}^{\rm o}(0)\lesssim 10$ ${\rm Mpc}^{-3}{\rm Myr}^{-1}$. However, if EOS BSk21 is assumed, the SGWB may be detectable by the ET for MFR1 with the maximal local formation rate. Moreover, the background spectra show cutoffs at about 350 Hz in the case of EOS BSk21, and at 124 Hz for CDDM2, respectively. We suggest that if the cutoff at $\sim100$ Hz in the background spectrum from massive magnetars could be detected, then the quark star EOS CDDM2 seems to be favorable. Moreover, the EOSs, which present relatively small TOV maximum masses, would be excluded.

Use of the Gibbs thermodynamic potential to express the equation of state in atmospheric models

The thermodynamics of moist processes is complicated, and in typical atmospheric models numerous approximations are made. However, they are not always made in a self‐consistent way, which could lead to spurious sources or sinks of energy and entropy. One way to ensure self‐consistency is to derive all thermodynamic quantities from a thermodynamic potential such as the Gibbs function. Approximations may be made to the Gibbs function; these approximations are inherited by all derived quantities in a way that guarantees self‐consistency. Here, the feasibility of using the Gibbs function in an atmospheric model is demonstrated through the development of a semi‐implicit, semi‐Lagrangian vertical slice model, and its application to a standard buoyant bubble test case. The flexibility of the approach is also demonstrated by running the test case with four different equations of state corresponding to dry air, moist air that is saturated, a pseudo‐incompressible fluid, and an incompressible fluid. A recently presented ‘blended’ equation set that unifies the dry fully compressible case and the pseudo‐incompressible case is also easily accommodated.

R -mode frequencies of rapidly and differentially rotating relativistic neutron stars

R-modes of neutron stars could be a source of gravitational waves for ground based detectors. If the precise frequency $\sigma$ is known, guided gravitational wave searches with enhanced detectability are possible. Because of its physical importance many authors have calculated the r-mode frequency. For the dominant mode, the associated gravitational wave frequency is 4/3 times the angular velocity of the star $\Omega$, subject to various corrections of which relativistic and rotational corrections are the most important. This has led several authors to investigate the dependence of the r-mode frequency on factors such as the relativistic compactness parameter ($M/R$) and the angular velocity of stars with different equations of state. The results found so far, however, are almost independent of the equation of state. Here we investigate the effect of rapid rotation and differential rotation on $\sigma$. We evolve the perturbation equations using the Cowling approximation by applying finite differencing methods to compute the r-mode frequency for a series of rotating neutron stars with polytropic equations of state. We find that rotational effects in the r-mode frequency can be larger than relativistic effects for rapidly spinning stars with low compactness, reducing the observed frequency. Differential rotation also acts to decrease $\sigma$, but its effect inscreases with the compactness. The results presented here are relevant to the design of gravitational wave and electromagnetic r-mode searches.

Rayleigh–Bénard stability and the validity of quasi-Boussinesq or quasi-anelastic liquid approximations

The linear stability threshold of the Rayleigh–Bénard configuration is analysed with compressible effects taken into account. It is assumed that the fluid under investigation obeys a Newtonian rheology and Fourier’s law of thermal transport with constant, uniform (dynamic) viscosity and thermal conductivity in a uniform gravity field. Top and bottom boundaries are maintained at different constant temperatures and we consider here mechanical boundary conditions of zero tangential stress and impermeable walls. Under these conditions, and with the Boussinesq approximation, Rayleigh (Phil. Mag., vol. 32 (192), 1916, pp. 529–546) first obtained analytically the critical value $27\unicode[STIX]{x03C0}^{4}/4$ for a dimensionless parameter, now known as the Rayleigh number, at the onset of convection. This paper describes the changes of the critical Rayleigh number due to the compressibility of the fluid, measured by the dimensionless dissipation parameter ${\mathcal{D}}$ and due to a finite temperature difference between the hot and cold boundaries, measured by a dimensionless temperature gradient $a$. Different equations of state are examined: ideal gas equation, Murnaghan’s model (often used to describe the interiors of solid but convective planets) and a generic equation of state with adjustable parameters, which can represent any possible equation of state. In the perspective to assess approximations often made in convective models, we also consider two variations of this stability analysis. In a so-called quasi-Boussinesq model, we consider that density perturbations are solely due to temperature perturbations. In a so-called quasi-anelastic liquid approximation model, we consider that entropy perturbations are solely due to temperature perturbations. In addition to the numerical Chebyshev-based stability analysis, an analytical approximation is obtained when temperature fluctuations are written as a combination of only two modes, one being the original symmetrical (between top and bottom) mode introduced by Rayleigh, the other one being antisymmetrical. The analytical solution allows us to show that the antisymmetrical part of the critical eigenmode increases linearly with the parameters $a$ and ${\mathcal{D}}$, while the superadiabatic critical Rayleigh number departs quadratically in $a$ and ${\mathcal{D}}$ from $27\unicode[STIX]{x03C0}^{4}/4$. For any arbitrary equation of state, the coefficients of the quadratic departure are determined analytically from the coefficients of the expansion of density up to degree three in terms of pressure and temperature.

The general class of Bianchi cosmological models with dark energy and variable Λ and G in viscous cosmology

The general class of Bianchi cosmological models with dark energy in the form of modified Chaplygin gas with variable Λ and G and bulk viscosity have been considered. We discuss three types of average scale factor by using a special law for deceleration parameter which is linear in time with negative slope. The exact solutions to the corresponding field equations are obtained. We obtain the solution of bulk viscosity (ξ), cosmological constant (Λ), gravitational parameter (G) and deceleration parameter (q) for different equations of state. The model describes an accelerating Universe for large value of time t, wherein the effective negative pressure induced by Chaplygin gas and bulk viscous pressure are driving the acceleration.

Hybrid metric-Palatini stars

We consider the internal structure and the physical properties of specific classes of neutron, quark and Bose-Einstein condensate stars in the recently proposed hybrid metric-Palatini gravity theory, which is a combination of the metric and Palatini $f(R)$ formalisms. It turns out that the theory is very successful in accounting for the observed phenomenology, since it unifies local constraints at the Solar System level and the late-time cosmic acceleration, even if the scalar field is very light. In this paper, we derive the equilibrium equations for a spherically symmetric configuration (mass continuity and Tolman-Oppenheimer-Volkoff) in the framework of the scalar-tensor representation of the hybrid metric-Palatini theory, and we investigate their solutions numerically for different equations of state of neutron and quark matter, by adopting for the scalar field potential a Higgs-type form. It turns out that the scalar-tensor definition of the potential can be represented as an Clairaut differential equation, and provides an explicit form for $f(\mathcal{R})$ given by $f(\mathcal{R})\ensuremath{\sim}\mathcal{R}+{\mathrm{\ensuremath{\Lambda}}}_{\mathrm{eff}}$, where ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{eff}}$ is an effective cosmological constant. Furthermore, stellar models, described by the stiff fluid, radiation-like, bag model and the Bose-Einstein condensate equations of state are explicitly constructed in both general relativity and hybrid metric-Palatini gravity, thus allowing an in-depth comparison between the predictions of these two gravitational theories. As a general result it turns out that for all the considered equations of state, hybrid gravity stars are more massive than their general relativistic counterparts. Furthermore, two classes of stellar models corresponding to two particular choices of the functional form of the scalar field (constant value, and logarithmic form, respectively) are also investigated. Interestingly enough, in the case of a constant scalar field the equation of state of the matter takes the form of the bag model equation of state describing quark matter. As a possible astrophysical application of the obtained results, we suggest that stellar mass black holes, with masses in the range of 3.8 and $6\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, respectively, could be in fact hybrid metric-Palatini gravity neutron or quark stars.

Charged gravastars in higher dimensions

We explore possibility to find out a new model of gravastars in the extended $D$-dimensional Einstein-Maxwell spacetime. The class of solutions as obtained by Mazur and Mottola of a neutral gravastar \cite{Mazur2001,Mazur2004} have been observed as an alternative to $D$-dimensional versions of the Schwarzschild-Tangherlini black hole. To tackle the spherical system in a convenient way we have configured that the gravastar consists of three distinct regions with different equations of state as follows: [I] Interior region $0 \leq r < r_1$,$\rho = -p$, [II] Thin shell region $r_1 \leq r < r_2$,$\rho = p$, and [III] Exterior region $r_2 < r$,$\rho = p =0$. The outer region of this gravastar model therefore corresponds to a higher dimensional Reissner-Nordstr{\"o}m black hole. In connection to this junction conditions are provided and therefore we have formulated mass and the related Equation of State of the gravastar. It has been shown that the model satisfies all the requirements of the physical features. However, overall observational survey of the results also provide probable indication of non-applicability of higher dimensional approach for construction of a gravastar with or without charge from an ordinary $4$-dimensional seed as far as physical ground is concerned.

Neutron stars in Scalar-Tensor-Vector Gravity

Scalar-Tensor-Vector Gravity (STVG), also referred as MOdified Gravity (MOG), is an alternative theory of the gravitational interaction. Its weak field approximation has been successfully used to described Solar System observations, galaxy rotation curves, dynamics of clusters of galaxies, and cosmological data, without the imposition of dark components. The theory was formulated by John Moffat in 2006. In this work, we derive matter-sourced solutions of STVG and construct neutron star models. We aim at exploring STVG predictions about stellar structure in the strong gravity regime. Specifically, we represent spacetime with a static, spherically symmetric manifold, and model the stellar matter content with a perfect fluid energy-momentum tensor. We then derive the modified Tolman-Oppenheimer-Volkoff equation in STVG and integrate it for different equations of state. We find that STVG allows heavier neutron stars than General Relativity (GR). Maximum masses depend on a normalized parameter that quantifies the deviation from GR. The theory exhibits unusual predictions for extreme values of this parameter. We conclude that STVG admits suitable spherically symmetric solutions with matter sources, relevant for stellar structure. Since recent determinations of neutron stars masses violate some GR predictions, STVG appears as a viable candidate for a new gravity theory.

Dynamical ejecta from precessing neutron star-black hole mergers with a hot, nuclear-theory based equation of state

Neutron star-black hole binaries are among the strongest sources of gravitational waves detectable by current observatories. They can also power bright electromagnetic signals (gamma-ray bursts, kilonovae), and may be a significant source of production of r-process nuclei. A misalignment of the black hole spin with respect to the orbital angular momentum leads to precession of that spin and of the orbital plane, and has a significant effect on the properties of the post-merger remnant and of the material ejected by the merger. We present a first set of simulations of precessing neutron star-black hole mergers using a hot, composition dependent, nuclear-theory based equation of state (DD2). We show that the mass of the remnant and of the dynamical ejecta are broadly consistent with the result of simulations using simpler equations of state, while differences arise when considering the dynamics of the merger and the velocity of the ejecta. We show that the latter can easily be understood from assumptions about the composition of low-density, cold material in the different equations of state, and propose an updated estimate for the ejecta velocity which takes those effects into account. We also present an updated mesh-refinement algorithm which allows us to improve the numerical resolution used to evolve neutron star-black hole mergers.

Examined the Ability of Some Different Equations of State in Predicting Thermodynamic Properties of Nitrogen Gas at Different Conditions Rang of Pressure and Temperature

Examined the Ability of Some Different Equations of State in Predicting Thermodynamic Properties of Nitrogen Gas at Different Conditions Rang of Pressure and Temperature

Maxwell Equation Violation by Density Dependent Magnetic Fields in Neutron Stars

We show that the widely used density dependent magnetic field prescriptions, necessary to account for the variation of the field intensity from the crust to the core of neutron stars violate one of the Maxwell equations. We estimate how strong the violation is when different equations of state are used and check for which cases the pathological problem can be cured. We then propose a simple solution that allows for the usual prescriptions to be used without violating a fundamental equation of physics.

Entropy production and effective viscosity in heavy-ion collisions

Entropy production and an effective viscosity in central Au+Au collisions are estimated in a wide range of incident energies 3.3 GeV $\le \sqrt{s_{NN}}\le$ 39 GeV. The simulations are performed within a three-fluid model employing three different equations of state with and without deconfinement transition, which are equally good in reproduction of the momentum-integrated elliptic flow of charged particles in the considered energy range. It is found that more that 80\% entropy is prodused during a short early collision stage which lasts $\sim$1 fm/c at highest considered energies $\sqrt{s_{NN}}\ge$ 20 GeV. The estimated values of the viscosity-to-entropy ratio ($\eta/s$) are approximately the same in all considered scenarios. At final stages of the system expansion they range from $\sim$0.05 at highest considered energies to $\sim$0.5 lowest ones. It is found that the $\eta/s$ ratio decreases with the temperature ($T$) rise approximately as $\sim 1/T^4$ and exhibits a rather weak dependence on the net-baryon density.

Jupiter internal structure: the effect of different equations of state

Heavy elements, even though its smaller constituent, are crucial to understand Jupiter formation history. Interior models are used to determine the amount of heavy elements in Jupiter interior, nevertheless this range is still subject to degeneracies due to uncertainties in the equations of state. Prior to Juno mission data arrival, we present Jupiter optimized calculations exploring the effect of different model parameters in the determination of Jupiter's core and heavy element's mass. We perform comparisons between equations of state published recently. The interior model of Jupiter is calculated from the equations of hydrostatic equilibrium, mass and energy conservation, and energy transport. The mass of the core and heavy elements is adjusted to match Jupiter's observational constrains radius and gravitational moments. We show that the determination of Jupiter interior structure is tied to the estimation of its gravitational moments and the accuracy of equations of state of hydrogen, helium and heavy elements. The location of the region where Helium rain occurs as well as its timescale are important to determine the distribution of heavy elements and helium in the interior of Jupiter. We show that differences find when modeling Jupiter's interior with recent EOS are more likely due to differences in the internal energy and entropy calculation. The consequent changes in the thermal profile lead to different estimations of the mass of the core and heavy elements, explaining differences in recently published Jupiter interior models. Our results help clarify differences find in Jupiter interior models and will help the interpretation of upcoming Juno data.

Numerical approach to reproduce instabilities of partial cavitation in a Venturi 8° geometry

Unsteady partial cavitation is mainly formed by an attached cavity which present periodic oscillations. Under certain conditions, the instabilities are characterized by the formation of vapour clouds, convected downstream the cavity and which collapse in higher pressure region. In order to gain a better understanding of the complex physics involved, many experimental and numerical studies have been carried out. These identified two main mechanisms responsible for the break-off cycles. The development of a liquid re-entrant jet is the most common type of instabilities, but more recently, the role of pressure waves created by the cloud collapses has been highlighted. This paper presents a one-fluid compressible Reynolds- Averaged NavierStokes (RANS) solver closed by two different equations of state (EOS) for the mixture. Based on experimental data, we investigate the ability for our simulations to reproduce the instablities of a self-sustained oscillating cavitation pocket. Two cavitation models are firstly compared. The importance of considering a non-equilibrium state for the vapour phase is also exhibited. To finish, the role played by the added transport equation to compute void ratio is emphasised. In case of partially cavitating flows with detached cavitation clouds, the reproduction of convective mechanisms is clearly improved.

Three-dimensional numerical simulation of the instability of the interface between two high-speed colliding metal plates

The dynamic processes which take place during high-speed impact of two metal plates with different densities are investigated using three-dimensional numerical simulations. It is shown that as a result of the impact the Rayleigh-Taylor instability forms which leads to the formation of three-dimensional ring-shaped structures on the surface of the metal with smaller density. The comparative analysis of the metals interface deformation process with the use of different equations of state is performed.

MILLIHERTZ QUASI-PERIODIC OSCILLATIONS IN 4U 1636–536: PUTTING POSSIBLE CONSTRAINTS ON THE NEUTRON STAR SIZE

ABSTRACT Based on previous studies of quasi-periodic oscillations (QPOs) in neutron star (NS) low-mass X-ray binaries, mHz QPOs are believed to be related to “marginally stable” burning on the NS surface. Our study of phase-resolved energy spectra of these oscillations in 4U 1636–53 shows that the oscillations are not caused by variations in the blackbody temperature of the NS, but reveals a correlation between the change of the count rate during the mHz QPO pulse and the spatial extent of a region emitting blackbody emission. The maximum size of the emission area, km2, provides direct evidence that the oscillations originate from a variable surface area constrained on the NS and are therefore not related to instabilities in the accretion disk. The obtained lower limit on the size of the NS (11.0 km) rules out equations of state that prefer small NS radii. Observations of mHz QPOs in NS LMXBs with NICER and eXTP will reduce the statistical uncertainty in the lower limit on the NS radius, which together with better estimates of the hardening factor and distance, will allow for improved discrimination between different equations of state and compact star models. Furthermore, future missions will allow us to measure the peak blackbody emission area for a single mHz QPO pulse, which will push the lower limit to larger radii.

The coupled non-isothermal, multiphase-multicomponent flow and reactive transport simulator OpenGeoSys–ECLIPSE for porous media gas storage

Numerical simulations are a viable tool to gain insights into complex coupled THMC processes prevailing in many geoscientific applications. In this work, a coupling approach for OpenGeoSys and ECLIPSE is presented, which combines the multiphase flow simulations of ECLIPSE with heat and reactive geochemical component transport simulations of OpenGeoSys. The coupled simulator is capable of dealing with multiphase-multicomponent systems with no specific limitations regarding the components used. Furthermore, thermal effects like the Joule–Thomson effect and geochemical feedback on fluid flow and mass transport are accounted for by the coupled simulator. The developed coupled code is validated in a series of benchmarks. It is found that the results of the coupled simulator are in very close agreement with those obtained from the reference simulations with the relative errors being smaller than 0.00001, 0.0002 and 0.003 % for phase pressures, saturations and component concentrations, respectively. Validation of the thermal coupling of the simulators shows the same good agreement, if no thermal feedback on fluid flow is considered with a maximum relative error of 0.0015 %. Including thermal feedback on fluid flow shows increased relative differences of up to 0.3 % due to the slightly different equations of states used in the simulators. Given the good accuracy of the validation runs, the coupled code can thus now be applied for reservoir simulations of coupled processes occurring in the subsurface.

Application of software complex turbo problem solver to rayleigh-taylor instability modeling

The dynamic processes which take place during high-speed impact of two metal plates with different densities are investigated using three-dimensional numerical simulations. It is shown that as a result of the impact the Rayleigh-Taylor instability forms which leads to the formation of three-dimensional ring-shaped structures on the surface of the metal with smaller density. The comparative analysis of the metals interface deformation process with the use of different equations of state is performed. The numerical study is carried out by means of special software complex Turbo Problem Solver developed by the authors. The software complex Turbo Problem Solver implements generalized approach to the construction of hydrodynamic code for various computational fluid dynamics problems. Turbo Problem Solver provides several numerical schemes and software blocks to set initial, boundary conditions and mass forces. The solution of test problem about Rayleigh-Taylor instability growth and development for the case of very rapid density growth is also presented.