Various Equations Of State Research Articles

Exact regular black hole solutions with de sitter cores and hagedorn fluid

Abstract In this paper, we present three exact solutions to the Einstein field equations, each illustrating different black hole models. The first solution introduces a black hole with a variable equation of state, $P = k(r)\rho$, which can represent both singular and regular black holes depending on the parameters $M_0$ and $w_0$. The second solution features a black hole with Hagedorn fluid, relevant to the late stages of black hole formation, and reveals similarities to the first solution by also describing both singular and regular black holes in a specific case. Furthermore, we investigate the shadows cast by these black hole solutions to constrain their parameters. Recognizing that real astrophysical black holes are dynamic, we developed a third, dynamical solution that addresses gravitational collapse and suggests the potential formation of naked singularities. This indicates that a black hole can transition from regular to singular and back to regular during its evolution.

Inflationary dynamics of Mutated Hilltop inflation in Einstein–Gauss–Bonnet Gravity under new slow-roll approximations with generalized reheating

The advancement in the observational cosmology of the early universe such as Cosmic Microwave Background (CMB) observations, puts severe constraints on the inflationary models. Many inflationary models have been ruled out by CMB, nevertheless the models ruled out in standard cold inflationary scenarios can be resurrected in modified gravity models. In this regard we examine the dynamics of inflation within the framework of Einstein–Gauss–Bonnet (EGB) Gravity using the new slow-roll approximation methods proposed in Pozdeeva et al. (2024). We consider the Mutated Hilltop inflation model (Pal et al., 2010; Pinhero and Pal, 2019) due to its origin from super-gravity, a naturally perfect choice to study the impact of EGB on inflationary observables such as tensor-to-scalar ratio (r) and scalar spectral index (ns). The period of reheating following the inflationary phase is also examined, and for the Planck’18 permitted values of ns, constraints on the reheating temperature (Tre) are computed for various equations of states during reheating (ωre).

Impact of cold dark matter and variable equations of state on the stability of thin-shell wormholes

The goal of this research is to better understand how two identical black hole copies, bounded by a cold dark matter halo, produce and stabilize thin-shell wormholes. The occurrence of a cold dark matter halo is discovered to increase the black hole’s horizon radius. Investigating the stable geometry of these wormholes by linearized radial perturbation analysis is the main objective of the work. It is noteworthy that the development of thin-shell wormholes with reduced energy limitations is associated with the presence of a cold dark matter halo. We study how the stability of the wormholes is affected by variable equations of state, including phantom-like, variable Chaplygin, and barotropic equations of state. The question emphasizes how crucial the existence of a cold dark matter halo is to preserving stable thin-shell wormhole configurations. The findings shed light on the interactions between a cold dark matter halo and wormholes, which improved our knowledge of both phenomena and their possible consequences for extraterrestrial travel.

Realistic models of general-relativistic differentially rotating stars

ABSTRACT General-relativistic equilibria of differentially rotating stars are expected in a number of astrophysical scenarios, from core-collapse supernovae to the remnant of binary neutron-star mergers. The latter, in particular, have been the subject of extensive studies where they were modelled with a variety of laws of differential rotation with varying degree of realism. Starting from accurate and fully general-relativistic simulations of binary neutron-star mergers with various equations of state and mass ratios, we establish the time when the merger remnant has reached a quasi-stationary equilibrium and extract in this way realistic profiles of differential rotation. This allows us to explore how well traditional laws reproduce such differential-rotation properties and to derive new laws of differential rotation that better match the numerical data in the low-density Keplerian regions of the remnant. In this way, we have obtained a novel and somewhat surprising result: the dynamical stability line to quasi-radial oscillations computed from the turning-point criterion can have a slope that is not necessarily negative with respect to the central rest-mass density, as previously found with traditional differential-rotation laws. Indeed, for stellar models reproducing well the properties of the merger remnants, the slope is actually positive, thus reflecting remnants with angular momentum at large distances from the rotation axis, and hence with cores having higher central rest-mass densities and slower rotation rates.

Thermodynamic Theory of Curvature-Dependent Surface Tension: Tolman's Theory Revisited.

An exact equation for determining the Tolman length (TL) as a function of radius is obtained within the framework of classical thermodynamics and a computational procedure for solving it is proposed. As a result of implementing this procedure, the dependences of the TL and surface tension on radius are obtained for the drop and bubble cases and various equations of state. As one of the results of the thermodynamic study, a new equation for the dependence of surface tension on radius (curvature effect) alternative to the corresponding Tolman equation and associated with the spinodal point is obtained. The fundamental impossibility to determine the curvature effect analytically from the binodal point, i.e., using the Tolman equation, is established; it is calculated only from the spinodal point and is determined by the characteristics of the system at this point. The sign of the TL asymptotic value debated in the literature in recent decades is uniquely determined in the theory: it is negative for drops and positive for bubbles.

How macroscopic limits on neutron-star baryon loss yield microscopic limits on non-standard-model baryon decay

We investigate how our baryon-loss limits from anomalous binary-pulsar period lengthening can be interpreted microscopically to yield specific constraints on the particle physics of baryon number violation within a neutron star. We focus on the possibility of anomalous baryon disappearance via dark baryon processes and on scenarios in which the produced dark-sector particles do not survive to influence the response of the star to baryon-number-violating effects. We flesh out the conditions for which this may occur, as well as other key assumptions. We then turn to the analysis of particle processes in the dense nuclear medium found at the core of a neutron star, employing the techniques of relativistic mean-field theory. Using our study of in-medium effects and limits on macroscopic baryon number violation, we extract limits on in-vacuum baryon-number-violating processes, and we determine them for various equations of state. We conclude by noting the implications of our results for models of dark-sector-enabled baryogenesis. Published by the American Physical Society 2024

High-Pressure Calibration TiN Equation of State

High pressure is becoming an interesting area of research for originating vital properties in crystalline solids. In the present study, the pressure equation of the state of TiN was investigated by employing various equations of state (EoS) presented in the literature, such as Dodson EoS, Barden EOS, Birch-Murnaghan (B-M) EoS. The EoSs were processed to find the high-pressure effects on the characterizations of TiN such as volume compression ratio, bulk modulus B, Grüneisen parameter, and phonon frequency spectrum. It was shown that a gigantic pressure results in a significant reduction in the volume of the TiN material, and the volume compression ratio reduction, is almost the same for the existing equations of state and the comparative literature results up to a pressure of 80 GPa. The maximum pressure difference is observed to be 4.85 GPa. over the entire pressure of 120GPa. Increasing the bulk modulus with high pressure was expected by the present EoSs, and up to the pressure of about 60 GPa, all curves of bulk modulus are matched with each other. Eventually, a fair comparison has been made between the present results and the first principle approximation along with the generalized gradient approximation method in which a perfect agreement was observed. Finally, the feasibility of TiN EoS as a standard pressure calibration was demonstrated.

NEUTRON STARS IN A UNIFORM DENSITY APPROXIMATION

Models of neutron stars are considered in the case of a uniform density distribution. A universal algebraic equation is obtained that is valid for any equation of state. This equation allows us to find the approximate mass of a star of a given density without resorting to the integration of differential equations. Solutions for various equations of state, including more realistic ones, are presented in the paper and differ from the exact solutions obtained by numerical integration of differential equations by no more than 20%.

2022 Joint Barringer Medal for Kai Wünnemann and Gareth S. Collins

2022 Joint Barringer Medal for Kai Wünnemann and Gareth S. Collins

Study of single-component two-phase free energy lattice Boltzmann models using various equations of state

In single-component two-phase flow simulations by the lattice Boltzmann method (LBM), one key topic of interest is the equation of state (EOS), which has been studied more in the pseudo-potential approach but much less in the free energy approach. Here, we conducted fair assessment of several popular non-ideal gas EOS in free energy LBM. The inability to independently tune the surface tension and interface thickness was identified for existing free energy formulation using most EOS. A simple modification was proposed and incorporated into three free energy LBM models, including the pressure tensor model, Lee–Fischer's model, and Guo's well-balanced model. Good compatibility with all of them was demonstrated by numerical simulations. In addition, a piecewise-linear (PWL) EOS proposed in pseudo-potential LBM was found to be also feasible in free energy LBM. Extensive numerical experiments on diverse problems (some containing contact lines) revealed that the influence of EOS was rather limited when key parameters are nearly the same (easily achievable with the proposed modification). The capability of the Lee–Fischer and well-balanced models to reduce the spurious currents down to machine accuracy (for static drop tests) was found to be independent of the EOS (including the customized PWL EOS). Overall, the pressure tensor LBM is associated with larger spurious currents and deviations in the density and chemical potential, thus less accurate than the other two. However, it is less sensitive to the relaxation parameter and grid number, thus more robust.

Net zero Flow Assurance - Validation of various equations of state for the prediction of VLE and density of CO2-rich mixtures for CCUS applications

Carbon dioxide management is becoming a major topic of interest in the energy industry and carbon capture is part of this process. Carbon capture utilization and storage is considered a promising technique to mitigate the impact of the hard-to-abate industries. Despite the high level of accuracy of predictions of the thermodynamic behaviour of pure CO2, there are still several uncertainties when dealing with CO2-rich mixtures. The impact of impurities in the captured stream can impact considerably the sizing and the design of components such as pipelines and related costs. The scope of this work is to assess the capabilities of the most acknowledged Equations of State (EoS) in the energy industry to predict CO2-rich mixtures behaviour. In this work we assess their accuracy in the prediction of Vapour-Liquid Equilibrium (VLE) and density validating numerical results with detailed experimental data available in literature. A quantitative estimation of deviations from experimental data is provided for density and bubble points. The results show that, based on experimental data available, multi-parameters Equations of State, such as GERG-2008 and CSMA, are generally more accurate in the description of both VLE and density if compared with cubic EoS.

Supercritical carbon dioxide utilization in drug delivery: Experimental study and modeling of paracetamol solubility

In the present study, the solubility of paracetamol in supercritical CO2 is measured at temperatures between 311 and 358 K and pressures between 95 and 265 bar. It was shown that the solubility of paracetamol through a static solubility measurement method was between 0.3055 × 10−6 to 16.3582 × 10−6 based on mole fraction. The obtained experimental solubility data revealed the direct effect of pressure on the paracetamol experimental data, while the temperature has a dual effect of both increasing and decreasing effect considering the shifting point known as crossover pressure which was measured to be around 110 bar for paracetamol. Besides, two theoretical approaches were applied to predict the paracetamol experimental results. The experimental data were modeled with two various equations of state (EoSs) i.e. Peng-Robinson EoS and the simplified perturbed chain statistical associating fluid theory (sPC-SAFT) EoS, which their binary interaction parameters were optimized by using genetic algorithm. The obtained results demonstrated the sPC-SAFT EoS predicted the solubility of paracetamol with more accuracy (the average percent deviation was equal to 2.5215), especially at higher pressures. Furthermore, four well-known semi-empirical density-based correlations namely Mendez-Santiago and Teja (MST), Kumar-Johnston (KJ), Bartle et al., and Garlapati and Madras models were applied for modeling the solubility of paracetamol experimental data. According to self-consistency test, KJ model presented more accurate correlative capability with average percent deviation about 4.09%. As a final point, the rapid expansion of supercritical solution process was performed to reduce particle size of paracetamol and mean particle size of paracetamol was calculated based on EoSs and mathematical modeling.

The Influence of Equation of State on the Giant Impact Simulations

AbstractWe explore the role of various equations of state (EoS) in controlling the composition of the Moon formed by a giant impact (GI) using a density‐independent SPH code. A limitation in our previous model Hosono et al. (2019), https://doi.org/10.1038/s41561-019-0354-2 is improved by replacing the EoS of the solid from Tillotson EoS to M‐ANEOS, and we also explored two recently proposed EoSs by Stewart et al. (2020), https://doi.org/10.1063/12.0000946 and Wissing and Hobbs (2020a), https://doi.org/10.1051/0004-6361/201935814; Wissing and Hobbs (2020b), https://doi.org/10.1051/0004-6361/201936227. The goal is to investigate to what extent we can explain the observed composition of the Moon including the similarity in the isotopic composition and the dissimilarity in the FeO/(FeO + MgO) ratio as compared to that of Earth by the different types of EoS assuming the conventional collision conditions. We found that changing the EoS for solids from Tillotson to M‐ANEOS EoS resolves the issues of latent heat, but its effect on the composition of the disk is small compared to the influence of the hard‐sphere EoS of magma ocean in controlling the composition of the disk. Similarly, two recently proposed EoSs have small effects on the composition of the disk in comparison to the model where the hard‐sphere EoS is used for preexisting magma ocean. We attribute this difference to a fundamental difference in thermodynamic behavior of silicate melts captured by the hard‐sphere EoS and by newly proposed EoSs; in the hard‐sphere model of silicate melts, configurational entropy dominates in free energy, whereas in the newly proposed model, entropy is dominated by vibrational entropy similar to entropy of solids.

Thin-shell wormhole satisfying the null-energy condition unconditionally

Null energy condition (NEC) is revisited in the context of thin-shell wormholes (TSW). In a generic spherically symmetric configuration we introduce the condition upon which NEC is satisfied. Also, we present a general condition which specifies the stability of the generic spherically symmetric TSW against a radial linear perturbation. Furthermore, we introduce a specific bulk metric in the framework of gravity coupled minimally with nonlinear electrodynamics such that the corresponding TSW satisfies NEC, unconditionally. We study the mechanical stability of this TSW and show that, with a variable equation of state of the fluid present at the throat, this TSW remains stable irrespective of the value of the speed of sound.

Experimental measurement and compositional modeling of bubble point pressure in crude oil systems: Soft computing approaches, correlations, and equations of state

No one can deny the ever-increasing importance of oil since it has influenced every aspect of humans' life. One of the most important pressure-volume-temperature (PVT) properties of crude oil, which is needed in a majority of production and reservoir engineering calculations, is the saturation pressure (bubble point pressure (Pb)). Having accurate knowledge about Pb is significant for both academia and industry. This communication concentrates on providing reliable experimental data from constant composition expansion (CCE) test as well as rigorous compositional models to predict saturation pressure of crude oils based on oil composition (H2S, N2, CO2, C1 to C7+), reservoir temperature, C7+ specifications (molecular weight and specific gravity). Seven advanced machine learning approaches, namely, decision trees (DTs), random forest (RF), extra trees (ETs), cascade-forward back-propagation network (CFBPN), and generalized regression neural networks (GRNN) as well as multilayer perceptron (MLP) and radial basis function (RBF) neural networks were used for modeling. The CFBPN and MLP models were trained by three different training algorithms, namely scaled conjugate gradient (SCG), Bayesian regularization (BR), and Levenberg-Marquardt (LM). The modeling was done based on a databank consisting of 206 data points (130 points were previously published in the literature plus 76 points determined experimentally in this study). The results show that the DT model could provide the most reliable prediction with an average absolute percent relative error (AAPRE) of 4.43%. The efficiency of various equations of state (EoS) and empirical correlations were checked. According to the results, Peng-Robinson (PR) and the correlation developed by Elsharkawy were the most efficient EoS and empirical correlation with AAPRE values of 8.46% and 12.05%, respectively. Then, the sensitivity analysis revealed that the Pb was extremely affected by methane and C7+ mole percent. Finally, the Leverage approach confirmed the validity of the employed data, detecting only 7 points as outliers.

Effect of the Nuclear Equation of State and Relativistic Turbulence on Core-Collapse Supernovae

The nuclear Equation of State (EoS) is an important component in the evolution and subsequent explosion of core collapse supernovae. We make a survey of various equations of state that can be found in the literature and analyze their effect on the explosion. To simulate the supernovae, we use the general relativistic spherically-symmetric code GR1D, modified to take into account the effects of three-dimensional turbulence through a new mixing length theory approach (STIR). We show that the viability of the explosion is quite EoS dependent and that the strength of explosions correlate best with the central entropy density right after bounce and the onset of turbulent mixing in the proto-neutron star.

ИССЛЕДОВАНИЕ ЭФФЕКТОВ КЛАСТЕРНОЙ ПОЛЯРИЗАЦИИ В ЯДРЕ 6Li

In this work we consider various equations of state of neutron star matter, which include from the point of neutron drops formation to supra nuclear densities. Particular attention is paid to the nucleon – nucleon interaction since, in addition to the kinetic energies of the particles, the interactions among nucleons play a key role. Moreover, we investigate the properties of super-dense matter with diverse sets of particles such as electrons, protons, and the contribution of various particles-carriers of interaction. In order to achieve these goals, different potentials were considered, which are in a good agreement with experimental data. Furthermore, we find the energy of the system by using a variety of multi-particle methods, including the interaction of nucleons. Thanks to this information, thermodynamic parameters such as pressure, energy density and the speed of sound in the star are calculated. We compared similar equations of state of matter so that we could demonstrate the difference from each other. The Tolman-Oppenheimer-Volkoff system of equations has been solved numerically to construct mass-central density, radius-central density and mass-radius relations using different equations of state. In conclusion, the latest observational constraints on the equation of state are taken into account and we show that the observational data require that the equation of state be stiff, despite the fact that all stiff equations of state violate the principle of causality at high central densities, unlike soft ones.

Stability of [formula omitted]-dimensional gravastars with variable equation of state

In this paper, we are interested to explore stable configurations of d-dimensional gravastars constructed from the interior d-dimensional de Sitter and exterior d-dimensional Schwarzschild/Reissner–Nordström (de Sitter) black holes through cut and paste approach. We consider the linearized radial perturbation preserving the original symmetries to explore their stability by using three different types of matter distributions. The resulting frameworks represent unstable structures for barotropic, Chaplygin, and phantomlike models for every considered choice of exterior geometries. However, matter contents with variable equations of state have a remarkable role to maintain the stability of gravastars. We conclude that stable structures of gravastars are obtained only for generalized variable models with exterior d-dimensional Schwarzschild/Reissner–Nordström–de Sitter black holes.

Prediction of Joule–Thomson coefficients and inversion curves of natural gas by various equations of state

The Joule-Thomson effect is an important thermodynamic phenomenon for natural gas-related industries. Hence, accurate prediction of the Joule–Thomson coefficient (JTC) and the Joule–Thomson inversion curve (JTIC) are of great importance in various industries. In this contribution, we apply six equations of state (EOSs) including SAFT, PρT-SAFT, SAFT-CP, PC-SAFT, and I-PC-SAFT, as well as SRK, to predict JTC and JTIC of eight main pure components of natural gas including methane, ethane, propane, n-butane, isobutane, pentane, carbon dioxide, and nitrogen. We also predict the JTC and JTIC for four and six synthetic mixtures of natural gas, respectively. By comparing the results of the six EOSs for prediction of natural gas-related pure and mixtures JTC and JTIC with literature data, we can conclude that although all the EOSs were in reasonable agreement with the literature data, in general, to predict the JTC and JTIC for all studies systems, SAFT-CP and original SAFT equations of state had the best results.

Study of cavitation inception using multiphase lattice Boltzmann method with incorporating equations of state

The study of cavitation inception is crucial in several hydraulic machines, e.g. pumps, nozzles and sprays. In the present study, a multiphase lattice Boltzmann method (LBM) is implemented for simulation of the cavitation bubbles dynamics and characteristics of cavitating flows. The effect of employing various equations of state (EoS) is investigated on the computing of interaction forces and the phase separation between the liquid and its vapor in the cavitating flows. Herein, the cubic EoSs of Shan-Chen (SC) and Carnahan-Starling (CS) and the non-cubic EoS of Peng-Robinson (PR) are applied. The exact difference method is imposed to improve the numerical stability for simulation of two-phase flow systems. The accuracy and efficiency of the present method are examined by comparison of the results obtained for the homogeneous and heterogeneous cavitation with those of reported in the literature. Then, the implemented multiphase LBM is used for studying the inception and growth of the cavitation bubbles in the throat of a venturi. The effect of hydrophobicity and hydrophobicity of the nozzle wall on the cavitation dynamics is investigated and a detail discussion is made for the results from the numerical and physical point of view. Evaluation of the present results shows that the multiphase LBM with incorporating an appropriate equation of state has excellent capability for prediction of the bubble dynamics and cavitating flow characteristics in applied geometries.