Different Equations Of State Research Articles

Effects of magnetic fields and slow rotation in white dwarfs

In this work we use Hartle’s formalism to study the effects of rotation in the structure of magnetized white dwarfs within the framework of general relativity. We describe the inner matter by means of an equation of state for electrons under the action of a constant magnetic field, which introduces an anisotropy in the pressures. Solutions correspond to typical densities of white dwarfs and values of magnetic field below [Formula: see text][Formula: see text]G considering perpendicular and parallel pressures independently, as if associated to two different equations of state. Rotation effects obtained account for an increase of the maximum mass for both magnetized and nonmagnetized stable configurations, up to about [Formula: see text]. Further effects studied include the deformation of the stars, which become oblate spheroids and the solutions for other quantities of interest, such as the moment of inertia, quadrupolar momentum and eccentricity. In all cases, rotation effects are dominant with respect to those of the magnetic field.

Density and Compressibility of Multicomponent n-Alkane Mixtures up to 463 K and 140 MPa

Density measurements of two ternary alkane mixtures (methane/n-butane/n-decane and methane/n-butane/n-dodecane) and two multicomponent mixtures composed of methane/n-butane/n-octane/n-dodecane/n-hexadecane/n-eicosane were performed in the temperature range from (278.15 to 463.15) K and pressures up to 140 MPa. The isothermal compressibility values of these mixtures were obtained by differentiation from a Tait-type fitting of experimental densities as a function of temperature and pressure. Excess volume of the studied mixtures was also determined. Four different equations of state, that is, Soave–Redlich–Kwong (SRK), Peng–Robinson (PR), Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT), and Soave-Benedict-Webb-Rubin (Soave-BWR) were used for predicting the experimental density values as well as the excess volumes.

Assessing thermodynamic models and introducing novel method for prediction of methane hydrate formation

Transmission of natural gas with methane as the main constituent has been a subject of interest to industrial companies. Predicting hydrate formation conditions is important to prevent formation of methane hydrate in gas pipeline. Also, attention has been taken to account for capture and storage of pure methane. In this paper, a comprehensive comparison is performed between empirical correlations and different equation of state in van der Waals Platteeuw (VdW-P) thermodynamic model to determine the most accurate method of hydrate formation condition of methane. In addition, a novel, simple and accurate correlation is developed to predict methane hydrate formation temperature using genetic programming. Error analysis on a wide range of experimental data indicates that the new proposed correlation is superior over existing correlations and all VdW-P models with R2 = 0.999.

Modelling the thermodynamics of air-component mixtures (N2, O2 and Ar): Comparison and performance analysis of available models

With a view to finding which of the available equations of state is the most suitable for the representation of the thermodynamics of mixtures containing nitrogen, oxygen and argon, this paper mainly intends to address the comparison of the performance of the - already optimized - GERG-2008, Bender and Peng-Robinson (PR) Equations of State (EoS) in the calculation of Vapour-Liquid Equilibrium (VLE) and volumetric properties of N2-O2-Ar mixtures. The comparison between experimental measurements collected in the literature and model calculations has led to conclude about the overall superiority of GERG-2008. It is also shown that the Peng-Robinson EoS leads to comparable results in VLE calculations and that the use of Bender EoS should be avoided as it leads, despite its complex multiparameter formulation, to very inaccurate results in the calculation of VLE properties of the binary Ar-O2 and of volumetric properties. For completeness, the paper also shows the poor accuracy of the PR EoS in calculating VLE properties when zero-kij are selected. Moreover, the paper evaluates the impact of deviations on densities, calculated with the different equations of state, on the computation of transport properties (thermal conductivity, viscosity), in turns determined by means of correlations which are typically applied. Liquid thermal conductivity is highly affected by errors on liquid density calculations while the liquid viscosity is independent of density. Differently, errors on vapour thermal conductivity and dynamic viscosity are lower than those observed on vapour density.

Light fragment production at CERN Super Proton Synchrotron

Recent data on the deutron and $^3$He production in central Pb+Pb collisions at the CERN Super Proton Synchrotron (SPS) energies measured by the NA49 collaboration are analyzed within the model of the three-fluid dynamics (3FD) complemented by the coalescence model for the light-fragment production. The simulations are performed with different equations of state---with and without deconfinement transition. It is found that scenarios with the deconfinement transition are preferable for reproduction rapidity distributions of deuterons and $^3$He, the corresponding results well agree with the experimental data. At the same time the calculated transverse-mass spectra of $^3$He at midrapidity do not that nice agree with the experimental data. The latter apparently indicates that coalescence coefficients should be temperature and/or momentum dependent.

Photon electrodynamics and photon structure as a bunch of one of many possible states of electromagnetic field

Fundamental laws of conservation are used to show that electromagnetic field is generally represented (even in vacuum at ρ = 0 and j = 0) using four vectors D, E, B, and H with different equations of state (material equations) that are linear for electromagnetic waves and nonlinear for photons and particles. An equation that describes different states of electromagnetic field (i.e., different but not arbitrary relationships of field vectors E, H, D, and B) is derived. It is shown that electromagnetic wave and photon are different states of electromagnetic field that exhibit different dependences of energy density on field vectors. Partial analytical solutions are obtained for a photon (spatially localized bunch of electromagnetic field energy) that propagates at a velocity of light along a single (as distinct from electromagnetic wave) direction.

Thermodynamic modeling of phase equilibria of clathrate hydrates formed from CH4, CO2, C2H6, N2 and C3H8, with different equations of state

Abstract A thermodynamic model to predict three phase (L-H-V and I-H-V) equilibria of gas hydrates is presented. In this model we have employed a fugacity based approach where the hydrate phase is modeled using van der Waals-Platteeuw solid solution theory and the liquid phase activity coefficients are determined from the modified UNIFAC method. For the vapour phase fugacity calculations we have investigated three equations of state (EOS): Peng-Robinson-Stryjek-Vera (PRSV), Patel-Teja (PT) and Soave-Redlich-Kwong (SRK). This model employs only parameters reported in the literature. The coexistence pressures predicted by our model for the sI hydrates of methane, carbon dioxide and ethane are in reasonable agreement with experiments, whereas our model overestimates the coexistence pressures for the sII clathrates of nitrogen and propane. The predicted cage occupancies are found to increase with increasing temperature in the L-H-V equilibria. For I-H-V equilibria the cage occupancy is observed to decrease with temperature. We have also estimated the solubility of each guest in the liquid phase (for L-H-V equilibria) using the Henry’s law. The solubilities predicted using all three EOS are in good agreement for all guest molecules, with the exception of nitrogen where at relatively higher temperatures the estimates from the PRSV EOS are noticeably lower than the corresponding predictions from the PT and SRK EOS.

Study of the magnetic equation of state as precursor of the area under the isothermal magnetocaloric potential

The isothermal evolution of magnetization under different magnetic fields, described by an equation of state, not only defines de entropy change ΔS(T) (magnetocaloric effect) but also the cooling power (area enclosed by the ΔS(T) curve). In fact, the area under the MT0(H) curve limited by the initial (Hi) and final (Hf) fields equals the area under the ΔS(T) curve above T>T0 for the same field range. This “sum rule” has been used to compare magnetocaloric curves for a number of materials. We based this study in the prediction that MT0(H) contains all the information to the establishment of the cooling power above T0 over the whole range of considered magnetic fields. To perform a check, we studied here some magnetic systems described by different equations of state including that around the transition region (power law). We show results of theoretical calculations in GdAl2-like ferromagnetic material with equation of state in the framework of Brillouin and Oguchi models. An intricate phenomenological equation of state for polycrystalline NdAl2 under hydrostatic pressure is also used to validate the sum-rule.

SPH calculations of Mars-scale collisions: The role of the equation of state, material rheologies, and numerical effects

We model large-scale ( ≈ 2000 km) impacts on a Mars-like planet using a Smoothed Particle Hydrodynamics code. The effects of material strength and of using different Equations of State on the post-impact material and temperature distributions are investigated. The properties of the ejected material in terms of escaping and disc mass are analysed as well. We also study potential numerical effects in the context of density discontinuities and rigid body rotation. We find that in the large-scale collision regime considered here (with impact velocities of 4 km/s), the effect of material strength is substantial for the post-impact distribution of the temperature and the impactor material, while the influence of the Equation of State is more subtle and present only at very high temperatures.

Solutions of supercritical CO2 flow through a convergent-divergent nozzle with real gas effects

Supercritical CO2 (S-CO2) has a density as high as that of its liquid phase while the viscosity remains closer to its gaseous phase. S-CO2 has the potential to be used as a working fluid in compressor as it requires much less work due to its low compressibility as well as relatively small flow resistance. Besides the material properties and design calculations, the thermodynamic properties of working gases play a vital role in the design and efficiency of various machinery such as compressors, turbines, etc. Equation of state (EOS) which accounts the real gas effects is used in computational analysis to estimates the thermodynamic properties of the working fluid. Each EOS gives priority to real gas effects phenomena differently and for the analysis of the fluid dynamic machinery, as of today, there is no standard procedure for selecting a suitable equation of state (EOS). To understand the influence of real gas effects on the formation of a shock wave, S-CO2 flow through a convergent-divergent nozzle, is theoretically analyzed. The thermophysical and transport properties calculated with the six different equation of state (EOS) are used to estimate the flow characteristics.An in-house code based on the real gas approach which solves gas dynamics equations with variable gas properties is used to analytically analyze the compressible flow of S-CO2 through nozzle. The solution for the shock strength, total pressure loss, and location of the normal shock wave at different back pressure conditions is obtained. Using Becker’s solutions with varying viscosity and thermal conductivity estimated from each EOS, the properties inside the normal shock wave are calculated. Numerical results of supersonic S-CO2 flow varies with different EOS candidates and the formation of shock wave is found to be significantly influenced by the real gas effects.

K⁎(892) and ϕ(1020) production and their decay into the hadronic medium at the Large Hadron Collider

The production of the K⁎(892) strange resonance in Pb+Pb collisions at sNN=2.76 TeV LHC energy is analyzed within the integrated hydrokinetic model (iHKM) at different equations of state of superdense matter. The similar analysis is done also for the RHIC top energy sNN=200 GeV for comparison purposes. A modification of experimental K⁎(892)-identification is studied for different centralities in view of possible re-scattering of the decay products at the afterburner stage of the fireball evolution. We see quite intensive rescattering of the decay products as well as recombination processes for K⁎(892). In addition, the production of the much longer-long-lived ϕ(1020) resonance with hidden strange quark content is investigated.

A model with interaction of dark components and recent observational data

In the proposed model with interaction between dark energy and dark matter, we consider cosmological scenarios with different equations of state ($w_d$) for dark energy. For both constant and variable equation of state, we analyze solutions for dark energy and dark matter in seven variants of the model. We investigate exact analytic solutions for $w_d={}$ constant equation of state, and several variants of the model for variable $w_d$. These scenarios are tested with the current astronomical data from Type Ia Supernovae, baryon acoustic oscillations, Hubble parameter $H (z)$ and the cosmic microwave background radiation. Finally, we make a statistical comparison of our interacting model with $\Lambda$CDM as well as with some other well known non-interacting cosmological models.

Modeling wormholes in f(R,T) gravity

In this work we propose the modelling of static wormholes within the $f(R,T)$ extended theory of gravity perspective. We present some models of wormholes, which are constructed from different hypothesis for their matter content, i.e., different relations for their pressure components (radial and lateral) and different equations of state. The solutions obtained for the shape function of the wormholes obey the necessary metric conditions. They show a behaviour similar to those found in previous references about wormholes, which also happens to our solutions for the energy density of such objects. We also apply the energy conditions for the wormholes physical content.

Dependence of pulsar death line on the equation of state

Pulsar death line can be defined in $P-\dot{P}$ diagram. Traditionally, radio-loud pulsars are supposed to locate above the death line where is the radio-loud region. With the development of observational equipment, the observational properties of the neutron star are remarkably diverse. In $P-\dot{P}$ diagram, some of the special sources are radio-quiet but lie above the death line. From the definition of the pulsar death line, different equation of states for neutron star or strange star results in different death lines. We discuss the influence of the equation of state on the pulsar death line and the possible link between different neutron star groups. The results show that central compact objects would be the small mass of self-bound strange stars, and rotating radio transients might be old pulsars on the verge of death. We suggest that PSR J2144-3933 is likely to be a large mass pulsar, which would be larger than $2.0\rm{M_{\odot}}$. Multiple observational facts would help us to reveal the nature of pulsars.

Numerical investigation of the pseudopotential lattice Boltzmann modeling of liquid–vapor for multi-phase flows

The incorporation of different equations of state into single-component multiphase lattice Boltzmann model is considered in this paper. The original pseudopotential model is first detailed, and several cubic equations of state, the Redlich–Kwong, Redlich–Kwong–Soave, and Peng–Robinson are then incorporated into the lattice Boltzmann model. A comparison of the numerical simulation achievements on the basis of density ratios and spurious currents is used for presentation of the details of phase separation in these non-ideal single-component systems. The paper demonstrates that the scheme for the inter-particle interaction force term as well as the force term incorporation method matters to achieve more accurate and stable results. The velocity shifting method is demonstrated as the force term incorporation method, among many, with accuracy and stability results. Kupershtokh scheme also makes it possible to achieve large density ratio (up to 104) and to reproduce the coexistence curve with high accuracy. Significant reduction of the spurious currents at vapor–liquid interface is another observation. High-density ratio and spurious current reduction resulted from the Redlich–Kwong–Soave and Peng–Robinson EOSs, in higher accordance with the Maxwell construction results.

Last stable orbit around rapidly rotating neutron stars

We compute the binding energy and angular momentum of a test-particle at the last stable circular orbit (LSO) on the equatorial plane around a general relativistic, rotating neutron star (NS). We present simple, analytic, but accurate formulas for these quantities that fit the numerical results and which can be used in several astrophysical applications. We demonstrate the accuracy of these formulas for three different equations of state (EOS) based on nuclear relativistic mean-field theory models and argue that they should remain still valid for any NS EOS that satisfy current astrophysical constraints. We compare and contrast our numerical results with the corresponding ones for the Kerr metric characterized by the same mass and angular momentum.

The pseudoforce approach to fully nonlinear plasma excitations

In this paper, we develop a technique to study the dynamic structure of oscillations in plasmas. We consider the hydrodynamic model and reduce the system of closed equations to the system of differential equations with integrable Hamiltonian. Then, using the analogy of pseudoparticle oscillation in the pseudoforce field, we generalize the Hamiltonian to include the dissipation and external driving force effects. The developed method is used to study various features of electron-ion plasmas with different equations of state for ions. It is shown that this method can be used in the analysis of superposed fully nonlinear oscillations and even the sheath structure of plasmas. The generalized pseudoforce equation is then used to study the dynamics of damped periodically forced nonlinear ion acoustic oscillations in plasmas with adiabatic and isothermal ion fluids. We found striking differences in dynamics of oscillations in these plasmas. The fundamental difference in the dynamic character of oscillations between adiabatic and isothermal ion fluids is described based on the fast ion fluid response to external perturbations in the case of adiabatic ion fluid compression. The current approach may be easily extended to more complex situations with different species and in the presence of electromagnetic interactions.

Transport of CO2: Presentation of New Thermophysical Property Measurements and Phase Diagrams

CO2 transportation is an integral part of the CCS chain. After capture, CO2 needs to be transported to locations whereby it is stored or alternatively used in various processes. CO2 can be transported via ship or pipeline. In both cases, the required compression pressure can be 100–300bar, depending on the distance and intended disposal or use of CO2. The CO2 rich stream can contain a number of impurities which can modify the phase diagram and change the thermophysical properties of the stream in comparison with the ones of pure CO2. Indeed, along with carbon dioxide, a great number of compounds such as water, O2, N2, Ar, SOx, NOx, H2 and CO can be present at different levels of concentration. During transportation by pipeline, if the pipe suffers a major fracture due to an accidental release or a failure, CO2 can rapidly expand and cool: vapour cloud followed by solid formation of CO2 may appear. The impurities could change the characteristics of the leak and change the conditions and compositions of CO2 clouds and solid. The presence of water can also be a source of gas hydrate formation, ice or corrosion. In this communication we will present new experimental data and their modelling concerning the phase diagrams of systems rich in CO2 and their thermophysical properties. Comparisons of the results obtained using different equations of state are also reported.

Impact of the equation of state on calculated adsorption isotherm using DFT

In the early state of process development, usually high quality experimental data are often missing, especially, if the experimental effort is quite large. This situation occurs for the separation of very similar components, which must be separated applying adsorption. In principle, adsorption isotherms can be predicted using the density functional approach in combination with a suitable thermodynamic model in order to describe the fluid properties. In this paper, we study the adsorption of propanal, where no experimental data for comparison are available for verification of the modelling results. Therefore, we use three different equations of state (EOS), namely the Peng-Robinson and two versions out of the SAFT framework. The two versions are the Perturbed Chain – Statistical Association Fluid Theory (PC-SAFT) and the Perturbed Chain Polar – Statistical Association Fluid Theory (PCP-SAFT) including an additional dipole contribution. Although both SAFT versions are superior in modelling the phase behavior, especially the saturated liquid volume, the predicted adsorption isotherms were close together. However, the calculated condensation pressure in the pore depends on the chosen EOS. All equations of state lead to similar surface tensions, if they are coupled with the density gradient theory. The calculated surface tensions using one of the two SAFT versions are in excellent agreement with experimental data taken from the literature.

Perturbative instability of inflationary cosmology from quantum potentials

It was argued that the Raychaudhuri equation with a quantum correction term seems to avoid the Big Bang singularity and to characterize an everlasting Universe [PLB741,276(2015)]. Critical comments on both conclusions and on the correctness of the key expressions of this work were discussed in literature [MPLA31(2016)1650044]. In the present work, we have analyzed the perturbative (in)stability conditions in the inflationary era of the early Universe. We conclude that both unstable and stable modes are incompatible with the corresponding ones obtained in the standard FLRW Universe. We have shown that unstable modes do exist at small (an)isotropic perturbation and for different equations of state. Inequalities for both unstable and stable solutions with the standard FLRW space were derived. They reveal that in the FLRW flat Universe both perturbative instability and stability are likely. While negative stability modes have been obtained for radiation- and matter-dominated eras, merely, instability modes exist in case of a finite cosmological constant and also if the vacuum energy dominates the cosmic background geometry.