Different Equations Of State Research Articles

Effects of equation of state on hydrodynamic expansion, spectra, flow harmonics and two-pion interferometry

We perform an extensive study of the role played by the equation of state (EoS) in the hydrodynamic evolution of the matter produced in relativistic heavy ion collisions. By using the same initial conditions and freeze-out scenario, the effects of different equations of state are compared by calculating their respective hydrodynamical evolution, particle spectra, harmonic flow coefficients [Formula: see text], [Formula: see text] and [Formula: see text] and two-pion interferometry radius parameters. The equations of state investigated contain distinct features, such as the nature of the phase transition, as well as strangeness and baryon density contents, which are expected to lead to different hydrodynamic responses. The results of our calculations are compared to the data recorded at two RHIC energies, 130[Formula: see text]GeV and 200[Formula: see text]GeV. The three equations of state used in the calculations are found to describe the data reasonably well. Differences can be observed among the studied observables, but they are quite small. In particular, the collective flow parameters are found not to be sensitive to the choice of the EOS, whose implications are discussed.

Exact solutions for spherical gravitational collapse around a black hole: the effect of tangential pressure**Supported by National Natural Science Foundation of China (11373036, 11133002), the National Program on Key Research and Development Project (2016YFA0400802) and the Key Research Program of Frontier Sciences, CAS, (QYZDY-SSW-SLH008)

Spherical gravitational collapse towards a black hole with non-zero tangential pressure is studied. Exact solutions corresponding to different equations of state are given. We find that when taking the tangential pressure into account, the exact solutions have three qualitatively different outcomes. For positive tangential pressure, the shell around a black hole may eventually collapse onto the black hole, or expand to infinity, or have a static but unstable solution, depending on the combination of black hole mass, mass of the shell and the pressure parameter. For vanishing or negative pressure, the shell will collapse onto the black hole. For all eventually collapsing solutions, the shell will cross the event horizon, instead of accumulating outside theeventhorizon, even if clocked by a distant stationary observer.

Beam energy dependence of the squeeze-out effect on the directed and elliptic flow in Au + Au collisions in the high baryon density region

We present a detailed analysis of the beam energy dependence of the mechanisms for the generation of directed and elliptic flows in Au+Au collisions focusing on the role of hadronic rescattering and spectator shadowing within a microscopic transport model JAM with different equation of state. A systematic study of the beam energy dependence is performed for Au+Au collisions at $\sqrt{s_{NN}} =2.3 - 62.4$ GeV. The transition of the dynamical origin of the directed flow is observed. We find that the initial Glauber type nucleon-nucleon collisions generate negative $v_1$ for nucleons at midrapidity due to the presence of spectator matter, and this negative nucleon $v_1$ is turned to be positive by the meson-baryon interactions at the beam energy region of $\sqrt{s_{NN}} < 30$ GeV. In contrast, above 30 GeV there is no spectator shadowing at midrapidity, and initial nucleon-nucleon collisions do not generate directed flow, but subsequent rescatterings among produced particles generate negative $v_1$ for nucleons. It is demonstrated that negative pion-directed flows are mostly generated by the interaction with the spectator matter. It is also shown that the squeeze-out effect is largely suppressed in the case of softening, which leads to the enhancement of elliptic flow around $\sqrt{s_{NN}}=5-7$ GeV. The elliptic flow at midrapidity above 10 GeV is not influenced by the squeeze-out due to spectator matter, while its effect is seen at the forward rapidity range of $y/y_\mathrm{c.m.}>0.5$, which decreases as beam energy increases.

Particle production at energies available at the CERN Large Hadron Collider within an evolutionary model

The particle yields and particle number ratios in Pb+Pb collisions at the LHC energy $\sqrt{s_{NN}}=2.76$ TeV are described within the integrated hydrokinetic model (iHKM) at the two different equations of state (EoS) for the quark-gluon matter and the two corresponding hadronization temperatures, $T=165$ MeV and $T=156$ MeV. The role of particle interactions at the final afterburner stage of the collision in the particle production is investigated by means of comparison of the results of full iHKM simulations with those where the annihilation and other inelastic processes (except for resonance decays) are switched off after hadronization/particlization, similarly as in the thermal models. An analysis supports the picture of continuous chemical freeze-out in the sense that the corrections to the sudden chemical freeze-out results, which arise because of the inelastic reactions at the subsequent evolution times, are noticeable and improve the description of particle and number ratios. An important observation is that although the particle number ratios with switched-off inelastic reactions are quite different at different particlization temperatures which are adopted for different equations of state to reproduce experimental data, the complete iHKM calculations bring very close results in both cases.

Constraints on the nuclear symmetry energy and its density slope from the decay process

We study the impact of the nuclear symmetry energy and its density dependence on the α-decay process. Within the framework of the preformed cluster model and the energy density formalism, we use different parameterizations of the Skyrme energy density functionals that yield different equations of state (EOS). Each EOS is characterized by a particular symmetryenergy coefficient (asym) and a corresponding density-slope parameter L. The stepwise trends of the neutron (proton) skin thickness of the involved nuclei with both asym and L do not clarify the oscillating behaviors of the α-decay half-life Tα with these quantities. We find that the change of the skin thickness after α-decay satisfactorily explains these behaviors. The presented results provide constraints on asym centered around an optimum value asym=32 MeV, and on L between 41 and 57 MeV. These values of asym and L, which indicate larger reduction of the proton-skin thickness and less increase in the neutron-skin thickness after an α-decay, yield a minimum calculated half-life with the same extracted value of the α-preformation factor inside the parent nucleus.

Axial quasinormal modes of static neutron stars in the nonminimal derivative coupling sector of Horndeski gravity: Spectrum and universal relations for realistic equations of state

We study axial quasinormal modes of static neutron stars in the nonminimal derivative coupling sector of Horndeski theory. We focus on the fundamental curvature mode, which we analyse for ten different equations of state with different matter content. A comparison with the results obtained in pure General Relativity reveals that, apart from modifying the spectrum of the frequencies and the damping times of the stars, this theory modifies several universal relations between the modes and physical parameters of the stars, that are otherwise matter-independent.

Оценка применимости различных уравнений состояния реального газа для этилена

Оценка применимости различных уравнений состояния реального газа для этилена

Modeling of the phase behavior of CO2 in water, methanol, ethanol and acetone by different equations of state

This paper deals with the modeling of the phase behavior of CO2 in water, methanol, ethanol and acetone. The phase equilibria of pure substances and binary mixtures are correlated using different equations of state: PC-SAFT, PCP-SAFT, CPA and GEOS. The adjustable specific coefficients of pure fluids are determined by regression of vapor pressure and saturated liquid and vapor densities data. For binary mixtures, the binary cross-interaction parameters are deduced by regression of the vapor-liquid equilibrium data for wide ranges of temperature and pressure. The obtained results show that the GEOS equation of state appears to be the most adequate in the modeling and prediction of the isothermal vapor-liquid phase behavior in the vicinity of the critical region. Moreover, the GEOS model is most adequate in the prediction of the three-phase liquid-liquid-vapor equilibria of CO2/water system at temperatures around and below the critical temperature of CO2 and a formation of a second rich-CO2 liquid phase. In addition, the dew curves of the water/CO2 system were most accurately predicted by the GEOS model. The isothermal-isobaric vapor-liquid equilibria of CO2/methanol/water and CO2/ethanol/water were predicted and the comparison with the literature data demonstrated some advantages to the GEOS equation of state.

Equations of state and pressure dependence of bulk modulus for aggregated diamond nanorods

In the present paper study of the high pressure behaviour of aggregated diamond nanorods (ADNRs) and diamond have been carried out. A comparative study of different equations of state is discussed to understand the high pressure behaviour of diamond and the aggregated diamond nanorods. In the present study the usual Tait’s equation of state has been modified to predict the high pressure behaviour of carbon material ADNRs and diamond. The results obtained in the present study are compared with available experimental evidences. Bulk moduli as a function of pressure are also computed for ADNRs and natural diamond in the light of recent investigations. Present study reveals that ADNRs are less compressible than diamond.

Effect of air gap on the structural response of aluminum foam protected reinforced concrete panels

ABSTRACTThis paper comprises computational investigation on the effect of air gap clearance on the dynamic behavior of aluminum foam- air gap- reinforced concrete (RC) panel interaction under the effect of various blast loads. A parametric study was performed using hydro-code software (i.e. AUTODYN 3D) in order to investigate the effect of considering material of low mechanical impedance (i.e. Air) between the protection panel and RC panel. The parameters studied are the thickness of aluminum foam, air gap thickness, the weight of explosive charge, and thickness of RC panel. A set of published experimental tests was used to validate the developed numerical models of protected and unprotected RC panels. In the numerical simulations, the dynamic behavior of reinforced concrete and aluminum foam materials as porous materials were defined utilizing different Equations of State (EOS) and strength models. Time-dependent results of the response of the tested RC panels are analyzed, discussed and utilized to obtain the suitable aluminum foam and air gap thicknesses for each case to maintain the maximum deflection of each RC panel within its elastic limit.

A model of Saturn inferred from its measured gravitational field

We present an interior model of Saturn with an ice-rock core, a metallic region, an outer molecular envelope and a thin transition layer between the metallic and molecular regions. The shape of Saturn’s 1 bar surface is irregular and determined fully self-consistently by the required equilibrium condition. While the ice-rock core is assumed to have a uniform density, three different equations of state are adopted for the metallic, molecular and transition regions. The Saturnian model is constrained by its known mass, its known equatorial and polar radii, and its known zonal gravitational coefficients, J2n, n = 1, 2, 3. The model produces an ice-rock core with equatorial radius 0.203 RS, where RS is the equatorial radius of Saturn at the 1-bar pressure surface; the core density ρc = 10388.1 kgm−3 corresponding to 13.06 Earth masses; and an analytical expression describing the Saturnian irregular shape of the 1-bar pressure level. The model also predicts the values of the higher-order gravitational coefficients, J8, J10 and J12, for the hydrostatic Saturn and suggests that Saturn’s convective dynamo operates in the metallic region approximately defined by 0.2 RS < re < 0.7 RS, where re denotes the equatorial radial distance from the Saturnian center of figure.

Comparison of several methods for obtaining hydrate formation pressure

ABSTRACTIn petroleum engineering hydrate is referred to as crystalline and snow like compounds Which consists of the capture of gaseous molecules among water molecules. The primary requirement for the prevention of hydrate is to recognize the conditions for its formation. Hydrate formation conditions include the presence of water, small gas molecules and the appropriate conditions of temperature and pressure. Several models have been proposed to determine the hydration pressure and temperature. Van der waals-platteeuw is a model base on statistical thermodynamics. In this model, the determinant is the fugacity of the gas phase. In this paper, the fugacity is obtained with different equations of state and replaced by the pattern provided by Parish and Prasnitz, to obtain the pressure and temperature of hydrate formation. In the end, results are compared with laboratory data and results from the CSMHyd Software and the experimental data to Check the accuracy of the model.

Evaluation of Spinodal Pressure for Gallium nitride in the Zinc-blend and Wurtzite Structures by Using Different Equations of State (EOSs)

According to the definition of spinodal pressure as the negative pressure at which bulk modulus (of a substance) go to zero. Extrapolation of variation of bulk modulus results with pressure has been used to evaluate spinodal pressure for GaN in zinc-blende and wurtzite structures using different equations of state (EOS) (Birch-Murnaghan, Bardeen, Libby and Libby, and Born-Mie). Result obtained in the present work for GaN in the zinc-blende structure using Born-Mie equation of state shows a good agreement with literature. While results for wurtzite structure, obtained by using Birch-Murnaghan and Bardeen EOSs are in a good agreement with literature. Present results and many literature show that (Jiuxun, 2005) approach for evaluation of spinodal pressure yield results in less agreement with other works

A new equation of state to predict S-CO2 flow with real gas effects

The accuracy of the thermodynamic properties prediction from the different Equation of state (EOS) varies upon the range of temperature and pressure. Despite the variety of EOS available, there is no de facto for selecting an EOS for particular computational modeling. The EOS model recently developed by Kumar and Kim (K-K EOS) determines more accurately the thermodynamic properties of CO2 than earlier models. In this present study, K-K EOS is successfully implemented in the computational analysis of compressible supercritical CO2 flow (S-CO2) in the thermodynamic region near and away from the vapour-liquid critical point. Computational results of SCO2 flow with the real gas properties predicted with the K-K EOS is compared with Span and Wagner (SW EOS) and ideal EOS.

Bulk properties of the matter produced at energies of the beam energy scan program

Recent STAR data on the bulk observables in the energy range of the Beam-Energy Scan Program at the Relativistic Heavy-Ion Collider are analyzed within the model of the three-fluid dynamics (3FD). The simulations are performed with different equations of state (EoS). The purely hadronic EoS fails to reproduce the data. A good, though imperfect, overall reproduction of the data is found within the deconfinement scenarios. The crossover EoS turns out to be slightly preferable. For this reproduction a fairly strong baryon stopping in the quark-gluon phase is required. The 3FD model does not need two separate freeze-outs (i.e. kinetic and chemical ones) to describe the STAR data. A unified freeze-out is applied at all energies.

Magnetothermodynamics: measurements of the thermodynamic properties in a relaxed magnetohydrodynamic plasma

We have explored the thermodynamics of compressed magnetized plasmas in laboratory experiments and we call these studies ‘magnetothermodynamics’. The experiments are carried out in the Swarthmore Spheromak eXperiment device. In this device, a magnetized plasma source is located at one end and at the other end, a closed conducting can is installed. We generate parcels of magnetized plasma and observe their compression against the end wall of the conducting cylinder. The plasma parameters such as plasma density, temperature and magnetic field are measured during compression using HeNe laser interferometry, ion Doppler spectroscopy and a linear ${\dot{B}}$ probe array, respectively. To identify the instances of ion heating during compression, a PV diagram is constructed using measured density, temperature and a proxy for the volume of the magnetized plasma. Different equations of state are analysed to evaluate the adiabatic nature of the compressed plasma. A three-dimensional resistive magnetohydrodynamic code (NIMROD) is employed to simulate the twisted Taylor states and shows stagnation against the end wall of the closed conducting can. The simulation results are consistent to what we observe in our experiments.

Modeling of physical properties and vapor – liquid equilibrium of ethylene and ethylene mixtures with equations of state

Ethylene (C2H4) is one of the most important compounds for the chemical and petrochemical industry, since it has found extensive use in the production of polymers, functionalized hydrocarbons and many other basic and intermediate products. As a result, significant amounts of ethylene are being transported, mainly through pipelines, from the site of production to the relevant industrial areas for exploitation and conversion to products of higher value. Accurate knowledge of the physical properties of the chemical systems involved, as well as the conditions for which two or more phases are formed, is a key aspect to the design and operation of a safe and optimal transportation process. In this work, the capability of three different Equations of State (EoS) in predicting the various physical properties (density, heat capacity, speed of sound, Joule-Thomson coefficient, and isothermal compressibility coefficient) of pure ethylene was assessed. The EoS considered include the Peng-Robinson (PR), the Perturbed Chain – Statistical Association Fluid Theory (PC-SAFT), and the SAFT with the Mie potential of variable range (SAFT-VR Mie) EoS, all of them in their original forms, with respect to the parameterization procedure. Furthermore, the vapor - liquid equilibrium (VLE) of pure ethylene and binary ethylene mixtures with hydrocarbons (CH4, C2H6, C3H6, C3H8, 1-C4H8) and gaseous components (H2, CO2) was calculated and the binary interaction parameters (BIPs) were regressed to optimize the performance of each EoS. Finally, the VLE of ternary mixtures with the components mentioned above and ethylene was predicted using the optimized BIPs. Most of the physical properties of pure C2H4 are predicted with relatively high accuracy by PC-SAFT and SAFT-VR Mie EoS, with none being clearly superior to the other. Both SAFT EoS are more accurate than PR in predicting the pure C2H4 physical properties overall. For phase equilibrium predictions, SAFT-VR Mie is overall the most accurate EoS, but when BIPs are used, the performance of all EoS is of comparable accuracy.

A mesoscopic numerical analysis for combustion reaction of multi-component PBX explosives

A mesoscopic combustion reaction model of multi-component PBX explosives by using a coupled thermo-mechanical constitutive model is studied. Thereinto, based on the heat balance equation, the present temperature can be calculated; the changing physical state of different materials is described by establishing different equations of state, and based on specially appointed constitutive equations, the microcracks in PBXs are described. Furthermore, the concept of combustion reaction degree is established, which takes temperature as a criterion for changing physical state. The model is implemented within the framework of the material point method so that the different gradient in the governing differential equations could be discretized in a single computational domain and that continuous remeshing is not required with increasing reaction time. The proposed model-based simulation procedure is verified with the burn rate, the peak pressure, and temperature of PBX explosives under macroscopic scale.

Diffuse-Interface Capturing Methods for Compressible Two-Phase Flows

Simulation of compressible flows became a routine activity with the appearance of shock-/contact-capturing methods. These methods can determine all waves, particularly discontinuous ones. However, additional difficulties may appear in two-phase and multimaterial flows due to the abrupt variation of thermodynamic properties across the interfacial region, with discontinuous thermodynamical representations at the interfaces. To overcome this difficulty, researchers have developed augmented systems of governing equations to extend the capturing strategy. These extended systems, reviewed here, are termed diffuse-interface models, because they are designed to compute flow variables correctly in numerically diffused zones surrounding interfaces. In particular, they facilitate coupling the dynamics on both sides of the (diffuse) interfaces and tend to the proper pure fluid–governing equations far from the interfaces. This strategy has become efficient for contact interfaces separating fluids that are governed by different equations of state, in the presence or absence of capillary effects, and with phase change. More sophisticated materials than fluids (e.g., elastic–plastic materials) have been considered as well.

Effects of Different Equations of State on the Oblique Shock Wave Reflection in Solids

The equations of state of solids under high pressure are more complicated than that of gases in a variety of forms. While the existing studies on the oblique shock wave reflection usually take just one of the equations of state, lacking of the comparisons among them. This paper aims at the investigation of oblique shock wave reflection in solids through shock polar methodology. Four different forms of equations of state are considered, principal shock taking with vN particle velocity relationship and second shock taking with Grüneisen equation of state(1Du2Grüneisen), principal and second shock both taking with vN particle velocity relationship (1Du2Du), principal shock taking with vN particle velocity relationship and second shock taking with stiffened gas equation of state (1Du2Gamma), and principal and second shock both taking with stiffened gas equation of state (1Gamma2Gamma). The effects of different equations of state on the pressure behind the reflected shock show: different combination of EOS may lead to diverse results. In our opinion, the 1Du2Grüneisen and 1Du2Du shows almost the same trends in most conditions and is suitable for the theoretical analysis of oblique reflection, and 1Du2Gamma and 1Gamma2Gamma should be carefully employed in studies to avoid the incorrect result.