Equation Of State Model Research Articles

Premelting, solid-fluid equilibria, and thermodynamic properties in the high density region based on the Lennard-Jones potential.

The Lennard-Jones potential is used to study the high density fluid and face centered cubic solid state region, including solid-fluid equilibria. Numerous thermodynamic properties are considered, elucidating the behavior of matter in this poorly studied region. The present molecular simulation results are extensively compared to the latest and most accurate equation of state models for fluid and solid phases. It is shown that current models do not cover the thermodynamics of the system adequately near the solid-fluid phase transition. Furthermore, thermodynamic stability is analyzed, indicating that published solid-fluid coexistence data may not be correct at high temperatures. Particular attention is paid to the premelting zone, a range of states close to the melting line, which is characterized by strong variations of several thermodynamic properties. Because the underlying microscopic mechanisms are not yet fully understood, it is hoped that these data may contribute to the development of a theoretical framework for describing premelting effects.

Shock equation of state of LiH6 to 1.1 TPa

Using laser-generated shock waves, we have measured pressure, density, and temperature of LiH on the principal Hugoniot between 260 and 1100 GPa (2.6--11 Mbar) and on a second-shock Hugoniot up to 1400 GPa to near fivefold compression, extending the maximum pressure reached in non-nuclear experiments by a factor of two. We observe the onset of metal-like reflectivity consistent with temperature-induced ionization of the Li 2s electron, and no sign of additional changes in ionization up to the maximum pressure. Our measurements are in good agreement with gas gun, Z-machine, and underground test data and are accurately described by quantum molecular dynamics simulations. The results confirm the validity of equation of state models built on an average-atom description of the electron-thermal contribution to the free energy and a density-dependent Gr\uneisen parameter to describe shock response of LiH over this pressure range.

Relativistic Disc Line: A Tool to Constrain Neutron Star Equation of State Models

Relativistic iron K$\alpha$ spectral emission line from the inner disc of a neutron star low-mass X-ray binary (LMXB) was first detected in 2007. This discovery opened up new ways to probe strong gravity and dense matter. The past decade has seen detections of such a line from many neutron star LMXBs, and confirmation of this line from the same source with several X-ray satellites. These have firmly established the new field of relativistic disc line from neutron star systems in only ten years. Fitting the shape of such a line with an appropriate general relativistic model provides the accretion disc inner edge radius to the stellar mass ratio. In this review, we briefly discuss how an accurate measurement of this ratio with a future larger area X-ray instrument can be used to constrain neutron star equation of state models.

UAS based Li-ion battery model parameters estimation

Estimation of Lithium-ion (Li-ion) battery model parameters is key for accurately determining battery state of charge (SOC). Estimating these parameters requires substantial experimental effort. This work reduces the experimentation required, by using universal adaptive stabilization (UAS) for estimating parameters appearing in battery model state equations. Accuracy of estimated model parameters is verified by comparing the estimated and measured battery terminal voltage. SOC obtained using the estimated model parameters, and open circuit EMF vs SOC curve, captures effects due to discharge currents of small magnitude, which Coulomb counting, well known filtering methods ignore. Rigorous mathematical analysis supports the experimental results presented.

Effect of cerebrospinal fluid modeling on spherically convergent shear waves during blunt head trauma.

The MRI-based computational model, previously validated by tagged MRI and harmonic phase imaging analysis technique on in vivo human brain deformation, is used to study transient wave dynamics during blunt head trauma. Three different constitutive models are used for the cerebrospinal fluid: incompressible solid elastic, viscoelastic, and fluid-like elastic using an equation of state model. Three impact cases are simulated, which indicate that the blunt impacts give rise not only to a fast pressure wave but also to a slow, and potentially much more damaging, shear (distortional) wave that converges spherically towards the brain center. The wave amplification due to spherical geometry is balanced by damping due to tissues' viscoelasticity and the heterogeneous brain structure, suggesting a stochastic competition of these 2 opposite effects. It is observed that this convergent shear wave is dependent on the constitutive property of the cerebrospinal fluid, whereas the peak pressure is not as significantly affected.

Predictive model for gas and vapor sorption and swelling in glassy polymers: II. Effect of sample previous history

The solubility of various gases in several glassy polymers has been analyzed by the nonequilibrium thermodynamics for glassy polymers (NET-GP) framework, coupled with a lattice fluid equation of state model. Moreover, a simple rheological tool recently introduced for the a priori evaluation of the penetrant induced swelling is employed to predict the volumetric behavior of the solute/polymer mixture below Tg. Such model accounts for an additional nonequilibrium parameter for the description of polymer phase that represents its pseudoequilibrium compressibility, and it can be retrieved from pure component pressure–volume–temperature data below Tg. More in detail, the effect of polymer pretreatment and its prior history (e.g. annealing or conditioning by preswelling) on the resulting solubility behavior has been thoroughly analyzed and discussed, and the experimental data obtained for several penetrant/polymer couples have been well described by the present model.

단일 인버터로 두 대의 영구자석 동기전동기 병렬운전에 대한 공진특성해석

This pap4er analyzes resonance characteristics of a slave motor that is not controlled by load and parameter differences between Dual motors during parallel operation in middle-low speed. Dual SPMSMs(Surface mounted Permanent Magnet Synchronous Motor) connected in parallel to a single inverter controlled by the master and slave control in this paper. Based on the stability analysis of the SPMSM for a variation of torque angle, the 6th nonlinear state equation of the torque angle variation in the SIMM(Single Inverter Multi Motor) structure is derived according to a mathematical model for the dual motors. In general, an analysis of the 6th order nonlinear state equation is complex. Therefore, a resonance frequency generated from the slave motor is found from the characteristic equation of the 2nd order system obtained by linearization and model reduction near steady state operation point. Through simulations and experiments, it is confirmed that the stability analysis of the SPMSMs and state equation models are useful for the variation of the torque angle analyzed in this paper.

Dimerization of Carboxylic Acids: An Equation of State Approach.

The association term of the nonrandom hydrogen bonding theory, which is an equation of state model, is extended to describe the dimerization of carboxylic acids in binary mixtures with inert solvents and in systems of two different acids. Subsequently, the model is applied to describe the excess enthalpies and the vapor-liquid equilibrium of relevant binary mixtures containing low molecular weight organic acids. The model sheds light on the interplay of intermolecular interactions through the calculation of the various contributions to the mixing enthalpies, namely from hydrogen bonding and non-hydrogen bonding (dipolar, induced polar or dispersive) interactions. According to model predictions, the acid molecules are so strongly associated that the addition of inert solvents to carboxylic acids with small carbon numbers at ambient temperature does not dramatically alter their degree of association. Consequently, the observed endothermic dissolution process is mainly attributed to the hindering of polar interactions. Furthermore, upon mixing of two carboxylic acids, the rearrangement of hydrogen bonds due to the formation of cross associating species results in an insignificant contribution to the heats of mixing due to the rather constant dimerization enthalpy that is revealed by the available experimental data for low molecular weight compounds.

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.

Estimating the solubility of different solutes in supercritical CO2 covering a wide range of operating conditions by using neural network models

A new neural network-based model is proposed for solute solubility in supercritical carbon dioxide (CO2). The solubility of fifteen solutes in supercritical carbon dioxide at different temperatures and pressures are estimated. Four neural network models have been tested to investigate the generalize-ability of each network. The results from different semi-empirical models, namely Chrastil, Kumar and Johnston, Bartle, Mendez-Santiago and Teja, the Peng–Robinson and Soave–Redlich–Kwong equation of state models are compared to the one estimated by using the proposed neural network model. The average absolute deviation (AAD) of 5.42% compared to those of density-based and equation of state models, representing the reasonable accuracy of the developed model for estimating the solubility of solutes in supercritical fluid extraction process.

Millisecond radio pulsars with known masses: Parameter values and equation of state models

The recent fast growth of a population of millisecond pulsars with precisely measured mass provides an excellent opportunity to characterize these compact stars at an unprecedented level. This is because the stellar parameter values can be accurately computed for known mass and spin rate and an assumed equation of state (EoS) model. For each of the 16 such pulsars and for a set of EoS models from nucleonic, hyperonic, strange quark matter and hybrid classes, we numerically compute fast spinning stable stellar parameter values considering the full effect of general relativity. This first detailed catalogue of the computed parameter values of observed millisecond pulsars provides a testbed to probe the physics of compact stars, including their formation, evolution and EoS. We estimate uncertainties on these computed values from the uncertainty of the measured mass, which could be useful to quantitatively constrain EoS models. We note that the largest value of the central density ρc in our catalogue is ∼5.8 times the nuclear saturation density ρsat, which is much less than the expected maximum value 13ρsat. We argue that the ρc-values of at most a small fraction of compact stars could be much larger than 5.8ρsat. Besides, we find that the constraints on EoS models from accurate radius measurements could be significantly biased for some of our pulsars, if stellar spinning configurations are not used to compute the theoretical radius values.

The State of Matter in Simulations of Core-Collapse supernovae—Reflections and Recent Developments

AbstractIn this review article, we discuss selected developments regarding the role of the equation of state in simulations of core-collapse supernovae. There are no first-principle calculations of the state of matter under supernova conditions since a wide range of conditions is covered, in terms of density, temperature, and isospin asymmetry. Instead, model equation of state are commonly employed in supernova studies. These can be divided into regimes with intrinsically different degrees of freedom: heavy nuclei at low temperatures, inhomogeneous nuclear matter where light and heavy nuclei coexist together with unbound nucleons, and the transition to homogeneous matter at high densities and temperatures. In this article, we discuss each of these phases with particular view on their role in supernova simulations.

Rotation-Driven Phase Transitions in the Cores of Pulsars

In this paper, we discuss the impact of rotation on the particle composition of rotating neutron stars (pulsars). Particular emphasis is put on the formation of quark matter during stellar spin-down, driven by continuous gravitational compression. Our study is based on modern models for the nuclear equation of state whose parameters are tightly constrained by nuclear data, neutron star masses, and the latest estimates of neutron star radii.

Stellar Structure Models of Deformed Neutron Stars

Traditional stellar structure models of non-rotating neutron stars work under the assumption that these stars are perfect spheres. This assumption of perfect spherical symmetry is not correct if the matter inside neutron stars is described by an anisotropic model for the equation of state. Certain classes of neutron stars such as Magnetars and neutron stars which contain color-superconducting quark matter cores are expected to be deformed making them oblong spheroids. In this work, we investigate the stellar structure of these deformed neutron stars by deriving stellar structure equations in the framework of general relativity. Using a non-isotropic equation of state model, we solve these structure equations numerically in two dimensions. We calculate stellar properties such as masses and radii along with pressure profiles and investigate changes from standard spherical models.

Behavior of universal critical parameters in the QCD phase diagram

We determine the dependence of important parameters for critical fluctuations on temperature and baryon chemical potential in the QCD phase diagram. The analysis is based on an identification of the fluctuations of the order parameter obtained from the Ising model equation of state and the Ginzburg-Landau effective potential approach. The impact of the mapping from Ising model variables to QCD thermodynamics is discussed.

Shock compression experiments on Lithium Deuteride (LiD) single crystals

Shock compression experiments in the few hundred GPa (multi-Mbar) regime were performed on Lithium Deuteride single crystals. This study utilized the high velocity flyer plate capability of the Sandia Z Machine to perform impact experiments at flyer plate velocities in the range of 17–32 km/s. Measurements included pressure, density, and temperature between ∼190 and 570 GPa along the Principal Hugoniot—the locus of end states achievable through compression by large amplitude shock waves—as well as pressure and density of reshock states up to ∼920 GPa. The experimental measurements are compared with density functional theory calculations, tabular equation of state models, and legacy nuclear driven results that have been reanalyzed using modern equations of state for the shock wave standards used in the experiments.

Shock-wave processes evolution in fused quartz under intense energy action

The paper considers gas-dynamical processes evolving as a result of laser action in fused quartz. A conventional approach is used to construct a model for equation of state which provides an adequate description of the silica state at high densities of energy typical for local optical silica damage. Shock-wave processes generated in the medium due to the local laser energy deposition are calculated using fully conservative numerical technique. The obtained results provide relatively accurate description of the process in a wide range of parameters and allow further research to get clear interpretation of high-speed propagation of the laser absorbing front through the silica optical fiber.

Radial stability of anisotropic strange quark stars

The influence of the anisotropy in the equilibrium and stability of strange stars is investigated through the numerical solution of the hydrostatic equilibrium equation and the radial oscillation equation, both modified from their original version to include this effect. The strange matter inside the quark stars is described by the MIT bag model equation of state. For the anisotropy two different kinds of local anisotropic σ = pt−pr are considered, where pt and pr are respectively the tangential and the radial pressure: one that is null at the star's surface defined by pr(R) = 0, and one that is nonnull at the surface, namely, σs = 0 and σs ≠ 0. In the case σs = 0, the maximum mass value and the zero frequency of oscillation are found at the same central energy density, indicating that the maximum mass marks the onset of the instability. For the case σs ≠ 0, we show that the maximum mass point and the zero frequency of oscillation coincide in the same central energy density value only in a sequence of equilibrium configurations with the same value of σs. Thus, the stability star regions are determined always by the condition dM/dρc > 0 only when the tangential pressure is maintained fixed at the star surface's pt(R). These results are also quite important to analyze the stability of other anisotropic compact objects such as neutron stars, boson stars and gravastars.

Mechanical response of lithium fluoride under off-principal dynamic shock-ramp loading

Single crystal lithium fluoride (LiF), oriented [100], was shock loaded and subsequently shocklessly compressed in two experiments at the Z Machine. Velocimetry measurements were employed to obtain an impactor velocity, shock transit times, and in-situ particle velocities for LiF samples up to ∼1.8 mm thick. A dual thickness Lagrangian analysis was performed on the in-situ velocimetry data to obtain the mechanical response along the loading path of these experiments. An elastic response was observed on one experiment during initial shockless compression from 100 GPa before yielding. The relatively large thickness differences utilized for the dual sample analyses (up to ∼1.8 mm) combined with a relative timing accuracy of ∼0.2 ns resulted in an uncertainty of less than 1% on density and stress at ∼200 GPa peak loading on one experiment and <4% on peak loading at ∼330 GPa for another. The stress-density analyses from these experiments compare favorably with recent equation of state models for LiF.

Zero-Kelvin Compression Isotherms of the Elements 1 ≤ Z ≤ 92 to 100 GPa

Most of the chemical elements have now been compressed close to or above 100 GPa (1 Mbar) pressure in diamond-anvil cells and the pressure–volume room-temperature isotherms have been measured. We collect these data and use simple lattice-dynamics models to reduce the isotherms to 0 K. We have extended the published work by making new diamond-anvil-cell measurements on Cr and Rh, and by conducting density-functional calculations on the elements Po, At, Rn, Fr, Ra, and Ac. The 0 K data are tabulated for all elements 1 ≤ Z ≤ 92 and 0 ≤ P ≤ 100 GPa. These data are useful for generating wide-range equation of state models and for studying the stability of chemical compounds at high pressure (“Megabar chemistry”). The tables presented here are intended to be reference thermodynamic tables for use in high-pressure research. Further experimental and theoretical work will be needed to extend the tables to higher pressure and to improve accuracy.