Analysis of K-prime equations of state

We present an analysis of the $K$-prime equations of state (EOS) due to Keane and Stacey. It is found that the two EOS differ significantly from each other in some important respects. $K$-prime represents the pressure derivative of the bulk modulus. It is shown that the volume dependence of $K$-prime and higher derivative properties predicted from the Keane EOS are compatible with those predicted from Stacey’s reciprocal $K$-prime EOS only when the Murnaghan approximation is valid. It has been emphasized that the Stacey EOS is more appropriate for describing the relationship between pressure and the bulk modulus and its pressure derivative. The results based on the two EOS have been compared and discussed.     

Applicability of equation of state in extreme compression region and study of diatomic solids under pressure

In the present study, the expression of first pressure derivative of bulk modulus B′?earlier derived by Goyal and Gupta EoS [7] is corrected and the validity of the EoS is then verified in extreme compression region. The expressions of second and third order pressure derivative $(B^{{}^{″}},B^{″\prime })$of bulk modulus are obtained. The values of B′, B²B? to BB″,?Grunesien parameters?λ_∞,?γ_∞,?q_∞ at infinite pressure (P?→?∞)?are calculated using the identities [11–13] to check the validity of the equation in extreme compression region. The Goyal and Gupta EoS is then used to study the volume compression in diatomic solids, LiH and MgO. The values of pressure, bulk modulus and its first order pressure derivative at different compressions are calculated and compared with the results obtained from Hama–Suito EoS. The results justify the validity of the present EoS in high pressure region and the results for diatomic solids are also found in good consistency with the compared results.     

Thermo-elastic property of Ca(OH)2 portlandite

An equation of state (EoS) for Ca(OH)₂ portlandite has been obtained through measurements of pressure and temperature dependence of volume by means of in-situ X-ray observation. The bulk modulus and its pressure derivative at zero pressure calculated using third-order Birch-Murnaghan's equation of state is 33.1 GPa and 4.2 at 300 K, respectively. The unit cell parameters and the volumes have been also determined at 573 K and 673 K. Temperature derivatives of the bulk modulus and its pressure derivative have been calculated to be ?0.022 GPa/K and 0.0072 K^?1, respectively. Thermal expansion coefficient of portlandite has been calculated from the EoS. The pressure dependence of entropy has been obtained from the present thermo-elastic parameters.     

Directed flow of baryons from high-energy heavy-ion collisions

The collective motion of nucleons from high-energy heavy-ion collisions is analyzed within a relativistic two-fluid model for different equations of state (EoS). As function of beam energy the theoretical slope parameter F _y of the differential directed flow is in good agreement with experimental data, when calculated for the QCD-consistent EoS described by the statistical mixed-phase model. Within this model, which takes the deconfinement phase transition into account, the excitation function of the directed flow (P _x ) turns out to be a smooth function in the whole range from SIS till SPS energies. This function is close to that for pure hadronic EoS and exhibits no minimum predicted earlier for a two-phase bag-model EoS. Attention is also called to a possible formation of nucleon antiflow (F _y < 0) at energies ? 100 A·GeV.     

Thermal equation of state of goethite (α-FeOOH)

ABSTRACT

The pressure–volume–temperature (P–V–T) equation of state (EoS) of natural goethite (α-FeOOH) has been determined by an X-ray diffraction study using synchrotron radiation. Fitting the volume data to the third-order Birch–Murnaghan EoS yielded an isothermal bulk modulus, B₀ of 85.9(15)?GPa, and a pressure derivative of the bulk modulus, B′, of 12.6(8). The temperature derivative of the bulk modulus, (?B/?T)_P, was –0.022(9)?GPa?K^?1. The thermal expansion coefficient α₀ was determined to be 4.0(5)?×?10^?5?K^?1.     

Sensitivity of electromagnetic spectra to equation of state and initial energy density in the Pb + Pb collisions at SPS

We study Pb + Pb collisions at 158 A GeV/c using hydrodynamical approach. We test different equations of state (EoSs) and different initial conditions and show that there are more than one initial state for each EoS which reproduce the observed hadronic spectra. We also find that different equations of state favor different freeze-out temperature. Simultaneously we calculate the thermal dilepton and photon spectra for each EoS and initial state. We compare the dilepton mass spectrum to data measured by the CERES collaboration and find that the differences in spectra obtained using different EoSs and initial states are not resolvable within the current experimental resolution. However, at invariant masses over 2 GeV the difference in the yield due to various initial states is close to an order of magnitude. We also study the rapidity distribution of lepton pairs and find that for masses around 800 MeV the shape of the distribution depends strongly on the EoS.     

Computation of partial molar properties using continuous fractional component Monte Carlo

ABSTRACT

An alternative method for calculating partial molar excess enthalpies and partial molar volumes of components in Monte Carlo (MC) simulations is developed. This method combines the original idea of Frenkel, Ciccotti, and co-workers with the recent continuous fractional component Monte Carlo (CFCMC) technique. The method is tested for a system of Lennard–Jones particles at different densities. As an example of a realistic system, partial molar properties of a [NH₃, N₂, H₂] mixture at chemical equilibrium are computed at different pressures ranging from P = 10 to 80 MPa. Results obtained from MC simulations are compared to those obtained from the PC-SAFT Equation of State (EoS) and the Peng–Robinson EoS. Excellent agreement is found between the results obtained from MC simulations and PC-SAFT EoS, and significant differences were found for PR EoS modelling. We find that the reaction is much more exothermic at higher pressures.     

Non-perturbative effects for the Quark-Gluon Plasma equation of state

The non-perturbative effects for the Quark-Gluon Plasma (QGP) equation of state (EoS) are considered. The modifications of the bag model EoS are constructed to satisfy the main qualitative features observed for the QGP EoS in the lattice QCD calculations. A quantitative comparison with the lattice results is done for the SU(3) gluon plasma and for the QGP with dynamical quarks. Our analysis advocates a negative value of the bag constant B.     

Bianchi type-III Dark Energy Model in f(R,T) Gravity

A dark energy model with EoS parameter is investigated in f(R,T) gravity in Bianchi type-III space-time in the presence of perfect fluid source. To obtain a determinate solution special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B 74:183, 1983) is used. We have also assumed that the scalar expansion is proportional to shear and the EoS parameter is proportional to skewness parameter. It is observed that the EoS parameter, skewness parameters in the model turn out to be functions of cosmic time. Some physical and kinematical properties of the model are also discussed.     

Pressure dependence of the electric field gradient and knight shift tensors of single crystal gallium

Nuclear pure quadrupole resonance has been observed in single crystal gallium as a function of hydrostatic pressure up to 7 kbar at temperatures of 77, 198 and 273 K. The resonance frequency v_Q increases linearly with pressure and the slope ($\text{δv}{}_{\mathrm{O}}\text{δP}$)_T is 13.7, 15.5 and 16.3 Hz/bar at 77, 198 and 273 K respectively. The asymmetry parameter decreases nonlinearly with pressure. Using compressibility and thermal expansion data, the volume dependence of the major principle component of the electric field gradient was deduced. The principal components K_x, K_y and K_z of the Knight shift tensor have been measured as a function of pressure to 6 kbar at 77 K. The isotropic and anisotropic components of the Knight shift were deduced as a function of pressure, and K_iso is found to vary with volume as V^{4.95 ± 0.80}.     

Holographic Dark Energy (DE) Cosmological Models with Quintessence in Bianchi Type-V Space Time

In this paper, author studied homogeneous and anisotropic Bianchi type-V universe filled with matter and holographic dark energy (DE) components. The exact solutions to the corresponding Einstein’s field equations are obtained for exponential and power-law volumetric expansion. The holographic dark energy (DE) EoS parameter behaves like constant, i.e. ω _Λ =?1, which is mathematically equivalent to cosmological constant (Λ) for exponential expansion of the model, whereas the holographic dark energy (DE) EoS parameter behaves like quintessence for power-law expansion of the model. A correspondence between the holographic dark energy (DE) models with the quintessence dark energy (DE) is also established. Quintessence potential and dynamics of the quintessence scalar field are reconstructed, which describe accelerated expansion of the universe. The statefinder diagnostic pair {r,s} is adopted to characterize different phases of the universe.     

Pressure dependence of the superconducting transition temperature of the stage-2 potassium mercurographitide intercalation compound

Measurements of the pressure (P) dependence of the superconducting transition temperature T_c of stage-two KHgC₈ are reported. T_c is found to decrease with applied pressure from a room pressure value of 1.85K at a rate dT_c/dP=-6.5 × 10^-5K/bar, similar to typical superconducting elements such as Sn. No superconductivity was detected for stage-one KHgC₄ or K_0.5Hg_0.5 amalgam to a limiting temperature T = 1.3K and a limiting pressure P = 22 kbar. These results are discussed in reference to the possible occurence of structural and charge density wave transitions in these materials and recent theoretical models of superconducting graphire intercalation compounds.     

X-ray diffraction study of molybdenum diselenide to 35.9 GPa

In situ high-pressure angle dispersive synchrotron X-ray diffraction studies of molybdenum diselenide (MoSe₂) were carried out in a diamond-anvil cell to 35.9 GPa. No evidence of a phase transformation was observed in the pressure range. By fitting the pressure-volume data to the third-order Birch-Murnaghan equation of state, the bulk modulus, K_0T, was determined to be 45.7±0.3 GPa with its pressure derivative, K′_0T, being 11.6±0.1. It was found that the c-axis decreased linearly with pressure at a slope of −0.1593 when pressures were lower than 10 GPa. It showed different linear decrease with the slope of a −0.0236 at pressures higher than 10 GPa.     

QCD equation of state for heavy ion collisions

In this work, we calculate the equation of state(EoS) of quark gluon-plasma(QGP) using the CornwallJackiw-Tomboulis(CJT) effective action. We get the quark propagator by using the rank-1 separable model within the framework of the Dyson-Schwinger equations(DSEs). The results from CJT effective action are compared with lattice QCD data. We find that, when μ is small, our results generally fit the lattice QCD data when TT_c,but show deviations at and below T_c. It can be concluded that the EoS of CJT is reliable when TT_c. Then,by adopting the hydrodynamic code UVH2+1, we compare the CJT results of the multiplicity and elliptic flow v2 with the PHENIX data and the results from the original EoS in UVH2+1. While the CJT results of multiplicities generally match the original UVH2+1 results and fit the experimental data, the CJT results of v2 are slightly larger than the original UVH2+1 results for centralities smaller than 40% and smaller than the original UVH2+1 results for higher centralities.     

Thermodynamics of Evolving Lorentzian Wormhole at Apparent and Event Horizons

We have investigated the non-static Lorentzian Wormhole model in presence of anisotropic pressure. We have presented some exact solutions of Einstein equations for anisotropic pressure case. Introducing two EoS parameters we have shown that these solutions give very rich dynamics of the universe yielding to the different expansion history of it in the r - direction and in the T - direction. The corresponding explicit forms of the shape function b(r) is presented.We have shown that the Einstein’s field equations and unified first law are equivalent for the dynamical wormhole model. The first law of thermodynamics has been derived by using the Unified first law. The physical quantities including surface gravity and the temperature are derived for the wormhole. Here we have obtained all the results without any choice of the shape function. The validity of generalized second law (GSL) of thermodynamics has been examined at apparent and event horizons for the evolving Lorentzian wormhole.     

A Study on the New Agegraphic Dark Energy Model in the Framework of Generalized Uncertainty Principle for Different Scale Factors

In this paper, we consider the New Agegraphic Dark Energy (NADE) model interacting with pressureless Dark Matter (DM) in the framework of generalized uncertainty principle. We consider different expressions of the scale factor a(t) pertaining to the emergent, the intermediate and the logamediate scenarios of the universe. We have derived the expressions for various cosmological parameters in all the three cases and plotted the equation of state (EoS) parameter ω _D and squared speed of the sound $v_{s}^{2}$ to check the stability of the model in each case. We have observed that for emergent and intermediate cases, the EoS parameter has a quintom-like behavior and in the logamediate case it has quintessence-like behavior. The negative squared speed of sound in all of the three cases has indicated that the model is classically unstable for each choice of scale factor.     

Equations of state of MgO,Au, Pt,NaCl-B1, and NaCl-B2: Internally consistent high-temperature pressure scales

Semiempirical equations of state (EoS) of Au, Pt, MgO, NaCl-B1, and NaCl-B2 based on expanded Mie–Grüneisen–Debye approach, which are consistent both with the Mie–Grüneisen–Bose–Einstein approach and the thermochemical, X-ray, ultrasonic and shock-wave data in a wide pressure-temperature range, have been constructed. It is shown that to determine the volume dependence of the Grüneisen parameter, not only shock-wave and static compression data, but also experimental information on heat capacity, bulk moduli, volume, and thermal expansion coefficient at zero pressure need to be taken into account. Intrinsic anharmonicity is of great importance at construction of EoS at high temperatures and x=V/V ₀>1. Cross-comparison of the current equations of state with independent measurements shows that these EoS may be used as the internally consistent and independent pressure scales in a wide range of temperatures and pressures.     

Isotropic and anisotropic dark energy models

In this review we discuss the evolution of the universe filled with dark energy with or without perfect fluid. In doing so we consider a number of cosmological models, namely Bianchi type I, III, V, VI₀, VI and FRW ones. For the anisotropic cosmological models we have used proportionality condition as an additional constrain. The exact solutions to the field equations in quadrature are found in case of a BVI model. It was found that the proportionality condition used here imposed severe restriction on the energy-momentum tensor, namely it leads to isotropic distribution of matter. Anisotropic BVI₀, BV, BIII and BIDE models with variable EoS parameter ω have been investigated by using a law of variation for the Hubble parameter. In this case the matter distribution remains anisotropic, though depending on the concrete model there appear different restrictions on the components of energy-momentum tensor. That is why we need an extra assumption such as variational a law for the Hubble parameter. It is observed that, at the early stage, the EoS parameter v is positive i.e. the universe was matter dominated at the early stage but at later time, the universe is evolving with negative values, i.e., the present epoch. DE model presents the dynamics of EoS parameter ω whose range is in good agreement with the acceptable range by the recent observations. A spatially homogeneous and anisotropic locally rotationally symmetric Bianchi-I space time filled with perfect fluid and anisotropic DE possessing dynamical energy density is studied. In the derived model, the EoS parameter of DE (ω^(de)) is obtained as time varying and it is evolving with negative sign which may be attributed to the current accelerated expansion of Universe. The distance modulus curve of derived model is in good agreement with SNLS type Ia supernovae for high redshift value which in turn implies that the derived model is physically realistic. A system of two fluids within the scope of a spatially flat and isotropic FRW model is studied. The role of the two fluids, either minimally or directly coupled in the evolution of the dark energy parameter, has been investigated. In doing so we have used three different ansatzs regarding the scale factor that gives rise to a variable decelerating parameter. It is observed that, in the non-interacting case, both the open and flat universes can cross the phantom region whereas in the interacting case only the open universe can cross the phantom region. The stability and acceptability of the obtained solution are also investigated.     

Dielectric properties and phase transitions in alkali cyanides and cyanospinels under the influence of hydrostatic pressure

The effect of hydrostatic pressure p on the low-frequency dielectric constant ? has been investigated for selected cyanides (NaCN, KCN) and cyanospinels [K₂M(CN)₄ with M = Zn, Cd, Hg and Rb₂Zn(CN)₄] for pressures up to 7 kbar In the low-pressure region (decreases monotomcally resulting in negative first-order pressure denvatives of the dielectric constant The second- and third-order pressure derivatives, however, proved to be positive in most cases Using the dielectric constant as a very sensitive probe we observed phase transitions from the cubic low-pressure phase to an orthorhombic (NaCN) resp trigonal (cyanospinels) high-pressure phase at the following transition pressures (for 293.2 K) 2 260 kbar for NaCN, 1 438 kbar for K₂Hg(CN)₄, 2 660 kbar for K₂Cd(CN)₄, 3 318 kbar for K₂Zn(CN)₄ and 0.690 kbar for Rb₂Zn(CN)₄ The transition temperature T_c, was found to increase strictly linear with pressure between 290 and 340 K at a rate of dT_c/dp = 120 2 and 105 3 Kkbar^?1 for K₂Zn(CN)₄ and K₂Cd(CN)₄, respectively.     

High pressure X-ray diffraction study of Fe2B

We report the results of a synchrotron based X-ray diffraction study of bct-Fe₂B under quasi-hydrostatic conditions from 0 to 50 GPa. Over this pressure range, no phase change or disproportionation has been observed. A weighted fit of the data to the Birch-Murnaghan equation of state yields a value of the bulk modulus, K, of 164±14 GPa and the first pressure derivative of the bulk modulus, K′, of 4.4±0.5. The compression is found to be anisotropic, with the a-axis being more incompressible than the c-axis.