Using Equations Of State Research Articles

Black hole-neutron star mergers using a survey of finite-temperature equations of state

Each of the potential signals from a black hole-neutron star merger should contain an imprint of the neutron star equation of state: gravitational waves via its effect on tidal disruption, the kilonova via its effect on the ejecta, and the gamma ray burst via its effect on the remnant disk. These effects have been studied by numerical simulations and quantified by semi-analytic formulae. However, most of the simulations on which these formulae are based use equations of state without finite temperature and composition-dependent nuclear physics. In this paper, we simulate black hole-neutron star mergers varying both the neutron star mass and the equation of state, using three finite-temperature nuclear models of varying stiffness. Our simulations largely vindicate formulae for ejecta properties but do not find the expected dependence of disk mass on neutron star compaction. We track the early evolution of the accretion disk, largely driven by shocking and fallback inflow, and do find notable equation of state effects on the structure of this early-time, neutrino-bright disk.

De Sitter universe described by a binary mixture with a variable cosmological constant λ $\lambda $

We have constructed a self-consistent system of Bianchi Type VI0 cosmology, and mingling of perfect fluid and dark energy in five dimensions. The usual equation of state \(p = \gamma \rho \) with \(\gamma \in [0, 1]\) is chosen by the perfect fluid. The dark energy assumed to be chosen is taken into consideration to be either the quintessence or Chaplygin gas. The same solutions pertaining to the corresponding the field equations of Einstein are obtained as a quadrature. State parameter’s equations for dark energy \(\omega \) is found to be consistent enough with the recent observations of SNe Ia data (SNe Ia data with CMBR anisotropy) and galaxy clustering statistics. Here our models predict that the rate of expansion of Universe would increase with passage of time. The cosmological constant \(\varLambda \) is traced as a declining function of time and it gets nearer to a small positive value later on which is supported by the results from the current supernovae Ia observations. Also a detail discussion is made on the physical and geometrical aspects of the models.

Emergent Universe with Particle Production

The possibility of an emergent universe solution to Einstein's field equations allowing for an irreversible creation of matter at the expense of the gravitational field is shown. With the universe being chosen as spatially flat FRW spacetime together with equation of state proposed in [17], the solution exists when the ratio of the phenomenological matter creation rate to the number density times the Hubble parameter is a number $\beta$ of the order of unity and independent of time. The thermodynamic behaviour is also determined for this solution. Interestingly, we also find that an emergent universe scenario is present with usual equation of state in cosmology when the matter creation rate is chosen to be a constant. More general class of emergent universe solutions are also discussed.

Bianchi Type VI0 Cosmological Models with Perfect Fluid and Dark Energy

We consider a self-consistent system of Bianchi Type VI0 cosmology and binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be one obeying the usual equation of state p=γρ with γ∈[0,1]. The dark energy is considered to be either the quintessence or Chaplygin gas. Exact solutions to the corresponding Einstein’s field equations are obtained as a quadrature. Models with power-law and exponential expansion have discussed in detail.

Bianchi type-V cosmological models with perfect fluid and dark energy

We consider a self-consistent system of Bianchi type-V cosmology and binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be one obeying the usual equation of state p=γρ with γ∈[0,1]. The dark energy is considered to be either the quintessence or Chaplygin gas. Exact solutions to the corresponding Einstein equations are obtained as a quadrature. The cases of disordered radiation and models with power-law and exponential expansion have discussed in detail. For large t, the models tend to be isotropic.

Anisotropic Cosmological Models with a Perfect Fluid and a Λ Term

We consider a self-consistent system of Bianchi type-I (BI) gravitational field and a binary mixture of perfect fluid and dark energy given by a cosmological constant. The perfect fluid is chosen to be the one obeying either the usual equation of state, i.e., $p = \zeta \ve$, with $\zeta \in [0, 1]$ or a van der Waals equation of state. Role of the $\Lambda$ term in the evolution of the BI Universe has been studied.

Upper bounds on the entropy of radiation systems

The upper bounds on the entropy of a radiation system confined to a spherical box are calculated in six cases by using the equation of state of radiation in flat spacetime and the equation of state of radiation near black-hole horizon, which was derived by Li and Liu (hereafter the Li-Liu equation). It turns out that the Li-Liu equation does have unique advantage in dealing with the entropy bound of critical self-gravitating radiation systems, while the usual equation of state will result in entropy divergence. In the case of non-self-gravitating radiation systems and non-critical self-gravitating radiation systems, there is no difference in the entropy bounds derived by these two equations of state.

New field theoretical method for spin 1/2

A new field theoretic method for spin 12, for which the propagator and the finite temperature perturbation theory rules have been recently derived, is analysed in some detail. This propagator can be diagonalised using a spherical basis with the third axis along the magnetic field direction. The diagrammatic representation of the spherical spin components is given. As an illustration of this method, we derive some single spin quantities and the usual equation of state and spin wave spectrum of the spin 12 Heisenberg model, using the Hartree-Fock and the random phase approximations. We show how the field theoretic renormalisation group techniques can be applied to renormalise the different quantities of interest and to derive renormalisation group equations. As an example of their application, we consider the commutative and noncommunicative models of two-level systems in metallic glasses.

Mechanical Behavior of a Polymer at Temperatures through the Glass Transition Temperature

Abstract Stress-temperature (constant strain) and length-temperature (constant stress) measurements have been made on Paracril-35 (a butadiene-acrylonitrile copolymer) in the temperature range −80° C to 25° C, which includes the glasslike, transition, and rubberlike states for this material (Tg∼−25°C). Time effects are observed in the transition region, but for temperature gradients used (down to about 1° C in 4 hours) the behavior at low temperatures is unique, indicating the existence of a real transition. This behavior is independent of the strain imposed at room temperature. The shift in transition temperature (in the length-temperature work) with extension is found to give quantitative support to the theory that the transition occurs at a certain minimum volume. In the rubberlike region, behavior is represented by the usual equation of state.

Mechanical Behavior of a Polymer at Temperatures through the Glass Transition Temperature

Stress-temperature (constant strain) and length-temperature (constant stress) measurements have been made on Paracril-35 (a butadiene-acrylonitrile copolymer) in the temperature range −80°C to 25°C, which includes the glass-like, transition, and rubber-like states for this material (Tg∼−25°C). Time effects are observed in the transition region, but for temperature gradients used (down to about 1°C in 4 hours) the behavior at low temperatures is unique, indicating the existence of a real transition. This behavior is independent of the strain imposed at room temperature. The shift in transition temperature (in the length-temperature work) with extension is found to give quantitative support to the theory that the transition occurs at a certain minimum volume. In the rubber-like region, behavior is represented by the usual equation of state.