Regular models with quadratic equation of state

We provide new exact solutions to the Einstein–Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is quadratic relating the radial pressure to the energy density. Earlier models, with linear and quadratic equations of state, are shown to be contained in our general class of solutions. The new solutions to the Einstein–Maxwell are found in terms of elementary functions. A physical analysis of the matter and electromagnetic variables indicates that the model is well behaved and regular. In particular there is no singularity in the proper charge density at the stellar centre unlike earlier anisotropic models in the presence of the electromagnetic field.     

Generalized isothermal models with strange equation of state

We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the electromagnetic field. New exact solutions are found to the Einstein-Maxwell system. A particular case is shown to be regular at the stellar centre. In the isotropic limit we regain the general relativistic isothermal Universe. We show that the mass corresponds to the values obtained previously for quark stars when anisotropy and charge are present.      

Quintessence models with an oscillating equation of state and their potentials

In this paper, we investigate the quintessence models with an oscillating equation of state (EOS) and its potentials. From the constructed potentials, which have an EOS of $\omega_{\phi}=\omega_0+\omega_1\sin z$, we find that they are all the oscillating functions of the field $\phi$, and the oscillating amplitudes decrease (or increase) with $\phi$. From the evolutive equation of the field $\phi$, we find that this is caused by the expansion of the universe. This also makes it very difficult to build a model whose EOS oscillates forever. However one can build a model with EOS oscillating for a certain period of time. Then we discuss three quintessence models, which are the combinations of the invert power law functions and the oscillating functions of the field $\phi$. We find that they all follow the oscillating EOS.     

New stellar models generated using a quadratic equation of state

In the present era, there has been a great demand of cost-effective, biodegradable, flexible and wearable electronics which may open the gate to many applications like flexible displays, RFID tags, health monitoring devices, etc. Due to the versatile nature of plastic substrates, they have been extensively used in packaging, printing, etc. However, the fabrication of electronic devices requires specially prepared substrates with high quality surfaces, chemical compositions and solutions to the related fabrication issues along with its non-biodegradable nature. Therefore, in this report, a cost-effective, biodegradable cellulose paper as an alternative dielectric substrate material for the fabrication of flexible field effect transistor (FET) is presented. The graphite and liquid phase exfoliated graphene have been used as the material for the realisation of source, drain and channel on cellulose paper substrate for its comparative analysis. The mobility of fabricated FETs was calculated to be \(83\,\hbox {cm}^{2}/\hbox {V}\,\hbox {s}\) (holes) and \(33\,\hbox {cm}^{2}/\hbox {V}\,\hbox {s}\) (electrons) for graphite FET and \(100\,\hbox {cm}^{2}/\hbox {V}\,\hbox {s}\) (holes) and \(52\,\hbox {cm}^{2}/\hbox {V}\,\hbox {s}\) (electrons) for graphene FET, respectively. The output characteristic of the device demonstrates the linear behaviour and a comprehensive increase in conductance as a function of gate voltages. The fabricated FETs may be used for strain sensing, health care monitoring devices, human motion detection, etc.     

New classes of anisotropic models with generalized polytropic equation of state

In this paper, we investigate the gravitational behavior of compact objects with the help of generalized polytropic equation of state in isotropic coordinates. We found three exact solutions of Einstein field equations by taking into account the different values of polytropic index with spherically symmetric anisotropic inner fluid distribution. We have regained the masses of PSR \(\hbox {J}1614-2230\), Vela X-1, Vela 4U, PSR J1903+327 and 4U 1820-30. Speed of sound has been used to analyze the stability of models. The comprehensive analysis indicates that all the models are physically viable and well behaved.     

Effective dark energy equation of state in interacting dark energy models

In models where dark matter and dark energy interact non-minimally, the total amount of matter in a fixed comoving volume may vary from the time of recombination to the present time due to energy transfer between the two components. This implies that, in interacting dark energy models, the fractional matter density estimated using the cosmic microwave background assuming no interaction between dark matter and dark energy will in general be shifted with respect to its true value. This may result in an incorrect determination of the equation of state of dark energy if the interaction between dark matter and dark energy is not properly accounted for, even if the evolution of the Hubble parameter as a function of redshift is known with arbitrary precision. In this Letter we find an exact expression, as well as a simple analytical approximation, for the evolution of the effective equation of state of dark energy, assuming that the energy transfer rate between dark matter and dark energy is described by a simple two-parameter model. We also provide analytical examples where non-phantom interacting dark energy models mimic the background evolution and primary cosmic microwave background anisotropies of phantom dark energy models.     

Structure and equation of state of interaction site models for disc-shaped lamellar colloids

We apply RISM (reference interaction site model) and PRISM (polymer-RISM) theories to calculate the site–site pair structure and the osmotic equation of state of suspensions of circular or hexagonal platelets (lamellar colloids) over a range of ratios of the particle diameter over thickness Dσ. Despite the neglect of edge effects, the simpler PRISM theory yields results in good agreement with the more elaborate RISM calculations, provided the correct form factor, characterizing the intramolecular structure of the platelets, is used. The RISM equation of state is sensitive to the number n of sites used to model the platelets, but saturates when the hard spheres, associated with the interaction sites, nearly touch; the limiting equation of state agrees reasonably well with available simulation data for all densities up to the isotropic–nematic transition. When properly scaled with the second virial coefficient, the equations of state of platelets with different aspect ratios Dσ nearly collapse on a single master curve.     

Ising models with two- and three-spin interactions: Mean field equation of state

The Ising model with pair and triplet interactions on the triangular lattice is solved in the mean-field approximation. With a sufficiently strong triplet interaction two first-order transitions take place at low temperature, and at intermediate temperatures one transition, terminating in a critical point. For J₂ > 0.75J₃ only the latter transition remains.     

The ϵ-expansion and parametric models for the ising equation of state in the critical region

The scaling equation of state for a system with short range interactions and a one-component order parameter is calculated to order ?³ in the ?-expansion. The results are not compatible with the linear parametric model.     

Wide-range equation of state of matter. I. Analysis of nonideality models

Models proposed for theoretical calculations and based on wide-range equations of state of matter are analyzed and compared. It is shown that all previously proposed models of nonideal plasma behavior fall short in terms of accuracy for the equation of state in the range above critical.This work has received financial support from the Fundamental Research Fund, Grant No. 93-012-861 TEFIS (the Computerized Library of Thermophysical Properties of Matter).Deceased.Institute of Mathematical Modeling, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 23–43, November, 1994.     

Fluctuations and the magnetic equation of state

The influence of inhomogeneity of magnetization on the equation of state for a magnetic system has been considered in the approximation of homogeneous fluctuations of magnetic moment. The fluctuations have been described in the molecular field approximation. It has been shown that taking into account the fluctuations of magnetic moment at the derivation of the equation of state changes the relation among the variablesM, H andT, the temperature dependence of the spontaneous magnetization near the critical point, and shifts the critical temperature.The author would like to thank Prof. J.Kocinski and Prof. L.Wojtczak for their interest in the subject of the paper and for numerous elucidating discussions. The author is indebted to Prof. L.Valenta for his helpful remarks concerning this paper.     

Selfconsistent equation of state

We investigate the effects of a selfconsistent single-particle potential and the Pauli principle on the equation of state for dense systems at low temperatures. It is found that the selfconsistent potential plays an extremely important role for the equation of state near nuclear matter density.     

Two-component cosmological models with a variable equation of state of matter and with thermal equilibrium of components

A class of models describing the evolution of the homogeneous and isotropic spatially flat Universe filled with a scalar field and matter and changing the equation of state during its evolution from a vacuum-like form to an ideal liquid is proposed under the assumption that both components of matter are in thermal equilibrium. The main characteristics of such models are analyzed and their asymptotic behavior in the vicinity of a cosmological singularity and at the postinflation stage is investigated. It is shown that the thermal equilibrium condition and the requirement of asymptotic decrease of the field with time unambiguously lead to secondary inflation at the final stage of evolution, which is accompanied by accelerated expansion of the Universe and an increase in the temperature of matter.     

Chemical-potential dependence of the pairing gap in a nuclear-matter slab

The equation for the pairing gap Δ in a slab of nuclear matter governed by the Paris nucleon-nucleon potential is solved for various values of the chemical potential μ in the range from −8 MeV, which corresponds to stable nuclei, to −0.1 MeV, which corresponds to nuclei in the vicinity of the nucleon drip line. The slab is placed in a one-dimensional Woods-Saxon potential whose parameters are set to values typical of nuclei. Two models are considered. In the first, the potential-well depth is fixed at U ₀ = −50 MeV, the density within the slab growing as |μ| is reduced. In the second model, the density is fixed at the center of the slab, |U ₀| decreasing as |μ| is reduced. The behavior of the gap Δ as a function of μ is model-dependent. In the first model, Δ decreases with decreasing |μ|, while, in the second, it increases. At the same time, the effect of the surface enhancement of Δ becomes more pronounced with decreasing |μ| in both models. Original Russian Text ? S.S. Pankratov, E.E. Saperstein, M.V. Zverev, 2006, published in Yadernaya Fizika, 2006, Vol. 69, No. 12, pp. 2052–2063.     

Deducing the nuclear-matter incompressibility coefficient from data on isoscalar compression modes

Accurate assessment of the value of the incompressibility coefficient, K, of symmetric nuclear matter, which is directly related to the curvature of the equation of state (EOS), is needed to extend our knowledge of the EOS in the vicinity of the saturation point. We review the current status of K as determined from experimental data on isoscalar giant monopole and dipole resonances (compression modes) in nuclei, by employing the microscopic theory based on the random-phase approximation (RPA).     

Incomplete fusion and nuclear equation of state

A microscopic model based on the molecular dynamics concept was applied to study linear momentum transfer in nuclear reactions for a range of incident energies and several systems. It appears that this quantity is sensitive to the incompressibility of nuclear matter. The comparison of the model calculation with a substantial body of data favors a soft equation of state (K=200MeV).