Corresponding Equations Of State Research Articles

Exploration of GUP-corrected Casimir wormholes in extended teleparallel gravity with matter coupling

In this manuscript, we investigate the properties of Casimir wormholes within the framework of extended teleparallel gravity, incorporating the Generalized Uncertainty Principle. Both the Casimir effect and the Generalized Uncertainty Principle (GUP) originate from the concept of a fundamental minimum length. Our analysis explores the geometric and physical traits of these wormholes, examining two distinct GUP constructions namely the Kempf, Mangano, and Mann (KMM) model and the Detournay, Gabriel, and Spindel (DGS) model and their corresponding equations of state. We find that the resulting wormhole solutions exhibit anisotropic effects and violate the null energy condition, implying the presence of exotic fluid. By employing volume integral techniques, we compute the quantity of exotic fluid, providing new insights into the nature of these wormholes. Our study sheds light on the implications of GUP-corrected Casimir wormholes for our understanding of gravity and the structure of spacetime.

Perfect-fluid, generalized Robertson-Walker space-times, and Gray’s decomposition

We give new necessary and sufficient conditions on the Weyl tensor for generalized Robertson-Walker (GRW) space-times to be perfect-fluid space-times. For GRW space-times, we determine the form of the Ricci tensor in all the O(n)-invariant subspaces provided by Gray's decomposition of the gradient of the Ricci tensor. In all but one, the Ricci tensor is Einstein or has the form of perfect fluid. We discuss the corresponding equations of state that result from the Einstein equation in dimension 4, where perfect-fluid GRW space-times are Robertson-Walker.

Equations of State of different phases of dense quark matter

Compact stars with significant high densities in their interiors can give rise to quark deconfined phases that can open a window for the study of strongly interacting dense nuclear matter. Recent observations on the mass of two pulsars, PSR J1614-2230 and PSR J0348+0432, have posed a great restriction on their composition, since their equations of state must be hard enough to support masses of about at least two solar masses. The onset of quarks tends to soften the equation of state, but due to their strong interactions, different phases can be realized with new parameters that affect the corresponding equations of state and ultimately the mass-radius relationships. In this paper I will review how the equation of state of dense quark matter is affected by the physical characteristics of the phases that can take place at different baryonic densities with and without the presence of a magnetic field, as well as their connection with the corresponding mass-radius relationship, which can be derived by using different models.

Spatially open Friedmann–Robertson–Walker Universe fueled with interacting sources

In the present paper, we are analyzing the $k=-1-$FRW Universe with two interacting ideal fluids. The energy densities and the pressures are used to derive the corresponding Equations of State. For a particular form of the interaction term between the two fluids, it turns out that the Universe is filled with a mixture of dust and radiation.

Nonlinear positive/negative thermal expansion and equations of state of a chain with longitudinal and transverse vibrations

AbstractThermal expansion of a classical chain with pair interactions performing longitudinal and transverse vibrations is investigated. Corresponding equations of state are derived analytically using series expansions of pressure and thermal energy with respect to deformations of the bonds caused by thermal motion. In the first approximation the equation of state has Mie–Grüneisen form. The dependence of Grüneisen parameter on deformation of the chain is obtained. For Lennard‐Jones‐like potential Grüneisen parameter varies with deformation from minus infinity (at zero stretching) to plus infinity (at the breakage point). Necessary and sufficient condition for negative thermal expansion at low thermal energies is formulated. Using this condition the potential giving rise to negative thermal expansion in the given range of deformations can be designed. It is shown that at small deformations and finite thermal energies Mie–Grüneisen equation of state strongly overestimates the absolute value of pressure. More accurate nonlinear equation of state is derived for this case. The equation implies that thermal pressure in the unstretched chain is proportional to square root of thermal energy. In the vicinity of the deformation, corresponding to zero Grüneisen parameter, the chain demonstrates negative thermal expansion at low temperatures and positive thermal expansion at higher temperatures. This phenomenon is qualitatively described by the nonlinear equation of state derived in the present paper. The theoretical findings are supported by the results of molecular dynamics simulations.

Efficient implementation of high order unstructured WENO schemes for cavitating flows

In this article we present a new efficient implementation of high order accurate Godunov-type WENO finite volume schemes on unstructured triangular and tetrahedral meshes for the simulation of real fluids with complex equations of state. The main focus of this paper is the efficient computation of flows in compressible mixtures of liquid and vapor in multiple space-dimensions, including the onset of cavitation. In the present article we use the full equation of state (EOS) for water, vapor and wet steam in thermal equilibrium based on the industrial and scientific standard IAPWS-IF97, as well as the real equation of state for n-heptane provided by Span and Wagner. Since the direct evaluation of these very complex EOS is computationally very expensive, we propose a new robust, accurate and particularly efficient approach for their evaluation in high order Godunov type finite volume schemes. It is based on the L2 projection of the EOS (ρ, e)→(p, T) onto the space of piecewise polynomials of degree q using an adaptive mesh refinement (AMR) approach together with Cartesian cut-cells, which adjusts the grid of the phase space (ρ, e) so that the L∞ error of the L2-projection of the EOS is less than a given error threshold ∊. For a thorough validation of our numerical approach we construct several quasi-exact solutions to the Riemann problem for water and n-heptane using the corresponding detailed equations of state. We furthermore present numerical convergence results of third and fourth order schemes for an unsteady two-dimensional test problem for water with real EOS. We furthermore show the onset of cavitation on a simple model problem with an initially purely liquid fluid at ambient conditions at rest using a strong heat source term in the energy equation as well as the development of a cavitation bubble due to strong rarefaction. Finally, some numerical test problems are solved with the new approach on unstructured triangular and tetrahedral meshes in multiple space dimensions.

Statistical mechanics of Beltrami flows in axisymmetric geometry: equilibria andbifurcations

We characterize the thermodynamical equilibrium states of axisymmetric Euler–Beltramiflows. They have the form of coherent structures presenting one or several cells. We find therelevant control parameters and derive the corresponding equations of state. Weprove the coexistence of several equilibrium states for a given value of the controlparameter like in 2D turbulence (Chavanis and Sommeria 1996 J. Fluid Mech.314 267). We explore the stability of these equilibrium states and show that allstates are saddle points of entropy and can, in principle, be destabilized by aperturbation with a larger wavenumber, resulting in a structure at the smallestavailable scale. This mechanism is reminiscent of the 3D Richardson energy cascadetowards smaller and smaller scales. Therefore, our system is truly intermediatebetween 2D turbulence (coherent structures) and 3D turbulence (energy cascade).We further explore numerically the robustness of the equilibrium states withrespect to random perturbations using a relaxation algorithm in both canonical andmicrocanonical ensembles. We show that saddle points of entropy can be veryrobust and therefore play a role in the dynamics. We evidence differences in therobustness of the solutions in the canonical and microcanonical ensembles. Ascenario of bifurcation between two different equilibria (with one or two cells) isproposed and discussed in connection with a recent observation of a turbulentbifurcation in a von Kármán experiment (Ravelet et al 2004 Phys. Rev. Lett. 93 164501).

Structures, compressibilities and relative stabilities of the , and phases of Mg2SiO4 deduced from an electron-gas ionic Hamiltonian

The properties of forsterite (α-Mg2SiO4) and its high-pressure polymorphs wadsleyite (β-Mg2SiO4) and ringwoodite (γ-Mg2SiO4) play an important role in the chemical, dynamic and elastic behaviour of the upper 660 km of the Earth's mantle. Mineralogists have tended to rationalize their structures in terms of empirical ionic models, guided by Pauling's rules. Modern electron-gas theory of ionic interactions is accurate enough to encourage a detailed study of the structure and properties of these minerals within an intuitively appealing ionic model that is independent of empirical data. We therefore undertook to obtain the minimum-energy lattice structures, and their corresponding equations of state, of electron-gas models of the Mg2SiO4 polymorphs. We find that the model densities compare very well with actual observations, while compressibilities are somewhat underestimated. Unit cell geometries are also accurately represented, but coordination polyhedra tend to be more distorted than those observed, mainly because of excessive bond-angle variance. We also found that Pauling's rules do not offer a complete accounting for the observed stability of olivine at low pressures. Instead, in the model crystals it is a difference in the magnitude of the Mg–O repulsions that give olivine the energetic advantage. The higher density of ringwoodite, and a rapidly increasing Mg–O repulsion energy in olivine stabilize ringwoodite at high pressure.

Non-newtonian shear viscosity, normal stress coefficients and corresponding states in rheology

A set of mutually consistent material functions, i.e., shear viscosity, primary normal stress, and secondary normal stress coefficients, is presented. They were originally derived by means of a dense-simple-fluid kinetic theory. It is shown that in spite of their origin the material functions can account for the shear rate dependences of rheological material functions for some polymer solutions, if the formulas are treated as phenomenological functions of shear rate. It is also shown that the material functions used are in fact a set of corresponding state rheological equations of state to a good accuracy for the materials examined.