General Equation Of State Research Articles

A coupled thermal-elastic-plastic-damage model for concrete subjected to dynamic loading

A coupled thermal-elastic-plastic-damage model for concrete subjected to dynamic loading is proposed. This model is formulated in the thermodynamic framework, with the adoption of critical state concept, bounding surface plasticity and continuum damage model (small strain being assumed). The contributions of temperature change, plasticity hardening/softening, damage evolution have been taken into account, with cross coupling effects among temperature, damage, strain rate and plasticity being considered through the consistent condition of thermodynamic model. Specifically, the variation of dynamic yield surface depends on the level of mean pressure, damage evolution, strain rate and plastic strain, which can be expressed through a general hardening law in bounding surface plasticity. The extension or contraction of dynamic bounding surface has been described by both compression and extension parts. For the consideration of higher strain rates and ultimately high pressures, the relationship between volumetric strain-mean pressure has been expressed through a more general equation of state (GEOS), which is different from traditional equation of state (EOS) under impact loading. This model has been validated through modelling extensive experimental results in literature, with good agreement among modelling results and experimental data being achieved. All model parameters are measurable physical entities and can be calibrated through conventional experimental approach or taken from literature.

Hyperbolic discretization of simplified Euler equation via Riemann invariants

We are interested in numerical schemes for the simulation of large scale gas networks. Gas transport is described by a simplified Euler equation with a general equation of state for the pressure, including in particular the isentropic as well as the isothermal case. The numerical scheme is based on transformation of conservative variables in Riemann invariants and its corresponding numerical discretization. A novelty of the proposed method is the possibility to allow for an efficient discretization of the boundary and coupling conditions at nodal points of the network, as well as obtaining well balanced schemes. The proposed discretization is analysed in view of its property to correctly recover steady states as well as to resolve possible analytic solutions. Comparisons with existing methods are presented.

A general equation of state for high density matter from thermodynamic symmetry

A general and simple equation of state (EOS) is a rich source for research and discussion. Experience shows that high-density matter exhibits simple regularities and some “universal” EOSs have been established. Here, we present an ideal dense matter EOS that is symmetric to the ideal gas EOS by means of Oettingen's dual approach. The ideal dense matter EOS makes no assumptions about the structure of matter and is, therefore, general. Thermodynamic symmetry requires that the ideal dense matter EOS has better agreements with matter at higher densities, which is supported by some empirical equations and actual property data of various substances. Two derivative variables that have historically been overlooked, i.e., the specific work at constant entropy and the specific work at constant temperature, are rejuvenated in the ideal dense matter EOS. Additionally, we find another physical constant related to thermodynamic property of matter symmetric to the ideal gas constant and further give its estimated values for several common substances. Thermodynamic symmetry suggests that the ideal dense matter EOS has the same theoretical location as the ideal gas EOS. It is another basis for the EOS theory and enriches the dual framework of thermodynamics.

Shock polars for non-polytropic compressible potential flow

<p style='text-indent:20px;'>We consider compressible potential flow for general equations of state. Assuming hyperbolicity and convex equation of state, we prove that shock polars have a unique critical point (in each half), as well as a unique sonic point, with critical and strong shocks always on the subsonic side. We also show existence of normal and oblique shocks, as well as monotonicity of density, enthalpy, pressure along each half-polar, with Mach number monotone only along the subsonic part.</p>

Separable Hamiltonian PDEs and Turning Point Principle for Stability of Gaseous Stars

AbstractWe consider stability of nonrotating gaseous stars modeled by the Euler‐Poisson system. Under general assumptions on the equation of states, we proved a turning point principle (TPP) that the stability of the stars is entirely determined by the mass–radius curve parametrized by the center density. In particular, the stability can only change at extrema (i.e., local maximum or minimum points) of the total mass. For a very general equations of state, TPP implies that for increasing center density the stars are stable up to the first mass maximum and unstable beyond this point until the next mass extremum (a minimum). Moreover, we get a precise counting of unstable modes and exponential trichotomy estimates for the linearized Euler‐Poisson system. To prove these results, we develop a general framework of separable Hamiltonian PDEs. The general approach is flexible and can be used for many other problems, including stability of rotating and magnetic stars, relativistic stars, and galaxies. © 2021 Wiley Periodicals LLC.

New opportunities for axion dark matter searches in nonstandard cosmological models

We study axion dark matter production from a misalignment mechanism in scenarios featuring a general nonstandard cosmology. Before the onset of Big Bang nucleosynthesis, the energy density of the universe is dominated by a particle field ϕ described by a general equation of state ω. The ensuing enhancement of the Hubble expansion rate decreases the temperature at which axions start to oscillate, opening this way the possibility for axions heavier than in the standard window. This is the case for kination, or in general for scenarios with ω > 1/3. However, if ω < 1/3, as in the case of an early matter domination, the decay of ϕ injects additional entropy relative to the case of the standard model, diluting this way the preexisting axion abundance, and rendering lighter axions viable. For a misalignment angle 0.5 < θ_i < π/√(3), the usual axion window becomes expanded to 4 × 10-9 eV ≲ ma ≲ 2 × 10-5 eV for the case of an early matter domination, or to 2 × 10-6 eV ≲ ma ≲ 10-2 eV for the case of kination. Interestingly, the coupling axion-photon in such a wider range can be probed with next generation experiments such as ABRACADABRA, KLASH, ADMX, MADMAX, and ORGAN. Axion dark matter searches may therefore provide a unique tool to probe the history of the universe before Big Bang nucleosynthesis.

Determination of the symmetry groups of radiation hydrodynamics equations and the compatible equations of state and opacities

The purpose of this study was to find all the symmetry groups of the radiation hydrodynamics equations with no a priori assumptions on the equations of state (EOS) and opacities. As shown in earlier works, the application of the Lie group technique to such a system of equations leads to invariance conditions in the form of linear differential equations, which, up until now, were only partially solved. In this paper, using the same technique and under the same assumptions, but with a simpler formulation, we show that these equations can be entirely solved analytically. This result enables us to list all the one-parameter groups that may be symmetry groups of the system. To be actually so, they must be associated with suitable EOS and opacities whose general expressions are also given. The interesting point is that some of them can be chosen so as to fit realistic data for EOS and opacities. Using this property, we propose a method to design low-scale experiments to simulate radiative processes, which would involve too much energy to have experimented with at their full scale. In addition, we derive the reduced systems associated with the one-parameter symmetry groups found. We show that some classical self-similar problems can be extended to more general EOS and opacities, and we treat in detail the self-similar expansion of a semi-infinite medium submitted to an internal source of energy.

A 𝑃1 Finite Element Method for a Distributed Elliptic Optimal Control Problem with a General State Equation and Pointwise State Constraints

Abstract We investigate a P 1 P_{1} finite element method for an elliptic distributed optimal control problem with pointwise state constraints and a state equation that includes advective/convective and reactive terms. The convergence of this method can be established for general polygonal/polyhedral domains that are not necessarily convex. The discrete problem is a strictly convex quadratic program with box constraints that can be solved efficiently by a primal-dual active set algorithm.

The Effect of Functional Groups on the Phase Behavior of Carbon Dioxide Binaries and Their Role in CCS.

In recent years we have focused our efforts on investigating various binary mixtures containing carbon dioxide to find the best candidate for CO2 capture and, therefore, for applications in the field of CCS and CCUS technologies. Continuing this project, the present study investigates the phase behavior of three binary systems containing carbon dioxide and different oxygenated compounds. Two thermodynamic models are examined for their ability to predict the phase behavior of these systems. The selected models are the well-known Peng–Robinson (PR) equation of state and the General Equation of State (GEOS), which is a generalization for all cubic equations of state with two, three, and four parameters, coupled with classical van der Waals mixing rules (two-parameter conventional mixing rule, 2PCMR). The carbon dioxide + ethyl acetate, carbon dioxide + 1,4-dioxane, and carbon dioxide + 1,2-dimethoxyethane binary systems were analyzed based on GEOS and PR equation of state models. The modeling approach is entirely predictive. Previously, it was proved that this approach was successful for members of the same homologous series. Unique sets of binary interaction parameters for each equation of state, determined for the carbon dioxide + 2-butanol binary model system, based on k12–l12 method, were used to examine the three systems. It was shown that the models predict that CO2 solubility in the three substances increases globally in the order 1,4-dioxane, 1,2-dimethoxyethane, and ethyl acetate. CO2 solubility in 1,2-dimethoxyethane, 1.4-dioxane, and ethyl acetate reduces with increasing temperature for the same pressure, and increases with lowering temperature for the same pressure, indicating a physical dissolving process of CO2 in all three substances. However, CO2 solubility for the carbon dioxide + ether systems (1,4-dioxane, 1,2-dimethoxyethane) is better at low temperatures and pressures, and decreases with increasing pressures, leading to higher critical points for the mixtures. By contrast, the solubility of ethyl acetate in carbon dioxide is less dependent on temperatures and pressures, and the mixture has lower pressures critical points. In other words, the ethers offer better solubilization at low pressures; however, the ester has better overall miscibility in terms of lower critical pressures. Among the binary systems investigated, the 1,2-dimethoxyethane is the best solvent for CO2 absorption.

On quasineutral plasma flow in the magnetic nozzle

Exact solutions for quasineutral plasma acceleration of magnetized plasma in the paraxial magnetic nozzle are obtained. It is shown that the non-monotonic magnetic field with a local maximum of the magnetic field is a necessary condition for the formation of the quasineutral accelerating potential structure. A global nature of the accelerating potential that occurs as a result of the constraint due to the regularity condition at the sonic point is emphasized, and properties of such solutions are discussed for the case of general polytropic equation of state for electrons.

Probing non-Gaussianities with the high frequency tail of induced gravitational waves

We investigate in detail the spectrum of gravitational waves induced by a peaked primordial curvature power spectrum generated in single-field inflationary models. We argue that the f NL parameter can be inferred by measuring the high frequency spectral tilt of the induced gravitational waves. We also show that the intrinsically non-Gaussian impact of f NL in ΩGW is to broaden its peak, although at a negligible level in order not to overproduce primordial black holes. We discuss possible degeneracies in the high frequency spectral tilt between f NL and a general equation of state of the universe w. Finally, we discuss the constraints on the amplitude, peak and slope (or equivalently, f NL) of the primordial power spectrum by combining current and future gravitational wave experiments with limits on μ distortions from the cosmic microwave background.

Thin-shell wormhole from ABGB–de Sitter black holes

A thin shell wormhole is constructed utilizing the cut and paste technique from ABGB–de Sitter black hole derived by Matyjasek et al. The surface stress localized at the wormhole throat is determined using Darmois–Israel formalism. We examine the attractive and repulsive nature of the thin shell wormhole on which cosmological constant [Formula: see text] has a significant effect. For the fixed values of charge [Formula: see text] and mass [Formula: see text], the attractiveness of the wormhole decreases with increasing [Formula: see text]. We calculate the total amount of exotic matter in the shell, which is not much affected by [Formula: see text]. For the construction of the wormhole in de Sitter universe, the regular black holes have to be heavily charged with a light mass to minimize the amount of required exotic matter. The stability of the wormhole solution is explored by considering a general equation of state in the form of linear perturbation. The stability regions are shown in the figures.

Modeling and testing the equation of state for (Early) dark energy

A general equation of state is considered for analyzing the possible behaviors for (Early) dark energy that alleviates the Hubble parameter tension problem. By departing from the possible evolution for the (Early) dark energy density and the corresponding dynamical equations, the equation of state is obtained, which allow us to analyze qualitatively the cosmological evolution and the dominance of each term in the equation of state along the cosmic expansion, which show some interesting consequences as the occurrence of (past) future singularities. Then, by considering two general models, their free parameters are fit with different sources of data, showing the goodness of the fits in comparison to more standard models. Results might be considered as a promising starting point to get a better understanding of the cosmological evolution as a whole.

Minimally deformed wormholes

This work is devoted to the study of wormhole solutions in the framework of gravitational decoupling by means of the minimal geometric deformation scheme. As an example, to analyze how this methodology works in this scenario, we have minimally deformed the well-known Morris–Thorne model. The decoupler function f(r) and the theta -sector are determined considering the following approaches: (i) the most general linear equation of state relating the theta _{mu nu } components is imposed and (ii) the generalized pseudo-isothermal dark matter density profile is mimicked by the temporal component of the theta -sector. It is found that the first approach leads to a non-asymptotically flat space-time with an unbounded mass function. To address this issue we have matched both the wormhole and the Schwarzschild vacuum solutions, via a thin-shell at the junction surface. Using the second approach, it can be seen that, on one hand, the solution for gamma =1 does not give place to a bounded mass and it presents a topological defect at large distances; on the other hand, the wormhole manifold is asymptotically flat in the gamma =2 case. In order to satisfy the flare-out condition, we have found restrictions on the value of the alpha parameter, which is related with the amount of exotic matter distribution. Finally, the averaged weak energy condition has been analyzed by using the volume integral quantifier.

A multi-resolution method for two-phase fluids with complex equations of state by binomial solvers in three space dimensions

In this paper, we propose approximate solvers for two-phase fluids with general equations of state (EOS) in high dimension. The standard finite volume scheme is used for each fluid away from material interface. The two-phase interfaces are captured by the level set method coupled with a multi-resolution algorithm. For the Riemann solver of two-phase fluids with general equations of state, we construct an iterative approximation method by the solver for binomial equations of state. The velocity of the interface and the interface exchange fluxes are obtained precisely. With the help of the adaptive multi-resolution algorithms, we extend the method to three space dimensions conveniently. Numerical examples are carried out to demonstrate the strength and robustness of this method.

Interactions of Rarefaction Waves and Rarefaction Shocks of the Two-Dimensional Compressible Euler Equations with General Equation of State

We consider two types of wave interactions arising from the expansion of a wedge of gas to vacuum: interaction of rarefaction waves and interaction of shock-rarefaction composite waves. In order to construct the solutions to these wave interactions, we consider a standard Goursat problem and a discontinuous Goursat problem for the two-dimensional self-similar Euler system. Global solutions to these Goursat problems are constructed by the method of characteristics. The main difficulty to construct the global solutions is that the type of the 2D self-similar Euler system is a priori unknown. By constructing invariant regions of the characteristic angles, we obtain the hyperbolicity of the system in the interaction regions. The solutions constructed in this paper can be used as building blocks of solutions to 2D Riemann problems of the Euler equations with general equations of state.

Rheological characterization of coconut cream emulsion using steady-state shear and time-dependent modeling

The rheological properties of raw coconut-cream emulsion (RCCE) were evaluated under various shear rates (0–500 s −1 ) and temperatures (10 °C–50 °C) through steady-state shear and time-dependent modeling. Thixotropic behavior of the samples was observed at all temperatures tested, and it decreased with increased temperature. The Power law model was found to better fit the obtained data. The effects of temperature on regression parameters, namely, the Arrhenius and Turian relations were explored by approaches. The modeling parameters were assessed under the combined impacts of shearing and temperature, resulting in two generalized state equations governing the RCCE steady-state flow behavior. The extent and rate of thixotropy were measured with the Weltmann model, and the structural kinetics model was found to best describe the time-dependent behavior of RCCE. In conclusion, the structural breakdown was found in stress-decay tests at a high shear rate of 250 s −1 and a relatively high temperature of 50 °C. • Raw coconut cream emulsion exhibits thixotropic behavior at all temperatures tested. • Thixotropicity reduces with increasing temperature from 10 to 50 °C. • Weltmann model and SKM approach best describe time-dependent behavior. • The structural breakdown is evident in the high shearing & high temperature.

Transonic flows of single-phase supercritical fluids over thin airfoils

Abstract

Self-gravitating Equilibria of Non-minimally Coupled Dark Matter Halos

Abstract We investigate self-gravitating equilibria of halos constituted by dark matter (DM) non-minimally coupled to gravity. In particular, we consider a theoretically motivated non-minimal coupling that may arise when the averaging/coherence length L associated with the fluid description of the DM collective behavior is comparable to the local curvature scale. In the Newtonian limit, such a non-minimal coupling amounts to a modification of the Poisson equation by a term L 2∇2 ρ proportional to the Laplacian of the DM density ρ itself. We further adopt a general power-law equation of state p ∝ ρ Γ r α relating the DM dynamical pressure p to density ρ and radius r, as expected for phase-space density stratification during the gravitational assembly of halos in a cosmological context. We confirm previous findings that, in the absence of non-minimal coupling, the resulting density ρ(r) features a steep central cusp and an overall shape mirroring the outcomes of N-body simulations in the standard ΛCDM cosmology, as described by the classic Navarro–Frenk–White or Einasto profiles. Most importantly, we find that the non-minimal coupling causes the density distribution to develop an inner core and a shape that closely follows the Burkert profile out to several core scale radii. In fact, we highlight that the resulting mass distributions can fit, with an accuracy comparable to Burkert’s one, the coadded rotation curves of dwarf, DM-dominated galaxies. Finally, we show that non-minimally coupled DM halos are consistent with the observed scaling relation between the core radius r 0 and core density ρ 0, in terms of a universal core surface density ρ 0 × r 0 among different galaxies.

Two component phase equilibria for the 3-methoxy-3-methyl-1-butanol and 1-methoxy-2-methyl-2-propanol in supercritical carbon dioxide

Two component mixtures, 3-methoxy-3-methyl-1-butanol (MMB)+carbon dioxide and 1-methoxy-2-methyl-2-propanol (MMP)+carbon dioxide, were investigated at 313.2, 333.2, 353.2, 373.2 and 393.2 K and at 4.29 to 20.95 MPa to get phase equilibrium data. The phase separation of vapor+liquid behavior for the MMB and MMP plays a momentous function as the organic solvent in a diversity of industrial processes. The two MMB+carbon dioxide and MMP+carbon dioxide components have mixture critical curves that have maxima in the p-T plot between the Tc (critical temperatures) of MMB and carbon dioxide or MMP and carbon dioxide. The two component systems of MMB+ carbon dioxide and MMP+carbon dioxide mixture display type-I in simplest behavior. The measured results for the two component mixtures, MMB+carbon dioxide and MMP+carbon dioxide, are modelled with a general cubic equation of state, the Peng-Robinson, containing the kij, ηij adjustable factor.