Equation Of State In Order Research Articles

Evolution of magnetic fields and cosmic ray acceleration in supernova remnants

Observations show that the magnetic field in young supernova remnants (SNRs) is significantly stronger than can be expected from the compression of the circumstellar medium (CSM) by a factor of four expected for strong blast waves. Additionally, the polarization is mainly radial, which is also contrary to expectation from compression of the CSM magnetic field. Cosmic rays (CRs) may help to explain these two observed features. They can increase the compression ratio to factors well over those of regular strong shocks by adding a relativistic plasma component to the pressure, and by draining the shock of energy when CRs escape from the region. The higher compression ratio will also allow for the contact discontinuity, which is subject to the Rayleigh–Taylor (R–T) instability, to reach much further out to the forward shock. This could create a preferred radial polarization of the magnetic field. With an Adaptive Mesh Refinement MHD code (AMRVAC), we simulate the evolution of SNRs with three different configurations of the initial CSM magnetic field, and look at two different equations of state in order to look at the possible influence of a CR plasma component. The spectrum of CRs can be simulated using test particles, of which we also show some preliminary results that agree well with available analytical solutions.

Neutrino‐cooled Accretion Disk and Its Stability

We investigate the structure and stability of hypercritical accretion flows around stellar-mass black holes, taking into account neutrino cooling, lepton conservation, and firstly a realistic equation of state in order to properly treat the dissociation of nuclei. We obtain the radial distributions of physical properties, such as density, temperature and electron fraction, for various mass accretion rates $0.1\sim 10M_{\odot}{\rm s}^{-1}$. We find that, depending on mass accretion rates, different physics affect considerably the structure of the disk; most important physics is (1) the photodissociation of nuclei around $r\sim 100r_g$ for relatively low mass accretion rates ($\dot{M}\sim 0.01-0.1M_{\odot} {\rm s}^{-1}$), (2) efficient neutrino cooling around $r\sim 10-100r_g$ for moderately high mass accretion rate ($\dot{M}\sim 0.2-1.0M_{\odot}{\rm s}^{-1}$), and (3) neutrino trapping ($r\sim 3-10r_g$) for very high mass accretion rate ($\dot{M}\gtrsim 2.0M_{\odot}{\rm s}^{-1}$). We also investigate the stability of hypercritical accretion flows by drawing the thermal equilibrium curves, and find that efficient neutrino cooling makes the accretion flows rather stable against both thermal and viscous modes.

Fluctuation approach for the estimation of the dynamic heterogeneity in glass-forming liquids from the dispersion in o-Ps lifetimes: Free volume fluctuations in polymers

Positron annihilation lifetime spectra are analyzed with respect to the mean, τ3, and mean dispersion, σ3, of ortho-positronium lifetimes using the new routine LifeTime, version 9.0, which assumes a log-Gaussian distribution of annihilation rates λ=1/τ. From these data the size distribution of subnanometer local free volumes (holes) characterized by their mean, 〈vh〉, and mean dispersion, σh=〈δvh2〉1/2, is derived. Pressure–volume–temperature experiments are analyzed employing the Simha–Somcynsky equation of state in order to obtain the fractional, h, and the specific, Vf=hV, hole free volume and its expansivity and compressibility. From comparison of Vf with 〈vh〉 the specific number of holes Nh′ is estimated. It is assumed that the hole size dispersion mirrors directly the fluctuation in the free volume as long as the relaxation time of structural motion is larger than the ortho-positronium lifetime of a few nanoseconds. The mean fluctuation in the fractional and specific free volume is calculated. Starting from a fluctuation approach the mean size of the smallest subvolume 〈VSV〉 representative for structural relaxations is estimated. This volume is assumed to be closely related to the volume of a cooperatively rearranging region and to mirror the dynamic heterogeneity. Limits of this interpretation and specific features of PALS are discussed. The variation of the subvolume with temperature and pressure is analyzed. A different behavior of 〈vh〉 and σh is interpreted in terms of Donth’s theory of dynamic glass transition heterogeneity.

A Reference Multiparameter Viscosity Equation for R134a with an Optimized Functional Form

An optimization technique was applied to develop a functional form for a multiparameter viscosity equation η=η(ρ,T) for R134a. The results obtained are very promising, with an average absolute deviation of 0.55% for the currently available 549 primary data points. Compared to viscosity equations available in the literature, this is a significant improvement. Advantages become evident especially at gaseous states. As usual, both the development and the use of the viscosity equation require a highly accurate equation of state in order to convert the independent variables used for the experimental data and in most applications, (P,T), into the independent variables of the viscosity equation, (ρ,T). Though the equation was developed directly using the available data, the zero-density viscosity and the reduced second viscosity virial coefficient are correctly reproduced in the data range. The technique used to develop the equation, which is heuristic and not theoretically founded, is capable of selecting consistent data sets and thus is a powerful tool for screening the available experimental data. For the viscosity surface representation of a pure fluid this study shows that the limit in the achievement of a better accuracy is much more due to the present experimental uncertainty level for this property rather than to the effectiveness of the proposed modeling method.

A variational method in design optimization and sensitivity analysis for aerodynamic applications

Variational method is applied to the state equations in order to derive the costate equations and their boundary conditions. Thereafter, the analyses of the eigenvalues of the state and costate equations are performed. It is shown that the eigenvalues of the Jacobean matrices of the state and the transposed Jacobean matrices of the costate equations are analytically and numerically the same. Based on the eigenvalue analysis, the costate equations with their boundary conditions are numerically integrated. Numerical results of the eigenvalues problems of the state and costate equations and of a maximization problem are finally presented.

Adaptive nonlinear guidance law considering control loop dynamics

A new adaptive nonlinear guidance law is proposed here. The fourth order state equation for integrated guidance and control loop is formulated taking into consideration the target uncertainties and control loop dynamics. The state equation is further changed into the normal form by nonlinear coordinate transformation. Using the normal form of state equation, an adaptive nonlinear guidance law is proposed to compensate for the uncertainties in both target acceleration and control loop dynamics. The proposed law adopts the sliding mode control approach with adaptation for unknown bound of uncertainties. The present approach can effectively solve the existing guidance problem against target maneuver and the limited performance of control loop. We have provided the stability analyses and performed simulations comparing favorably our approach to the state of the art.

Instantaneous optimal method for vibration control of linear sampled-data systems with time delay in control

In an actively controlled system, time delay exists inevitably. Neglecting time delay may cause degradation of control performance or even induce instability to the dynamic system. In this paper, instantaneous optimal control method for vibration control of linear sampled-data systems with time delay in control is investigated. By a peculiar integral transformation, the first order state equation with time delay is transformed into the standard first order state equation, which contains no time delay. Then the optimal controller is designed based on the numerical algorithm of the regular fourth order Runge–Kutta method. Since the obtained controller contains integral term, which is not practical for control implementation, the numerical algorithm for this integral term is investigated too. Since the controller is deduced directly from the time-delay differential equation, the control method presented is prone to guarantee system stability. Thus the presented control method can be applicable to the case of large time delay. The performance of the control method is demonstrated by numerical simulation. Simulation results indicate that this control method is feasible and is an attractive strategy for dealing with the time delay in vibration control systems and is effective in suppressing maximum structural responses. Instability in structural responses may occur if the systems with time delay are controlled using the controller designed in the case of no time delay.

목표물의 불확실성과 제어루프 특성을 고려한 비선형 적응 유도기법

This paper proposes a new nonlinear adaptive guidance law. Fourth order state equation for integrated guidance and control loop is formulated considering target uncertainties and control loop dynamics. The state equation is further changed into the normal form by nonlinear coordinate transformation. An adaptive nonlinear guidance law is proposed to compensate for the uncertainties In both target acceleration and control loop dynamics. The proposed law adopts the sliding mode control approach with adaptation fer unknown bound of uncertainties. The present approach can effectively solve the existing guidance problem of target maneuver and the limited performance of control loop. We provide the stability analyses and demonstrate the effectiveness of our scheme through simulations.

Influence of the counter-ion on the effective charge of polyacrylic acid in dilute condition

Osmotic pressure measurements were satisfactorily used to compute the effective charge of poly(acrylic) acid (PAA) at different pHs and with different monovalent and divalent counterions. This experimental method is sensitive to the osmotically active species (polymer and counterions). After correction for the polymer contribution to the total osmotic pressure (solvency and excluded volume), the remaining pressure can be attributed to the polyelectrolyte counterions and processed with Donnan and equation of state in order to compute the effective charge number per polymeric chain ( Z eff). The behavior of Z eff against the chain concentration and pH was investigated after neutralization of PAA with LiOH, NaOH, and TMAOH. The results clearly indicate that the nature of the monovalent counterion has no effect on Z eff leading to the conclusion that the interaction between monovalent counterions and the acrylate functionality is purely electrostatic in agreement with conductimetric and potentiometric results reported in the literature. The behavior of Z eff against the degree of ionization of the polymer and its concentration is also in good agreement with the theoretical expectations of the theory of ionic condensation. Osmotic measurements were also used in order to understand the influence of divalent cations (Mg 2+, Ca 2+, Ba 2+) on Z eff of the sodium salt of PAA at pH 9 and at different divalent/acrylate molar ratio. All the divalent cations depress Z eff each of one at different degrees, confirming a specific divalent/polymer interaction. The energy of hydration of cations can explain most of the observed results with divalents.

A direct injection diesel combustion model for use in transient condition analysis

A phenomenological multizone combustion model is developed for use in the transient condition analysis of a turbocharged direct injection (DI) diesel engine. The main processes in the cylinder, such as spray penetration, droplet evaporation, air-fuel mixing, spray wall interaction, ignition and fuel combustion, are taken into consideration. In order to predict cylinder pressure and NOx emissions in a wide range of engine speeds, loads and air-fuel ratios under transient conditions, the model has been improved in many respects, especially in the velocity distribution of fuel spray, zonal entrainment and the calculation of gas properties and chemical equilibrium compositions of combustion products including solid carbon. With respect to the turbocharged engine with a high pressure in the cylinder, the compression factor is added to the ideal gas equation of state in order to simulate cylinder pressure accurately. Cylinder pressure, heat release and NOx emission histories for different operating conditions are calculated for two types of engines. The agreement between calculated and measured results is good for a wide range of operating conditions. This indicates that the model has the ability to predict cylinder pressures and NOx emissions in both steady state and transient operating conditions.

Statistical Associating Fluid Theory. 1. Application toward Describing Isoparaffins

We apply recent advances in perturbation theory-based equation of state models to correlate thermodynamic property data for pure compounds. Parameters for the equation of state were regressed for over 240 compounds, including a number of homologous series and branched paraffins. We find that the equation of state is capable of quantitatively correlating all of the pure-component experimental data we tested. Our primary interest, however, is to look for trends in the parameters of the equation of state in order to extrapolate to properties of other types of molecules. For isoparaffins, increased branching for a given carbon number leads to a SAFT model molecule with fewer segments but with larger segment volume and energy parameters. These trends correlate highly with topological descriptors characterizing the degree of branching, suggesting a route toward estimating parameters for molecules for which data are in short supply or do not exist.

One parameter friction theory models for viscosity

In this work the friction theory ( f-theory) for viscosity modeling is used in conjunction with the SRK, PR and PRSV cubic equations of state in order to develop three one parameter general models for viscosity prediction. The models are considered one parameter models because they only require a characteristic critical velocity, which is a parameter normally not tabulated. The models use these rather simple cubic equations of state as a basis to obtain accurate modeling of the viscosity of fluids for wide ranges of temperature and pressure. The general models presented in this work are based on the viscosity behavior of n-alkanes from methane to n-octadecane. Although best performance is obtained for the considered n-alkanes, a good model performance is also obtained for other systems. Thus, recommended characteristic critical viscosity values for several systems are also reported in this work. However, in the case of n-alkanes, an empirical equation for the characteristic critical viscosity is provided so that no additional parameters are required. In addition, with the use of simple mixing rules, the viscosity of several binary to quaternary n-alkane mixtures can also be predicted with a satisfactory accuracy.

Hyperon stars in the Brueckner-Bethe-Goldstone theory

In the framework of the Brueckner-Bethe-Goldstone theory, we determine a fully microscopic equation of state for asymmetric and $\beta$-stable nuclear matter containing $\sim$ and $\la$ hyperons. We use the Paris and the new Argonne $Av_{18}$ two-body nucleon interaction, whereas the nucleon-hyperon interaction is described by the Njimegen soft-core model. We stress the role played by the three-body nucleon interaction, which produces a strong repulsion at high densities. This enhances enormously the hyperon population, and produces a strong softening of the equation of state, which turns out almost independent on the nucleon-nucleon interaction. We use the new equation of state in order to calculate the structure of static neutron stars. We obtain a maximum mass configuration with $M_{\rm max}$ = 1.26 (1.22) when the Paris ($Av_{18}$) nucleon potential is adopted. Central densities are about 10 times normal nuclear matter density. Stellar rotations, treated within a perturbative approach, increase the value of the limiting mass by about 12%.

Numerical modelling of low-temperature laser-produced magnesium plasma

The two-dimensional laser-plasma-interaction hydrodynamic code POLLUX has been used to simulate the ablation of a magnesium target by a 30-ns, 248-nm KrF excimer laser at low laser fluences of ≤10 J cm2. This code, originally written for much higher laser intensities, has been recently extended to include a detailed description of the equation of state in order to treat changes of phase within the target material, and also includes a Thomas Fermi description of the electrons. The simulated temporal and spatial evolution of the plasma plume in the early phase of the expansion (≤100 ns) is compared with experimental interferometric measurements of electron density. The expansion dynamics are in good agreement, although the simulated electron number density is about 2.5 times higher than the experimental values.

An equation of state describing the critical region: extension to high pressure

In this paper, an equation of state is presented, which is able to model the pρT behaviour of fluids in the critical region, in the low-density limit and at high pressure. The equation is developed in the framework of a local mean field model describing density fluctuations in a fluid. This model is based on an earlier developed model, which was employed to describe the pρT behaviour in the critical region for several substances. It is extended here to high pressure. For the representation of the critical isotherm, argon is used as reference substance. In addition to the experimental data taken from the literature, some state points at high pressure are estimated by the Monte-Carlo simulation on the basis of ab-initio pair potentials. These data were included in the development of the equation of state in order to assure physically correct behaviour at high pressure. With this equation, the pρT behaviour of argon, sulfur hexafluoride, methane, ethylene, nitrous oxide and carbon dioxide is modeled.

Covariant solutions of the Bethe-Salpeter equation and an application to the nucleon stucture function

There is a need for covariant solutions of bound state equations in order to construct realistic QCD based models of mesons and baryons. Furthermore, we ideally need to know the structure of these bound states in all kinematical regimes, which makes a direct solution in Minkowski space (without any 3-dimensional reductions) desirable. The Bethe-Salpeter equation (BSE) for bound states in scalar theories is reformulated and solved for arbitrary scattering kernels in terms of a generalized spectral representation directly in Minkowski space This differs from the conventional Euclidean approach, where the BSE can only be solved in ladder approximation after a Wick rotation. An application of covariant Bethe-Salpeter solutions to a quark-diquark model of the nucleon is also briefly discussed.

The Wong-Sandler mixing rules and EOS which are thermodynamically consistent at infinite pressure

Recently, Wang et al. (1996) have developed three different equations of state (EOS) based on the hard-sphere model which, through a rescaling factor in the definition of the dimensionless density, yield the correct close-packed density in the limit of infinite pressure. We derive the expressions for the residual Helmholtz free energy for these three EOS in order to investigate their thermodynamic consistency at infinite pressure, and thus examine the applicability of the Wong-Sandler mixing rules.

Electrostatic Attraction between Two Charged Surfaces: A (N,V,T) Monte Carlo Simulation

We have performed (N,V,T) Monte Carlo simulations in order to study the stability of two parallel charged surfaces (lamellae) neutralized by exchangeable counterions. By varying each parameter characterizing the interface, i.e., the interlamellar separation, the surface charge density of the lamellae, the dielectric constant of the solvent, and the radius and charge of the counterions, we have determined the stability of a wide class of physical situations. The ion−ion, lamella−ion, and lamella−lamella interactions are described within the context of the “primitive model”. We give evidence that, despite the intrinsic simplicity of the primitive model, the phase diagram of such a system exhibits complex patterns. We have determined 2D contour maps of the equation of state in order to localize attracto/repulsive domains and optimize adhesive properties of the interface. This study concerns a large variety of lamellar materials, including hydrated cement and clays, and pillared and organo clays. At low diele...

The phase structure of the 3-d Thirring model

We study the phase structure of the Thirring model in 3-d and find it to be compatible with the existence of a non gaussian fixed point of RG. A Finite Size Scaling argument is included in the equation of state in order to avoid the assumptions usually needed to extrapolate to the thermodymical limit.

Kaon production in hadronic matter

Subthreshold kaon production has been studied in symmetric nucleus-nucleus collisions as a function of the nucleus mass, beam energy and centrality. In Au+Au collsions at 1 AGeV theK+ multiplicity increases more than linearly with increasing number of participating nucleons. Transport calculations have to assume a soft equation of state in order to reproduce the data. The in-mediumK− cross section measured in Ni+Ni collisions is enhanced by about a factor of 7 as compared to the free cross section when using theK+ cross section at equivalent beam energies as a normalization.