A simple and accurate equation of state for hard-disk fluids

A long-standing problem for hard-disk fluids is to find a simple and accurate equation of state. By observing the known updated virial coefficients from up to , we obtain an accurate empirical formula, with errors less than 0.5%. We further assume that the empirical formula is valid for all the virial coefficients. Using this assumption, we obtain a simple and accurate equation of state. In the density range 0<ρa²≤0.83, the predicted pressures are in good agreement with the simulation results. For 0<ρa²≤0.70, the errors are less than 0.007%. Even at ρa²=0.83, the error is only 0.5%.     

Modified hypernetted-chain equation for the ground state of Bose fluids

Summary The modified hypernetted-chain equation is used to study the ground state of Bose fluids in the Jastrow approximation. We test the equation for different forms of the pair interaction and of the Jastrow pseudopotential and in all cases the energy of⁴He is given with an error not larger than 0.1 K at all densities. The effect of a triplet term in the wavefunction is also studied.

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Riassunto L'equazione integrale HNC modificata è applicata allo studio dello stato fondamentale di un fluido di Bose nell'approssimazione di Jastrow per diverse espressioni della interazione binaria e forme diverse della correlazione di Jastrow. In tutti i casi l'energia per⁴He è calcolata con un errore non superiore a 0.1 K a tutte le densità. Si considera inoltre l'effetto di una correlazione a tre corpi nella funzione d'onda.

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Резюме модифицированное уравнение цепочки используется для исследования основного состояния Ъозе-жидкости в приближении Ястрова. Мы проверяем уравнение для различных форм парного взаимодействия и псевдопотенциала Ястрова. Во всех случаях приводится энергия⁴He с погрешностью не более, чем 0.1 K для всех плотностей. Также исследуется влияине триплетного члена на волновую функцию.

     

An equation of state contribution for dipolar and quadrupolar square-well fluids

A dipolar–quadrupolar contribution to the residual Helmholtz energy for a polar square well (a square well plus either a point dipole or a point quadrupole) fluid is developed based on the Padé approximation. Taking the square well system as reference, the contribution is formulated using an expansion for radial distribution function of the reference system. In addition to square well potential parameters the contribution depends only on dipole and quadrupole moments. This term is added as perturbation to a generalized equation of state for square well fluids. The results are then compared with the available simulation data in the literature. With the new equation obtained, it was possible to predict liquid–vapour equilibrium properties and critical properties of polar square well fluids more accurately than with available perturbation theories for multipolar square well systems. Application of the equation of state to a real dipolar (water) and a real quadrupolar (carbon dioxide) fluid indicated that the polar contribution greatly improved the predictions of saturation properties. Accurate prediction of critical properties for polar square well fluids remains as a challenge. This work can be useful in the development of better equations of state.     

Self-consistent density functional theory and the equation of state for simple fluids

The accuracy of the self-consistent density functional theory, based on the idea of universality of the so-called 'bridge functional', is tested by comparison with the extensive simulations for the Lennard-Jones bulk fluid (Johnson et al. 1993, Molec. Phys., 78, 591). In this benchmark test very good agreement with the simulation results is obtained, and thermodynamic consistency is accurately obeyed between the 'Energy', 'Virial (Pressure)', and 'Compressibility' independent routes to the equation of state.     

Empirical evidence for correction terms to the scaling equation of state for magnetic systems

Data in the critical region of magnets are analyzed to give evidence of deviations from scaling behavior. An estimate of the extent of the asymptotic region is obtained.     

On the compressibility equation of state for multi-component adhesive hard sphere fluids

The compressibility equation of state (EOS) for a multi-component sticky hard sphere model alternative to Baxter's one is investigated within the mean spherical approximation (MSA). For this model and this closure, as well as for a more general class of models and closures leading to Baxter functions q_ij(r) with density-independent stickiness coefficients, no compressibility EOS can exist for mixtures, unlike the one-component case (in view of this, an EOS recently reported in the literature turns out to be incorrect). The reason is the failure of the Euler reciprocity relation for the mixed second-order partial derivatives of the pressure with respect to the partial densities. This is in turn related to the inadequacy of the approximate closure (in particular, the MSA). A way out to overcome this drawback is presented in a particular example, leading to a consistent compressibility pressure, and a possible generalization of this result is discussed.     

Perturbation and variational approach for the equation of state for hard-sphere and Lennard-Jones fluids

The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state (EOS) for a mixture of hard sphere (HS), Lennard–Jones (LJ) fluids. A suitable flexible functional form for the radial distribution function G(R) is assumed for the mixture, with R as a variable. The function G(R) has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m. For m = 0.75 and m = 0.83 results are close to molecular dynamics (MD) result for pure HS and LJ fluid respectively.     

A scaling equation of state near the critical point and the stability boundary of a liquid

A new scaling equation of state is proposed to describe the equilibrium thermodynamic properties of liquids near the critical point. In distinction from the existing scaling equations, which are parametric, the new equation is nonparametric and is expressed directly in terms of the physical quantities (pressure, temperature, and so on). It creates a number of advantages for the traditional representation and data processing. The equation gives rise to a binodal, spinodal, and a curve of thermal capacity divergence (pseudospinodal). The equation is expressed in terms of reduced variables (the ratio of the deviation of a thermodynamic variable from its critical value to the critical value) and contains 3 system-dependent adjustable constants. With the help of this equation, we conducted an approximation of the experimental PVT data in the critical region of ⁴He, C₂H₄, and H₂O with a pressure error of 0.4% and carried out a calculation of the C _v ⁴He thermal capacity with no more than 4% error using a three-system constant determined from the PVT data.     

Thermodynamic regularities for non-polar and polar fluids from the modified SAFT-BACK equation of state

We have used the modified SAFT-BACK EOS for its ability to predict three important thermodynamic regularities for several fluids composed of molecules with different geometries and interactions. The studied regularities included: (i) the common bulk-modulus point on the isotherms of the reduced bulk modulus versus reduced density, (ii) near linearity of the reduced isothermal bulk-modulus as a function of reduced pressure, and (iii) Zeno line regularity which describes near linearity of a contour in the temperature-density plane along which the compressibility factor equals unity. In this work, we also reported the influence of the molecular size and shape on the displacement of intersection point of isothermal bulk-modulus curves versus density.     

Photoluminescence asymmetry with quantum state preparation

We show that the number of photons in a strongly coupled exciton–photon system is asymmetric with the detuning of the modes when, in the spontaneous emission regime, the two modes are entangled. As changing the detuning is easy in semiconductor microcavities–where on the other hand the nature of the strong-coupling in terms of single-particle effects is not yet resolved–we propose this effect as a test of the quantum character of microcavity polaritons.     

Solution of Ornstein-Zernike equation for one-dimensional fluids

The application of Wiener-Hopf factorisation procedure as adopted by Baxter has been used to solve the one-dimensional Ornstein and Zernike (oz) equation for a fluid of interacting hard rods. Exact solution is obtained for the Kac potential in the van der Waals limit. We also obtain perturbative results which agree exactly with the lowest order calculations of Kac, Uhlenbeck and Hemmer.     

A contribution to the equation of state of fluids at low temperatures based on thermodynamic Green's functions

In quantum statistical mechanics, the Green's function formalism provides an expression for the density of a fluid as a four-dimensional momentum-energy integral over the spectral function. This function can be expressed in terms of the complex self-energy of the single-particle excited states. By using the ladder diagram approximation, in a low activity limit at which Fermi-Dirac and Bose-Einstein distributions can be approximated by a Boltzmann distribution, the self-energy has been expressed in terms of the two-body scattering amplitude. Density and pressure can then be expressed in terms of the activity, the temperature, and the two-body scattering phase shifts. A complete numerical evaluation of these results has been made for the case of argon at 100K, represented by a hard-sphere plus square-well potential: results are presented for the complex self-energy, the density, and the pressure as a function of activity. The resulting equation of state is compared to experimental results represented by the Beattie-Bridgeman equation and good agreement is found for the gaseous part of the 100K isotherm. Furthermore, two simple analytic equations of state are derived from these expressions with additional (low-density) approximations, which resemble closely some of the equations obtained from the lattice gas theories.Work supported (in part) by the Defence Research Board of Canada, Grant No. DRB 9510-30, and by the Research Council of Texas A & M University.     

Integral equation approximations for fluids of hard spheres with linear quadrupoles

In this paper we solve numerically several integral equation theories for the dense quadrupolar hard-sphere fluid. Closure approximations obtained by expanding the hypernetted-chain equation are shown to give pair-correlation functions and internal energies in good agreement with Monte Carlo calculations. The mean spherical approximation, however, is found to be extremely poor.     

General relativistic pulsation equation for charged fluids

A general relativistic pulsation equation for determining the characteristic frequencies of a charged fluid is obtained. The equation is then applied to the case of charged dust.     

Fission barriers and the inclusion of axial asymmetry

The nuclear potential-energy surface has been calculated on the basis of the modified-oscillator model with the inclusion of the degrees of freedom of axial asymmetry. For the heavier actinides the inner barrier is found to be reduced by up to one MeV. This is in agreement with the results obtained by Pashkevich. For superheavy elements a similar reduction is obtained.     

Integral equation approximations for fluids of hard spheres with dipoles and quadrupoles

The LHNC, QHNC and mean spherical approximations are solved for fluids of hard spheres with dipoles and linear quadrupoles. The theories are evaluated by comparison with new Monte Carlo results. The dielectric constant is found to decrease rapidly with increasing quadrupole moment.