1,721,128 research outputs found
Thermodynamically self-consistent theory of structure for three-dimensional lattice gases
No full textRecently, methods were developed to solve with high accuracy the equations that describe a thermodynamically self-consistent theory for the two-body correlation function, and preliminary results were reported for three-dimensional lattice gases with nearest-neighbor attractive interaction [R. Dickman and G. Stell, Phys. Rev. Lett. 77, 996 (1996)]. Here we give a detailed description of our methods and of the results, which are found to be remarkably accurate for both the thermodynamics and structure of these systems. In particular, critical temperatures are predicted to within 0.2% of the best estimates from series expansions. Although above the critical temperature the theory yields the same critical exponents as the spherical model, this asymptotic behavior sets in only in a very narrow region around the critical point, so that the apparent exponents and the thermodynamics are well reproduced up to reduced temperatures of around 10(-2). On the coexistence curve, on the other hand, the exponents are nonspherical, and considerably more accurate than the spherical ones. For instance, the exponent beta(coex) predicted by the theory for the shape of the coexistence curve is beta(coex)=0.35
Globally accurate theory of structure and thermodynamics for soft-matter liquids
No full textStandard statistical mechanical approximations (e.g. mean-field approximations) for pair-correlation functions of strongly interacting systems that yield adequate thermodynamics away from critical points typically break down badly in critical regions. The self-consistent Ornstein-Zemike approximation (SCOZA) transcends this difficulty, yielding globally accurate Structure and thermodynamics. The SCOZA has been applied successfully to a variety of Hamiltonian models and the result will be briefly summarized. We end with a progress report on the applications of the SCOZA to some soft-matter systems
SCOZA critical exponents and scaling in three dimensions
No full textThe critical behavior of a self-consistent Ornstein-Zernike approach (SCOZA) that describes the pair correlation function and thermodynamics of a classical fluid, lattice gas, or Ising model is analyzed in three dimensions below the critical temperature, complementing our earlier analysis of the supercritical behavior. The SCOZA subcritical exponents describing the coexistence curve, susceptibility (compressibility), and specific heat are obtained analytically (beta=7/20, gamma'=7/5, alpha'=-1/10). These are in remarkable agreement with the exact values (beta approximate to 0.326, gamma' approximate to 1.24, alpha' approximate to 0.11) considering that the SCOZA uses no renormalization group concepts. The scaling behavior that describes the singular parts of the thermodynamic functions as the critical point is approached is also analyzed. The subcritical scaling behavior in the SCOZA is somewhat less simple than that expected in an exact theory, involving two scaling functions rather than one
Self-consistent approximation for fluids and lattice gases
No full textA self-consistent Ornstein-Zernike approximation (SCOZA) for the direct-correlation function, embodying consistency between the compressibility and the internal energy routes to the thermodynamics, has recently been quantitatively evaluated for a nearest-neighbor attractive lattice gas and for a fluid of Yukawa spheres, in which the pair potential has a hard core and an attractive Yukawa tail. For the lattice gas the SCOZA yields remarkably accurate predictions for the thermodynamics, the correlations, the critical point, and the coexistence curve. The critical temperature agrees to within 0.2% of the best estimates based on extrapolation of series expansions. Until the temperature is to within less than 1% of its critical value, the effective critical exponents do not differ appreciably from their estimated exact form, so that the thermodynamics deviates from the correct behavior only in a very narrow neighborhood of the critical point. For the Yukawa fluid accurate results are obtained as well, although a comparison as sharp as in the lattice-gas case has not been possible due to the greater uncertainty affecting the available simulation results, especially with regard to the position of the critical point and the coexistence curve
Self-consistent Ornstein-Zemike approximation for three-dimensional spins
No full textAn Ornstein-Zemike approximation for the two-body correlation function embodying thermodynamic consistency is applied to a system of classical Heisenberg spins on a three-dimensional lattice. The consistency condition determined in a previous work is supplemented by introducing a simplified expression for the mean-square spin fluctuations. The thermodynamics and the correlations obtained are then compared with approximants based on extrapolation of series expansions and with Monte Carlo simulations. Many properties of the model, including the critical temperature, are very well reproduced by this simple version of the theory, but it shows substantial quantitative error in the critical region, both above the critical temperature and with respect to its rendering of the spontaneous magnetization curve. A less simple but conceptually more satisfactory version of the SCOZA is then developed, but not solved, in which the effects of transverse correlations on the longitudinal susceptibility is included, yielding a more complete and accurate description of the spin-wave properties of the model
Thermodynamically self-consistent theories of fluids interacting through short-range forces
No full textThe self-consistent Ornstein-Zernike approximation (SCOZA), the generalized mean spherical approximation (GMSA), the modified hypernetted chain (MHNC) approximation, and the hierarchical reference theory (HRT) are applied to the determination of thermodynamic and structural properties, and the phase diagram of the hard-core Yukawa fluid (HCYF). We investigate different Yukawa-tail screening lengths lambda, ranging from lambda=1.8 (a value appropriate to approximate the shape of the Lennard-Jones potential) to lambda =9 (suitable for a simple one-body modelization of complex fluids like colloidal suspensions and globular protein solutions). The comparison of the results obtained with computer simulation data shows that at relatively low lambda's all the theories are fairly accurate in the prediction of thermodynamic and structural properties; as far as the phase diagram is concerned, the SCOZA and HRT are able to predict the binodal line and the critical parameters in a quantitative manner. At lambda=4 some discrepancies begin to emerge in the performances of the different theoretical approaches: the MHNC remains, on the whole, reasonably accurate in predicting the energy and the contact value of the radial distribution function; the SCOZA predicts well the equation of state up to the highest lambda values investigated. The GMSA and the MHNC underestimate and overestimate, respectively, the liquid coexisting density, while the SCOZA and HRT yield liquid branches that fall between the two former theoretical predictions, although both appear to overestimate the critical temperature somewhat. At higher lambda's the GMSA and MHNC binodals further worsen, while the SCOZA appears to remain usefully predictive. In general, the predictions of all the theories tend to slightly worsen at low temperatures and high density. The determination of the freezing line, performed by means of a one-phase "freezing criterion" (due to other authors) is not particularly satisfactory within either the SCOZA or the MHNC. The GMSA prediction for the freezing line at lambda=7 and 9 is instead able to follow in a qualitative manner the pattern of the solid-vapor coexistence line as determined through computer simulation studies. The necessity of further assessments of the freezing predictions is also discussed. Finally, versions of the GMSA, SCOZA, and HRT that can be expected to be more accurate for interactions with extremely short-ranged attractions are identified
A liquid-state theory that remains successful in the critical region
No full textA thermodynamically self-consistent Ornstein-Zernike approximaton (SCOZA) is applied to a fluid of spherical particles with a pair potential given by a hard core repulsion and a Yukawa attractive tail w(r) = - exp[-z(r - 1)]/r. This potential allows one to take advantage of the known analytical properties of the solution of the Ornstein-Zernike equation for the case in which the direct correlation function outside the repulsive core is given by a linear combination of two Yukawa tails and the radial distribution function g(r) satisfies the exact core condition g(r)= 0 for r < 1. The predictions for the thermodynamics, the critical point, and the coexistence curve are compared with other theories and with simulation results. In order to assess unambiguously the ability of the SCOZA to locate the critical point and the phase boundary of the system, a new set of simulations also has been performed. The method adopted combines Monte Carlo and finite-size scaling techniques, and is especially adapted to deal with critical fluctuations and phase separation. It is found that the version of the SCOZA considered here provides very good overall thermodynamics and remarkably accurate critical point and coexistence curve. For the interaction range considered here, given by z = 1.8, the critical density and temperature predicted by the theory agree with the simulation results to about 0.6%
Liquid-gas phase behavior of an argon-like fluid modelled by the hard-core two-Yukawa potential
No full textWe study a model for an argon-like fluid parameterized in terms of a hard-core repulsion and a two-Yukawa potential. The liquid-gas phase behavior of the model is obtained from the thermodynamically Self-Consistent Ornstein-Zernike Approximation (SCOZA) of Hoye and Stell, the solution of which lends itself particularly well to a pair potential of this form. The predictions for the critical point and the coexistence curve are compared to new high resolution simulation data and to other liquid-state theories, including the hierarchical reference theory (HRT) of Parola and Reatto. Both SCOZA and HRT deliver results that are considerably more accurate than standard integral-equation approaches. Among the versions of SCOZA considered, the one yielding the best agreement with simulation successfully predicts the critical point parameters to within 1%
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
- …
