A thermodynamically self-consistent theory for the Blume-Capel model

We use a self-consistent Ornstein-Zernike approximation to study the Blume-Capel ferromagnet on three-dimensional lattices. The correlation functions and the thermodynamics are obtained from the solution of two coupled partial differential equations. The theory provides a comprehensive and accurate description of the phase diagram in all regions, including the wing boundaries in non-zero magnetic field. In particular, the coordinates of the tricritical point are in very good agreement with the best estimates from simulation or series expansion. Numerical and analytical analysis strongly suggest that the theory predicts a universal Ising-like critical behavior along the $\lambda$-line and the wing critical lines, and a tricritical behavior governed by mean-field exponents.Comment: 11 figures. to appear in Physical Review

Phase diagram of a two-dimensional system with anomalous liquid properties

Using Monte Carlo simulation techniques, we calculate the phase diagram for a square shoulder-square well potential in two dimensions that has been previously shown to exhibit liquid anomalies consistent with a metastable liquid-liquid critical point. We consider the liquid, gas and five crystal phases, and find that all the melting lines are first order, despite a small range of metastability. One melting line exhibits a temperature maximum, as well as a pressure maximum that implies inverse melting over a small range in pressure.Comment: 11 pages, 13 figure

S98RS SGR No. 14 (Finals)

A RESOLUTION To recommend to Executive Vice-Chancellor and Provost Dan Fogel, Robert Doolos of the University Registrars Office, and the University Calendar Committee to begin finals the Saturday after Dead Week and end the following Friday

Collateral donor artery physiology and the influence of a chronic total occlusion on fractional flow reserve

Background— The presence of a concomitant chronic total coronary occlusion (CTO) and a large collateral contribution might alter the fractional flow reserve (FFR) of an interrogated vessel, rendering the FFR unreliable at predicting ischemia should the CTO vessel be revascularized and potentially affecting the decision on optimal revascularization strategy. We tested the hypothesis that donor vessel FFR would significantly change after percutaneous coronary intervention of a concomitant CTO. Methods and Results— In consecutive patients undergoing percutaneous coronary intervention of a CTO, coronary pressure and flow velocity were measured at baseline and hyperemia in proximal and distal segments of both nontarget vessels, before and after percutaneous coronary intervention. Hemodynamics including FFR, absolute coronary flow, and the coronary flow velocity–pressure gradient relation were calculated. After successful percutaneous coronary intervention in 34 of 46 patients, FFR in the predominant donor vessel increased from 0.782 to 0.810 (difference, 0.028 [0.012 to 0.044]; P=0.001). Mean decrease in baseline donor vessel absolute flow adjusted for rate pressure product: 177.5 to 139.9 mL/min (difference −37.6 [−62.6 to −12.6]; P=0.005), mean decrease in hyperemic flow: 306.5 to 272.9 mL/min (difference, −33.5 [−58.7 to −8.3]; P=0.011). Change in predominant donor vessel FFR correlated with angiographic (%) diameter stenosis severity (r=0.44; P=0.009) and was strongly related to stenosis severity measured by the coronary flow velocity–pressure gradient relation (r=0.69; P<0.001). Conclusions— Recanalization of a CTO results in a modest increase in the FFR of the predominant collateral donor vessel associated with a reduction in coronary flow. A larger increase in FFR is associated with greater coronary stenosis severity

Liquid-Liquid Phase Transition for an Attractive Isotropic Potential with Wide Repulsive Range

Recent experimental and theoretical results have shown the existence of a liquid-liquid phase transition in isotropic systems, such as biological solutions and colloids, whose interaction can be represented via an effective potential with a repulsive soft-core and an attractive part. We investigate how the phase diagram of a schematic general isotropic system, interacting via a soft-core squared attractive potential, changes by varying the parameters of the potential. It has been shown that this potential has a phase diagram with a liquid-liquid phase transition in addition to the standard gas-liquid phase transition and that, for a short-range soft-core, the phase diagram resulting from molecular dynamics simulations can be interpreted through a modified van der Waals equation. Here we consider the case of soft-core ranges comparable with or larger than the hard-core diameter. Because an analysis using molecular dynamics simulations of such systems or potentials is too time-demanding, we adopt an integral equation approach in the hypernetted-chain approximation. Thus we can estimate how the temperature and density of both critical points depend on the potential's parameters for large soft-core ranges. The present results confirm and extend our previous analysis, showing that this potential has two fluid-fluid critical points that are well separated in temperature and in density only if there is a balance between the attractive and repulsive part of the potential. We find that for large soft-core ranges our results satisfy a simple relation between the potential's parameters

Gel transitions in colloidal suspensions

The idealized mode coupling theory (MCT) is applied to colloidal systems interacting via short-range attractive interactions of Yukawa form. At low temperatures MCT predicts a slowing down of the local dynamics and ergodicity breaking transitions. The nonergodicity transitions share many features with the colloidal gel transition, and are proposed to be the source of gelation in colloidal systems. Previous calculations of the phase diagram are complemented with additional data for shorter ranges of the attractive interaction, showing that the path of the nonergodicity transition line is then unimpeded by the gas-liquid critical curve at low temperatures. Particular attention is given to the critical nonergodicity parameters, motivated by recent experimental measurements. An asymptotic model is developed, valid for dilute systems of spheres interacting via strong short-range attractions, and is shown to capture all aspects of the low temperature MCT nonergodicity transitions.Comment: 12 pages, LaTeX, 5 eps figures, uses ioplppt.sty, to appear in J. Phys.: Condens. Matte

A model for the atomic-scale structure of a dense, nonequilibrium fluid: the homogeneous cooling state of granular fluids

It is shown that the equilibrium Generalized Mean Spherical Model of fluid structure may be extended to nonequilibrium states with equation of state information used in equilibrium replaced by an exact condition on the two-body distribution function. The model is applied to the homogeneous cooling state of granular fluids and upon comparison to molecular dynamics simulations is found to provide an accurate picture of the pair distribution function.Comment: 29 pages, 11 figures Revision corrects formatting of the figure