Stability of the iterative solutions of integral equations as one phase freezing criterion

A recently proposed connection between the threshold for the stability of the iterative solution of integral equations for the pair correlation functions of a classical fluid and the structural instability of the corresponding real fluid is carefully analyzed. Direct calculation of the Lyapunov exponent of the standard iterative solution of HNC and PY integral equations for the 1D hard rods fluid shows the same behavior observed in 3D systems. Since no phase transition is allowed in such 1D system, our analysis shows that the proposed one phase criterion, at least in this case, fails. We argue that the observed proximity between the numerical and the structural instability in 3D originates from the enhanced structure present in the fluid but, in view of the arbitrary dependence on the iteration scheme, it seems uneasy to relate the numerical stability analysis to a robust one-phase criterion for predicting a thermodynamic phase transition.Comment: 11 pages, 2 figure

Optimized random phase approximations for arbitrary reference systems: extremum conditions and thermodynamic consistence

The optimized random phase approximation (ORPA) for classical liquids is re-examined in the framework of the generating functional approach to the integral equations. We show that the two main variants of the approximation correspond to the addition of the same correction to two different first order approximations of the homogeneous liquid free energy. Furthermore, we show that it is possible to consistently use the ORPA with arbitrary reference systems described by continuous potentials and that the same approximation is equivalent to a particular extremum condition for the corresponding generating functional. Finally, it is possible to enforce the thermodynamic consistence between the thermal and the virial route to the equation of state by requiring the global extremum condition on the generating functional.Comment: 8 pages, RevTe

Simple Fluids with Complex Phase Behavior

We find that a system of particles interacting through a simple isotropic potential with a softened core is able to exhibit a rich phase behavior including: a liquid-liquid phase transition in the supercooled phase, as has been suggested for water; a gas-liquid-liquid triple point; a freezing line with anomalous reentrant behavior. The essential ingredient leading to these features resides in that the potential investigated gives origin to two effective core radii.Comment: 7 pages including 3 eps figures + 1 jpeg figur

Effective Soft-Core Potentials and Mesoscopic Simulations of Binary Polymer Mixtures

Mesoscopic molecular dynamics simulations are used to determine the large scale structure of several binary polymer mixtures of various chemical architecture, concentration, and thermodynamic conditions. By implementing an analytical formalism, which is based on the solution to the Ornstein-Zernike equation, each polymer chain is mapped onto the level of a single soft colloid. From the appropriate closure relation, the effective, soft-core potential between coarse-grained units is obtained and used as input to our mesoscale simulations. The potential derived in this manner is analytical and explicitly parameter dependent, making it general and transferable to numerous systems of interest. From computer simulations performed under various thermodynamic conditions the structure of the polymer mixture, through pair correlation functions, is determined over the entire miscible region of the phase diagram. In the athermal regime mesoscale simulations exhibit quantitative agreement with united atom simulations. Furthermore, they also provide information at larger scales than can be attained by united atom simulations and in the thermal regime approaching the phase transition.Comment: 19 pages, 11 figures, 3 table

Nonergodicity transitions in colloidal suspensions with attractive interactions

The colloidal gel and glass transitions are investigated using the idealized mode coupling theory (MCT) for model systems characterized by short-range attractive interactions. Results are presented for the adhesive hard sphere and hard core attractive Yukawa systems. According to MCT, the former system shows a critical glass transition concentration that increases significantly with introduction of a weak attraction. For the latter attractive Yukawa system, MCT predicts low temperature nonergodic states that extend to the critical and subcritical region. Several features of the MCT nonergodicity transition in this system agree qualitatively with experimental observations on the colloidal gel transition, suggesting that the gel transition is caused by a low temperature extension of the glass transition. The range of the attraction is shown to govern the way the glass transition line traverses the phase diagram relative to the critical point, analogous to findings for the fluid-solid freezing transition.Comment: 11 pages, 7 figures; to be published in Phys. Rev. E (1 May 1999

Childhood craniopharyngioma: greater hypothalamic involvement before surgery is associated with higher homeostasis model insulin resistance index

<p>Abstract</p> <p>Background</p> <p>Obesity seems to be linked to the hypothalamic involvement in craniopharyngioma. We evaluated the pre-surgery relationship between the degree of this involvement on magnetic resonance imaging and insulin resistance, as evaluated by the homeostasis model insulin resistance index (HOMA). As insulin-like growth factor 1, leptin, soluble leptin receptor (sOB-R) and ghrelin may also be involved, we compared their plasma concentrations and their link to weight change.</p> <p>Methods</p> <p>27 children with craniopharyngioma were classified as either grade 0 (n = 7, no hypothalamic involvement), grade 1 (n = 8, compression without involvement), or grade 2 (n = 12, severe involvement).</p> <p>Results</p> <p>Despite having similar body mass indexes (BMI), the grade 2 patients had higher glucose, insulin and HOMA before surgery than the grade 0 (P = 0.02, <0.05 and 0.02 respectively) and 1 patients (P < 0.02 and <0.03 for both insulin and HOMA). The grade 0 (5.8 ± 4.9) and 1 (7.2 ± 5.3) patients gained significantly less weight (kg) during the year after surgery than did the grade 2 (16.3 ± 7.4) patients. The pre-surgery HOMA was positively correlated with these weight changes (P < 0.03).</p> <p>The data for the whole population before and 6–18 months after surgery showed increases in BMI (P < 0.0001), insulin (P < 0.005), and leptin (P = 0.0005), and decreases in sOB-R (P < 0.04) and ghrelin (P < 0.03).</p> <p>Conclusion</p> <p>The hypothalamic involvement by the craniopharyngioma before surgery seems to determine the degree of insulin resistance, regardless of the BMI. The pre-surgery HOMA values were correlated with the post-surgery weight gain. This suggests that obesity should be prevented by reducing inn secretion in those cases with hypothalamic involvement.</p