Path integral based calculations of symmetrized time correlation functions. I.

In this paper, we examine how and when quantum evolution can be approximated in terms of (generalized) classical dynamics in calculations of correlation functions, with a focus on the symmetrized time correlation function introduced by Schofield. To that end, this function is expressed as a path integral in complex time and written in terms of sum and difference path variables. Taylor series expansion of the path integral's exponent to first and second order in the difference variables leads to two original developments. The first order expansion is used to obtain a simple, path integral based, derivation of the so-called Schofield's quantum correction factor. The second order result is employed to show how quantum mechanical delocalization manifests itself in the approximation of the correlation function and hinders, even in the semiclassical limit, the interpretation of the propagators in terms of sets of guiding classical trajectories dressed with appropriate weights.

Path integral based calculations of symmetrized time correlation functions. II.

Schofield's form of quantum time correlation functions is used as the starting point to derive a computable expression for these quantities. The time composition property of the propagators in complex time is exploited to approximate Schofield's function in terms of a sequence of short time classical propagations interspersed with path integrals that, combined, represent the thermal density of the system. The approximation amounts to linearization of the real time propagators and it becomes exact with increasing number of propagation legs. Within this scheme, the correlation function is interpreted as an expectation value over a probability density defined on the thermal and real path space and calculated by a Monte Carlo algorithm. The performance of the algorithm is tested on a set of benchmark problems. Although the numerical effort required is considerable, we show that the algorithm converges systematically to the exact answer with increasing number of iterations and that it is stable for times longer than those accessible via a brute force, path integral based, calculation of the correlation function. Scaling of the algorithm with dimensionality is also examined and, when the method is combined with commonly used filtering schemes, found to be comparable to that of alternative semiclassical methods.

Transient hydrodynamical behavior by dynamical nonequilibrium molecular dynamics: the formation of convective cells.

We present a method based on dynamical nonequilibrium molecular dynamics (D-NEMD) that allows one to produce rigorous ensemble averages for the transient regimes. We illustrate the method by describing the formation of convective cells within a two-dimensional fluid system of soft disks in which a gravity field and a thermal gradient are present. We analyze two different physical settings, with the thermal gradient orthogonal or parallel to the gravity field. In both settings, we follow the formation of the convective flows from the initial time, when the perturbation is turned on, to the steady state. In the first setting (orthogonal fields) we investigate several different cases, varying the initial stationary ensemble and the perturbing field. We find that the final steady-state convective cell is independent of the specific sequence of perturbation fields, which only affects the transient behavior. In all cases, we find that the convective roll is formed through a sequence of damped oscillations of the local fields (density, temperature, and velocity), superimposed to an overall relaxation toward the local steady-state values. Then, we show how D-NEMD can be applied to the Rayleigh-Bénard (RB) setting (parallel fields). In these conditions, the convective flow only establishes above a threshold, without a preferred verse of rotation. We analyze only the response to the ignition of the gravity field in a stationary system under the action of a vertical thermal gradient. Also in this case we characterize the transient response by following the evolution of the density, temperature, and velocity fields until the steady-state RB convective cell is formed. The observed transients are similar to those observed in the case of orthogonal fields. However, the final steady states are quite different. Finally, we briefly discuss the conditions for the general applicability of the D-NEMD method.

Sphere versus cylinder: the effect of packing on the structure of nonionic C12E6 micelles.

Two independent series of calculations are performed simulating spherical and cylindrical C12E6 micelles in a temperature range around the experimental sphere-to-rod transition temperature for surfactant concentrations less than 20% by weight. A comparative analysis of these systems helps to shed light on the microscopic details of the micelle sphere-to-rod transition. In agreement with theoretical models, we find that spherical and cylindrical micelles have a different oil core packing; the core radius of a cylindrical micelle is reduced by a factor of 0.87 with respect to the core radius of a spherical micelle. Despite this contraction, the specific volume of the alkyl tails is larger in a cylindrical micelle than in a spherical micelle. In both geometries, this specific volume follows the same linear increase with temperature. Density measurement experiments are also performed in order to evaluate the specific volume of the hydrophobic tail of surfactants of the C12Ej family with j ranging from 5 to 8. We observe a good agreement between experimental data and simulation results. Our simulations also show that the spatial distribution of the head groups in the interface is more effective in screening the oil core in the cylindrical aggregate than in the spherical aggregate, reducing by a factor of 2 the oil surface per monomer exposed to water. This screening accounts for a free-energy difference of Deltafs=fssph-fscyl approximately +2.5kBT per monomer and mirrors the essential role that the hydrophobic interactions have on the shape transition. We also find that the different interface packing correlates with different conformations and flexibility of the hydrophilic fragments E6, that appear as an entropic reservoir for the transition. Finally, comparing the degree of hydration of a spherical micelle at T=283 K with that of a cylindrical micelle at T=318 K, we observe an amount of dehydration in agreement with reported experimental data across the sphere-to-rod transition. However, for aggregates of fixed shape, we find a much smaller amount of dehydration with temperature, suggesting that the shape transition is not a consequence of the measured temperature dehydration but rather the opposite.

Pressure-induced core packing and interfacial dehydration in nonionic C12E6 micelle in aqueous solution.

A spherical micelle of C12E6 is simulated at different pressures, from 0.001 to 3 kbar, by molecular dynamics. On increasing the pressure the alkyl tails of the surfactants pack tightly and stretch. At 3 kbar we observe dynamical slowing down of the oil core of the micelle. At that pressure the core is characterized by a high oil density, rho oil approximately 0.85 g/cm(3), regular density oscillation, and low chain entropy. Pressure affects the interfacial region as well. Dehydration, induced by the collapse of the hydrophilic head groups, is observed in the inner part of the interface. Such dehydration resembles temperature dehydration but differs in details. Our results support the interpretation of recent experiments on micellar solutions at high pressure.

Backflow correlations for the electron gas and metallic hydrogen.

We justify and evaluate backflow three-body wave functions for a two-component system of electrons and protons. Based on the generalized Feynman-Kacs formula, many-body perturbation theory, and band structure calculations, we analyze the use and the analytical form of the backflow function from different points of view. The resulting wave functions are used in variational and diffusion Monte Carlo calculations of the electron gas and of solid and liquid metallic hydrogen. For the electron gas, the purely analytic backflow and three-body form gives lower energies than those of previous calculations. For bcc hydrogen, analytical and optimized backflow-three-body wave functions lead to energies nearly as low as those from using local density approximation orbitals in the trial wave function. However, compared to wave functions constructed from density functional solutions, backflow wave functions have the advantage of only few parameters to estimate, the ability to include easily and accurately electron-electron correlations, and that they can be directly generalized from the crystal to a disordered liquid of protons.

Urokinase receptor is up-regulated in endothelial cells and macrophages associated with fibrinoid deposits in the human placenta.

Clearance of fibrin deposits within the human placenta is an ongoing process during normal placental development. Plasminogen is a circulating fibrinolytic protease zymogen activated in situ by plasminogen activators. We have previously reported that the receptor for urokinase plasminogen activator (uPAR) is expressed by cells either covering or enmeshed within the perivillous fibrinoid deposits. Whereas these cells seemed likely to be trophoblasts, a definitive identification was lacking, and this question is central to the understanding of the cellular mechanisms directing fibrinolysis in the placenta. In this study we have performed immunohistochemical co-localization studies and found that the uPAR-positive cells covering fibrinoid deposits are immunoreactive for CD31 and vWF, indicating that they are actually endothelial cells. In addition, we found that perivillous fibrinoid deposits not covered with uPAR-positive endothelial cells were covered with platelets identified by integrin alpha(IIb)beta(3)-immunoreactivity. Also surprisingly, the uPAR-positive cells enmeshed within fibrinoid deposits express a cell specific marker indicating that they are macrophages. Both uPAR-positive cell populations also express uPA immunoreactivity. Taken together, the data suggest that both fibrinoid-covering endothelial cells and fibrinoid-enmeshed macrophages can participate in the clearance process of perivillous fibrinoid deposits formed in the human placenta.

Free energy of the Fröhlich polaron in two and three dimensions.

We present a novel path integral Monte Carlo scheme to solve the Fröhlich polaron model. At intermediate and strong electron-phonon couplings, the polaron self-trapping is properly taken into account at the level of an effective action obtained by a preaveraging procedure with a retarded trial action. We compute the free energy at several couplings and temperatures in three and two dimensions. Our results show that the accuracy of the Feynman variational upper bound for the free energy is always within a few percent. The method can be generalized to the N-polarons case.

Different statistical mechanical ensembles for a stretched polymer.

Imposing to a single polymer chain of N monomers either a fixed pair of forces +/-f acting at the chain ends (stress ensemble) or a fixed end-to-end vector R (strain ensemble) does correspond to the use of different statistical mechanical ensembles. In particular, the two elasticity laws, R(f)=g(f) and f(R)=h(R), where R(f) is the length of the average end-to-end vector (f) in the stress ensemble and f(R) is the intensity of the average internal force (R) in the strain ensemble, are not equivalent. For these conjugated ensembles, the quantity Delta(f)=f-h(g(f)) and more generally Delta(O)=(f)-(R) where O is an arbitrary observable, is studied systematically in this paper for a wide class of polymer models corresponding to chains at temperatures equal or above the theta point. The leading term Delta((2))(O) of an expansion of Delta(O) in terms of the successive moments of the end-to-end vector fluctuations in the stress ensemble can be used to analyze the scaling properties of Delta(f). For the Gaussian and the freely jointed chain models, Delta(O) proportional to 1/N for large N with the particularity that, for the elasticity law, Delta(f) strictly vanishes for the Gaussian chain at any finite N. For chains in good solvent, the usual result Delta(f) proportional to 1/N at fixed f is only valid in the highly stretched chain regime (Pincus regime). N independent large ensemble differences of the order of 20% on Delta(f) are noticed when the chain is stretched over a distance of the order of the unstretched chain average end-to-end distance R0. These effects decrease to the 1% level for R(f)>3R(0). Monte Carlo calculations for a chain model containing both excluded volume and finite extensibility features illustrate the distinction between the elasticity laws in the two ensembles over all stretching regimes. Our study suggests that the nature of the constraints used in single chain micromanipulations could be relevant to the interpretation of experimental elasticity law data.

Fibronectins and basal lamina molecules expression in human subcutaneous white adipose tissue.

Adipose tissue is a type of connective tissue whose extracellular matrix (ECM) components are poorly characterized in vivo. Several in vitro studies have suggested a regulatory role for the ECM molecules during adipocyte differentiation. Since no data are available concerning the in vivo expression of the main ECM components such as fibronectin, collagen IV, laminin and heparan sulfate proteoglycan in the adipose tissue, we investigated the presence of these molecules by immunohistochemistry. We show that fibronectin isoforms are not expressed in fully differentiated subcutaneous adipocytes whereas collagen IV, laminin and heparan sulfate are detectable around single adipocytes, i.e. in the region corresponding to the basement membrane. These data are supported by previous in vitro studies showing a strong decrease of fibronectin synthesis during adipocyte development whereas basement membrane molecules seem to increase during adipocyte differentiation.

Immunohistochemical identification of the receptor for urokinase plasminogen activator associated with fibrin deposition in normal and ectopic human placenta.

The receptor for urokinase plasminogen activator (uPAR) is a key molecule in cell surface-directed plasminogen activation. uPAR binds urokinase plasminogen activator (uPA) and thereby focuses plasminogen activation on the cell surface. Plasmin dissolves fibrin deposits and facilitates cell migration during tissue repair processes by degrading the extracellular matrix. During human implantation and placental development, plasmin is considered important for both trophoblast migration/invasion and for fibrin surveillance. This study examined the expression of uPAR in normal and ectopic human placentae by immunohistochemistry. In first and third trimester normal placentae as well as in tubal ectopic placental tissues, a high uPAR expression was seen in the trophoblast associated with deposits of fibrin-type fibrinoid. Extravillous trophoblast of the basal plate, of the cell islands, and of the cell columns was also positive for uPAR in the first trimester whereas at term the expression of the protein was decreased. Moreover, uPAR immunostaining was observed in decidual cells throughout normal gestation and in endometrial tissues of patients with ectopic pregnancies. These findings suggest that uPAR participates in placental development and in trophoblast invasion particularly in the first trimester of pregnancy and that uPAR is involved in repair mechanisms of the trophoblast and fibrin surveillance.

BCL-2 expression in the human placenta and its correlation with fibrin deposits.

The human placenta performs numerous functions during its limited lifespan and its survival is a necessary prerequisite for fetal nutrition, even in unfavourable conditions. BCL-2 is a proto-oncogene implicated in the regulation of cell death and survival without affecting cell proliferation. An extracellular matrix molecule involved in the reparative and degenerative processes in the human placenta is fibrin. We have analysed by immunohistochemistry the expression of BCL-2 and correlated it with fibrin deposits in placental tissues. In first and third trimester placentas BCL-2 was expressed in the syncytiotrophoblast. Only a few mesenchymal villi (first trimester) or terminal villi (third trimester) showed no staining in the syncytiotrophoblast. Villous cytotrophoblast, mesenchymal cells of the villous cores and extravillous cytotrophoblast of cell columns and cell islands were all negative for BCL-2. BCL-2 expression was enhanced in the syncytiotrophoblast overlying subtrophoblastic fibrin deposits. However, discontinuities and/or variations in intensity of BCL-2 expression characterized not only the villi showing perivillous fibrinoid but also those villi with a massive presence of fibrinoid in their cores. These data suggest that BCL-2 may be necessary for the preservation of the placenta during gestation as well as for the reparative processes of the trophoblast.

Fasting inhibits natriuretic peptides clearance receptor expression in rat adipose tissue.

OBJECTIVE AND DESIGN: The early phase of weight loss induced by fasting is associated with diuresis, natriuresis and reduction in blood pressure through unclear mechanisms. Atrial natriuretic peptide (ANP) is a cardiac hormone with potent natriuretic, diuretic and hypotensive effects mediated by 'biologically active' receptors (NPr-A). A second type of receptor mediates the clearance of ANP (the clearance receptor, NPr-C). Since NPr-C appears to be abundant in adipose tissue, we analysed NPr-C and NPr-A gene expression in white and brown adipose tissue (WAT and BAT) as well as in renal cortex of fasting rats. Plasma ANP, cyclic GMP and aldosterone were also measured. METHODS: Twelve male Wistar rats were deprived of food for about 50 h, and 12 other rats were fed ad libitum. Periepididymal WAT, interscapular BAT and left renal cortex were used for RNA extraction and northern blot analysis with rat NPr-C and NPr-A complementary DNA probes labelled with 32P-dCTP. Densitometric analysis of hybridization signals was corrected by beta actin expression before statistical analysis. Blood was drawn for ANP, cyclic GMP (cGMP) and aldosterone radioimmunoassays, which were also measured in a group of six rats deprived of food for 25 h. RESULTS: A dramatic decrease in NPr-C steady-state messenger RNA levels was observed both in WAT (about 3.6-fold, P < 0.001) and in BAT (about threefold, P < 0.01), but fasting did not affect the expression of NPr-A in adipose tissues. In the renal cortex NPr-C and NPr-A messenger RNA levels were unaffected by fasting. ANP and aldosterone levels were reduced after fasting whereas cyclic GMP was increased at 25 h, but the differences did not reach statistical significance. CONCLUSIONS: Fasting exerts a tissue-specific and gene-specific suppression of NPr-C gene expression in adipose tissue that appears to be accompanied by an increased biological activity of ANP. The natriuresis and diuresis and reduction of blood pressure induced by fasting might result from a reduced expression of NPr-C in adipose fat pads.

The normal, cryptorchid and retractile prepuberal human testis: a comparative morphometric ultrastructural study of 101 cases.

Fifty-two surgical biopsies from retractile testes of patients in pediatric age (3-14 years), of which 25 were treated with hormonal therapy (RT) and 27 did not undergo therapy before orchidopexy (RNT), were compared with the biopsies of 18 normal (N) and 30 cryptorchid or ectopic (E) testes. A light and electron microscopic morphologic and morphometric study was performed. For the quantitative investigation 4 parameters were selected: a) the mean tubular diameter (on 20 cross-sections); b) the mean spermatogonial number per tubular section; c) the mean nucleolar area of the Sertoli cells; and d) the mean thickness of the tubular basal lamina. The 101 biopsies were collected for statistical evaluation into four age groups: 3-6 years, 7-10, 11-13 without spermatogenesis and 10-14 with signs of early spermatogenesis. In the RT category the mean tubular diameter and the mean spermatogonial number were similar to N in the first two age groups, but were significantly reduced in the RNT categories. The morphometric study of the Sertoli cell nucleolar area confirms the delay of maturation observed in the categories of RT, RNT and E. In normal biopsies, the basal lamina shows a progressive reduction of the thickness, with the lowest values around puberty, while constantly higher values were found in the other categories, although this increase is not statistically significant.