New discretization and solution techniques for incompressible viscous flow problems

Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned

Prediction of small-for-gestational-age neonates at 35-37 weeks' gestation: contribution of maternal factors and growth velocity between 20 and 36 weeks

Objective: To evaluate the performance of ultrasonographic estimated fetal weight (EFW) at 35+0 - 36+6 weeks’ gestation in the prediction of small for gestational age (SGA) neonates and assess the additive value of first, maternal risk factors and second, fetal growth velocity between 20 and 36 weeks’ gestation in improving such prediction. Methods: This was a prospective study of 44,043 singleton pregnancies that had undergone routine ultrasound examination at 19+0 - 23+6 and at 35+0 - 36+6 weeks’ gestation. Multivariable logistic regression analysis was used to determine whether addition of maternal risk factors and growth velocity, defined by a difference in EFW Z-scores or fetal abdominal circumference (AC) Z-scores between the third and second trimester scans divided by the time interval between them, improved the performance of EFW at 35+0 - 36+6 weeks in the prediction of delivery of SGA neonates with birthweight <10th and <3rd percentiles within two weeks and at any stage after assessment. Results: Screening by EFW at 35+0 - 36+6 weeks’ gestation <10th percentile predicted 63.4% (95% CI 62.0, 64.7) of neonates with birthweight <10th percentile and 74.2% (95% CI 72.2, 76.1) of neonates with birthweight <3rd percentile born at any stage after assessment, at screen positive rate of 10%. The respective values for SGA neonates born within two weeks of assessment were 76.8% (95% CI 74.4, 79.0) and 81.3% (95% CI 78.2, 84.0). In the group of fetuses with EFW <10th percentile, 43.7% were born with birthweight ≥10th percentile. For a desired 90% detection rate of SGA neonates delivering at any stage after assessment the necessary screen positive rate would be 33.7% for SGA <10th percentile and 24.4% for SGA <3rd percentile. Multivariable logistic regression analysis demonstrated that in the prediction of SGA neonates with birthweight <10th and <3rd percentiles there was a significant contribution from EFW Z-score at 35+0 - 36+6 weeks’ gestation, maternal risk factors and AC growth velocity, but not EFW growth velocity. However, the area under the receiver operating characteristic curves for SGA neonates in screening by maternal risk factors and EFW Z-score was not improved by addition of AC growth velocity. Conclusion: Screening for SGA neonates by EFW at 35+0 - 36+6 weeks’ gestation and use of a cut-off of the 10th percentile predicts 63% of affected neonates. Prediction of 90% of SGA neonates necessitates classification of about 35% of the population as being screen positive use of the 35th percentile cut-off in EFW. The predictive performance of EFW is not improved by addition of estimated growth velocity between the second and third trimesters of pregnancy

Prediction of small-for-gestational-age neonates at 35-37 weeks' gestation: contribution of maternal factors and growth velocity between 32 and 36 weeks

Objective: To assess the additive value of fetal growth velocity between 32 and 36 weeks’ gestation on the performance of ultrasonographic estimated fetal weight (EFW) at 35+0 - 36+6 weeks’ gestation for prediction of small for gestational age (SGA) neonates and adverse perinatal outcome. Methods: This was a prospective study of 14,497 singleton pregnancies that had undergone routine ultrasound examination at 28+0 - 34+6 and at 35+0 - 36+6 weeks’ gestation. Multivariable logistic regression analysis was used to determine whether addition of growth velocity, defined by a difference in EFW and abdominal circumference (AC) Z-scores between the early and late third trimester scans divided by the time interval between them, improved the performance of EFW at 35+0 - 36+6 weeks in the prediction of first, delivery of SGA neonates with birthweight <10th and <3rd percentiles within two weeks and at any stage after assessment and second, composite of adverse perinatal outcome defined as stillbirth, neonatal death or admission to the neonatal unit for ≥48 hours. Results Multivariable logistic regression analysis demonstrated that significant contributors to prediction of SGA neonates were EFW Z-score at 35+0 - 36+6 weeks’ gestation, fetal growth velocity by either AC or EFW Z-scores and maternal risk factors. The area under the receiver operating characteristic curves (AUROC) and detection rate (DR) with 95% confidence interval, at 10% screen positive rate, for prediction of SGA neonates <10th percentile born within two weeks of assessment achieved by EFW Z-score at 35+0 - 36+6 weeks (AUROC 0.938, 0.928 - 0.947; DR 80.7, 77.6 - 83.9) were not significantly improved by addition of EFW growth velocity and maternal risk factors (AUROC 0.941, 0.932 - 0.950; p=0.061; DR 82.5, 79.4 - 85.3). Similar results were obtained when growth velocity was defined by AC rather than EFW growth velocity. Similarly, there was no significant improvement in AUROC and DR, at 10% screen positive rate, for prediction of SGA neonates <10th percentile born at any stage after assessment or SGA neonates <3rd percentile born within two weeks or at any stage after assessment achieved by EFW Z-score at 35+0 - 36+6 weeks by addition of maternal factors and either EFW growth velocity of AC growth velocity. Multivariable logistic regression analysis demonstrated that the only significant contributor to adverse perinatal outcome was maternal risk factors. Multivariable logistic regression analysis in the group with EFW <10th percentile demonstrated that significant contribution to prediction of birth of neonates with birthweight <10th and <3rd percentiles and adverse perinatal outcome was provided by EFW Z-score at 35+0 - 36+6 weeks, but not by AC growth velocity <1st decile. Conclusion: The predictive performance of EFW at 35+0 - 36+6 weeks’ gestation for birth of SGA neonates and adverse perinatal outcome is not improved by addition of estimated growth velocity between 32 and 36 weeks’ gestation

Synoptic and dynamic characteristics of selected deep depressions over Cyprus

International audienceIn this study, the spatial and temporal distributions of dynamic and synoptic characteristics of a selection of 32 deep baroclinic depressions have been investigated. The study covers the cold period months of November till March, in the period from 1 November 1986 to 31 March 2003. For the needs of the study, several synoptic characteristics of these depressions have been extracted. Also, several dynamic characteristics during the evolution of the depressions were studied: relative vorticity, divergence, vertical motion and a static stability parameter. The results are presented in the form of isobaric distributions over, three tropospheric isobaric levels, namely the lower 850 hPa, the middle 500 hPa and the upper 300 hPa

Value of routine ultrasound examination at 35–37 weeks' gestation in diagnosis of non‐cephalic presentation

Background: Undiagnosed non-cephalic presentation in labor carries increased risks for both the mother and baby. Routine pregnancy care based on maternal abdominal palpation fails to detect the majority of non-cephalic presentations. Objective: To report the incidence of non-cephalic presentation at a routine scan at 35+0 - 36+6 weeks’ gestation and subsequent management of such pregnancies. Methods: This was a retrospective analysis of prospectively collected data in 45,847 singleton pregnancies that had undergone routine ultrasound examination at 35+0 - 36+6 weeks’ gestation. Patients with breech or transverse / oblique presentation were divided into two groups, first those that would have elective cesarean section for fetal or maternal indications other than the abnormal presentation, and second, those that would potentially require ECV. The latter group was reassessed in 1-2 weeks and if there was persistence of the abnormal presentation the parents were offered the options of ECV versus elective cesarean section at 38-40 weeks’ gestation. Multivariable logistic regression analysis was carried out to determine which of the factors from maternal and pregnancy characteristics provided a significant contribution in the prediction of first, non-cephalic presentation at the 35+0 - 36+6 weeks scan, second, successful ECV from non-cephalic to cephalic presentation, and third, spontaneous rotation from non-cephalic to cephalic presentation. Results: First, at 35+0 - 36+6 weeks the fetal presentation was cephalic in 43,416 (94.7%) pregnancies, breech in 1,987 (4.3%) and transverse or oblique in 444 (1.0%). Second, multivariable analysis demonstrated that the chance of non-cephalic presentation increased with increasing maternal age and weight, decreasing height, earlier gestational age at scan, and it was higher in the presence of placenta previa, oligohydramnios and polyhydramnios, in nulliparous than parous women and lower in women of South Asian and mixed racial origin than in White women. Third, 22% of cases of non-cephalic presentation were not eligible for ECV because of planned cesarean section for indications other than the malpresentation. Fourth, of those eligible for ECV only 48.5% (646/1,332) accepted the procedure and this was successful in 39.0% (252/646) of cases. Fifth, the chance of successful ECV increased with increasing maternal age and was lower in nulliparous than parous women. Sixth, in 33.9% (738/2,179) of pregnancies with non-cephalic presentation where successful ECV was not carried out there was a subsequent spontaneous rotation to cephalic presentation. Seventh, the chance of spontaneous rotation from non-cephalic to cephalic presentation increased with increasing interval between the scan and delivery and decreased with increasing birth weight, it was higher in women of Black than White racial origin, if the presentation was transverse or oblique than breech and if there was polyhydramnios and lower in nulliparous than parous women and in the presence of placenta previa. Eighth, in 109 (0.3%) of cephalic presentations there was subsequent rotation to non-cephalic presentation and in 41% of these the diagnosis was made during labor. Ninth, in the total of 2,431 cases of non-cephalic presentation at the time of the scan the presentation at birth was cephalic in 985 (40.5%); in 738 (74.9%) this was due to spontaneous rotation and in 247 (25.1%) due to successful ECV. Tenth, prediction of non-cephalic presentation at the 35+0 - 36+6 weeks scan and successful ECV from maternal and pregnancy factors was poor, but prediction of spontaneous rotation from non-cephalic to cephalic presentation was moderately good and this could be incorporated in the counselling of women prior to undertaking ECV. Conclusions: The problem of unexpected non-cephalic presentation in labor can to a great extent be overcome by a routine ultrasound examination at 35+0 - 36+6 weeks’ gestation. The incidence of non-cephalic presentation at the 35+0 - 36+6 weeks scan was about 5%, but, in about 40% of these cases the presentation at birth was cephalic, mainly due to subsequent spontaneous rotation and to a lesser extent as a consequence of successful ECV

Synoptic, thermodynamic and agroeconomic aspects of severe hail events in Cyprus

Hail is a hazardous weather element often accompanying a thunderstorm, as a result of either thermal instability or instability associated with baroclinic synoptic-scale systems (i.e. frontal depressions). Nevertheless, instability of any kind and thunderstorm activity does not always lead to the formation of hail of adequate size to reach the ground. The broader the knowledge concerning hail events the better the understanding of the underlying thermodynamic and dynamic mechanisms, as well as the physical processes associated with its formation. &lt;br&gt;&lt;br&gt; In the present study, the severe hail events that were recorded in Cyprus during the ten-year period from 1996 until 2005 were examined, first by grouping them into two clusters, namely, the &quot;thermal instability cluster&quot; and the &quot;frontal depression cluster&quot;. Subsequently, the spatial and temporal evolution of the synoptic, dynamic and thermodynamic characteristics of these hail events was studied in depth. Also, the impact of hailstorms on the local economy of the island is presented in terms of the compensations paid by the Agricultural Insurance Organization of the country

Calculations of time-dependent observables in non-Hermitian quantum mechanics: The problem and a possible solution

The solutions of the time independent Schrodinger equation for non-Hermitian (NH) Hamiltonians have been extensively studied and calculated in many different fields of physics by using L^2 methods that originally have been developed for the calculations of bound states. The existing non-Hermitian formalism breaks down when dealing with wavepackets(WP). An open question is how time dependent expectation values can be calculated when the Hamiltonian is NH ? Using the F-product formalism, which was recently proposed, [J. Phys. Chem., 107, 7181 (2003)] we calculate the time dependent expectation values of different observable quantities for a simple well known study test case model Hamiltonian. We carry out a comparison between these results with those obtained from conventional(i.e., Hermitian) quantum mechanics (QM) calculations. The remarkable agreement between these results emphasizes the fact that in the NH-QM, unlike standard QM, there is no need to split the entire space into two regions; i.e., the interaction region and its surrounding. Our results open a door for a type of WP propagation calculations within the NH-QM formalism that until now were impossible.Comment: 20 pages, 5 Postscript figures. To be Published in Physical Review

The Doubting Apostle 'Didymus' – Saint Thomas: theological, psychological and historical perspectives

Very little information is documented on Saint Thomas the Apostle, however the Gospel according to Saint John gives us a very good indication of his character. Saint Thomas was absent when Jesus appeared amongst his disciples the first time after His resurrection in the Upper Room. He would not accept as true, the numerous eye-witness reports concerning the risen Christ and stated that: "Unless I see the mark of the nails in his hands, and put my finger in the mark of the nails and my hand in his side, I will not believe" (John 20:25). He is thus termed ‘Doubting Thomas’, and his doubt was a distinct failure to believe in things he had not personally witnessed but that were attested to by others. Thomas’ primary significance thus arises from his position as a “doubter” and one lacking in requisite faith who found it necessary to have proof that Jesus had indeed risen from the dead. His doubt is important as it illustrates a profound denial of the Lord and a duplicity of the supremacy and indeed the very truth of what it means to possess proper faith. This paper argues that Thomas’ doubt (and his behaviour during the crucifixion of Jesus) has an internal disposition side, in other words his personality traits and cognition, as well as the external environment (the situation, including the abnormality of it, the nature of the communication and the group [the disciples]). The latter is often left out in the criticism of Thomas, resulting in him being portrayed as the symbol of the unfaithful and doubting individual. His behaviour could thus be evaluated in accordance with the attribution theory. Thomas clearly affirms the depth of his belief in his missionary activities, in especially India

The various power decays of the survival probability at long times for free quantum particle

The long time behaviour of the survival probability of initial state and its dependence on the initial states are considered, for the one dimensional free quantum particle. We derive the asymptotic expansion of the time evolution operator at long times, in terms of the integral operators. This enables us to obtain the asymptotic formula for the survival probability of the initial state $\psi (x)$, which is assumed to decrease sufficiently rapidly at large $|x|$. We then show that the behaviour of the survival probability at long times is determined by that of the initial state $\psi$ at zero momentum $k=0$. Indeed, it is proved that the survival probability can exhibit the various power-decays like $t^{-2m-1}$ for an arbitrary non-negative integers $m$ as $t \to \infty$, corresponding to the initial states with the condition $\hat{\psi} (k) = O(k^m)$ as $k\to 0$.Comment: 15 pages, to appear in J. Phys.

Relevance of soft modes for order parameter fluctuations in the Two-Dimensional XY model

We analyse the spin wave approximation for the 2D-XY model, directly in reciprocal space. In this limit the model is diagonal and the normal modes are statistically independent. Despite this simplicity non-trivial critical properties are observed and exploited. We confirm that the observed asymmetry for the probability density function for order parameter fluctuations comes from the divergence of the mode amplitudes across the Brillouin zone. We show that the asymmetry is a many body effect despite the importance played by the zone centre. The precise form of the function is dependent on the details of the Gibbs measure, giving weight to the idea that an effective Gibbs measure should exist in non-equilibrium systems, if a similar distribution is observed.Comment: 12 pages, 9 figure