Construction of higher order accurate vortex and particle methods

The standard point vortex method has recently been shown to be of high order of accuracy for problems on the whole plane, when using a uniform initial subdivision for assigning the vorticity to the points. If obstacles are present in the flow, this high order deteriorates to first or second order. New vortex methods are introduced which are of arbitrary accuracy (under regularity assumptions) regardless of the presence of bodies and the uniformity of the initial subdivision

Analysis and convergence of the MAC scheme. Part 1: The linear problem

The MAC discretization of fluid flow is analyzed for the stationary Stokes equations. It is proved that the discrete approximations do in fact converge to the exact solutions of the flow equations. Estimates using mesh dependent norms analogous to the standard H(sup 1) and L(sup 2) norms are given for the velocity and pressure, respectively

Iterative methods for elliptic finite element equations on general meshes

Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included

The Seventh Ecumenical Council and the veneration of icons in Orthodoxy

In the Orthodox Christian tradition, icons are not regarded as works of art; they are rather a visual gospel and windows into the spiritual realm. They are intended to assist believers to be more contemplative and prayerful. They guide believers into a life of prayer. There are, however, those who consider them to be idolatrous. Such a belief is erroneous, since the honouring of created beings does not detract from being totally devoted to the Creator in whose image they were created. Icons portraying God’s grace are sanctifying and help affirm the faith of Orthodox believers. Icons are a concrete theology that instructs and leads believers to a spiritual reality and ultimately sanctify them as they transform them. They ultimately serve as conduits to the healing of body and soul through the grace of God and are essentially a prelude to the final transfiguration of the world

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: screening by maternal factors, fetal biometry, and biomarkers at 35-37 weeks' gestation

Background: Small for gestational age (SGA) neonates are at increased risk of perinatal mortality and morbidity, but the risks can be substantially reduced if the condition is identified prenatally, because in such cases close monitoring and appropriate timing of delivery and prompt neonatal care can be undertaken. The traditional approach of identifying pregnancies with SGA fetuses is maternal abdominal palpation and serial measurements of symphysial-fundal height, but the detection rate of this approach is less than 30%. A higher performance of screening for SGA is achieved by sonographic fetal biometry during the third trimester; screening at 30-34 weeks’ gestation identifies about 80% of SGA neonates delivering preterm but only 50% of those delivering at term, at screen positive rate of 10%. There is some evidence that routine ultrasound examination at 36 weeks' gestation is more effective than that at 32 weeks in predicting birth of SGA neonates. Objective: To investigate the potential value of maternal characteristics and medical history, sonographycally estimated fetal weight (EFW) and biomarkers of impaired placentation at 35+0 - 36+6 weeks’ gestation in the prediction of delivery of small for gestational age (SGA) neonates. Methods: A dataset of 124,443 prospectively examined singleton pregnancies at 11+0 - 13+6 weeks’ gestation was used to derive, through multivariable logistic regression analysis, the patient-specific prior risk for delivery of SGA neonate with birthweight <10th percentile for gestational age from maternal characteristics and medical history. A dataset of 19,209 singleton pregnancies undergoing screening at 35+0 - 36+6 weeks’ gestation was divided into a training set and a validation set. The training dataset was used to develop models from multivariable logistic regression analysis to determine whether addition of uterine artery pulsatility index (UtA-PI), umbilical artery PI (UA-PI), fetal middle cerebral artery PI (MCA-PI), maternal serum placental growth factor (PlGF) and soluble fms-like tyrosine kinase-1 (sFLT) improved the performance of maternal factors and EFW in the prediction of delivery of SGA neonates. The models were then tested in the validation dataset to assess performance of screening. Results In the training dataset, in the SGA group, compared to those with birthweight ≥10th percentile, the median multiple of the median (MoM) values of PLGF and MCA-PI were reduced, whereas UtA-PI, UA-PI and sFLT were increased. Multivariable regression analysis demonstrated that in the prediction of SGA <10th there were significant contributions from maternal factors, EFW Z-score, UtA-PI MoM, MCA-PI MoM and PlGF MoM. In the validation dataset, prediction of 90% of SGA neonates delivering within two weeks of assessment was achieved by a screen positive rate of 67% in screening by maternal factors, 23% by maternal factors and EFW and 21% by the addition of biomarkers; the respective values for prediction of SGA neonates delivering at any stage after assessment were 66%, 32% and 30%. Conclusion: Addition of biomarkers of impaired placentation only marginally improves the predictive performance for delivery of SGA neonates achieved by maternal factors and fetal biometry at 35+0 - 36+6 weeks’ gestation