Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. II: The incompressible Navier-Stokes equations

This paper presents the construction of a correct-energy stabilized finite element method for the incompressible Navier-Stokes equations. The framework of the methodology and the correct-energy concept have been developed in the convective--diffusive context in the preceding paper [M.F.P. ten Eikelder, I. Akkerman, Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. I: The convective--diffusive context, Comput. Methods Appl. Mech. Engrg. 331 (2018) 259--280]. The current work extends ideas of the preceding paper to build a stabilized method within the variational multiscale (VMS) setting which displays correct-energy behavior. Similar to the convection--diffusion case, a key ingredient is the proper dynamic and orthogonal behavior of the small-scales. This is demanded for correct energy behavior and links the VMS framework to the streamline-upwind Petrov-Galerkin (SUPG) and the Galerkin/least-squares method (GLS). The presented method is a Galerkin/least-squares formulation with dynamic divergence-free small-scales (GLSDD). It is locally mass-conservative for both the large- and small-scales separately. In addition, it locally conserves linear and angular momentum. The computations require and employ NURBS-based isogeometric analysis for the spatial discretization. The resulting formulation numerically shows improved energy behavior for turbulent flows comparing with the original VMS method.Comment: Update to postprint versio

A space-time framework for periodic flows with applications to hydrofoils

In this paper we propose a space-time framework for the computation of periodic flows. We employ the isogeometric analysis framework to achieve higher-order smoothness in both space and time. The discretization is performed using residual-based variational multiscale modelling and weak boundary conditions are adopted to enhance the accuracy near the moving boundaries of the computational domain. We show conservation properties and present a conservative method for force extraction. We apply our framework to the computation of a heaving and pitching hydrofoil. Numerical results display very accurate results on course meshes

Supramolecular copolymers: structure and composition revealed by theoretical modeling

Supramolecular copolymers, non-covalent analogues of synthetic copolymers, constitute a new and promising class of polymers. In contrast to their covalent counterparts, the details of their mechanism of formation, as well as the factors determining their composition and length, are still poorly understood. Here, the supramolecular copolymerization between two slightly structurally different benzene-1,3,5-tricarboxamide (BTA) monomers functionalized with either oligodimethylsiloxane (oDMSi) or alkyl side chains is unraveled by combining experimental and theoretical approaches. By applying the “sergeant-and-soldiers” approach using circular dichroism (CD) experiments, we are able to obtain detailed insights into the structure and composition of these supramolecular copolymers. Moreover, we observe an unexpected chiral induction upon mixing two independently CD-silent solutions of the achiral (soldier) and chiral (sergeant) monomers. We find that the subtle differences in the chemical structure of the two monomers impact their homopolymerization mechanism: whereas alkyl-BTAs cooperatively self-assemble, oDMSi-BTAs self-assemble in an isodesmic manner. The effect of these mechanistic differences in the supramolecular copolymerization process is investigated as a function of the composition of the two monomers and explicitly rationalized by mathematical modeling. The results show that, at low fractions of oDMSi-BTA sergeants (25 mol%), the isodesmic assembly of the increasing amounts of sergeant becomes more dominant, and different species start to coexist in the copolymerization process. The analysis of the experimental data with a newly developed theoretical model allows us to quantify the thermodynamic parameters, the distribution of different species, and the compositions and stack lengths of the formed supramolecular copolymers existing at various feed ratios of the two monomers.This work was financially supported by The Netherlands Organization for Scientific Research (NWO-TOP PUNT Grant 10018944) and the Dutch Ministry of Education, Culture and Science (Gravity Program 024.001.035)

Mechanical methods for induction of labour

Background Mechanical methods were the first methods developed to ripen the cervix and induce labour.During recent decades they have been substituted by pharmacological methods. Potential advantages of mechanical methods, compared with pharmacological methods may include reduction in side effects that could improve neonatal outcomes. This is an update of a review first published in 2001, last updated in 2012. Objectives To determine the effectiveness and safety of mechanical methods for third trimester (> 24 weeks' gestation) induction of labour in comparison with prostaglandin E2 (PGE2) (vaginal and intracervical), low-dose misoprostol (oral and vaginal), amniotomy or oxytocin. Search methods For this update, we searched Cochrane Pregnancy and Childbirth’s Trials Register, ClinicalTrials.gov, the WHO International Clinical Trials Registry Platform (ICTRP), and reference lists of retrieved studies (9 January 2018). We updated the search in March 2019 and added the search results to the awaiting classification section of the review. Selection criteria Clinicaltrials comparingmechanicalmethodsusedforthirdtrimester cervicalripeningorlabourinductionwithpharmacologicalmethods. Mechanical methods include: (1) the introduction of a catheter through the cervix into the extra-amniotic space with balloon insufflation; (2) introduction of laminaria tents, or their synthetic equivalent (Dilapan), into the cervical canal; (3) use of a catheter to inject fluid into the extra-amniotic space (EASI). This review includes the following comparisons: (1) specific mechanical methods (balloon catheter, laminaria tents or EASI) compared with prostaglandins (different types, different routes) or with oxytocin; (2) single balloon compared to a double balloon; (3) addition of prostaglandins or oxytocin to mechanical methods compared with prostaglandins or oxytocin alone. Data collection and analysis Two review authors independently assessed trials for inclusion and assessed risk of bias. Two review authors independently extracted data and assessed the quality of the evidence using the GRADE approach. Main results This review update includes a total of 113 trials (22,373 women) contributing data to 21 comparisons. Risk of bias of trials varied. Overall, the evidence was graded from very-low to moderate quality. All evidence was downgraded f