An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

Interpolation estimate for a finite-element space with embedded discontinuities

We consider a recently proposed finite-element space that consists of piecewise affine functions with discontinuities across a smooth given interface Γ (a curve in two dimensions, a surface in three dimensions). Contrary to existing extended finite element methodologies, the space is a variant of the standard conforming Formula space that can be implemented element by element. Further, it neither introduces new unknowns nor deteriorates the sparsity structure. It is proved that, for u arbitrary in Formula, the interpolant Formula defined by this new space satisfies Graphic where h is the mesh size, Formula is the domain, Formula, Formula, Formula and standard notation has been adopted for the function spaces. This result proves the good approximation properties of the finite-element space as compared to any space consisting of functions that are continuous across Γ, which would yield an error in the Formula-norm of order Graphic. These properties make this space especially attractive for approximating the pressure in problems with surface tension or other immersed interfaces that lead to discontinuities in the pressure field. Furthermore, the result still holds for interfaces that end within the domain, as happens for example in cracked domains.

Numerical assessment of stability of interface discontinuous finite element pressure spaces

The stability of two recently developed pressure spaces has been assessed numerically: The space proposed by Ausas et al. [R.F. Ausas, F.S. Sousa, G.C. Buscaglia, An improved finite element space for discontinuous pressures, Comput. Methods Appl. Mech. Engrg. 199 (2010) 1019-1031], which is capable of representing discontinuous pressures, and the space proposed by Coppola-Owen and Codina [A.H. Coppola-Owen, R. Codina, Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functions, Int. J. Numer. Methods Fluids, 49 (2005) 1287-1304], which can represent discontinuities in pressure gradients. We assess the stability of these spaces by numerically computing the inf-sup constants of several meshes. The inf-sup constant results as the solution of a generalized eigenvalue problems. Both spaces are in this way confirmed to be stable in their original form. An application of the same numerical assessment tool to the stabilized equal-order P-1/P-1 formulation is then reported. An interesting finding is that the stabilization coefficient can be safely set to zero in an arbitrary band of elements without compromising the formulation's stability. An analogous result is also reported for the mini-element P-1(+)/P-1 when the velocity bubbles are removed in an arbitrary band of elements. (C) 2012 Elsevier B.V. All rights reserved.

Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures

We design and investigate a sequential discontinuous Galerkin method to approximate two-phase immiscible incompressible flows in heterogeneous porous media with discontinuous capillary pressures. The nonlinear interface conditions are enforced weakly through an adequate design of the penalties on interelement jumps of the pressure and the saturation. An accurate reconstruction of the total velocity is considered in the Raviart-Thomas(-Nedelec) finite element spaces, together with diffusivity-dependent weighted averages to cope with degeneracies in the saturation equation and with media heterogeneities. The proposed method is assessed on one-dimensional test cases exhibiting rough solutions, degeneracies, and capillary barriers. Stable and accurate solutions are obtained without limiters. (C) 2010 Elsevier B.V. All rights reserved.

Accurate velocity reconstruction for Discontinuous Galerkin approximations of two-phase porous media flows

We consider Discontinuous Galerkin approximations of two-phase, immiscible porous media flows in the global pressure/fractional flow formulation with capillary pressure. A sequential approach is used with a backward Euler step for the saturation equation, equal-order interpolation for the pressure and the saturation, and without any limiters. An accurate total velocity field is recovered from the global pressure equation to be used in the saturation equation. Numerical experiments show the advantages of the proposed reconstruction. To cite this article: A. Ern et al., C R. Acad. Sci. Paris, Ser. 1347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

SYNTHESIS OF N-15-ENRICHED UREA (CO((NH2)-N-15)(2)) FROM (NH3)-N-15, CO, AND S IN A DISCONTINUOUS PROCESS

CO((NH2)-N-15)(2) enriched with the stable isotope N-15 was synthesized based on a reaction involving CO, (NH3)-N-15, and S in the presence of CH3OH. The method differs from the industrial method; a stainless steel reactor internally lined with polytetrafluoroethylene (PTFE) was used in a discontinuous process under low pressure and temperature. The yield of the synthesis was evaluated as a function of the parameters: the amount of reagents, reaction time, addition of H2S, liquid solution and reaction temperature. The results showed that under optimum conditions (1.36, 4.01, and 4.48 g of (NH3)-N-15, CO, and S, respectively, 40 ml CH3OH, 40 mg H2S, 100 degrees C and 120 min of reaction) 1.82 g (yield 76.5%) of the compound was obtained per batch. The synthesized CO((NH2)-N-15)(2) contained 46.2% N, 0.55% biuret, melting point of 132.55 degrees C and did not exhibit isotopic fractionation. The production cost of CO((NH2)-N-15)(2) with 90.0 at. % N-15 was US$ 238.60 per gram.

A new enrichment space for the treatment of discontinuous pressures in multi-fluid flows

In this work, a new enrichment space to accommodate jumps in the pressure field at immersed interfaces in finite element formulations, is proposed. The new enrichment adds two degrees of freedom per element that can be eliminated by means of static condensation. The new space is tested and compared with the classical P1 space and to the space proposed by Ausas et al (Comp. Meth. Appl. Mech. Eng., Vol. 199, 10191031, 2010) in several problems involving jumps in the viscosity and/or the presence of singular forces at interfaces not conforming with the element edges. The combination of this enrichment space with another enrichment that accommodates discontinuities in the pressure gradient has also been explored, exhibiting excellent results in problems involving jumps in the density or the volume forces. Copyright (c) 2011 John Wiley & Sons, Ltd.

Synthesis of 15N-enriched urea (CO(15NH2)2) from 15NH3, CO, and S in a discontinuous process

CO(15NH2)2 enriched with the stable isotope 15N was synthesized based on a reaction involving CO, 15NH3, and S in the presence of CH3OH. The method differs from the industrial method; a stainless steel reactor internally lined with polytetrafluoroethylene (PTFE) was used in a discontinuous process under low pressure and temperature. The yield of the synthesis was evaluated as a function of the parameters: the amount of reagents, reaction time, addition of H2S, liquid solution and reaction temperature. The results showed that under optimum conditions (1.36, 4.01, and 4.48 g of 15NH3, CO, and S, respectively, 40 ml CH3OH, 40 mg H2S, 100 ºC and 120 min of reaction) 1.82 g (yield 76.5%) of the compound was obtained per batch. The synthesized CO(15NH2)2 contained 46.2% N, 0.55% biuret, melting point of 132.55 ºC and did not exhibit isotopic fractionation. The production cost of CO(15NH2)2 with 90.0 at. % 15N was US$ 238.60 per gram.

The effects of solar radiation pressure on the motion of an artificial satellite

This thesis documents an investigation of the effect of solar radiation pressure on the motion of an artificial satellite. Consideration is given to the methods required for the inclusion of the discontinuous effect of the Earth's shadow. The analysis resulting from the description of a deformed diffusely reflecting balloon satellite and an algorithm describing the effects of Earth reflected solar radiation pressure are developed, culminating in the application of the derived theory to the orbital data of the balloon satellite, Explorer 19.

Changes in intraocular pressure in study and fellow eyes in the IVAN trial

PURPOSE: To describe changes in intraocular pressure (IOP) in the 'alternative treatments to Inhibit VEGF in Age-related choroidal Neovascularisation (IVAN)' trial (registered as ISRCTN92166560). DESIGN: Randomised controlled clinical trial with factorial design. PARTICIPANTS: Patients (n=610) with treatment naïve neovascular age-related macular degeneration were enrolled and randomly assigned to receive either ranibizumab or bevacizumab and to two regimens, namely monthly (continuous) or as needed (discontinuous) treatment. METHODS: At monthly visits, IOP was measured preinjection in both eyes, and postinjection in the study eye. OUTCOME MEASURES: The effects of 10 prespecified covariates on preinjection IOP, change in IOP (postinjection minus preinjection) and the difference in preinjection IOP between the two eyes were examined. RESULTS: For every month in trial, there was a statistically significant rise in both the preinjection IOP and the change in IOP postinjection during the time in the trial (estimate 0.02 mm Hg, 95% CI 0.01 to 0.03, p<0.001 and 0.03 mm Hg, 95% CI 0.01 to 0.04, p=0.002, respectively). There was also a small but significant increase during the time in trial in the difference in IOP between the two eyes (estimate 0.01 mm Hg, 95% CI 0.005 to 0.02, p<0.001). There were no differences between bevacizumab and ranibizumab for any of the three outcomes (p=0.93, p=0.22 and p=0.87, respectively). CONCLUSIONS: Anti-vascular endothelial growth factor agents induce increases in IOP of small and uncertain clinical significance.

Nebivolol Reduces Central Blood Pressure In Stage I Hypertensive Patients: Experimental Single Cohort Study.

Assessment of central blood pressure (BP) has grown substantially over recent years because evidence has shown that central BP is more relevant to cardiovascular outcomes than peripheral BP. Thus, different classes of antihypertensive drugs have different effects on central BP despite similar reductions in brachial BP. The aim of this study was to investigate the effect of nebivolol, a β-blocker with vasodilator properties, on the biochemical and hemodynamic parameters of hypertensive patients. Experimental single cohort study conducted in the outpatient clinic of a university hospital. Twenty-six patients were recruited. All of them underwent biochemical and hemodynamic evaluation (BP, heart rate (HR), central BP and augmentation index) before and after 3 months of using nebivolol. 88.5% of the patients were male; their mean age was 49.7 ± 9.3 years and most of them were overweight (29.6 ± 3.1 kg/m2) with large abdominal waist (102.1 ± 7.2 cm). There were significant decreases in peripheral systolic BP (P = 0.0020), diastolic BP (P = 0.0049), HR (P < 0.0001) and central BP (129.9 ± 12.3 versus 122.3 ± 10.3 mmHg; P = 0.0083) after treatment, in comparison with the baseline values. There was no statistical difference in the augmentation index or in the biochemical parameters, from before to after the treatment. Nebivolol use seems to be associated with significant reduction of central BP in stage I hypertensive patients, in addition to reductions in brachial systolic and diastolic BP.

Effects Of High Pressure Homogenization On The Activity, Stability, Kinetics And Three-dimensional Conformation Of A Glucose Oxidase Produced By Aspergillus Niger.

High pressure homogenization (HPH) is a non-thermal method, which has been employed to change the activity and stability of biotechnologically relevant enzymes. This work investigated how HPH affects the structural and functional characteristics of a glucose oxidase (GO) from Aspergillus niger. The enzyme was homogenized at 75 and 150 MPa and the effects were evaluated with respect to the enzyme activity, stability, kinetic parameters and molecular structure. The enzyme showed a pH-dependent response to the HPH treatment, with reduction or maintenance of activity at pH 4.5-6.0 and a remarkable activity increase (30-300%) at pH 6.5 in all tested temperatures (15, 50 and 75°C). The enzyme thermal tolerance was reduced due to HPH treatment and the storage for 24 h at high temperatures (50 and 75°C) also caused a reduction of activity. Interestingly, at lower temperatures (15°C) the activity levels were slightly higher than that observed for native enzyme or at least maintained. These effects of HPH treatment on function and stability of GO were further investigated by spectroscopic methods. Both fluorescence and circular dichroism revealed conformational changes in the molecular structure of the enzyme that might be associated with the distinct functional and stability behavior of GO.

Taurine Supplementation Reduces Blood Pressure And Prevents Endothelial Dysfunction And Oxidative Stress In Post-weaning Protein-restricted Rats.

Taurine is a sulfur-containing amino acid that exerts protective effects on vascular function and structure in several models of cardiovascular diseases through its antioxidant and anti-inflammatory properties. Early protein malnutrition reprograms the cardiovascular system and is linked to hypertension in adulthood. This study assessed the effects of taurine supplementation in vascular alterations induced by protein restriction in post-weaning rats. Weaned male Wistar rats were fed normal- (12%, NP) or low-protein (6%, LP) diets for 90 days. Half of the NP and LP rats concomitantly received 2.5% taurine supplementation in the drinking water (NPT and LPT, respectively). LP rats showed elevated systolic, diastolic and mean arterial blood pressure versus NP rats; taurine supplementation partially prevented this increase. There was a reduced relaxation response to acetylcholine in isolated thoracic aortic rings from the LP group that was reversed by superoxide dismutase (SOD) or apocynin incubation. Protein expression of p47phox NADPH oxidase subunit was enhanced, whereas extracellular (EC)-SOD and endothelial nitric oxide synthase phosphorylation at Ser 1177 (p-eNOS) were reduced in aortas from LP rats. Furthermore, ROS production was enhanced while acetylcholine-induced NO release was reduced in aortas from the LP group. Taurine supplementation improved the relaxation response to acetylcholine and eNOS-derived NO production, increased EC-SOD and p-eNOS protein expression, as well as reduced ROS generation and p47phox expression in the aortas from LPT rats. LP rats showed an increased aortic wall/lumen ratio and taurine prevented this remodeling through a reduction in wall media thickness. Our data indicate a protective role of taurine supplementation on the high blood pressure, endothelial dysfunction and vascular remodeling induced by post-weaning protein restriction. The beneficial vascular effect of taurine was associated with restoration of vascular redox homeostasis and improvement of NO bioavailability.

Onset Of Hypertension During Pregnancy Is Associated With Long-term Worse Blood Pressure Control And Adverse Cardiac Remodeling.

Up to 20% of women with hypertensive pregnancy disorders might persist with chronic hypertension. This study compared clinical and echocardiographic features between women whose hypertension began as hypertensive pregnancy disorders (PH group) and women whose diagnosis of hypertension did not occur during pregnancy (NPH group). Fifty PH and 100 NPH women were cross-sectionally evaluated by clinical, laboratory, and echocardiography analysis, and the groups were matched by duration of hypertension. PH exhibited lower age (46.6 ± 1.4 vs. 65.3 ± 1.1 years; P < .001), but higher systolic (159.8 ± 3.9 vs. 148.0 ± 2.5 mm Hg; P = .009) and diastolic (97.1 ± 2.4 vs. 80.9 ± 1.3 mm Hg; P < .001) blood pressure than NPH, although used more antihypertensive classes (3.4 ± 0.2 vs. 2.6 ± 0.1; P < .001). Furthermore, PH showed higher left ventricular wall thickness and increased prevalence of concentric hypertrophy than NPH after adjusting for age and blood pressure. In conclusion, this study showed that PH may exhibit worse blood pressure control and adverse left ventricular remodeling compared with NPH.

Combined External Pressure And Cu-substitution Studies On Bafe2as2 Single Crystals.

We report a combined study of external pressure and Cu-substitution on BaFe2As2 single crystals grown by the in-flux technique. At ambient pressure, the Cu-substitution is known to suppress the spin density wave (SDW) phase in pure BaFe2As2(TSDW ≈ 140 K) and to induce a superconducting (SC) dome with a maximum transition temperature [Formula: see text]. This [Formula: see text] is much lower than the Tc ∼ 15-28 K achieved in the case of Ru, Ni and Co substitutions. Such a lower Tc is attributed to a Cu(2+) magnetic pair-breaking effect. The latter is strongly suppressed by applied pressure, as shown herein, Tc can be significantly enhanced by applying high pressures. In this work, we investigated the pressure effects on Cu(2+) magnetic pair-breaking in the BaFe2-xCuxAs2 series. Around the optimal concentration (xopd = 0.11), all samples showed a substantial increase of Tc as a function of pressure. Yet for those samples with a slightly higher doping level (over-doped regime), Tc presented a dome-like shape with maximum Tc ≃ 8 K. Remarkably interesting, the under-doped samples, e.g. x = 0.02 display a maximum pressure induced Tc ≃ 30 K which is comparable to the maximum Tc's found for the pure compound under external pressures. Furthermore, the magnetoresistance effect as a function of pressure in the normal state of the x = 0.02 sample also presented an evolution consistent with the screening of the Cu(2+) local moments. These findings demonstrate that the Cu(2+) magnetic pair-breaking effect is completely suppressed by applying pressure in the low concentration regime of Cu(2+) substituted BaFe2As2.