On an incompressible Navier-Stokes/Cahn-Hilliard system with degenerate mobility

We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain by allowing for a degenerate mobility. The model has been developed by Abels, Garcke and Grün for fluids with different densities and leads to a solenoidal velocity field. It is given by a nonhomogeneous Navier-Stokes system with a modifed convective term coupled to a Cahn-Hilliard system, such that an energy estimate is fulfilled which follows from the fact that the model is thermodynamically consistent

Mean curvature flow with triple junctions in higher space dimensions

We consider mean curvature flow of n-dimensional surface clusters. At (n-1)-dimensional triple junctions an angle condition is required which in the symmetric case reduces to the well-known 120 degree angle condition. Using a novel parametrization of evolving surface clusters and a new existence and regularity approach for parabolic equations on surface clusters we show local well-posedness by a contraction argument in parabolic Hoelder spaces.Comment: 31 pages, 2 figure

Effect of frequent hemodialysis on residual kidney function.

Frequent hemodialysis can alter volume status, blood pressure, and the concentration of osmotically active solutes, each of which might affect residual kidney function (RKF). In the Frequent Hemodialysis Network Daily and Nocturnal Trials, we examined the effects of assignment to six compared with three-times-per-week hemodialysis on follow-up RKF. In both trials, baseline RKF was inversely correlated with number of years since onset of ESRD. In the Nocturnal Trial, 63 participants had non-zero RKF at baseline (mean urine volume 0.76 liter/day, urea clearance 2.3 ml/min, and creatinine clearance 4.7 ml/min). In those assigned to frequent nocturnal dialysis, these indices were all significantly lower at month 4 and were mostly so at month 12 compared with controls. In the frequent dialysis group, urine volume had declined to zero in 52% and 67% of patients at months 4 and 12, respectively, compared with 18% and 36% in controls. In the Daily Trial, 83 patients had non-zero RKF at baseline (mean urine volume 0.43 liter/day, urea clearance 1.2 ml/min, and creatinine clearance 2.7 ml/min). Here, treatment assignment did not significantly influence follow-up levels of the measured indices, although the range in baseline RKF was narrower, potentially limiting power to detect differences. Thus, frequent nocturnal hemodialysis appears to promote a more rapid loss of RKF, the mechanism of which remains to be determined. Whether RKF also declines with frequent daily treatment could not be determined

Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities

We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain in two and three space dimensions. In contrast to previous works, we study a new model recently developed by Abels, Garcke, and Gr\"un for fluids with different densities, which leads to a solenoidal velocity field. The model is given by a non-homogeneous Navier-Stokes system with a modified convective term coupled to a Cahn-Hilliard system. The density of the mixture depends on an order parameter.Comment: 33 page

Plasma Levels of Middle Molecules to Estimate Residual Kidney Function in Haemodialysis without Urine Collection

© 2015 Vilar et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, (http://creativecommons.org/Licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.BACKGROUND: Residual Kidney Function (RKF) is associated with survival benefits in haemodialysis (HD) but is difficult to measure without urine collection. Middle molecules such as Cystatin C and β2-microglobulin accumulate in renal disease and plasma levels have been used to estimate kidney function early in this condition. We investigated their use to estimate RKF in patients on HD. DESIGN: Cystatin C, β2-microglobulin, urea and creatinine levels were studied in patients on incremental high-flux HD or hemodiafiltration(HDF). Over sequential HD sessions, blood was sampled pre- and post-session 1 and pre-session 2, for estimation of these parameters. Urine was collected during the whole interdialytic interval, for estimation of residual GFR (GFRResidual = mean of urea and creatinine clearance). The relationships of plasma Cystatin C and β2-microglobulin levels to GFRResidual and urea clearance were determined. RESULTS: Of the 341 patients studied, 64% had urine output>100 ml/day, 32.6% were on high-flux HD and 67.4% on HDF. Parameters most closely correlated with GFRResidual were 1/β2-micoglobulin (r2 0.67) and 1/Cystatin C (r2 0.50). Both these relationships were weaker at low GFRResidual. The best regression model for GFRResidual, explaining 67% of the variation, was: GFRResidual = 160.3 · (1/β2m) - 4.2. Where β2m is the pre-dialysis β2 microglobulin concentration (mg/L). This model was validated in a separate cohort of 50 patients using Bland-Altman analysis. Areas under the curve in Receiver Operating Characteristic analysis aimed at identifying subjects with urea clearance≥2 ml/min/1.73 m2 was 0.91 for β2-microglobulin and 0.86 for Cystatin C. A plasma β2-microglobulin cut-off of ≤19.2 mg/L allowed identification of patients with urea clearance ≥2 ml/min/1.73 m2 with 90% specificity and 65% sensitivity. CONCLUSION: Plasma pre-dialysis β2-microglobulin levels can provide estimates of RKF which may have clinical utility and appear superior to cystatin C. Use of cut-off levels to identify patients with RKF may provide a simple way to individualise dialysis dose based on RKF.Peer reviewe

Linearized stability analysis of surface diffusion for hypersurfaces with triple lines

The linearized stability of stationary solutions for surface diffusion is studied. We consider three hypersurfaces that lie inside a fixed domain and touch its boundary with a right angle and fulfill a non-flux condition. Additionally they meet at a triple line with prescribed angle conditions and further boundary conditions resulting from the continuity of chemical potentials and a flux balance have to hold at the triple line. We introduce a new specific parametrization with two parameters corresponding to a movement in tangential and normal direction to formulate the geometric evolution law as a system of partial differential equations. For the linearized stability analysis we identify the problem as an H−1-gradient flow, which will be crucial to show self-adjointness of the linearized operator. Finally we study the linearized stability of some examples

Stability analysis of geometric evolution equations with triple lines and boundary contact

In this doctoral thesis we investigate different area-minimizing geometric evolution equations for evolving hypersurfaces, which lie in a fixed domain and touch its boundary at a right angle. Additionally we consider situations where three evolving hypersurfaces meet each other at a triple line under prescribed angle conditions. We introduce appropriate parametrizations to formulate the geometric evolution laws mean curvature and surface diffusion flow as partial differential equations for unknown functions. These differential equationsare then examined qualitatively on linearized stability around a stationary state. More precisely, they are linearized around a stationary state and the arising linear differential equations are investigated on stability with the help of methods from spectral theory. As a result we get an equivalence of stability to positivity of a specific bilinear form, which is easier to verify in applications

Linearized stability analysis of surface diffusion for hypersurfaces with boundary contact

The linearized stability of stationary solutions for surface diffusion is studied. We consider hypersurfaces that lie inside a fixed domain, touch its boundary with a right angle and fulfill a no-flux condition. We formulate the geometric evolution law as a partial differential equation with the help of a parametrization from Vogel [Vog00], which takes care of a possible curved boundary. For the linearized stability analysis we identify as in the work of Garcke, Ito and Kohsaka [GIK05] the problem as an