On Sharp Interface Limits for Diffuse Interface Models for Two-Phase Flows

We discuss the sharp interface limit of a diffuse interface model for a two-phase flow of two partly miscible viscous Newtonian fluids of different densities, when a certain parameter \epsilon>0 related to the interface thickness tends to zero. In the case that the mobility stays positive or tends to zero slower than linearly in \epsilon we will prove that weak solutions tend to varifold solutions of a corresponding sharp interface model. But, if the mobility tends to zero faster than \epsilon^3 we will show that certain radially symmetric solutions tend to functions, which will not satisfy the Young-Laplace law at the interface in the limit.Comment: 27 pages, 1 figur

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

Magnet displacement: a rare complication following cochlear implantation

The purpose of this paper is to describe cases which reported complication after cochlear implantation in children: displacement of magnet from the receiver pocket, possibly aided by the use of magnetic toys. We observed magnet displacement in two female children from the same family and in one male child. Age at implantation was 23, 51, and 24months, respectively. Magnet displacement occurred at 37, 16, and 32months, respectively after the initial surgery. The magnets were replaced under general anaesthesia and we did not observe recurrent magnet dislodgement. Measurements indicated that forces required to remove the magnet from its pocket were not greater than those exerted by magnetic toys or the magnet used in the external sender coil. Although magnet displacement is not common after cochlear implantation, it is a major complication in children where subsequent general anaesthesia and surgery are necessary to replace the magnet. Therefore, we propose that pockets for removable magnets of cochlear implants used in children should be redesigned to increase forces to remove the magnet or that removable magnets not be used at al

On sharp interface limits for diffuse interface models for two-phase flows

We discuss the sharp interface limit of a diffuse interface model for a two-phase flow of two partly miscible viscous Newtonian fluids of different densities, when a certain parameter ϵ>0 related to the interface thickness tends to zero. In the case that the mobility stays positive or tends to zero slower than linearly in ϵ we will prove that weak solutions tend to varifold solutions of a corresponding sharp interface model. But, if the mobility tends to zero faster than ϵ3 we will show that certain radially symmetric solutions tend to functions, which will not satisfy the Young-Laplace law at the interface in the limit

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

Privacy and transparency in the 4th space : implications for conspirary theories

This article investigates the role of privacy and transparency in the 4th Space and outlines their implications for the development and dissemination of conspiracy theories. We argue that privacy can be exploited by individuals and organizations to spread conspiracy theories online, while organizational transparency, intended to increase accountability and ultimately trust, can have the adverse effect and nurture conspiracy beliefs. Through the lens of the 4th Space concept, we offer suggestions on how to approach those challenges which emerge as a result of the complex entanglements of both actual and virtual world across time

Verhandeln und Streiten im Erörterungstermin - Zur Bürgerbeteiligung in gentechnikrechtlichen Genehmigungsverfahren

Bora A. Verhandeln und Streiten im Erörterungstermin - Zur Bürgerbeteiligung in gentechnikrechtlichen Genehmigungsverfahren. In: Barben D, Abels G, eds. Biotechnologie - Globalisierung - Demokratie. Politische Gestaltung transnationaler Technologieentwicklung. Berlin: Edition Sigma; 2000: 335-357