Analytical investigations and numerical experiments for singularly perturbed convection-diffusion problems with layers and singularities using a newly developed FE-software

In the field of singularly perturbed reaction- or convection-diffusion boundary value problems the research area of a priori error analysis for the finite element method, has already been thoroughly investigated. In particular, for mesh adapted methods and/or various stabilization techniques, works have been done that prove optimal rates of convergence or supercloseness uniformly in the perturbation parameter epsilon. Commonly, however, it is assumed that the exact solution behaves nicely in that it obeys certain regularity assumptions although in general, e.g. due to corner singularities, these regularity requirements are not satisfied. So far, insufficient regularity has been met by assuming compatibility conditions on the data. The present thesis originated from the question: What can be shown if these rather unrealistic additional assumptions are dropped? We are interested in epsilon-uniform a priori estimates for convergence and superconvergence that include some regularity parameter that is adjustable to the smoothness of the exact solution. A major difficulty that occurs when seeking the numerical error decay is that the exact solution is not known. Since we strive for reliable rates of convergence we want to avoid the standard approach of the "double-mesh principle". Our choice is to use reference solutions as a substitute for the exact solution. Numerical experiments are intended to confirm the theoretical results and to bring further insights into the interplay between layers and singularities. To computationally realize the thereby arising demanding practical aspects of the finite element method, a new software is developed that turns out to be particularly suited for the needs of the numerical analyst. Its design, features and implementation is described in detail in the second part of the thesis

SiFo-Peers: A Social FOAF Based Peer-to-Peer Network

In this paper, an attempt is made to conceptually unite three different application areas for semantic technologies, namely personal Knowledge Management, social networking, and Peer-to-Peer information-sharing. Until now, semantic technology has been applied to each of these application areas separately or in binary combinations only. By functionally combining all three areas in a single application, it is hoped to sketch a compelling Semantic Web system that will help increase the spread and acceptance of the Semantic Web vision. A concrete usage scenario of a community of researchers is used to demonstrate the approach

Numerical analysis of a singularly perturbed convection diffusion problem with shift in space

We consider a singularly perturbed convection-diffusion problem that has in addition a shift term. We show a solution decomposition using asymptotic expansions and a stability result. Based upon this we provide a numerical analysis of high order finite element method on layer adapted meshes. We also apply a new idea of using a coarser mesh in places where weak layers appear. Numerical experiments confirm our theoretical results.Comment: 17 pages, 1 figur

Hydrogen-Poor Disks in Compact X-Ray Binaries

We show that accretion disks in several compact X-ray binaries with hydrogen-depleted donors are likely subject to a thermal ionization instability, unless they are strongly irradiated. These disks are particularly interesting in that their MHD-turbulent properties in the neutral phase may be quite different from those of standard, hydrogen-rich disks.Comment: 10 pages, accepted for publication in ApJ

Imaging for trans-catheter pulmonary stent-valve implantation without angiography: role of intravascular ultrasound

Patients with stenosed biologic pulmonary conduits require redo cardiac surgery to prevent severe right ventricular dysfunction. Following the latest trends, the trans-catheter pulmonary stent-valve implantation represents a new fascinating alternative carrying a lower operative risk, compared with the standard open-heart re-intervention. Traditionally, the pulmonary stent valve is positioned off pump, under fluoroscopic control, and requires angiographies. However, alternative tools not requiring contrast injections for the intra-operative cardiac imaging have to be also considered strongly. The usefulness of intravascular ultrasound for the positioning of aortic endoprosthesis has already been proven in previous reports and, following the same principle, we have started to routinely implant balloon-expandable stent valves (Edwards Sapien™ THV) in stenosed pulmonary valve conduits using intravascular ultrasound for the stent-valve positioning without angiography. We describe the intra-operative intravascular imaging technique with technical detail

Modified ‘dumbbell' technique: a simple and intuitive method to position balloon-expandable stent valves

Intraoperative cardiac imaging plays a key role during transcatheter aortic valve replacement. In recent years, new techniques and new tools for improved image quality and virtual navigation have been proposed, in order to simplify and standardize stent valve positioning and implantation. But routine performance of the new techniques may require major economic investments or specific knowledge and skills and, for this reason, they may not be accessible to the majority of cardiac centres involved in transcatheter valve replacement projects. Additionally, they still require injections of contrast medium to obtain computed images. Therefore, we have developed and describe here a very simple and intuitive method of positioning balloon-expandable stent valves, which represents the evolution of the ‘dumbbell' technique for echocardiography-guided transcatheter valve replacement without angiography. This method, based on the partial inflation of the balloon catheter during positioning, traps the crimped valve in the aortic valve orifice and, consequently, very near to the ideal landing zone. It does not require specific echocardiographic knowledge; it does not require angiographies that increase the risk of postoperative kidney failure in elderly patients, and it can be also performed in centres not equipped with a hybrid operating roo

An Architecture of FoaF-based Peer 2 Peer Knowledge Management System

A number of researches have been focused on improving the productivity of knowledge workers. Effective communication is determinative, and one important problem has been to find the right person for collaboration. The Semantic Web efforts improve it by better wide-range knowledge management. Through extending the FoaF (Friend of a Friend) vocabulary, knowledge workers can share their machine-readable knowledge world widely, so that their PCs can facilitate effective collaboration efficiently. This paper presents an approach to support networked personal knowledge management. An example of extended FoaF is also describe

aLFQ: an R-package for estimating absolute protein quantities from label-free LC-MS/MS proteomics data

Motivation: The determination of absolute quantities of proteins in biological samples is necessary for multiple types of scientific inquiry. While relative quantification has been commonly used in proteomics, few proteomic datasets measuring absolute protein quantities have been reported to date. Various technologies have been applied using different types of input data, e.g. ion intensities or spectral counts, as well as different absolute normalization strategies. To date, a user-friendly and transparent software supporting large-scale absolute protein quantification has been lacking. Results: We present a bioinformatics tool, termed aLFQ, which supports the commonly used absolute label-free protein abundance estimation methods (TopN, iBAQ, APEX, NSAF and SCAMPI) for LC-MS/MS proteomics data, together with validation algorithms enabling automated data analysis and error estimation. Availability and implementation: aLFQ is written in R and freely available under the GPLv3 from CRAN (http://www.cran.r-project.org). Instructions and example data are provided in the R-package. The raw data can be obtained from the PeptideAtlas raw data repository (PASS00321). Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics onlin

Hydrodynamics of charged two-dimensional Dirac systems I: thermo-electric transport

In this paper we study thermo-electric transport in interacting two-dimensional Dirac-type systems using a phenomenological Boltzmann approach. We consider a setup that can accommodate electrons, holes, and collective modes. In the first part of the paper we consider the electron-hole hydrodynamics, a model that is popular in the context of graphene, and its transport properties. In a second part, we propose a novel type of hydrodynamics. In that setup, the `fluid' consists of electrons, holes, and plasmons. We study its transport properties, especially the thermo-electric behavior. The results of this part can also be adapted to the study of a fluid consisting of electrons and phonons. This paper is accompanied by a technical paper in which we give a detailed derivation of the Boltzmann equations and the encoded conservation laws.Comment: This is part I of two parallel paper