Rigorous Derivation of Discrete Fracture Models for Darcy Flow in the Limit of Vanishing Aperture

We consider single-phase flow in a fractured porous medium governed by Darcy's law with spatially varying hydraulic conductivity matrices in both bulk and fractures. The width-to-length ratio of a fracture is of the order of a small parameter $\varepsilon$ and the ratio $K_\mathrm{f}^\star / K_\mathrm{b}^\star$ of the characteristic hydraulic conductivities in the fracture and bulk domains is assumed to scale with $\varepsilon^\alpha$ for a parameter $\alpha \in \mathbb{R}$. The fracture geometry is parameterized by aperture functions on a submanifold of codimension one. Given a fracture, we derive the limit models as $\varepsilon \rightarrow 0$. Depending on the value of $\alpha$, we obtain five different limit models as $\varepsilon \rightarrow 0$, for which we present rigorous convergence results

Flow in Porous Media with Fractures of Varying Aperture

We study single-phase flow in a fractured porous medium at a macroscopic scale that allows to model fractures individually. The flow is governed by Darcy's law in both fractures and porous matrix. We derive a new mixed-dimensional model, where fractures are represented by $(n-1)$-dimensional interfaces between $n$-dimensional subdomains for $n\ge 2$. In particular, we suggest a generalization of the model in [22] by accounting for asymmetric fractures with spatially varying aperture. Thus, the new model is particularly convenient for the description of surface roughness or for modeling curvilinear or winding fractures. The wellposedness of the new model is proven under appropriate conditions. Further, we formulate a discontinuous Galerkin discretization of the new model and validate the model by performing two- and three-dimensional numerical experiments

Synthesis of Functionalized 1,4-Azaborinines by the Cyclization of Di-tert-butyliminoborane and Alkynes

Di-tert-butyliminoborane is found to be a very useful synthon for the synthesis of a variety of functionalized 1,4-azaborinines by the Rh-mediated cyclization of iminoboranes with alkynes. The reactions proceed via [2 + 2] cycloaddition of iminoboranes and alkynes in the presence of [RhCl(PiPr3)2]2, which gives a rhodium η4-1,2-azaborete complex that yields 1,4-azaborinines upon reaction with acetylene. This reaction is compatible with substrates containing more than one alkynyl unit, cleanly affording compounds containing multiple 1,4-azaborinines. The substitution of terminal alkynes for acetylene also led to 1,4-azaborinines, enabling ring substitution at a predetermined location. We report the first general synthesis of this new methodology, which provides highly regioselective access to valuable 1,4-azaborinines in moderate yields. A mechanistic rationale for this reaction is supported by DFT calculations, which show the observed regioselectivity to arise from steric effects in the B-C bond coupling en route to the rhodium η4-1,2-azaborete complex and the selective oxidative cleavage of the B-N bond of the 1,2-azaborete ligand in its subsequent reaction with acetylene.</p

Bamberg in the Early Modern Period. New Essays on the History of Town and Bishopric

Die Beiträge dieses Bandes behandeln Aspekte der Verwaltungs-, Herrschafts-, Wirtschafts-, Sozial- und Kulturgeschichte Bambergs zwischen 1500 und 1800 und schließen damit einige der weißen Flecken auf der Landkarte der frühneuzeitlichen Stadt- und Regionalforschung. Zugleich werden aktuelle geschichtswissenschaftliche Fragestellungen und Konzepte empirisch erprobt. Damit sollen die Möglichkeiten, die Bamberg als Forschungsfeld bietet, und das Potential, das sich mit der Anwendung von Konzepten und Methoden der modernen Geschichtswissenschaft auf das reichhaltige Bamberger Material verbindet, aufgezeigt und Anregungen für künftige Forschungen gegeben werden.The essays in this volume cover aspects of Bamberg’s political, administrative, economic, social and cultural history from 1500 to 1800 and thus close some of the gaps in the city’s and region’s historiography. At the same time the essays provide empirical explorations of current scholarly concepts and approaches. They intend to point out the possibilities which Bamberg offers as a field of research and the potentials inherent in the application of modern historical concepts and methods on the rich source materials available for Bamberg

A randomized, placebo-controlled, double-blind, prospective trial to evaluate the effect of vildagliptin in new-onset diabetes mellitus after kidney transplantation

<p>Abstract</p> <p>Background</p> <p>New-onset diabetes mellitus after transplantation (NODAT), a frequent and serious complication after transplantation, is associated with decreased graft and patient survival. Currently, it is diagnosed and treated primarily according to existing guidelines for type II diabetes. To date, only a few trials have studied antidiabetic drugs in patients with NODAT. Vildagliptin is a novel dipeptidyl peptidase-4 (DPP-4) inhibitor that improves pancreatic islet function by enhancing both α- and β-cell responsiveness to increased blood glucose. Experimental data show potential protective effects of DPP-4 inhibitors on islet function after exogenous stress stimuli including immunosuppressants. Therefore, the therapy of NODAT with this class of compounds seems attractive. At present, vildagliptin is used to treat type II diabetes as monotherapy or in combination with other antidiabetic drugs, since that it efficiently decreases glycated hemoglobin (HbA1c) values. Additionally, vildagliptin has been shown to be safe in patients with moderately impaired kidney function. This study will evaluate the safety and efficacy of vildagliptin monotherapy in renal transplant recipients with recently diagnosed NODAT.</p> <p>Methods/Design</p> <p>This study is a randomized, placebo-controlled, double-blind, prospective phase II trial. Using the results of routinely performed oral glucose tolerance tests (OGTT) in stable renal transplant patients at our center, we will recruit patients without a history of diabetes and a 2 h glucose value surpassing 200 mg/dl (11.1 mmol/l). They are randomized to receive either 50 mg vildagliptin or placebo once daily. A total of 32 patients with newly diagnosed NODAT will be included. The primary endpoint is the difference in the 2 h glucose value between baseline and the repeated OGTT performed 3 months after treatment start, compared between the vildagliptin- and the placebo-group. Secondary endpoints include changes in HbA1c and fasting plasma glucose (FPG). The safety of vildagliptin in renal transplant patients will be assessed by the number of symptomatic hypoglycemic episodes (glucose <72 mg/dl or 4 mmol/l), the number of adverse events, and possible medication-associated side-effects.</p> <p>Discussion</p> <p>NODAT is a severe complication after kidney transplantation. Few trials have assessed the safety and efficacy of antidiabetic drugs for these patients. The purpose of this study is to assess the safety and efficacy of vildagliptin in renal transplant patients with NODAT.</p> <p>Trial Registration</p> <p>ClinicalTrials.gov NCT00980356</p

Biomarkers of Nutrition for Development (BOND)—Iron Review

This is the fifth in the series of reviews developed as part of the Biomarkers of Nutrition for Development (BOND) program. The BOND Iron Expert Panel (I-EP) reviewed the extant knowledge regarding iron biology, public health implications, and the relative usefulness of currently available biomarkers of iron status from deficiency to overload. Approaches to assessing intake, including bioavailability, are also covered. The report also covers technical and laboratory considerations for the use of available biomarkers of iron status, and concludes with a description of research priorities along with a brief discussion of new biomarkers with potential for use across the spectrum of activities related to the study of iron in human health. The I-EP concluded that current iron biomarkers are reliable for accurately assessing many aspects of iron nutrition. However, a clear distinction is made between the relative strengths of biomarkers to assess hematological consequences of iron deficiency versus other putative functional outcomes, particularly the relationship between maternal and fetal iron status during pregnancy, birth outcomes, and infant cognitive, motor and emotional development. The I-EP also highlighted the importance of considering the confounding effects of inflammation and infection on the interpretation of iron biomarker results, as well as the impact of life stage. Finally, alternative approaches to the evaluation of the risk for nutritional iron overload at the population level are presented, because the currently designated upper limits for the biomarker generally employed (serum ferritin) may not differentiate between true iron overload and the effects of subclinical inflammation

Synthesis and reactivity of heteroaromatic-substituted boroles and diborenes

Im Rahmen dieser Arbeit konnten erstmals die Eigenschaften von 1-heteroaromatisch-substituierten, freien Borolen des Typs R′BC4Ph4 untersucht werden. Der Rest R′ wurde unter Verwendung von bekannten Synthesemethoden (Zinn-Bor-Austausch, Salzeliminierung) variiert und die Borolderivate 45 (R′ = Thien-2-yl), 46 (R′ = 5-Methylfuran-2-yl), 47 (R′ = 5-Trimethylsilylthien-2-yl) und 49 (R′ = N-Methylpyrrol-3-yl) erfolgreich synthetisiert und vollständig charakterisiert (Multikern-NMR-Spektroskopie, Elementaranalyse, Röntgenstrukturanalyse am Einkristall). Des Weiteren ist es gelungen, die ersten Bis(borole) mit den heteroaromatischen Brückeneinheiten 2,5-Thienyl (54) und 5,5′-Bithiophen (55) mittels Zinn-Bor-Austausch-Reaktion darzustellen. Die Molekülstruktur von 54 bestätigt dabei nicht nur die erfolgreiche Synthese, sondern auch die coplanare Ausrichtung der drei Ringsysteme zueinander. Anhand von cyclovoltammetrischen Messungen konnte gezeigt werden, dass in diesem -konjugierten Akzeptor-Donor-Akzeptor-System (54) eine ausgeprägte Kommunikation zwischen den beiden Borzentren vorliegt. Dadurch ergeben sich vier irreversible Reduktionsereignisse, die ausgehend von 54, dem Monoanion [54]•−, dem Dianion [54]2−, dem Trianion [54]3− und dem Tetraanion [54]4− zugewiesen werden können. Das Verhalten von 54 gegenüber Reduktion wurde außerdem nicht nur elektrochemisch, sondern auch mithilfe unterschiedlicher Reduktionsmittel analysiert. Die Reduktion mit einem halben Äquivalent des Zwei-Elektronen-Reduktionsmittels Magnesiumanthracen führte dabei zu dem vollständig delokalisierten Monoanion Mg0.5[54], welches ESR-spektroskopisch charakterisiert werden konnte. Die Reduktion mit einem Äquivalent Magnesiumanthracen bzw. zwei Äquivalenten des Ein-Elektronen-Reduktionsmittels CoCp*2 lieferte das Dianion [54]2−, das für den Fall von [CoCp*2]2[54] im Festkörper studiert werden konnte. Die Molekülstruktur belegt, dass es sich bei Dianion [54]2− nicht um ein diradikalisches, sondern ein diamagnetisches, chinoides System handelt, welches auch als Bipolaron beschrieben werden kann. Der Einfluss von heteroaromatischen Substituenten wurde außerdem im Hinblick auf die Synthese neuartiger Basen-stabilisierter Diborene untersucht. Durch reduktive Kupplung geeigneter NHC-stabilisierter Dihalogenborane 77 und 78 (NHC = IMe) konnten die beiden Thienyl-substituierten Diborene 81 und 82 in sehr guten Ausbeuten (81: 82%; 82: 89%) dargestellt werden. UV-Vis-spektroskopische Untersuchungen und quantenchemische Rechnungen belegen, dass das HOMO der Diborene durch die -Bindung der BB-Bindung repräsentiert wird. Im Gegensatz zu den bekannten Aryl-substituierten Diborenen (73, 74) zeigt die Festkörperstruktur von 82 eine coplanare Ausrichtung der Heterocyclen relativ zur BB-Bindungsebene. Dadurch wird die sterische Abschirmung der reaktiven BB-Doppelbindung vermindert und weitere Reaktivitätsuntersuchungen in Analogie zur Reaktivität von CC-Doppelbindungen können durchgeführt werden.In this thesis, the properties of 1-heteroaromatic-substituted, non-annulated boroles with a R′BC4Ph4 framework have been studied for the first time. The variation of the R′ substituent was achieved with established synthetic procedures (tin-boron exchange, salt elimination) and the borole derivatives 45 (R′ = thien-2-yl), 46 (R′ = 5-methylfuran-2-yl), 47 (R′ = 5-trimethylsilylthien-2-yl) and 49 (R′ = N-methylpyrrol-3-yl) were successfully synthesized and characterized (multinuclear NMR spectroscopy, elemental analysis, single-crystal X-ray diffraction). In addition, the isolation of the first bis(borole)s with the heteroaromatic spacer units 2,5-thienyl (54) and 5,5′-bithiophene (55) via tin-boron exchange reaction was accomplished. The solid-state structure of 54 confirms not only the successful synthesis, but also the coplanar arrangement of the three five-membered rings with respect to each other. The measurement of a cyclic voltammogram for this compound revealed the existence of distinct communication between the two boron atoms in this acceptor-donor-acceptor system (54). Thus, the four irreversible reduction events of 54 were assigned to the formation of the monoanion [54]•−, the dianion [54]2−, the trianion [54]3− and the tetraanion [54]4−. Moreover, the reduction behavior of 54 was analyzed chemically with a selection of diverse reducing agents. The reduction with half an equivalent of the two-electron reducing agent magnesium anthracene results in the fully delocalized monoanion Mg0.5[54], which was characterized by EPR spectroscopy. The dianion [54]2− is accessible via reduction with one equivalent of magnesium anthracene or two equivalents of the one-electron reducing agent CoCp*2. In the case of [CoCp*2]2[54], the molecular structure revealed that the dianion is not a diradical, but rather has a diamagnetic, quinoidal structural motif across the thiophene spacer, which is characteristic of so-called bipolarons. The effect of heteroaromatic substituents was also explored with respect to the synthesis of novel base-stabilized diborenes. After reductive coupling of appropriate NHC-stabilized dihalogen-boranes 77 and 78 (NHC = IMe) the thienyl-substituted diborenes 81 and 82 were isolated in excellent yields (81: 82%; 82: 89%). UV-vis spectroscopy and DFT calculations independently substantiate that the HOMO of the diborenes is represented by the -bond of the BB double bond (Figure 4). In contrast with the common aryl-substituted diborenes (73, 74), the solid-state structure of 82 exhibits a coplanar alignment of the heterocyclic substituents with respect to the BB bond plane. Thus, the steric shielding of the reactive BB double bond is significantly reduced and enables further reactivity studies in analogy to the well-known reactivity of CC double bonds