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The present thesis considers the modelling of gas mixtures via a kinetic description. Fundamentals about the Boltzmann equation for gas mixtures and the BGK approximation are presented. Especially, issues in extending these models to gas mixtures are discussed. A non-reactive two component gas mixture is considered. The two species mixture is modelled by a system of kinetic BGK equations featuring two interaction terms to account for momentum and energy transfer between the two species. The model presented here contains several models from physicists and engineers as special cases. Consistency of this model is proven: conservation properties, positivity of all temperatures and the H-theorem. The form in global equilibrium as Maxwell distributions is specified. Moreover, the usual macroscopic conservation laws can be derived.
In the literature, there is another type of BGK model for gas mixtures developed by Andries, Aoki and Perthame, which contains only one interaction term. In this thesis, the advantages of these two types of models are discussed and the usefulness of the model presented here is shown by using this model to determine an unknown function in the energy exchange of the macroscopic equations for gas mixtures described in the literature by Dellacherie. In addition, for each of the two models existence and uniqueness of mild solutions is shown. Moreover, positivity of classical solutions is proven.
Then, the model presented here is applied to three physical applications: a plasma consisting of ions and electrons, a gas mixture which deviates from equilibrium and a gas mixture consisting of polyatomic molecules.
First, the model is extended to a model for charged particles. Then, the equations of magnetohydrodynamics are derived from this model. Next, we want to apply this extended model to a mixture of ions and electrons in a special physical constellation which can be found for example in a Tokamak. The mixture is partly in equilibrium in some regions, in some regions it deviates from equilibrium. The model presented in this thesis is taken for this purpose, since it has the advantage to separate the intra and interspecies interactions. Then, a new model based on a micro-macro decomposition is proposed in order to capture the physical regime of being partly in equilibrium, partly not. Theoretical results are presented, convergence rates to equilibrium in the space-homogeneous case and the Landau damping for mixtures, in order to compare it with numerical results.
Second, the model presented here is applied to a gas mixture which deviates from equilibrium such that it is described by Navier-Stokes equations on the macroscopic level. In this macroscopic description it is expected that four physical coefficients will show up, characterizing the physical behaviour of the gases, namely the diffusion coefficient, the viscosity coefficient, the heat conductivity and the thermal diffusion parameter. A Chapman-Enskog expansion of the model presented here is performed in order to capture three of these four physical coefficients. In addition, several possible extensions to an ellipsoidal statistical model for gas mixtures are proposed in order to capture the fourth coefficient. Three extensions are proposed: An extension which is as simple as possible, an intuitive extension copying the one species case and an extension which takes into account the physical motivation of the physicist Holway who invented the ellipsoidal statistical model for one species. Consistency of the extended models like conservation properties, positivity of all temperatures and the H-theorem are proven. The shape of global Maxwell distributions in equilibrium are specified.
Third, the model presented here is applied to polyatomic molecules. A multi component gas mixture with translational and internal energy degrees of freedom is considered. The two species are allowed to have different degrees of freedom in internal energy and are modelled by a system of kinetic ellipsoidal statistical equations. Consistency of this model is shown: conservation properties, positivity of the temperature, H-theorem and the form of Maxwell distributions in equilibrium. For numerical purposes the Chu reduction is applied to the developed model for polyatomic gases to reduce the complexity of the model and an application for a gas consisting of a mono-atomic and a diatomic gas is given.
Last, the limit from the model presented here to the dissipative Euler equations for gas mixtures is proven.
In 3 Maccabees, kingship as a form of rule is addressed on two levels: On the political level the question about a good king is addressed against the background of Hellenistic understandings of kingship, using the example of Ptolemy IV Philopator. This king is portrayed at the beginning of 3 Maccabees as a successful, positive, Hellenistic ruler, but one whose good rule goes off the rails. This analysis of the ideal of Hellenistic rule (cf. 3 Macc. 3:12-29; 6:24-28; 7:1-9) is then taken to a theological level: the God of Israel is portrayed as the true good king, the Soter who saves his people in their time of greatest trial (6:29, 32; 7:16). By these means the many divine epithets that are a striking feature of 3 Maccabees are incorporated into the narrative (cf. 2:2-3). Thereby 3 Maccabees not only thematises the conflict with a Hellenistic king who exploits his power in diverse ways but also focuses in a concentrated way the notion of a good (Hellenistic) king into the notion of God as king and ruler.
Epichloë endophytes associated with cool-season grass species can protect their hosts from herbivory and can suppress mycorrhizal colonization of the hosts’ roots. However, little is known about whether or not Epichloë endophyte infection can also change the foliar fungal assemblages of the host. We tested 52 grassland study sites along a land-use intensity gradient in three study regions over two seasons (spring vs. summer) to determine whether Epichloë infection of the host grass Lolium perenne changes the fungal community structure in leaves. Foliar fungal communities were assessed by Next Generation Sequencing of the ITS rRNA gene region. Fungal community structure was strongly affected by study region and season in our study, while land-use intensity and infection with Epichloë endophytes had no significant effects. We conclude that effects on non-systemic endophytes resulting from land use practices and Epichloë infection reported in other studies were masked by local and seasonal variability in this study’s grassland sites.
Progranulin (PGRN) is a secreted anti-inflammatory protein which can be processed by neutrophil proteases to various granulins. It has been reported that at least a significant portion of the anti-inflammatory effects of PGRN is due to direct high affinity binding to tumor necrosis factor receptor-1 (TNFR1) and TNFR2 and inhibition of tumor necrosis factor (TNF)-induced TNFR1/2 signaling. Two studies failed to reproduce the interaction of TNFR1 and TNFR2 with PGRN, but follow up reports speculated that this was due to varying experimental circumstances and/or the use of PGRN from different sources. However, even under consideration of these speculations, there is still a striking discrepancy in the literature between the concentrations of PGRN needed to inhibit TNF signaling and the concentrations required to block TNF binding to TNFR1 and TNFR2. While signaling events induced by 0.2–2 nM of TNF have been efficiently inhibited by low, near to equimolar concentrations (0.5–2.5 nM) of PGRN in various studies, the reported inhibitory effects of PGRN on TNF-binding to TNFR1/2 required a huge excess of PGRN (100–1,000-fold). Therefore, we investigated the effect of PGRN on TNF binding to TNFR1 and TNFR2 in highly sensitive cellular binding studies. Unlabeled TNF inhibited >95% of the specific binding of a Gaussia princeps luciferase (GpL) fusion protein of TNF to TNFR1 and TNFR2 and blocked binding of soluble GpL fusion proteins of TNFR1 and TNFR2 to membrane TNF expressing cells to >95%, too. Purified PGRN, however, showed in both assays no effect on TNF–TNFR1/2 interaction even when applied in huge excess. To rule out that tags and purification- or storage-related effects compromise the potential ability of PGRN to bind TNF receptors, we directly co-expressed PGRN, and as control TNF, in TNFR1- and TNFR2-expressing cells and looked for binding of GpL-TNF. While expression of TNF strongly inhibited binding of GpL-TNF to TNFR1/2, co-expression of PGRN had not effect on the ability of the TNFR1/2-expressing cells to bind TNF.
Lagrange Multiplier Methods for Constrained Optimization and Variational Problems in Banach Spaces
(2018)
This thesis is concerned with a class of general-purpose algorithms for constrained minimization problems, variational inequalities, and quasi-variational inequalities in Banach spaces.
A substantial amount of background material from Banach space theory, convex analysis, variational analysis, and optimization theory is presented, including some results which are refinements of those existing in the literature. This basis is used to formulate an augmented Lagrangian algorithm with multiplier safeguarding for the solution of constrained optimization problems in Banach spaces. The method is analyzed in terms of local and global convergence, and many popular problem classes such as nonlinear programming, semidefinite programming, and function space optimization are shown to be included as special cases of the general setting.
The algorithmic framework is then extended to variational and quasi-variational inequalities, which include, by extension, Nash and generalized Nash equilibrium problems. For these problem classes, the convergence is analyzed in detail. The thesis then presents a rich collection of application examples for all problem classes, including implementation details and numerical results.
Crop diversification has been proposed as farm management tool that could mitigate the externalities of conventional farming while reducing productivity-biodiversity trade-offs. Yet evidence for the acclaimed biodiversity benefits of landscape-level crop diversity is ambiguous. Effects may strongly depend on spatial scale and the level of landscape heterogeneity (e.g. overall habitat diversity). At the same time, contrasting within-taxon responses obscure benefits to specific functional groups (i.e. species with shared characteristics or requirements) if studied at the community level. The objectives of this study were to 1) disentangle the relative effects of crop diversity and landscape heterogeneity on avian species richness across five spatial scales ranging from 250 to 3000 m radii around focal winter wheat fields; and 2) assess whether functional groups (feeding guild, conservation status, habitat preference, nesting behaviour) determine the strength and direction of responses to crop diversity and landscape heterogeneity. In central Germany, 14 landscapes were selected along independent gradients of crop diversity (annual arable crops) and landscape heterogeneity. Bird species richness in each landscape was estimated using four point counts throughout the breeding season. We found no effects of landscape-level crop diversity on bird richness and functional groups. Instead, landscape heterogeneity was strongly associated with increased total bird richness across all spatial scales. In particular, insect-feeding and non-farmland birds were favoured in heterogeneous landscapes, as were species not classified as endangered or vulnerable on the regional Red List. Crop-nesting farmland birds, however, were less species-rich in these landscapes. Accordingly, crop diversification may be less suitable for conserving avian diversity and associated ecosystem services (e.g. biological pest control), although confounding interactions with management intensity need yet to be confirmed. In contrast, enhancement of landscape heterogeneity by increasing perennial habitat diversity, reducing field sizes and the amount of cropland has the potential to benefit overall bird richness. Specialist farmland birds, however, may require more targeted management approaches.
Background:
The treatment strategies for colorectal cancer located in the right side of the colon have changed dramatically during the last decade. Due to the introduction of complete mesocolic excision (CME) with central ligation of the vessels and systematic lymph node dissection, the long-term survival of affected patients has increased significantly. It has also been proposed that right-sided colon resection can be performed laparoscopically with the same extent of resection and equal long-term results.
Methods:
A retrospective evaluation of a prospectively expanded database on right-sided colorectal cancer or adenoma treated at the University Hospital of Wuerzburg between 2009 and 2016 was performed. All patients underwent CME. This data was analyzed alone and in comparison to the published data describing laparoscopic right-sided colon resection for colon cancer.
Results:
The database contains 279 patients, who underwent right-sided colon resection due to colorectal cancer or colorectal adenoma (255 open; 24 laparoscopic). Operation data (time, length of stay, time on ICU) was equal or superior to laparoscopy, which is comparable to the published results. Surprisingly, the surrogate parameter for correct CME (the number of removed lymph nodes) was significantly higher in the open group. In a subgroup analysis only including patients who were feasible for laparoscopic resection and had been operated with an open procedure by an experienced surgeon, operation time was significantly shorter and the number of removed lymph nodes is significantly higher in the open group.
Conclusion:
So far, several studies demonstrate that laparoscopic right-sided colon resection is comparable to open resection. Our data suggests that a consequent CME during an open operation leads to significantly more removed lymph nodes than in laparoscopically resected patients and in several so far published data of open control groups from Europe. Further prospective randomized trials comparing the long-term outcome are urgently needed before laparoscopy for right-sided colon resection can be recommended ubiquitously.
In diabetic cardiomyopathy, left ventricular (LV) diastolic dysfunction is one of the earliest signs of cardiac involvement prior to the definitive development of heart failure (HF). We aimed to explore the LV diastolic function using electrocardiography (ECG)-gated \(^{18}\)F-fluorodeoxyglucose positron emission tomography (\(^{18}\)F-FDG PET) imaging beyond the assessment of cardiac glucose utilization in a diabetic rat model. ECG-gated \(^{18}\)F-FDG PET imaging was performed in a rat model of type 2 diabetes (ZDF fa/fa) and ZL control rats at age of 13 weeks (n=6, respectively). Under hyperinsulinemic-euglycemic clamp to enhance cardiac activity, \(^{18}\)F-FDG was administered and subsequently, list-mode imaging using a dedicated small animal PET system with ECG signal recording was performed. List-mode data were sorted and reconstructed into tomographic images of 16 frames per cardiac cycle. Left ventricular functional parameters (systolic: LV ejection fraction (EF), heart rate (HR) vs. diastolic: peak filling rate (PFR)) were obtained using an automatic ventricular edge detection software. No significant difference in systolic function could be obtained (ZL controls vs. ZDF rats: LVEF, 62.5±4.2 vs. 59.4±4.5%; HR: 331±35 vs. 309±24 bpm; n.s., respectively). On the contrary, ECG-gated PET imaging showed a mild but significant decrease of PFR in the diabetic rats (ZL controls vs. ZDF rats: 12.1±0.8 vs. 10.2±1 Enddiastolic Volume/sec, P<0.01). Investigating a diabetic rat model, ECG-gated \(^{18}\)F-FDG PET imaging detected LV diastolic dysfunction while systolic function was still preserved. This might open avenues for an early detection of HF onset in high-risk type 2 diabetes before cardiac symptoms become apparent.
Background:
Conventional parameters including Ki67, hormone receptor and Her2/neu status are used for risk stratification for breast cancer. The serine protease urokinase plasminogen activator (uPA) and the plasminogen activator inhibitor type-1 (PAI-1) play an important role in tumour invasion and metastasis. Increased concentrations in tumour tissue are associated with more aggressive potential of the disease. Multigene tests provide detailed insights into tumour biology by simultaneously testing several prognostically relevant genes. With OncotypeDX\(^{®}\), a panel of 21 genes is tested by means of quantitative real-time polymerase chain reaction.
The purpose of this pilot study was to analyse whether a combination of Ki67 and uPA/PAI-1 supplies indications of the result of the multigene test.
Methods:
The results of Ki67, uPA/PAI-1 and OncotypeDX\(^{®}\) were analysed in 25 breast carcinomas (luminal type, pT1/2, max pN1a, G2). A statistical and descriptive analysis was performed.
Results:
With a proliferation index Ki67 of < 14%, the recurrence score (RS) from the multigene test was on average in the low risk range, with an intermediate RS usually resulting if Ki67 was > 14%. Not elevated values of uPA and PAI-1 showed a lower rate of proliferation (average 8.5%) than carcinomas with an increase of uPA and/or PAI-1 (average 13.9%); p = 0.054, Student’s t-test. When Ki67 was > 14% and uPA and/or PAI-1 was raised, an intermediate RS resulted. These differences were significant when compared to cases with Ki67 < 14% with non-raised uPA/PAI-1 (p < 0.03, Student’s t-test). Without taking into account the proliferative activity, an intermediate RS was also verifiable if both uPA and PAI-1 showed raised values.
Conclusion:
A combination of the values Ki67 and uPA/PAI-1 tended to depict the RS to be expected. From this it can be deduced that an appropriate analysis of this parameter combination may be undertaken before the multigene test in routine clinical practice. The increasing cost pressure makes it necessary to base the implementation of a multigene test on ancillary variables and to potentially leave it out if not required in the event of a certain constellation of results (Ki67 raised, uPA and PAI-1 raised).
Stories are a powerful means to change recipients’ views on themselves by being transported into the story world and by identifying with story characters. Previous studies showed that recipients temporarily change in line with a story and its characters (assimilation). Conversely, assimilation might be less likely when recipients are less identified with story protagonists or less transported into a story by comparing themselves with a story character. This may lead to changes, which are opposite to a story and its characters (contrast). In two experiments, we manipulated transportation and experience taking via two written reviews (Experiment 1; N = 164) and by varying the perspective of the story’s narrator (Experiment 2; N = 79) of a short story about a negligent student. Recipients’ self-ratings in comparison to others, motives, and problem-solving behavior served as dependent variables. However, neither the review nor the perspective manipulation affected transportation or experience taking while reading the story. Against our expectations, highly transported recipients (in Study 1) and recipients with high experience taking (in Study 2) showed more persistency working on an anagram-solving task, even when controlling for trait conscientiousness. Our findings are critically discussed in light of previous research.