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Finite volume methods for compressible Euler equations suffer from an excessive diffusion in the limit of low Mach numbers. This PhD thesis explores new approaches to overcome this.
The analysis of a simpler set of equations that also possess a low Mach number limit is found to give valuable insights. These equations are the acoustic equations obtained as a linearization of the Euler equations. For both systems the limit is characterized by a divergencefree velocity. This constraint is nontrivial only in multiple spatial dimensions. As the Jacobians of the acoustic system do not commute, acoustics cannot be reduced to some kind of multi-dimensional advection. Therefore first an exact solution in multiple spatial dimensions is obtained. It is shown that the low Mach number limit can be interpreted as a limit of long times.
It is found that the origin of the inability of a scheme to resolve the low Mach number limit is the lack a discrete counterpart to the limit of long times. Numerical schemes whose discrete stationary states discretize all the analytic stationary states of the PDE are called stationarity preserving. It is shown that for the acoustic equations, stationarity preserving schemes are vorticity preserving and are those that are able to resolve the low Mach limit (low Mach compliant). This establishes a new link between these three concepts.
Stationarity preservation is studied in detail for both dimensionally split and multi-dimensional schemes for linear acoustics. In particular it is explained why the same multi-dimensional stencils appear in literature in very different contexts: These stencils are unique discretizations of the divergence that allow for stabilizing stationarity preserving diffusion.
Stationarity preservation can also be generalized to nonlinear systems such as the Euler equations. Several ways how such numerical schemes can be constructed for the Euler equations are presented. In particular a low Mach compliant numerical scheme is derived that uses a novel construction idea. Its diffusion is chosen such that it depends on the velocity divergence rather than just derivatives of the different velocity components. This is demonstrated to overcome the low Mach number problem. The scheme shows satisfactory results in numerical simulations and has been found to be stable under explicit time integration.
Sarcoidosis is a multisystem granulomatous disorder of unknown etiology that can involve virtually all organ systems. Whereas most patients present without symptoms, progressive and disabling organ failure can occur in up to 10% of subjects. Somatostatin receptor (SSTR)-directed peptide receptor radionuclide therapy (PRRT) has recently received market authorization for treatment of SSTR-positive neuroendocrine tumors.
Methods:
We describe the first case series comprising two patients with refractory multi-organ involvement of sarcoidosis who received 4 cycles of PRRT.
Results:
PRRT was well-tolerated without any acute adverse effects. No relevant toxicities could be recorded during follow-up. Therapy resulted in partial response accompanied by a pronounced reduction in pain (patient #1) and stable disease regarding morphology as well as disease activity (patient #2), respectively.
Conclusion:
Peptide receptor radionuclide therapy in sarcoidosis is feasible and might be a new valuable tool in patients with otherwise treatment-refractory disease. Given the long experience with and good tolerability of PRRT, further evaluation of this new treatment option for otherwise treatment-refractory sarcoidosis in larger patient cohorts is warranted.
Introduction
The goals of successful bi-compartmental knee arthroplasty are to achieve correct fit and positioning of the implant, while appropriately correcting the mechanical alignment of the leg after surgery. As these requirements are not always reliably fulfilled using off-the-shelf implant systems, newer approaches for bi-compartmental resurfacing have been explored.
Material and methods
In this article we report the radiographic results of 30 patients with anteromedial osteoarthritis (OA) who were treated with a novel patient-specific fixed-bearing bi-compartmental knee resurfacing system using custom-made implants and instruments. Utilizing standardized pre- and postoperative radiographic analyses (based on anterior-posterior and lateral, anterior-posterior weight-bearing full-length radiographs, patella skyline views and preoperative computed tomography (CT) scanning) implant fit and positioning as well as correction of the mechanical axis (hip-knee-ankle angle, HKA) were determined.
Results
On average, HKA was corrected from 173.4 ±3.47° preoperatively to 179.4 ±2.85° postoperatively. The coronal femoro-tibial angle was corrected on average 5.61°. The preoperative tibial slope measured on lateral views was 6.38 ±2.4°, while the average slope in the CT-based planning protocol (iView) was 6.14 ±2.40°. Postoperative lateral tibial slope was determined to be 5.77 ±1.97°. The thickness of the posterior femoral cuts was measured intraoperatively and, in all cases, corresponded well to the targeted thickness of the cuts provided by the iView. The joint line was preserved in all cases and the average Insall-Salvati index was 1.078 ±0.11 pre- and 1.072 ±0.11 postoperatively. The fit of the implant components measured by over- or underhang was excellent throughout (< 1.01 mm).
Conclusions
Custom-made bicompartmental knee arthroplasty can ensure optimized fitting and positioning of the implant with restoration of the leg axis. These implants could be considered as an alternative primary solution for knee surgeons treating bi-compartmental disease.
Neuste Studien haben ergeben, dass Asc-1 Knock-out Mäuse aufgrund einer verminderten intrazellulären Glycinkonzentration in synaptischen Boutons im Gehirn, einen Hyperekplexie-ähnlichen Phänotyp entwickeln. Aufgrund nicht vollständig geklärter Ursachen für die Entstehung des Krankheitsbildes der Hyperekplexie beim Menschen, wurde eine Kohorte von 51 Patienten zusammengetragen, um vor dem Hintergrund der Forschungsergebnisse zu Asc-1 im Tiermodell, das kodierende Gen beim Menschen SLC7A10 als mögliches Kandidatengen auf Sequenzalterationen zu untersuchen. Hierfür wurde aus Vollblut der an Hyperekplexie erkrankten Patienten genomische DNA isoliert, um mittels PCR und anschließendem Screening der Sequenzen, Mutationen innerhalb funktionell wichtiger Bereiche des Gens zu eruieren. Neben weiteren Sequenzunterschieden, die meist in Introns gefunden wurden, wurde die codierende Mutation G307R innerhalb von Exon 7 identifiziert, die letztendlich der Grund für eine Versuchsreihe war, um zu hinterfragen, ob dieser Aminosäureaustausch in der Proteinsequenz funktionelle Konsequenzen zur Folge hat. HEK293-Zellen wurden mit dem zuvor hergestellten Klon G307R transfiziert, um über Biotinylierung, immuncytochemische Färbungen und funktionelle Untersuchungen die Aktivität des Transporters zu beurteilen. Hier zeigte sich ein Funktionsverlust von über 95 %, bei uneingeschränkter Oberflächenexpression. ASC-1 bestätigt sich damit als neue Ursache in der Ausprägung von Hyperekplexie. Ferner können Zusammenhänge mit geistiger Retardierung und eingeschränkter neuronaler Plastizität bestehen.
In rodents, low doses of CD28-specific superagonistic monoclonal antibodies (CD28 superagonists, CD28SA) selectively activate regulatory T cells (Treg). This observation has recently been extended to humans, suggesting an option for the treatment of autoimmune and inflammatory diseases. However, a mechanistic explanation for this phenomenon is still lacking. Given that CD28SA amplify T cell receptor (TCR) signals, we tested the hypothesis that the weak tonic TCR signals received by conventional CD4\(^{+}\) T cells (Tconv) in the absence of cognate antigen require more CD28 signaling input for full activation than the stronger TCR signals received by self-reactive Treg. We report that in vitro, the response of mouse Treg and Tconv to CD28SA strongly depends on MHC class II expression by antigen-presenting cells. To separate the effect of tonic TCR signals from self-peptide recognition, we compared the response of wild-type Treg and Tconv to low and high CD28SA doses upon transfer into wild-type or H-2M knockout mice, which lack a self-peptide repertoire. We found that the superior response of Treg to low CD28SA doses was lost in the absence of self-peptide presentation. We also tested if potentially pathogenic autoreactive Tconv would benefit from self-recognition-induced sensitivity to CD28SA stimulation by transferring TCR transgenic OVA-specific Tconv into OVA-expressing mice and found that low-dose CD28SA application inhibited, rather than supported, their expansion, presumably due to the massive concomitant activation of Treg. Finally, we report that also in the in vitro response of human peripheral blood mononuclear cells to CD28SA, HLA II blockade interferes with the expansion of Treg by low-dose CD28SA stimulation. These results provide a rational basis for the further development of low-dose CD28SA therapy for the improvement of Treg activity.
The focus of this analysis is on the early detection of forest health changes, specifically that of Norway spruce (Picea abies L. Karst.). In this analysis, we planned to examine the time (degree of early detection), spectral wavelengths and appropriate method for detecting vitality changes. To accomplish this, a ring-barking experiment with seven subsequent laboratory needle measurements was carried out in 2013 and 2014 in an area in southeastern Germany near Altötting. The experiment was also accompanied by visual crown condition assessment. In total, 140 spruce trees in groups of five were ring-barked with the same number of control trees in groups of five that were selected as reference trees in order to compare their development. The laboratory measurements were analysed regarding the separability of ring-barked and control samples using spectral reflectance, vegetation indices and derivative analysis. Subsequently, a random forest classifier for determining important spectral wavelength regions was applied. Results from the methods are consistent and showed a high importance of the visible (VIS) spectral region, very low importance of the near-infrared (NIR) and minor importance of the shortwave infrared (SWIR) spectral region. Using spectral reflectance data as well as indices, the earliest separation time was found to be 292 days after ring-barking. The derivative analysis showed that a significant separation was observed 152 days after ring-barking for six spectral features spread through VIS and SWIR. A significant separation was detected using a random forest classifier 292 days after ring-barking with 58% separability. The visual crown condition assessment was analysed regarding obvious changes of vitality and the first indication was observed 302 days after ring-barking as bark beetle infestation and yellowing of foliage in the ring-barked trees only. This experiment shows that an early detection, compared with visual crown assessment, is possible using the proposed methods for this specific data set. This study will contribute to ongoing research for early detection of vitality changes that will support foresters and decision makers.
Transforming modern agriculture towards both higher yields and greater sustainability is critical for preserving biodiversity in an increasingly populous and variable world. However, the intensity of agricultural practices varies strongly between crop systems. Given limited research capacity, it is crucial to focus efforts to increase sustainability in the crop systems that need it most. In this study, we investigate the match (or mismatch) between the intensity of pesticide use and the availability of knowledge on the ecosystem service of natural pest control across various crop systems. Using a systematic literature search on pest control and publicly available pesticide data, we find that pest control literature is not more abundant in crops where insecticide input per hectare is highest. Instead, pest control literature is most abundant, with the highest number of studies published, in crops with comparatively low insecticide input per hectare but with high world harvested area. These results suggest that a major increase of interest in agroecological research towards crops with high insecticide input, particularly cotton and horticultural crops such as citrus and high value-added vegetables, would help meet knowledge needs for a timely ecointensification of agriculture.
The invention of laser pulse shapers allowed for various quantum control experiments, where a chemical reaction is guided by specifically tailored laser pulses. However, despite of the prominent role of the liquid phase in chemistry, no successful attempt for controlling the selectivity of a bond-fission reaction has yet been reported in this state of matter. Promising candidates for such an experiment are C$_{\infty\mathrm{v}}$-symmetric trihalide anions with two different chemical bonds like $\ce{I2Cl-}$, because these molecules notionally offer the most simplest selectivity-control scenario of breaking either the one or the other bond and they are expected to dissociate under ultraviolet (UV) irradiation like it is known for the most-studied trihalide $\ce{I3-}$.
In order to investigate in this thesis the possibility that the dissociation reaction of such trihalides branches into two different photofragments, the ultrafast photodissociation dynamics of $\ce{I3-}$, $\ce{Br3-}$, $\ce{IBr2-}$ and $\ce{ICl2-}$ (point group D$_{\infty\mathrm{h}}$) as well as of $\ce{I2Br-}$ and $\ce{I2Cl-}$ (point group C$_{\infty\mathrm{v}}$) in dichloromethane solution were measured with broadband transient absorption spectroscopy in magic-angle configuration. The identification of the reaction pathway(s) relies on vibrational wavepacket oscillations, which survive the dissociation process and therefore carry not only informations about the reactant trihalides but also about the fragment dihalides.
These characteristic vibrational wavenumbers were extracted from the measured transient absorption spectra by globally fitting the population dynamics together with the wavepacket dynamics. Until recently, such a combined model function was not available in the well-established fitting tool Glotaran. This made it inevitable to develop a custom implementation of the underlying variable-projection fitting algorithm, for which the computer-algebra software Mathematica was chosen. Mathematica's sophisticated built-in functions allow not only for a high flexibility in constructing arbitrary model functions, but also offer the possibility to automatically calculate the derivative(s) of a model function. This allows the fitting procedure to use the exact Jacobian matrix instead of approximating it with the finite difference method.
Against the expectation, only one of the two thinkable photodissociation channels was found for each of the investigated C$_{\infty\mathrm{v}}$ trihalides. Since the photofragments recombine, their absorption signal as well as the reactant ground state bleach recover. This happens in a biexponential manner, which in the case of $\ce{I3-}$ was interpreted by Ruhman and coworkers with the direct formation of a neutral dihalogen fragment $\ce{I2}$ beside the negatively charged dihalide fragment $\ce{I2-}$. In this thesis, such a direct reaction channel was not found and instead the fast component of the biexponential decay is explained with vibrational excess energy mediating the recombination-preceding electron transfer process $\ce{I2- + I -> I2 + I-}$, while the slow component is attributed to cooled-down fragments.
In addition to the trihalide experiments, the possibility of a magic-angle configuration for polarization-shaping control experiments was theoretically investigated in this thesis by deriving magic-angle conditions for the third-order electric-dipole response signal of arbitrarily polarized laser pulses. Furthermore, the subtleties of anisotropy signals violating the well-known range of \numrange{-0.2}{0.4} were studied.