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Analysis and computation of the transmission eigenvalues with a conductive boundary condition
(2022)
We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a conductive boundary condition. The goal is to study how these eigenvalues depend on the material parameters in order to estimate the refractive index. The analytical questions we study are: deriving Faber–Krahn type lower bounds, the discreteness and limiting behavior of the transmission eigenvalues as the conductivity tends to infinity for a sign changing contrast. We also provide a numerical study of a new boundary integral equation for computing the eigenvalues. Lastly, using the limiting behavior we will numerically estimate the refractive index from the eigenvalues provided the conductivity is sufficiently large but unknown.
Lolium perenne (perennial ryegrass) is aproductive and high-quality forage grass indigenous to Southern Europe, temperate Asia, and North Africa. Nowadays it is widespread and the dominant grass species on green areas in temperate climates. This abundant source of biomass is suitable for the development of bioeconomic processes because of its high cellulose and water-soluble carbohydrate content. In this work, novel breeds of the perennial ryegrass are being examined with regards to their quality parameters and biotechnological utilization options within the context of bioeconomy. Three processing operations are presented. In the first process, the perennial ryegrass is pretreated by pressing or hydrothermal extraction to derive glucosevia subsequent enzymatic hydrolysis of cellulose. A yield of up to 82 % glucose was achieved when using the hydrothermal ex-traction as pretreatment. In a second process, the ryegrass is used to produce lactic acid in high concentrations. The influence of the growth conditions and the cutting time on the carboxylic acid yield is investigated. A yield of lactic acid of above 150 g kg⁻¹ dry matter was achieved. The third process is to use Lolium perenne as a substrate in the fermentation of K. marxianus for the microbial production of single-cell proteins. The perennial ryegrass is screw-pressed and the press juice is used as medium. When supplementing the press juice with yeast media components, a biomass concentration of up to 16 g L⁻¹ could be achieved.
Hydrogen is playing an increasingly important role in research and politics as an energy carrier of the future. Since hydrogen has commonly been produced from methane by steam reforming, the need for climate-friendly, alternative production routes is emerging. In addition to electrolysis, fermentative routes for the production of so-called biohydrogen are "green" alternatives. The application of microorganisms offers the advantage of sustainable production from renewable resources using easily manageable technologies. In this project, the hyperthermophilic, anaerobic microorganism Thermotoga neapolitana is used for the productio nof biohydrogen from renewable resources. The enzymatically hydrolyzed resources were used in fermentation leading to yield coefficients of 1.8 mole H₂ per mole glucose when using hydrolyzed straw and ryegrass supplemented with medium, respectively. These results are similar to the hydrogen yields when using Thermotoga basal medium with glucose (TBGY) as control group. In order to minimize the supplementation of the hydrolysate and thus increase the economic efficiency of the process, the essential media components were identified. The experiments revealed NaCl, KCl, and glucose as essential components for cell growth as well as biohydrogen production. When excluding NaCl, a decrease of 96% in hydrogen production occured.
On the basis of independent and identically distributed bivariate random vectors, where the components are categorial and continuous variables, respectively, the related concomitants, also called induced order statistic, are considered. The main theoretical result is a functional central limit theorem for the empirical process of the concomitants in a triangular array setting. A natural application is hypothesis testing. An independence test and a two-sample test are investigated in detail. The fairly general setting enables limit results under local alternatives and bootstrap samples. For the comparison with existing tests from the literature simulation studies are conducted. The empirical results obtained confirm the theoretical findings.
Im Handel mit Kraftfahrzeugen gehören Aspekte des gutgläubigen Erwerbs zu den beinahe alltäglichen Standardproblemen. Der BGH fügt in seiner Entscheidung v. 23.9.2022–VZR148/21, MDR 2022, 1541 diesem im Detail breit gefächerten Themenfeld einen weiteren Mosaikstein hinzu: Der Erwerber erhielt das verkaufte Kfz ohne Übergabe einer Zulassungsbescheinigung Teil II, behauptet aber, diese Bescheinigung sei dem vom ihm eingeschalteten Vermittler bei Erwerb (als Fälschung) vorgelegt worden. Tatsächlich befand sich das Original durchgängig beim wahren Eigentümer, der nunmehr Herausgabe des Fahrzeugs verlangt. Der BGH schützt in dieser Gestaltung im Ergebnis den Erwerber. Die Entscheidung ist in mehrfacher Hinsicht bemerkenswert.
The replacement of existing spillway crests or gates with labyrinth weirs is a proven techno-economical means to increase the discharge capacity when rehabilitating existing structures. However, additional information is needed regarding energy dissipation of such weirs, since due to the folded weir crest, a three-dimensional flow field is generated, yielding more complex overflow and energy dissipation processes. In this study, CFD simulations of labyrinth weirs were conducted 1) to analyze the discharge coefficients for different discharges to compare the Cd values to literature data and 2) to analyze and improve energy dissipation downstream of the structure. All tests were performed for a structure at laboratory scale with a height of approx. P = 30.5 cm, a ratio of the total crest length to the total width of 4.7, a sidewall angle of 10° and a quarter-round weir crest shape. Tested headwater ratios were 0.089 ≤ HT/P ≤ 0.817. For numerical simulations, FLOW-3D Hydro was employed, solving the RANS equations with use of finite-volume method and RNG k-ε turbulence closure. In terms of discharge capacity, results were compared to data from physical model tests performed at the Utah Water Research Laboratory (Utah State University), emphasizing higher discharge coefficients from CFD than from the physical model. For upstream heads, some discrepancy in the range of ± 1 cm between literature, CFD and physical model tests was identified with a discussion regarding differences included in the manuscript. For downstream energy dissipation, variable tailwater depths were considered to analyze the formation and sweep-out of a hydraulic jump. It was found that even for high discharges, relatively low downstream Froude numbers were obtained due to high energy dissipation involved by the three-dimensional flow between the sidewalls. The effects of some additional energy dissipation devices, e.g. baffle blocks or end sills, were also analyzed. End sills were found to be non-effective. However, baffle blocks with different locations may improve energy dissipation downstream of labyrinth weirs.
The emerging environmental issues due to the use of fossil resources are encouraging the exploration of new renewable resources. Biomasses are attracting more interest due to the low environmental impacts, low costs, and high availability on earth. In this scenario, green biorefineries are a promising platform in which green biomasses are used as feedstock. Grasses are mainly composed of cellulose and hemicellulose, and lignin is available in a small amount. In this work, a perennial ryegrass was used as feedstock to develop a green bio-refinery platform. Firstly, the grass was mechanically pretreated, thus obtaining a press juice and a press cake fraction. The press juice has high nutritional values and can be employed as part of fermentation media. The press cake can be employed as a substrate either in enzymatic hydrolysis or in solid-state fermentation. The overall aim of this work was to demonstrate different applications of both the liquid and the solid fractions. For this purpose, the filamentous fungus A. niger and the yeast Y. lipolythica were selected for their ability to produce citric acid. Finally, the possibility was assessed to use the press juice as part of fermentation media to cultivate S. cerevisiae and lactic acid bacteria for ethanol and lactic acid fermentation.
With proven impact of statistical fracture analysis on fracture classifications, it is desirable to minimize the manual work and to maximize repeatability of this approach. We address this with an algorithm that reduces the manual effort to segmentation, fragment identification and reduction. The fracture edge detection and heat map generation are performed automatically. With the same input, the algorithm always delivers the same output. The tool transforms one intact template consecutively onto each fractured specimen by linear least square optimization, detects the fragment edges in the template and then superimposes them to generate a fracture probability heat map.
We hypothesized that the algorithm runs faster than the manual evaluation and with low (< 5 mm) deviation. We tested the hypothesis in 10 fractured proximal humeri and found that it performs with good accuracy (2.5 mm ± 2.4 mm averaged Euclidean distance) and speed (23 times faster). When applied to a distal humerus, a tibia plateau, and a scaphoid fracture, the run times were low (1–2 min), and the detected edges correct by visual judgement. In the geometrically complex acetabulum, at a run time of 78 min some outliers were considered acceptable. An automatically generated fracture probability heat map based on 50 proximal humerus fractures matches the areas of high risk of fracture reported in medical literature.
Such automation of the fracture analysis method is advantageous and could be extended to reduce the manual effort even further.
Introduction
In regard of surgical training, the reproducible simulation of life-like proximal humerus fractures in human cadaveric specimens is desirable. The aim of the present study was to develop a technique that allows simulation of realistic proximal humerus fractures and to analyse the influence of rotator cuff preload on the generated lesions in regards of fracture configuration.
Materials and methods
Ten cadaveric specimens (6 left, 4 right) were fractured using a custom-made drop-test bench, in two groups. Five specimens were fractured without rotator cuff preload, while the other five were fractured with the tendons of the rotator cuff preloaded with 2 kg each. The humeral shaft and the shortened scapula were potted. The humerus was positioned at 90° of abduction and 10° of internal rotation to simulate a fall on the elevated arm. In two specimens of each group, the emergence of the fractures was documented with high-speed video imaging. Pre-fracture radiographs were taken to evaluate the deltoid-tuberosity index as a measure of bone density. Post-fracture X-rays and CT scans were performed to define the exact fracture configurations. Neer’s classification was used to analyse the fractures.
Results
In all ten cadaveric specimens life-like proximal humerus fractures were achieved. Two III-part and three IV-part fractures resulted in each group. The preloading of the rotator cuff muscles had no further influence on the fracture configuration. High-speed videos of the fracture simulation revealed identical fracture mechanisms for both groups. We observed a two-step fracture mechanism, with initial impaction of the head segment against the glenoid followed by fracturing of the head and the tuberosities and then with further impaction of the shaft against the acromion, which lead to separation of the tuberosities.
Conclusion
A high energetic axial impulse can reliably induce realistic proximal humerus fractures in cadaveric specimens. The preload of the rotator cuff muscles had no influence on initial fracture configuration. Therefore, fracture simulation in the proximal humerus is less elaborate. Using the presented technique, pre-fractured specimens are available for real-life surgical education.
In der aktuellen Gesellschaft ist ein Konsens davon spürbar, wie „Männlichkeit“ aussehen soll. In der fotografischen Arbeit wird hinterfragt, ob dieses Bild von Maskulinität flexibler gestaltet werden kann und muss. Über verschiede Online-Plattformen wurde nach männlich gelesenen Personen gesucht, die bereit waren, ihre „feminine“ Seite in Bezug auf ihr Aussehen innerhalb eines geschützten Raumes porträtieren zu lassen. Die Arbeit wird in einem Bildband und einem Ausstellungskonzept präsentiert und besteht aus einem 18-monatigem Prozess, 4 bereisten Städten und 30 Shootings. 80 Fotografien zeigen das Experiment, die Freude, aber auch die Überwindungskraft der Porträtierten, die notwendig ist, um Genderklischees zu brechen. Die Individualität der Menschen wird in den bühnenartigen Darstellungen hervorgehoben und gibt einen Denkanstoß zur Neugestaltung und Öffnung des Begriffes „Maskulinität“.