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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.
Fields of asymmetric tensors play an important role in many applications such as medical imaging (diffusion tensor magnetic resonance imaging), physics, and civil engineering (for example Cauchy-Green-deformation tensor, strain tensor with local rotations, etc.). However, such asymmetric tensors are usually symmetrized and then further processed. Using this procedure results in a loss of information. A new method for the processing of asymmetric tensor fields is proposed restricting our attention to tensors of second-order given by a 2x2 array or matrix with real entries. This is achieved by a transformation resulting in Hermitian matrices that have an eigendecomposition similar to symmetric matrices. With this new idea numerical results for real-world data arising from a deformation of an object by external forces are given. It is shown that the asymmetric part indeed contains valuable information.
An alternative method is presented to numerically compute interior elastic transmission eigenvalues for various domains in two dimensions. This is achieved by discretizing the resulting system of boundary integral equations in combination with a nonlinear eigenvalue solver. Numerical results are given to show that this new approach can provide better results than the finite element method when dealing with general domains.
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.
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.
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.
A method for the integrated extraction and separation of fatty acids from algae using supercritical CO2 is presented. Desmodesmus obliquus and Chlorella sorokiniana were used as algae. First, a method for chromatographic separation of fatty acids of different degrees of saturation was established and optimized. Then, an integrated method for supercritical extraction was developed for both algal species. It was also verified whether prior cell disruption was beneficial for extraction. In developing the method for chromatographic separation, statistical experimental design was used to determine the optimal parameter settings. The methanol content in the mobile phase proved to be the most important parameter for successful separation of the three unsaturated fatty acids oleic acid, linoleic acid, and linolenic acid. Supercritical extraction with dried algae showed that about four times more fatty acids can be extracted from C. sorokiniana relative to the dry mass used.
New materials often lead to innovations and advantages in technical applications. This also applies to the particle receiver proposed in this work that deploys high-temperature and scratch resistant transparent ceramics. With this receiver design, particles are heated through direct-contact concentrated solar irradiance while flowing downwards through tubular transparent ceramics from top to bottom. In this paper, the developed particle receiver as well as advantages and disadvantages are described. Investigations on the particle heat-up characteristics from solar irradiance were carried out with DEM simulations which indicate that particle temperatures can reach up to 1200 K. Additionally, a simulation model was set up for investigating the dynamic behavior. A test receiver at laboratory scale has been designed and is currently being built. In upcoming tests, the receiver test rig will be used to validate the simulation results. The design and the measurement equipment is described in this work.
The Solar-Institut Jülich (SIJ) and the companies Hilger GmbH and Heliokon GmbH from Germany have developed a small-scale cost-effective heliostat, called “micro heliostat”. Micro heliostats can be deployed in small-scale concentrated solar power (CSP) plants to concentrate the sun's radiation for electricity generation, space or domestic water heating or industrial process heat. In contrast to conventional heliostats, the special feature of a micro heliostat is that it consists of dozens of parallel-moving, interconnected, rotatable mirror facets. The mirror facets array is fixed inside a box-shaped module and is protected from weathering and wind forces by a transparent glass cover. The choice of the building materials for the box, tracking mechanism and mirrors is largely dependent on the selected production process and the intended application of the micro heliostat. Special attention was paid to the material of the tracking mechanism as this has a direct influence on the accuracy of the micro heliostat. The choice of materials for the mirror support structure and the tracking mechanism is made in favor of plastic molded parts. A qualification assessment method has been developed by the SIJ in which a 3D laser scanner is used in combination with a coordinate measuring machine (CMM). For the validation of this assessment method, a single mirror facet was scanned and the slope deviation was computed.
Concentrated Solar Power (CSP) systems are able to store energy cost-effectively in their integrated thermal energy storage (TES). By intelligently combining Photovoltaics (PV) systems with CSP, a further cost reduction of solar power plants is expected, as well as an increase in dispatchability and flexibility of power generation. PV-powered Resistance Heaters (RH) can be deployed to raise the temperature of the molten salt hot storage from 385 °C up to 565 °C in a Parabolic Trough Collector (PTC) plant. To avoid freezing and decomposition of molten salt, the temperature distribution in the electrical resistance heater is investigated in the present study. For this purpose, a RH has been modeled and CFD simulations have been performed. The simulation results show that the hottest regions occur on the electric rod surface behind the last baffle. A technical optimization was performed by adjusting three parameters: Shell-baffle clearance, electric rod-baffle clearance and number of baffles. After the technical optimization was carried out, the temperature difference between the maximum temperature and the average outlet temperature of the salt is within the acceptable limits, thus critical salt decomposition has been avoided. Additionally, the CFD simulations results were analyzed and compared with results obtained with a one-dimensional model in Modelica.