Abstract: Starting from logarithmic, sinusoidal and power spirals, it is shown how these spirals are connected directly with Chebyshev polynomials, Lamé curves, with allometry and Antonelli-metrics in Finsler geometry. Curvature is a crucial concept in geometry both for closed curves and equiangular spirals, and allowed Dillen to give a general definition of spirals. Many natural shapes can be described as a combination of one of two basic shapes in nature—circle and spiral—with Gielis transformations. Using this idea, shape description itself is used to develop a novel approach to anisotropic curvature in nature. Various examples are discussed, including fusion in flowers and its connection to the recently described pseudo-Chebyshev functions.

Abstract: Exposure to volatile organic compounds (VOCs) remains a major public health concern. Indoor VOC concentrations typically far exceed outdoor levels due to a variety of emission sources and the stringent insulation measures that are imposed today. Many attempts have been made to use photocatalysis for indoor air purification. In an ideal situation, photocatalysis is capable of complete mineralization of VOCs to H2O and CO2, without any byproduct formation. Moreover, the process can take place at standard atmospheric conditions, i.e. ambient temperature and atmospheric pressure. However, successful exploitation is still impeded due to low conversion efficiency, significant pressure loss (and hence a high energy consumption) and byproduct formation. In the first part of this thesis an attempt was made to tackles these problems by designing a novel type of photocatalytic (PCO) reactor. The PCO device consists of a cylindrical vessel filled with TiO2-coated glass tubes and equipped with UV fluorescence lamps. It was investigated in terms of fluid dynamics, coating properties, UV-light distribution and photocatalytic activity. Experimental data was later used to develop and calibrate a Multiphysics model. The model proved to be a useful tool for designing and upscaling the PCO reactor. Consequently, an optimized prototype reactor was constructed and tested according the CEN-EN-16846-1 standard for VOC removal. Although the prototype showed promising results for lab-scale conditions, it struggled with byproduct formation when purifying ppb-level VOCs. In the second part of this thesis, activated carbon adsorption was investigated in order to combine it with photocatalysis. Activated carbon fiber was opted for its fast kinetics, high adsorption capacity and thermo-electrical regeneration. The filter was studied in detail regarding the adsorption of polar and apolar VOCs at indoor air concentration levels and regeneration capabilities. Experimental data was used to develop a Multiphysics model for activated carbon adsorption as well. Consequently, a novel type of ACF filter was developed using the Multiphysics model, which was equipped with electrodes in the tips of the pleats for effective thermal regeneration. In the last part, the combination of both ACF and PCO was studied using a realistic case study. Based on the Multiphysics model, the feasibility of a so-called hybrid air purification device could be investigated. The Multiphysics model shows promising results for this hybrid PCO-ACF system and hence, a demo setup was constructed for future research.

Abstract: Gielis transformations are a generalization of Lame curves. To combine domains, we can make use of the natural alliance between Lame's work and Rvachev's R-functions. A logical next step is the extension to n-valued logic dening dierent partitions.

Abstract: The human population is projected to grow to 9.7 billion by 2050, resulting in an estimated increase in protein demand of 50%. From an environmental perspective, the current and future demand of protein cannot be sustainably met as the conventional food production chain is severely altering biogeochemical cycles of nitrogen and phosphorus, biodiversity and land-use, with flows towards the biosphere and oceans that are exceeding the planetary boundaries. Microbial protein (protein derived from microorganisms) has been suggested as an excellent sustainable protein source, a fortiori when produced in a land- and fossil free manner. The photoautohydrogenotrophic cultivation (i.e. with light, CO2 and H2) of purple bacteria links up perfectly with the upcoming green electrification of industry (green H2) and the need for carbon capture and utilization. However, this metabolism represented a gap in literature, and thus this thesis aimed to establish a basic knowledge platform on its kinetic, stoichiometric and nutritional performance. At first, three originally photoheterotrophically enriched purple bacteria were studied of which Rhodobacter capsulatus reached the highest protein productivity of 0.16 g protein/L/d, which aligned well with the commonly-known photoautotrophic microalgae. Moreover, a full dietary essential amino acid match was found for human food, while the fatty acid content was dominated by the health-stimulating vaccenic acid (82-86%). Lastly, the achieved protein yield in photoautohydrogenotrophic purple bacteria was 2.3 times higher compared to hydrogen oxidizing bacteria, indicating a resource-efficient use of H2. Next, a photoautohydrogenotrophic enrichment of wastewater treatment microbiomes was performed in search for specialist species. While the isolates of this enrichment showed improvements in their performance during acclimation, the kinetic and nutritional performance of Rhodobacter capsulatus still excelled. Subsequently, the influence of nutrient limitations (C or N) and nitrogen gas fixation was studied on the nutritional tuning potential. Both the limitations as well as the N2 fixation resulted in the shift of the essential amino acid profiles. Additionally, the limitations significantly decreased the pigment content, while an increase in the storage of poly-P was seen in case of carbon limitations. The next major challenge was the production intensification in a photobioreactor of which the design was linked to minimizing both H2 and light limitations. The chosen bubble-column photobioreactor already resulted in a doubled biomass productivity. Finally, the remaining technological and non-technological challenges ahead for the production of a high-value, cost-efficient, environment-friendly microbial protein that complies with legislative requirements and appeals to future consumers were discussed.

Abstract: A uniform description of natural shapes and phenomena is an important goal in science. Such description should check some basic principles, related to 1) the complexity of the model, 2) how well its fits real objects, phenomena and data, and 3) ia direct connection with optimization principles and the calculus of variations. In this article, we present nine principles, three for each group, and we compare some models with a claim to universality. It is also shown that Gielis Transformations and power laws have a common origin in conic sections

Abstract: In this paper, we consider the bulky knots and bulky links, which appear after cutting of a Generalized MöbiusListing GMLn2 body (with the radial cross section a convex plane 2-symmetric figure with two vertices) along a different Generalized MöbiusListing surfaces GMLn2 situated in it. The aim of this report is to investigate the number and geometric structure of the independent objects that appear after such a cutting process of GMLn2 bodies. In most cases we are able to count the indices of the resulting mathematical objects according to the known classification for the standard knots and links.

Abstract: In the biogeochemical flows on Earth, the reactive nitrogen (Nr) level has three times surpassed the safe boundary. The severe transgression of this boundary goes against sustainable planetary development. The modern food production process excessively relies on synthetic Nr fertilizers from the Haber– Bosch process. However, the massive loss of valuable nitrogen resources (i.e., 78-89%) from agriculture has been causing severe nitrogen cascade. Besides, the domestic wastewater in some local areas is discharged without proper treatment, making it a nonnegligible source of Nr pollution for local water bodies. Anthropogenic activities keep pumping out Nr pollution via point-source and non-point-source (NPS) emissions. Compared to the NPS emissions, point sources give visible and identified waste streams. It is vital to intervene the nitrogen cascade from point sources and facilitate humanity back to the safe Nr boundary. The collected and collectible Nr streams from food production, waste management, and recycling secondary raw materials can be used as waste-based fertilizers for agricultural cultivation. Besides the well-investigated recovery of inorganic Nr, organic Nr accounts for a massive Nr proportion on the Earth. Proper handling and treatment make these useful organic fertilizers for soil-based cultivation. However, these organic Nr fertilizers cannot directly apply to fertigation or hydroponic cultivation systems, and further biological conversion via nitrogen mineralization and nitrification to nitrate is essential. Besides the direct Nr cycling, the indirect Nr cycling ‘over the atmosphere’ should also be considered. In this way, the nitrogen cycle can be completed via converting the waste Nr back to nitrogen gas (i.e., Nr removal) and then synthesizing into Nr again. The municipal wastewater treatment plants receive a vast amount of low-strength Nr wastewater (mainly as ammonium) daily. Compared to the conventional nitrification/denitrification process, partial nitritation/anammox (PN/A) is considered a resource- and cost-effective technology for wastewater with a low COD/N ratio. Moreover, the novel autotrophic denitratation/anammox process could be a good Nr removal process for wastewater containing both ammonium and nitrate. This Ph.D. thesis aimed to develop Nr recovery, conversion, and removal bioreactor strategies for different types of waste streams and biomass. Nr recovery was investigated on high-strength Nr waste streams for fertigation or hydroponic applications in Chapters 2 and 3. On the other hand, Nr removal was studied on the medium- to low-strength Nr waste streams in Chapters 4 and 5. In Chapter 2, a novel mineralization and nitrification system was proposed, producing nutrient solutions from solid organic fertilizers for hydroponic systems. Batch tests showed that aerobic incubation at 35°C could realize the NO₃⁻-N production efficiency above 90% from a novel microbial fertilizer. Subsequently, in the stirred tank bioreactor test, NO₃⁻-N production efficiency stabilized in a range of 44-51% under the influent loading rate of 400 mg TN L⁻¹ d⁻¹ at a 5-day HRT. Using Ca(OH)₂ and Mg(OH)₂ as pH control reagents generated the nutrient solutions with different P, Ca, and Mg nutrient levels. After modeling the nutrient balancing process, the proportion of organic-sourced NO₃⁻-N in the Hoagland nutrient solution (HNS) of Ca(OH)₂ scenario was 92.7%, while only 37.4% in the Mg(OH)₂ scenario. Compared to commercial scenarios, the total costs of the organic-sourced HNS can be cost-competitive for hydroponic cultivation. In Chapter 3, the Nr recovery as nitrate (NO₃⁻-N) from diluted human urine (around 670 mg N L⁻¹) was explored in a trickling filter (TF) for the first time. A novel concept of in-situ integrating the TF system into hydroponic systems was proposed as meaningful progress towards sustainable agriculture. The difference between synthetic and real urine in nitrification efficiency was found to be negligible. The full nitrification of alkalinized real urine was realized in the pH-controlled TF by calcium hydroxide (Ca(OH)₂) at around pH 6. The TF could handle different urine collection batches and maintain relatively stable nitrification performance, with NO₃⁻-N production efficiency and rate of 88±3% and 136±4 mg N L⁻¹ d⁻¹, respectively. The optimal HLR to realize this nitrification performance was 2 m³ m⁻² h⁻¹, with energy consumption of 1.8 kWh electricity kg⁻¹ NO₃⁻-N production. Ca(OH)₂, as a cheap base, its triple advantages on urine alkalinization, full nitrification, and macronutrient supplementation were successfully demonstrated in our proposed concept. In Chapter 4, towards more sustainable wastewater treatment, the feasibility of one-stage partial nitritation/anammox (PN/A) was investigated in three parallel packed-bed trickling filters (TFs), with three types of carrier materials of different specific surface areas. Synthetic wastewater containing 100-250 mg NH₄⁺-N L⁻¹ was tested to mimic medium-strength household waste streams after carbon removal. Interestingly, the cheap carrier based on expanded clay achieved similar rates as commercially used plastic carrier materials. The top passive ventilation combined with an optimum hydraulic loading rate of 1.8 m³ m⁻² h⁻¹ could reach approximately 60% total nitrogen (TN) removal at a rate of 300 mg N L⁻¹ d⁻¹. A relatively low NO₃⁻-N production (13%) via PN/A was achieved in TFs. Most of the TN removal took place in the top compartment, where anammox activity was the highest. Energy consumption estimation (0.78 kWh electricity g⁻¹ N removed) suggested that the proposed process could be a suitable low-cost alternative for nitrogen removal. In Chapter 5, coupling sulfur-driven denitratation (SDN) with anammox was proposed to treat the wastewater containing both NO₃⁻-N and NH₄⁺-N, like the secondary effluents of mainstream PN/A processes. To explore the feasibility of sufficient and stable NO₂⁻-N accumulation via SDN in the long term, the effects of pH setpoints, residual NO₃⁻-N level, and biomass-specific NO₃⁻-N loading rate (BSNLR) were investigated. Alternating the pH setpoints between 7.0 and 8.5 could temporarily stimulate the NO₂⁻-N accumulation. Both the residual NO₃⁻-N and BSNLR showed highly positive correlations with the NO₂⁻-N accumulation efficiency. Under the control of pH 8.5, 1.0±0.8 mg NO₃⁻-N L⁻¹ and 150±42 mg NO₃⁻-N g⁻¹ VSS d⁻¹, SDN could produce 6.4±1.0 mg NO₂⁻-N L⁻¹ in the short term. Thiobacillus members may play a crucial role in managing the NO₂⁻-N accumulation, but the reduction of abundance and possible adaptation significantly impaired the efficacy of control strategies in the long run. Overall, novel technologies have been proposed to sustainably convert Nr in waste streams and biomass. The decision for Nr recovery versus removal and synthesis should be based on specific cases with the best environmental, economic, and human-health sustainability. In the future, the Nr management concepts should be further improved to make the nitrogen cycle more sustainable with higher resource use efficiency and less Nr emissions to the environment. Although the thesis is mainly focused on limited types of Nr waste streams, it pointed out the direction of sustainable Nr management and could facilitate the Nr back to the safe boundary in the long run.

Abstract: In this report we describe the basics of biological carbon fixation in bamboo forests. Confusing carbon stock with carbon flux has led to false expectations on the significance of bamboo forests as carbon sinks. Furthermore, misunderstandings about the growth of bamboo culms can lead to highly exaggerated expectations on the productivity of bamboo.