Abstract: Electron-withdrawing perfluoroalkyl peripheral groups grafted on phthalocyanine (Pc) macrocycles improve their single-site isolation, solubility, and resistance to self-oxidation, all beneficial features for catalytic applications. A high degree of fluorination also enhances the reducibility of Pcs and could alter their singlet oxygen (1O2) photoproduction. The ethanol/toluene 20:80 vol % solvent mixture was found to dissolve perfluorinated FnPcZn complexes, n = 16, 52, and 64, and minimize the aggregation of the sterically unencumbered F16PcZn. The 1O2 production ability of FnPcZn complexes was examined using 9,10-dimethylanthracene (DMA) and 2,2,6,6-tetramethylpiperidine (TEMP) in combination with UV–vis and electron paramagnetic resonance (EPR) spectroscopy, respectively. While the photoreduction of F52PcZn and F64PcZn in the presence of redox-active TEMP lowered 1O2 production, DMA was a suitable 1O2 trap for ranking the complexes. The solution reactivity was complemented by solid-state studies via the construction of photoelectrochemical sensors based on TiO2-supported FnPcZn, FnPcZn|TiO2. Phenol photo-oxidation by 1O2, followed by its electrochemical reduction, defines a redox cycle, the 1O2 production having been found to depend on the value of n and structural features of the supported complexes. Consistent with solution studies, F52PcZn was found to be the most efficient 1O2 generator. The insights on reactivity testing and structural–activity relationships obtained may be useful for designing efficient and robust sensors and for other 1O2-related applications of FnPcZn.

Abstract: Electroporation technique is widely used in biotechnology and medicine for the transport of various molecules through the membranes of biological cells. Different mathematical models of electroporation have been proposed in the literature to study pore formation in plasma and nuclear membranes. These studies are mainly based on models using a single isolated cell with a canonical shape. In this work, a spacetime (x,y,t) multiphysics model based on quasi-static Maxwells equations and nonlinear Smoluchowskis equation has been developed to investigate the electroporation phenomenon induced by pulsed electric field in multicellular systems having irregularly shape. The dielectric dispersion of the cell compartments such as nuclear and plasmatic membranes, cytoplasm, nucleoplasm and external medium have been incorporated into the numerical algorithm, too. Moreover, the irregular cell shapes have been modeled by using the Gielis transformations.

Abstract: Energy-lean nitrogen removal technologies, such as partial nitritation/anammox, often encounter effluent issues due to elevated nitrate and ammonium levels. This study proposed a novel autotrophic polishing strategy coupling sulfur-driven denitratation with anammox. To explore the denitratation potential in obtaining stable and sufficient nitrite accumulation, the effects of pH, residual nitrate level, and biomass-specific nitrate loading rate (BSNLR) were investigated in an S0-packed bed reactor at low hydraulic retention time (i.e., 0.2 h). Implementing pH and residual nitrate control strategies would be easier in practice than BSNLR control to polish secondary effluent. Alkaline pH values could realize successful nitrite accumulation without residual nitrate, and further intensify the accumulation under increased residual nitrate levels. The nitrate level was positively correlated with the nitrite accumulation efficiency. At pH 8.5 and nitrate concentration of 1.0 ± 0.8 mg N L−1, sulfur-driven denitratation could successfully maintain nitrite accumulation of 6.4 ± 1.0 mg NO2−-N L−1, ideally for the downstream anammox in case of residual ammonium levels of around 5 mg N L−1. Since Thiobacillus members play a key role in managing nitrite accumulation, their abundance should be guaranteed in the practical application.

Abstract: Enhanced pollutants removal from saline wastewater was investigated in simultaneous anammox and denitrification (SAD) process with glycine betaine (GB) addition. Long-term operation indicated the optimal GB dose was around 0.4 mM, which enhanced both anammox and denitrifying activity by 30% and 45%, respectively. The total nitrogen and organic removal rates were 0.38 +/- 0.2 kgN/m(3)/d and 0.34 +/- 0.3 kgCOD/m(3)/d, respectively, which increased by 34.5% and 20.5%. Independent of GB dose, denitrifying activity was promoted, but anammox activity was drastically deteriorated after excessive GB addition. The optimal GB dose predicated by both Gaussian and Modified-Boltzmann models were 0.42-0.45 mM. Besides, the bacterial activity recovery after excessive GB addition could be analyzed by the Modified-Boltzmann model. With 1.5 mM GB, granular floatation occurred since numerous gas bubbles were inside the granules. In general, exogenous GB addition can mitigate salinity inhibition and promote pollutants removal from saline wastewater.

Abstract: Enzyme cost is considered to be one of the most significant factors defining the final product price in lignocellulose hydrolysis and fermentation. Enzyme immobilization and recycling can be a tool to decrease costs. However, high solid loading is a key factor towards high product titers, and recovery of immobilized enzymes from this thick liquid is often overlooked. This paper aims to evaluate the economic feasibility of immobilized enzymes in simultaneous saccharification and fermentation (SSF) of lignocellulose biomass in general, as well as the recuperation of magnetic immobilized enzymes (m-CLEAs) during high solid loading in simultaneous saccharification, detoxification and fermentation processes (SSDF) of lignocellulose biomass. Enzyme prices were obtained from general cost estimations by Klein-Marcuschamer et al. [Klein-Marcuschamer et al. (2012) Biotechnol. Bioeng. 109, 10831087]. During enzyme cost analysis, the influence of inoculum recirculation as well as a shortened fermentation time was explored. Both resulted in 15% decrease of final enzyme product price. Enzyme recuperation was investigated experimentally and 99.5 m/m% of m-CLEAs was recovered from liquid medium in one step, while 88 m/m% could still be recycled from a thick liquid with high solid concentrations (SSF fermentation broth). A mathematical model was constructed to calculate the cost of immobilized and free enzyme utilization and showed that, with current process efficiencies and commercial enzyme prices, the cost reduction obtained by enzyme immobilization can reach around 60% compared to free enzyme utilization, while lower enzyme prices will result in a lower percentage of immobilization related savings, but overall enzyme costs will decrease significantly. These results are applied in a case study, estimating the viability of shifting from sugar to lignocellulose substrate for a 100 t lactic acid fermentation batch. It was concluded that it will only be economically feasible if the enzymes are produced at the most optimistic variable cost and either the activity of the immobilized catalyst or the recovery efficiency is further increased.

Abstract: EU strategies for waste management have long recognized the key role of recycling to move towards sustainable consumption and production. This resulted in a range of regulatory measures, among which the Waste Electrical and Electronic Equipment (WEEE) directive, which sets weight-based targets for recovery, preparation for re-use and recycling. The increasing strategic relevance of the supply of raw materials has, however, spurred a more integrated approach towards resource efficiency. In addition to the prevention of disposal, recycling practices are now also meant to contribute to sustainable materials management by pursuing (i) a higher degree of material cycle closure, (ii) an improved recovery of strategically relevant materials, and (iii) the avoidance of environmental burdens associated with the extraction and refining of primary raw materials. In response to this evolution, this paper reports about the development of an indicator set that allows to quantitatively demonstrate these recycling benefits, hence going further than the weight-based objectives employed in the WEEE directive. The indicators can be calculated for WEEE recycling processes for which information is available on both input and output fractions. It offers a comprehensive framework that aims to support decision making processes on product design, to identify opportunities for the optimization of WEEE End-of-Life scenarios, and to assess the achieved (or expected) results of implemented (or planned) recycling optimization strategies. The paper is illustrated by a case study on the recycling of LCD televisions. (C) 2014 Elsevier Ltd. All rights reserved.

Abstract: Exposure to air pollution, such as particulate matter (PM), causes adverse health effects, particularly to the respiratory tract and cardiovascular system. PM is the collective name for all kinds of particles ranging from small particles and liquid droplets, which contain organic compounds, acids and metals, to soil or dust particles. One distinguishes PM10, PM2.5 and PM0.1, which have aerodynamic particle sizes smaller than 10, 2.5 and 0.1 µm, respectively. It is mainly the latter that is the most harmful, as PM0.1 penetrates deep into the respiratory system and carries relatively more toxic substances than the other PM fractions. Over a 15-year period, PM concentrations in European member states have fallen by about 30%. Nevertheless, the World Health Organisation (WHO) air quality guidelines, which became stricter in 2021, are exceeded in most places around the world. Particularly in cities, excessive levels of PM are measured and it is here that PM mitigation should be investigated. For this, the implementation of urban green infrastructure, including trees, shrubs, green roofs and green walls, is being looked at. Plants hinder airflow and remove PM from the air by deposition on their leaves and branches. This process is known as dry deposition. Plants can capture PM very efficiently, due to their complex structure of leaves and branches. Green walls offer significant advantages over other types of urban green infrastructure because they can grow on the huge available wall area and, because they do not hinder air circulation, as we sometimes see with trees. Green walls are believed to have a much greater, untapped potential to reduce PM pollution. However, a literature review showed that we do not know the quantitative impact of green walls and lack the tools and/or general methodology to do so. The objective of this thesis is therefore to develop a method for assessing PM removal by green walls, based on predictive models and based on relevant parameters that are experimentally determined. Computational fluid dynamics (CFD) is a numerical method to simulate airflow in complex environments such as cities. These models can also simulate the vegetation-wind interaction in detail and are interesting tools to assess the effect of green walls on PM concentrations in real environments. It is important to first study the aerodynamic effect of green walls and parameterise it correctly in CFD models. Plants decrease the wind speed and create turbulence through a combination of viscous and form drag, which are determined by the permeability (K) and drag coefficient (Cd), respectively. Wind tunnel experiments were conducted with three commonly found climbers (Hedera helix, Parthenocissus tricuspidata and Parthenocissus quinquefolia) and the variation of leaf area density was investigated for two of them. It was observed that the air resistance depended on plant species, leaf area density and wind speed. The difference between the plant species was assigned to the functional leaf size (FLS), the ratio of the largest circle within the boundaries of the leaf to the total leaf area. FLS is likely associated with other morphological characteristics of plants that, when considered collectively, provide a more comprehensive representation of leaf complexity. The pressure and velocity measurements obtained were used to optimise the permeability and drag coefficient in a CFD model. At wind speeds below 0.6 m s-1, the resistance was mainly determined by viscous drag and a larger leaf size resulted in a higher viscous drag. At wind speeds above 1.5 m s-1, form drag was dominant and the parameterised Cd decreased with increasing wind speed due to the sheltering effect of successive plant elements. The leaf area density had a significant effect on K and Cd and, is therefore an important plant parameters in CFD models. The main conclusion here is that the common practice of using a constant Cd to model the influence of plants on the air flow leads to deviations from reality. Wind tunnels are highly suitable to study the impact of green walls on PM concentration under controlled environmental conditions. For this purpose, a new wind tunnel setup was built and great attention was paid to obtaining a uniform air flow. Thus, based on CFD models, appropriate flow controllers were chosen, consisting of honeycombs and screens with different mesh sizes. New PM generation devices and measuring equipment were installed and set up appropriately. Devices were available for generating and measuring ultrafine dust (<0.1 µm, i.e. PM0.1) and fine dust (<0.3 µm, i.e. PM0.3) consisting of soot particles, and, on the other hand, fine dust with particle sizes smaller than 2.5 (PM2.5) and 10 µm (PM10) consisting of 'Arizona fine test dust'. With the new wind tunnel setup, it was possible to measure the influence of Hedera helix (common ivy), grown in a planter against a climbing aid, on the PM concentration and this was expressed by a collection efficiency, i.e. the difference in concentration in front and behind the plants normalised for the incoming concentration. The collection efficiency of H. helix depended on the particle size of the PM and wind speed. The collection efficiency decreased when the particle size increased from 0.02 to 0.2 µm and increased again for particle sizes above 0.3 µm. The collection efficiency also increased with increasing wind speed, especially for particle sizes > 0.03 µm. On the other hand, relative humidity and the type of PM (soot or dust) did not significantly affect the collection efficiency. The main objective of this study was to obtain an optimised size-resolved deposition model. Dry deposition occurs through several mechanisms, in particular gravity, diffusion, impaction and interception, and the subsequent resuspension of deposited PM back to the environment. The modelling of these mechanisms was described by \citet{Zhang2001} and \citet{Petroff2010}. The data obtained from the wind tunnel experiments allowed validating these deposition models. It was for the first time that deposition of real PM on green walls was studied. The different PM deposition mechanisms were found to be strongly dependent on particle size and wind speed. The models of \citet{Zhang2001} and \citet{Petroff2010} each matched PM concentration measurements for only certain particle sizes. Therefore, a combination of the two models was investigated and the root mean square error was lower by on average 3.5% (PM < 0.03 µm) and 46% (PM > 0.03 µm) compared to the original models at wind speeds greater than 1.5 m s-1. For wind speeds less than 1.5 m s-1, the optimised model did not differ from the original models. The optimised model was able to meet the imposed criteria for air quality models, where a correct model exhibits low deviation from measurements ('normalised mean square error' < 1.5), low bias ('fractional bias' between -0.3 and 0.3) and high R2. In comparison, the R$2$ of the optimised model was 0.57, while that of Zhang et al. (2001) and Petroff et al. (2010) was 0.23 and 0.31, respectively. The optimised model was however characterised by a high scatter, with the fraction of modeled results located within a factor of two of the measurements being lower than 50. A model study with a green façade oriented parallel to the incoming airflow showed that deposition by interception and impaction reduced remarkably, but that the orientation had no effect on deposition by Brownian diffusion. A promising green wall form for PM mitigation is the living wall system (LWS). LWS consist of supporting structures with substrate to grow plants in and can be planted with a variety of plant species. This allows to select plant species with optimal characteristics to achieve PM deposition. These characteristics refer to the macro- and microstructure of the leaves, and research has been conducted mainly on these. On the other hand, the influence of the supporting structure and substrate on PM concentrations has rarely been studied. With the new wind tunnel setup, LWS from different manufacturers were tested for their ability to capture PM. The setups were subjected for three hours to an air flow with a low PM concentration (resuspension phase) and then for three hours to an air flow to which additional PM was added (deposition phase). Some setups were able to decrease the PM concentration during both phases, while others just caused the concentration to increase. Some systems were able to reduce particulate matter concentration during both phases, namely LWS consisting of planters (-2% and -4% for PM0.1 and PM2.5, respectively) and textile cloths (-23% and -5% for PM0.1 and PM2.5, respectively). While other systems actually resulted in an increase in concentration especially LWS existing textile fabrics consisting of geotextiles (+11% for both PM fractions) and with moss as substrate (+2% and +5% for PM0.1 and PM2.5, respectively). This highlights the importance of careful selection of suspension systems to reduce particulate matter concentrations. Further research is therefore needed on the materials used in these systems in relation to their particulate content, as well as on plant development in these systems. In addition to air measurements, measurements were taken of the amount of PM deposited on the leaves and suspension system of LWS. This allowed the difference in PM resuspension and deposition between plant species to be investigated. The amount of deposited particulate matter was determined based on 'saturation isothermal remanent magnetisation' (SIRM), a measure of magnetisable particulate matter. This was possible because the added 'Arizona fine test dust' contained iron oxide. However, no significant difference was observed between the SIRM values measured before the wind tunnel experiment, after resuspension and after deposition. This suggested that the iron oxide content in the Arizona fine test dust was too low to measure a significant difference in the SIRM values on leaves after three hours. The plant species did give rise to different SIRM values ranging between 5 and 260 µ A. In particular, SIRM values above 26 µ A were observed for the plant species that were grouped due to their significantly higher accumulation of PM. 'Specific leaf area' (SLA), specifically the ratio of the one-sided 'fresh' leaf area to its dry mass, was the significant leaf characteristic. SLA correlated with leaf complexity. In particular, plant species with elongated leaves were characterized by low SLA, high FLS and high complexity and showed significantly higher SIRM values. Finally, the optimised size-resolved deposition model was also tested in an urban model to get an idea of the impact of a green wall on PM concentrations in a so-called 'street canyon'. These are narrow streets with high buildings on both sides, making air pollution more persistent. To this end, an ideal scenario was tested in which a green wall was introduced along both sides of the street over a length of about 270 m. The model result showed a decrease in PM2.5 and PM10 of 46 ± 12% and 52 ± 14%. This result is of course for a very optimal scenario where the green wall covers the entire building façades. Since this is not feasible in reality, other ways of promoting contact between green walls and polluted air can be explored. The insights obtained illustrate that the use of climbing plants can be a cost-effective and environmentally friendly solution to reduce PM concentrations. Moreover, the findings showed that models can be used to investigate the impact of green walls on PM levels. These findings fit within the broader context of designing healthy and sustainable urban environments and developing innovative solutions based on solid scientific knowledge.

Abstract: Extensive research has been carried on the molecular adsorption in high surface area materials such as carbonaceous materials and MOFs as well as atomic bonded hydrogen in metals and alloys. Clathrates stand among the ones to be recently suggested for hydrogen storage. Although, the simulations predict lower capacity than the expected by the DOE norms, the additional benefits of clathrates such as low production and operational cost, fully reversible reaction, environmentally benign nature, low risk of flammability make them one of the most promising materials to be explored in the next decade. The inherent ability to tailor the properties of clathrates using techniques such as addition of promoter molecules, use of porous supports and formation of novel reverse micelles morphology provide immense scope customisation and growth. As rapidly evolving materials, clathrates promise to get as close as possible in the search of “holy grail” of hydrogen storage. This review aims to provide the audience with the background of the current developments in the solid-state hydrogen storage materials, with a special focus on the hydrogen clathrates. The in-depth analysis of the hydrogen clathrates will be provided beginning from their discovery, various additives utilised to enhance their thermodynamic and kinetic properties, challenges in the characterisation of hydrogen in clathrates, theoretical developments to justify the experimental findings and the upscaling opportunities presented by this system. The review will present state of the art in the field and also provide a global picture for the path forward.

Abstract: Field water flow processes can be precisely delineated with proper sets of soil hydraulic properties derived from in situ and/or laboratory experiments. In this study we analyzed and compared soil hydraulic properties obtained by traditional laboratory experiments and inverse optimization tension infiltrometer data along the vertical direction within two typical Podzol profiles with sand texture in a potato field. The main goal was to identify proper sets of hydraulic parameters and to evaluate their relevance on hydrological model performance for irrigation management purposes. Tension disc infiltration experiments were carried out at four and five different depths for both profiles at consecutive negative pressure heads of 12, 6, 3 and 0.1 cm. At the same locations and depths undisturbed samples were taken to determine Mualem-van Genuchten (MVG) hydraulic parameters (theta(r), residual water content, theta(s), saturated water content, alpha and n, shape parameters and K-ls, saturated hydraulic conductivity) in the laboratory. Results demonstrated horizontal differences and vertical variability of hydraulic properties. The tension disc infiltration data fitted well in inverse modeling using Hydrus 2D/3D in combination with final water content at the end of the experiment, theta(f). Four MVG parameters (theta(s), alpha, n and field saturated hydraulic conductivity K-fs) were estimated (theta(r) set to zero), with estimated K-ls and alpha values being relatively similar to values from Wooding's solution which used as initial value and estimated theta(s) corresponded to (effective) field saturated water content, theta(f). The laboratory measurement of K-ls yielded 2-30 times higher values than the field method K-fs from top to subsoil layers, while there was a significant correlation between both K-s values (r = 0.75). We found significant differences of MVG parameters theta(s), n and alpha values between laboratory and field measurements, but again a significant correlation was observed between laboratory and field MVG parameters namely K-s, n, theta(s) (r >= 0.59). Assessment of the parameter relevance in 1-D model simulations, illustrated that the model over predicted and under predicted top soil-water content using laboratory and field experiments data sets respectively. The field MVG parameter data set resulted in better agreement to observed soil-water content as compared to the laboratory data set at nodes 10 and 20 cm. However, better simulation results were achieved using the laboratory data set at 30-60 cm depths. Results of our study do not confirm whether laboratory or field experiments data sets are most appropriate to predict soil water fluctuations in a complete soil profile, while field experiments are preferred in many studies. (C) 2016 Elsevier B.V. All rights reserved.

Abstract: Finding a correspondence between soil hydraulic properties, such as saturated hydraulic conductivity (Ks) and apparent electrical conductivity (ECa) as an easily measurable parameter, may be a way forward to estimate the spatial distribution of hydraulic properties at the field scale. In this study, the spatial distributions of Ks, of soil ECa measured by a DUALEM-21S sensor and of soil physical properties were investigated in a sandy grassland. To predict field scale Ks, the statistical relationship between co-located soil Ks, and EMI-ECa was evaluated. Results demonstrated the large spatial variability of all studied properties with Ks being the most variable one (CV = 86.21%) followed by ECa (CV >= 53.77%). A significant negative correlation was found between In-transformed Ks and ECa (r = 0.83; P <= 0.01) at two depths of exploration (0-50 and 0-100 cm). This site specific relation between In Ks and ECa was used to predict saturated hydraulic conductivity over 0-50 cm depth for the whole field. The empirical relation was validated using an independent dataset of measured Ks. The statistical results demonstrate the robustness of this empirical relation with mean estimation error MEE = 0.46 (cm h(-1)), root-mean-square estimation errors RMSEE = 0.74 (cm h(-1)), coefficient of determination r(2) = 0.67 and coefficient of model efficiency Ce = 0.64. The relationship was then used to produce a detailed map of Ks for the whole field. The result will allow model predictions of spatially distributed water content in view of irrigation management. (C) 2016 Elsevier B.V. All rights reserved.

Abstract: For many years, photocatalysis has been proposed as one of the promising techniques to abate environmental pollutants. To improve these reactions it is vital to know the reaction mechanisms of the photocatalytic degradation. This new reactor will make it possible to study the catalytic surface at the moment the reactions occur. By the means of UV LED illumination there is no need of an external UV lamp and thus lowers the cost. The validation of this newly developed reactor is done by investigating the photocatalytic reaction mechanism of nitric oxide (NO) and comparing these findings with those already discussed in literature. From these results, it became clear that the newly developed FTIR in situ reactor allows real time study of photocatalytic degradations.

Abstract: Functionalization of photocatalytic metal oxide nanoparticles of TiO 2 , ZnO, WO 3 and CuO with amine‐terminated (oleylamine) and thiol‐terminated (1‐dodecanethiol) alkyl chained ligands was studied under ambient conditions. A high selectivity was observed in the binding specificity of a ligand towards nanoparticles of these different oxides. It was observed that oleylamine binds stably to only TiO 2 and WO 3 , while 1‐dodecanethiol binds stably only to ZnO and CuO. Similarly, polar to non‐polar solvent phase transfer of TiO 2 and WO 3 nanoparticles could be achieved by using oleylamine, but not by 1‐dodecanethiol, while the contrary holds for ZnO and CuO. The surface chemistry of ligand functionalized nanoparticles was probed by ATR‐FTIR spectroscopy, that enabled to elucidate the occupation of the ligands at the active sites. The photo‐stability of the ligands on the nanoparticle surface was determined by the photocatalytic self‐cleaning properties of the material. While TiO 2 and WO 3 degrade the ligands within 24 hours under both UV and visible light, ligands on ZnO and CuO remain unaffected. The gathered insights are also highly relevant from an application point of view. As an example, since the ligand functionalized nanoparticles are hydrophobic in nature, they can thus be self‐assembled at the air‐water interface, for obtaining nanoparticle films with demonstrated photocatalytic as well as anti‐fogging properties.

Abstract: Generalized Möbius-Listing surfaces and bodies generalize Möbius bands, and this research was motivated originally by solutions of boundary value problems. Analogous to cutting of the original Möbius band, for this class of surfaces and bodies, results have been obtained when cutting such bodies or surfaces. In general, cutting leads to interlinked and intertwined different surfaces or bodies, resulting in very complex systems. However, under certain conditions, the result of cutting can be a single surface or body, which reduces complexity considerably. These conditions are based on congruence and rotational symmetry of the resulting cross sections after cutting, and on the knife cutting the origin

Abstract: Gielis curves (GC) can represent a wide range of shapes and patterns ranging from star shapes to symmetric and asymmetric polygons, and even self intersecting curves. Such patterns appear in natural objects or phenomena, such as flowers, crystals, pollen structures, animals, or even wave propagation. Gielis curves and surfaces are an extension of Lamé curves and surfaces (superquadrics) which have benefited in the last two decades of extensive researches to retrieve their parameters from various data types, such as range images, 2D and 3D point clouds, etc. Unfortunately, the most efficient techniques for superquadrics recovery, based on deterministic methods, cannot directly be adapted to Gielis curves. Indeed, the different nature of their parameters forbids the use of a unified gradient descent approach, which requires initial pre-processings, such as the symmetry detection, and a reliable pose and scale estimation. Furthermore, even the most recent algorithms in the literature remain extremely sensitive to initialization and often fall into local minima in the presence of large missing data. We present a simple evolutionary algorithm which overcomes most of these issues and unifies all of the required operations into a single though efficient approach. The key ideas in this paper are the replacement of the potential fields used for the cost function (closed form) by the shortest Euclidean distance (SED, iterative approach), the construction of cost functions which minimize the shortest distance as well as the curve length using R-functions, and slight modifications of the evolutionary operators. We show that the proposed cost function based on SED and R-function offers the best compromise in terms of accuracy, robustness to noise, and missing data.

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.