On differential equations associated with perturbations of orthogonal polynomials on the unit circle

In this contribution, we propose an algorithm to compute holonomic second-order differential equations satisfied by some families of orthogonal polynomials. Such algorithm is based in three properties that orthogonal polynomials satisfy: a recurrence relation, a structure formula, and a connection formula. This approach is used to obtain second-order differential equations whose solutions are orthogonal polynomials associated with some spectral transformations of a measure on the unit circle, as well as orthogonal polynomials associated with coherent pairs of measures on the unit circle.Comunidad de MadridUniversidad de Alcal

Ride-through-fault capabilities of DFIG wind farm connected to a VSC station during a DC fault

This work analyzes the capabilities of ride-through-fault (RTF) of a double-fed induction machine (DFIG), -based wind farm connected to a VSC-, in case of a fault in the DC side of the VSC. The modelling of the DFIG wind turbine takes into account key aspects that intervene in succeeding the fault ride-through such as the power capacity of its electronic converter and its control scheme. As result a better understanding of the behaviour and capabilities of such system to perform a successful RTF is achieved. This work also analyzes the behaviour of the momentary islanding of the system composed by the wind farm and the ac filters of the VSC station. Using that information, a novel control scheme for the offshore VSC station is proposed in order to enhance RTF capabilities of the wind farm in case of such DC faults

Ride-through-fault capabilities of DFIG wind farm connected to a VSC station during a DC fault

This work analyzes the capabilities of ride-through-fault (RTF) of a double-fed induction machine (DFIG), -based wind farm connected to a VSC-, in case of a fault in the DC side of the VSC. The modelling of the DFIG wind turbine takes into account key aspects that intervene in succeeding the fault ride-through such as the power capacity of its electronic converter and its control scheme. As result a better understanding of the behaviour and capabilities of such system to perform a successful RTF is achieved. This work also analyzes the behaviour of the momentary islanding of the system composed by the wind farm and the ac filters of the VSC station. Using that information, a novel control scheme for the offshore VSC station is proposed in order to enhance RTF capabilities of the wind farm in case of such DC faults

An empirical examination of the relation between attention and motivation in computer-based education: a modeling approach

Attention is considered a pre-requisite to achieve greater motivation in the classroom. However, empirical evidence of this relationship in educational setting is scarce since the measurement of attention requires specialized equipment such as clinical electroencephalograms (EEG) or fMR1. With the advent of portable, consumer-oriented EEG it is now possible to estimate levels of attention and shed light onto this relationship in the context of a computer-based educational setting. To that end, students (N=40) interacted for an average of 9.48 minutes (SD = .0018) with an assessment exercise in a virtual world. Participants' attention levels were monitored via a portable EEG and incorporated into an attention model capable of deciding on strategies to correct low levels of attention. The participants' motivation was assessed using a self-reported motivation questionnaire at pre-test and post-test times. The results indicated that students with higher self-reported motivation and self-reported attention answered significantly more correct answers. However, no direct evidence was found of a relation between EEG readings and self-reported attention or self-reported motivation. This suggests student's own perceptions of motivation and attention influence performance. Future work consists of defining new models of attention considering self-perceived attention and motivation as baseline as well as improving the model of attention combining EEG reading with an indication of the students' gaze

Impact of the degradation leachate of the polyacrylonitrile-based material UP2W on the retention of Ni(II), Eu(III) and Pu(IV) by cement

The uptake of $^{63}$Ni(II), $^{152}$Eu(III) and $^{242}$Pu(IV) by hardened cement paste (HCP, CEM I) in the degradation stage II (pH ≈ 12.5, [Ca] ≈ 0.02 M) was investigated in the presence of a degradation leachate of UP2W, a polyacrylonitrile-based (PAN) material used as a filter aid in nuclear power plants. The degradation leachate with a concentration of dissolved organic carbon of ∼40 ppm was obtained from the degradation of UP2W in portlandite-buffered solutions for ca. 1100 days. Redox conditions in the Pu systems were buffered with hydroquinone, which defines mildly reducing conditions (pe + pH ≈ 10) where Pu(IV) is the predominant oxidation state. The degradation leachate investigated in this work is moderately sorbed by cement, with distribution ratios (R$_d$) of (0.35 ± 0.15) m$^3$ kg$^{−1}$. These values are 30 to 100 times greater than distribution ratios previously reported for proxy ligands of PAN degradation products, i.e., glutaric acid, α-hydroxyisobutyric acid and 3-hydroxybutyric acid. The presence of the degradation leachate induces a moderate decrease in the uptake of $^{63}$Ni(II), $^{152}$Eu(III) and $^{242}$Pu(IV) by cement, as compared to the sorption in the presence of the proxy ligands. Nevertheless, retention in the presence of the degradation leachate remains high for all investigated radionuclides, with Rd($^{63}$Ni(II)) ≈ 2 m$^3$ kg$^{−1}$, Rd($^{152}$Eu(III)) ≈ 100 m$^3$ kg$^{−1}$ and Rd($^{242}$Pu(IV)) ≈ 30 m$^3$ kg$^{−1}$. These observations possibly reflect that the multiple functionalities (–COOH, –OH, amide groups) expected in the macromolecules (10–15 kDa) present in the degradation leachate, can offer further binding/chelating capabilities compared to the small organic proxy ligands with at most bidentate binding

Solubility of Ca( ii ), Ni( ii ), Nd( iii ) and Pu( iv ) in the presence of proxy ligands for the degradation of polyacrylonitrile in cementitious systems

The solubility of Ca(OH)$_{2}$(cr), β-Ni(OH)$_{2}$(cr), Nd(OH)$_{3}$(s) and PuO$_{2}$(ncr, hyd) was investigated in cement porewater solutions containing glutarate (GTA), α-hydroxyisobutarate (HIBA) and 3-hydroxybutarate (HBA). These ligands were proposed as probable degradation products of UP2W, a polyacrylonitrile-based filter aid used in nuclear power plants. Results obtained in this work are compared with reported solubility data in the presence of iso-saccharinic acid (ISA), a polyhydroxocarboxylic acid resulting from cellulose degradation. None of the investigated proxy ligands shows any significant impact on the solubility of Ca(II), Nd(III) or Pu(IV) in cement porewater solutions. Although the formation of binary complexes M–L (M = Ca(II), Nd(III), An(IV); L = GTA, HIBA, HBA) under acidic conditions is described in the literature, these organic ligands cannot outcompete hydrolysis under hyperalkaline conditions. GTA, HIBA and HBA induce a slight increase in the solubility of β-Ni(OH)$_{2}$(cr) at [L]$_{tot}$ = 0.1 M. This observation supports the formation of stable Ni(II)–GTA, –HIBA and –HBA complexes in hyperalkaline conditions, although the exact stoichiometry of these complexes remains unknown. The comparison of these results with solubility data in the presence of ISA confirms the stronger complexation properties of the latter ligand. Even though HIBA and HBA are carboxylic acids containing one alcohol group, this comparison shows that additional alcohol groups are required to efficiently chelate the metal ion and outcompete hydrolysis. This conclusion is supported by DFT calculations on the Pu(IV)-OH–L systems (L = GTA, HIBA and HBA), which indicate that the complexation with the proxy ligands takes places through the carboxylate group. XRD of selected solid phases after equilibration with proxy ligands at [L]$_{tot}$ = 0.1 M confirms that Ca(II), Ni(II), Nd(III) and Pu(IV) starting solid materials remained mostly unaltered in the course of the experiments. However, the presence of new XRD features suggests the possible formation of secondary phases. These results allow assessment of the effect of the proposed proxy ligands on the solubility of key radionuclides and metal ions in cementitious systems relevant for low and intermediate level waste, and feed into on-going sorption studies evaluating the impact of UP2W degradation products on the uptake of radionuclides by cement

Fractal Metrology for biogeosystems analysis

The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes of this complex system. In the present research, we studied the aggregation process as self-organizing and operating near a critical point. The structural pattern is extracted from the digital images of three soils (<i>Chernozem, Solonetz</i> and <i>"Chocolate" Clay</i>) and compared in terms of roughness of the gray-intensity distribution quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them measured in terms of standard deviation. Some of the applied methods are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc.) while the others have been recently developed by our Group. The combination of these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper <i>Fractal Metrology</i> (FM). We show the usefulness of FM for complex systems analysis through a case study of the soil's physical and chemical degradation applying the selected toolbox to describe and compare the structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites