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In skill acquisition, instructing individuals the stimulus-response mappings indicating how to perform and act, yields better performance. Additionally, performance is helped by repeated practice. Whether providing instructions and repeated practice interact to achieve optimal performance remains debated. This paper addresses that question by analyzing the learning curves of individuals learning stimulus-response mappings of varying complexity. We particularly focus on the question whether instructions lead to improved performance in the longer run. Via evidence accumulation modeling, we find no evidence for this assertion. Instructions seem to provide individuals with a head start, leading to better initial performance in the early stages of learning, without long-lasting effects on behavior. We discuss the results in light of related studies that do report long-lasting effects of instructions, and propose that the complexity of a skill determines whether long-lasting benefits of initial instructions exist.

With a growing interest in carbon membranes for gas separation, understanding their performance and behaviour is essential for proper design of the membrane separation. Currently not many models exist that correctly describe transport through carbon membranes due to its complex nature. This work attempts to implement a general modelling approach which describes several key transport phenomena inside carbon membranes. The approach assumes a membrane wall to be a bundle of pores with parallel transport mechanisms using the pore size distribution as a weight factor to sum the different transport phenomena. This work adapts this approach specifically for carbon membranes, additionally accounting for molecular sieving and pore blocking effects. Imposing realistic boundary conditions, the model is solved using global optimization algorithms. For testing, four different CMSMs have been produced with hydroquinone and novolac precursors. Pure- and mixed gas permeation tests are done for these CMSMs with H2, N2, and CO2 and the model is fit to this permeation data. Fitting results with pure gas measurements show the model is able to predict the contributions of different mass transport mechanism for the different membranes. This is validated by comparing these results to gas-pair permselectivity data. The model is furthermore fit to mixed gas data. Existence of multi-component effects shows that the model could be further improved. Overall, the model presented in this work is shown to be able to describe complex mass transport behaviour for various different carbon membranes.

The scarcity of natural resources, rising energy prices and strict environmental policies are incentives for the food industry to reform current production strategies. As part of this shift, the eco-industrial park concept is gaining momentum. Industrial aquaponics, integrating aquaculture and hydroponics, emerges as a pioneering food production system. Its focus on reusing and conserving resources aligns with eco-industrial parks. The novel concept of an aquaponics-centered eco-industrial food park fits into a biobased circular economy and supports large-scale exploitation to overcome current economic constraints that prevent commercial adoption. However, balancing aquaponics-centered eco-industrial food parks to minimize external inputs as well as waste is challenging. The present study aims to investigate how a quasi-dynamic optimization method can be used in the design of aquaponics-centered eco-industrial food parks under different seasonal weather conditions. The food park encompasses an aquaculture-hydroponic and anaerobic digestion system that mineralizes internal waste streams. The study prioritizes enhancing nitrogen and phosphorus use-efficiency and self-sufficiency. The results unveil specific optimal hydroponic system sizes for a standardized 100 m3 aquaculture volume. Cooler regions thrive around 0.6–1.0 ha hydroponic system, while warmer areas excel at 0.2–0.3 ha with corresponding nitrogen and phosphorus use-efficiencies of 90% and 67% and self-sufficiencies of 88% and 95%, respectively. A supernatant nitrification step with light supplementation improved the design with maximum self-sufficiency and high water use-efficiency of 88% for a hydroponic-aquaculture area-volume ratio of 0.22:100. Complete nitrogen and phosphorus self-sufficient, near zero-waste, food park was achieved by introducing mineralization of chicken manure for a hydroponic-aquaculture ratio of 1.1:100. Moreover, the food park yielded a 6.7-fold lower carbon footprint compared to a

Self-compacting concrete (SCC) is commonly known for its high flowability and resistance to segregation. Using SCC in constructing large structural members where reinforcements are congested offers several benefits, including reduced project time and a better work environment due to the lack of vibration. However, the concern is the presumably higher pressure exerted on the formwork during casting. This thesis presents the results of a study on the form pressure exerted by SCC, which included the literature review to evaluate existing theoretical design models, laboratory testing, and modelling. A laboratory setup was developed, including a 2-meter circular column instrumented with a wireless pressure system. Two types of SCC were tested: with and without ground granulated blast furnace slag (GGBFS). The pressure was recorded by novel pressure sensors attached to transmitters to send real-time data to the cloud. The system was equipped with a pressure membrane that was in direct contact with the concrete. Several material and environmental parameters were recorded before and during casting. The collected data were used to assess the accuracy of the following models, including DIN1821 (2010), Khayat et al. (2009), Gardner et al. (2012), Teixeira et al. (2017), Beitzel (2010), Ovarlez and Roussel (2006), and Proske (2010). Most models were conservative, calculating higher pressures than recorded. In the next step, machine learning methods were developed to monitor and predict the pressure during casting continuously. These models showed significantly higher accuracy and flexibility than the existing prediction models.

Applying mathematical modelling to the Anthropocene should give students tools to under-stand and reflect on their own role in causes and effects related to the Anthropocene. Three Anthropocene-related phenomena discussed in the media are, for example, transportation, food supply and mass extinction of species. This paper formulates mathematical modelling tasks for these three phenomena. It discusses them with respect to four key features of mathematical modelling, namely understanding, description, abstraction, and negotiation, and finds that each task includes several of these key features. An example of ‘describe’ is to translate extinction of species into a net change equation between formation and extinc-tion of species. An example of ‘abstraction’ is to calculate and find the maybe surprising re-sult that for producing the same amount of protein, cheese requires more land than tomato. The key feature of ‘negotiation’ is that when going by car, time for physical activity must be added corresponding to that of cycling the same distance. This promotes ‘understand’ in the sense of identifying factors that are crucial in explaining the dynamics of the phenome-non., L'application de la modélisation mathématique à l'anthropocène devrait donner aux étu-diants des outils pour comprendre et réfléchir sur leur propre rôle dans les causes et les ef-fets liés à l'anthropocène. Trois phénomènes liés à l'anthropocène discutés dans les médias, par exemple, sont le transport, l'approvisionnement alimentaire et l'extinction massive d'es-pèces. Cet article formule des tâches de modélisation mathématique pour ces trois phéno-mènes et les discute par rapport à quatre caractéristiques clés de la modélisation mathéma-tique, à savoir la compréhension, la description, l'abstraction et la négociation, et constate que chaque tâche comprend plusieurs de ces caractéristiques clés. Un exemple de descrip-tion consiste à traduire l’extinction d’espèces en une équation de changement net entre la formation et l’extinction d’espèces. Un exemple d’abstraction consiste à calculer et à trou-ver le résultat, peut-être surprenant, pour produire la même quantité de protéines, le fromage nécessite plus de terre que la tomate. La caractéristique clé de la négociation est que lors-qu’on voyage en voiture, il faut ajouter un temps d’activité physique correspondant à celui du vélo sur la même distance. Cela favorise la caractéristique clé de la compréhension dans le sens de l’identification des facteurs cruciaux pour expliquer la dynamique du phénomène.

High hardness, low friction coefficient and chemical resistance are only a few of the exceptional mechanical qualities of diamond. Diamonds can be artificially created to have different levels of conductivity, or they can be single, micro or nanocrystalline and highly electrically insulating. It also has high biocompatibility and is famous for being mechanically robust. Due to its high hardness, lack of ductility and difficulty in welding, diamond is a challenging material to construct devices with. Diamonds have experienced a rise in attention as a biological material in recent decades due to new synthesis and fabrication techniques that have eliminated some of these disadvantages. In general, entropic measurements are used for investigating the chemical or biological properties of molecular structures. This study calculates several important K-Banhatti entropies, redefined Zagreb entropies and atom-bond sum connectivity entropy for diamond crystals. We also present a numeric and graphical explanations of obtain indices., Validerad;2024;Nivå 2;2024-09-09 (hanlid);Funder: KingSaud University, Riyadh, Saudi Arabia (RSP2024R401);Full text licens: CC BY-NC

This study investigated the effect of compaction effort and soaking time on the shear strength properties of fine-grained gypsum-containing soils. The objective was to demonstrate that increasing compaction effort increases soil strength, specifically cohesion and the angle of shear strength, when subjected to soaking in freshwater. Unconsolidated undrained triaxial tests were carried out on CBR soil samples with different soaking times. The results showed a transition from brittle to ductile failure behaviour as the soaking time increased. Mohr–Coulomb failure envelopes showed reduced cohesion and angle of shear strength with increasing soak time. Regression models were developed to establish correlations between soaked and unsoaked strength parameters. Strong relationships were found between soil strength properties, compaction effort and soaking time. Empirical equations were proposed to estimate the cohesion and angle of shear strength from compaction effort and soaking time. This study highlighted the importance of considering gypsum-rich soils in civil engineering design. Gypsum dissolution during wetting significantly affected soil strength parameters. The regression models and empirical equations provide engineers with tools to assess the influence of compaction effort and soaking time on soil strength, thus aiding decision making when designing structures on gypsum-rich soils.

This book contains the proceedings of the 18th Social Simulation Conference (SSC) and covers the state of the art of social simulation modeling. The SSC is the annual conference of the European Social Simulation Association (ESSA) and the major global conference devoted to this topic. It is aimed at promoting social simulation and computational social science. The book is the biggest collection of agent-based modeling research. It covers all aspects of modeling, from theory and philosophy of modeling to question of model design, purpose, and structure, using data, visualization, model interrelation, and open modeling. This book is targeted at researchers in social simulation regardless of disciplinary backgrounds, across career stages and different sectors, such as academia, industry, and policy

In this chapter, we challenge the view of mathematical modelling as a neutral practice and argue that ethical reasoning is an important part of the process. Using six cases, each describing different sharing scenarios, we analysed children’s mathematical reasoning and ethical reasoning. The cases were designed to cover a variety of aspects of mathematics and allow different types of ethics to be used. The results show that ethical reasoning plays a crucial part in task-solving, both when the children advocated for division or when they decided on sharing in unequal-sized parts.

This study investigated the effect of compaction effort and soaking time on the shear strength properties of fine-grained gypsum-containing soils. The objective was to demonstrate that increasing compaction effort increases soil strength, specifically cohesion and the angle of shear strength, when subjected to soaking in freshwater. Unconsolidated undrained triaxial tests were carried out on CBR soil samples with different soaking times. The results showed a transition from brittle to ductile failure behaviour as the soaking time increased. Mohr–Coulomb failure envelopes showed reduced cohesion and angle of shear strength with increasing soak time. Regression models were developed to establish correlations between soaked and unsoaked strength parameters. Strong relationships were found between soil strength properties, compaction effort and soaking time. Empirical equations were proposed to estimate the cohesion and angle of shear strength from compaction effort and soaking time. This study highlighted the importance of considering gypsum-rich soils in civil engineering design. Gypsum dissolution during wetting significantly affected soil strength parameters. The regression models and empirical equations provide engineers with tools to assess the influence of compaction effort and soaking time on soil strength, thus aiding decision making when designing structures on gypsum-rich soils.

Optical coherence tomography (OCT) is a non-invasive high-resolution imaging technology. It utilises the coherence property of light to visualise biological tissue cross-sections and produce A-scans. A-scans contain numerous peaks that are associated with layer interfaces in a given sample. Trained medical staff may be able to make a qualitative interpretation of an OCT A-scan. However, this interpretation is not always reliable in terms of identifying the key features of the sample structure. To provide an accurate prognosis and a potential treatment scheme, a more objective measure is in order. The process of inferring sample structure from an A-scan is known as the inverse scattering problem. There are two stages to mathematically solve the OCT inverse scattering problem. The first stage is to establish an OCT model as a means to simulate the A-scan of a known sample structure. This is known as the direct scattering problem. The OCT model is of significant importance in providing a quantitative measure of how well a sample structure fits the available A-scan. The second stage is to develop an efficient and reliable algorithm to infer the sample structure from the A-scan. Solving the inverse scatting problem is about establishing an algorithm to systematically search the space of feasible optical properties of the sample to best fit the available A-scan, thus inferring the tissue structure. Aligning with the two stages, the research proceeds under two main foci. The first focus is the development of the OCT models for the direct scattering problem. This includes extending the first principle OCT model to incorporate absorption, scattering and multiple reflections to create simulated A-scans. The extended OCT model will be used to study the impact of light sources, and the impact of absorption, scattering and multiple reflections on the simulated A-scans. The second focus is the solutions to the inverse scattering problem. This includes investigating and implementi

Problem solving at the crossroads between chemistry and mathematics presents significant challenges for students at all levels of education. This licentiate thesis aims to enhance our understanding of such problem solving, with a focus on how university students approach problems in the context of chemical kinetics. The thesis is based on two papers. The video data analysed in these papers were collected from problem-solving sessions where second-year chemistry students worked in pairs to solve tasks centred around a key concept in chemical kinetics. The first paper aimed to develop a framework suitable for analysing problem solving at the interface of chemistry and mathematics. Deductive and inductive analysis of the collected video data resulted in the extended mathematical modelling cycle (MMC). This empirically derived framework offers a fine-grained picture of the processes and resources at play during problem solving in chemical kinetics, suggesting that students: (1) engage in a range of (sub)processes beyond those typically outlined in the classical MMC; and (2) employ extra-mathematical resources (EMRs) in all stages of the MMC. The EMRs can be divided into chemical and other resources. While chemical resources are essential in translating chemical information into mathematical relationships, they also play a crucial role during mathematical work, offering guidance to the mathematical operations. The purpose of the second paper was to further characterise the nature and roles of other resources. Findings suggest that other resources can be divided into: implicit models of results, explicit examples from experience, and superficial procedural resources. Analysing their roles in problem solving revealed that implicit models primarily influence students’ ideas of where they are going, while explicit examples and superficial procedural resources provide a basis of strategies for how to get there.

This thesis consists of four papers in the field of mathematical biology. All papers aim to advance our understanding of biological systems through the development and application of innovative mathematical models. These models cover a diverse range of biological scales, from the nuclei of unicellular organisms to the collective behaviours of animal populations, showcasing the broad applicability and potential of mathematical approaches in biology. While the first three papers study mathematical models of very different applications and at various scales, all models contribute to the understanding of how oscillations and/or feedback mechanisms on the individual level give rise to complex emergent patterns on the collective level. In Paper I, we propose a mathematical model of basal cognition, inspired by the true slime mould, Physarum polycephalum. The model demonstrates how a combination of oscillatory and current-based reinforcement processes can be used to couple resources in an efficient manner. In Paper II, we propose a model of social burst-and-glide motion in pairs of swimming fish by combining a well-studied model of neuronal dynamics, the FitzHugh-Nagumo model, with a model of fish motion. Our model, in which visual stimuli of the position of the other fish affect the internal burst or glide state of the fish, captures a rich set of swimming dynamics found in many species of fish. In Paper III, we study a class of spatially explicit individual-based models with contest competition. Based on measures of the spatial statistics, we develop two new approximate descriptions of the spatial population dynamics. Paper IV takes a reflective turn, advocating from a philosophical perspective the importance of developing new mathematical models in the face of current scientific challenges.

Problem solving at the crossroads between chemistry and mathematics presents significant challenges for students at all levels of education. This licentiate thesis aims to enhance our understanding of such problem solving, with a focus on how university students approach problems in the context of chemical kinetics. The thesis is based on two papers. The video data analysed in these papers were collected from problem-solving sessions where second-year chemistry students worked in pairs to solve tasks centred around a key concept in chemical kinetics. The first paper aimed to develop a framework suitable for analysing problem solving at the interface of chemistry and mathematics. Deductive and inductive analysis of the collected video data resulted in the extended mathematical modelling cycle (MMC). This empirically derived framework offers a fine-grained picture of the processes and resources at play during problem solving in chemical kinetics, suggesting that students: (1) engage in a range of (sub)processes beyond those typically outlined in the classical MMC; and (2) employ extra-mathematical resources (EMRs) in all stages of the MMC. The EMRs can be divided into chemical and other resources. While chemical resources are essential in translating chemical information into mathematical relationships, they also play a crucial role during mathematical work, offering guidance to the mathematical operations. The purpose of the second paper was to further characterise the nature and roles of other resources. Findings suggest that other resources can be divided into: implicit models of results, explicit examples from experience, and superficial procedural resources. Analysing their roles in problem solving revealed that implicit models primarily influence students’ ideas of where they are going, while explicit examples and superficial procedural resources provide a basis of strategies for how to get there.

El "Three-Sphere micro-swimmer" és un "swimmer" artificial a micro-escala, amb potencials aplicacions en la biomedicina, que consisteix en tres esferes unides per dos braços rígids les longituds dels quals varien entre dos valors. El comportament físic d'aquest dispositiu en un fluid està modelat pel "flow de Stokes" en règims de nombre de Reynolds petit, on les forces de viscositat dominen la dinàmica enfront de la inèrcia. Aquest "swimmer" és simulat tant en un domini infinit de tres dimensions com en un cilindre confinat, sent aquest últim el principal cas d'estudi. En aquest treball es presenta la modelització matemàtica del "micro-swimmer" com un conjunt de sistemes d'equacions diferencials parcials (EDP) que se solucionen numèricament amb el mètode de "Face Centered Finite Volumes" (FCFV) i generant les malles amb el software Gmsh. L'objectiu d'aquest treball és calcular els camps de velocitat i pressió de l'equació de Stokes així com les forces d'arrossegament exercides pel fluid sobre cada esfera en algunes configuracions geomètriques del model per analitzar qualitativament i numèricament la dinàmica del “swimmer”. Posteriorment, es presenta un estudi numèric per avaluar la qualitat de les solucions obtingudes mitjançant mètodes d'alt ordre., El “Three-Sphere micro-swimmer” es un “swimmer” artificial a micro-escala, con potenciales aplicaciones en la biomedicina, que consiste en tres esferas unidas por dos brazos rígidos cuyas longitudes varían entre dos valores. El comportamiento físico de este dispositivo en un fluido está modelado por el ”flow de Stokes” en regímenes de número de Reynolds pequeño, donde las fuerzas de viscosidad dominan la dinámica frente a la inercia. Este “swimmer” es simulado tanto en un dominio infinito de tres dimensiones como en un cilindro confinado, siento este último el principal caso de estudio. En este trabajo se presenta la modelización matemática del “micro-swimmer” como un conjunto de sistemas de ecuaciones diferenciales parciales (EDP) que se solucionan numéricamente con el método “Face Centered Finite Volumes” (FCFV) y generando las mallas con el software Gmsh. El objetivo de este trabajo es calcular los campos de velocidad y presión de la ecuación de Stokes así como las fuerzas de arrastre ejercidas por el fluido sobre cada esfera para algunas configuraciones geométricas del modelo para analizar cualitativamente y numéricamente la dinámica del “swimmer”. Posteriormente, se presenta un estudio numérico para evaluar la calidad de las soluciones obtenidas usando métodos de alto orden., The Three-Sphere micro-swimmer is an artificial swimmer at the micro-scale, with potential applications in bio-medicine, which consists of three spheres linked by rigid rods whose lengths vary between two values. The physical behavior of this device in a fluid is modeled by the Stokes flow at low-Reynolds number regimes, where viscous forces dominate over inertia. This swimmer is simulated both for an infinite three-dimensional domain and a confined capillary tube, being the latter the main case of study. In this work, the mathematical modeling of the micro-swimmer is stated as a set of PDE problems whose solution is tackled numerically with the Face Centered Finite Volume (FCFV) method and its computational meshes generated with Gmsh software. The aim of this work is to compute the velocity and pressure fields from the Stokes equations as well as the drag applied by the fluid over each of the spheres for some geometrical configurations, leading to a qualitative and numerical analysis of its locomotion. Afterwards, a numerical study to assess the quality of the solutions will be made using High Order methods.

Angiogenesis, i.e. the formation of blood vessels from existing ones, plays a vital role in bone or wound healing. The expansion of vascularization facilitates the healing process through the delivery of oxygen and nutrients to the injured site and through the removal of waste products. Clinical observations indicate that impaired angiogenesis can impede the healing process, or can result in non-healing outcomes. The computational model developed in this thesis predicts tip/stalk cell patterning, marking the initial phase of sprouting angiogenesis. Growth factors signal endothelial cells to differentiate into tip and stalk cells. Tip cells branch from the existing vessel, leading the sprout, while stalk cells proliferate and follow behind, forming the newly emerged blood vessel. Understanding tip/stalk cell patterning is vital to ensure successful angiogenesis, as an excess or deficiency in tip cells leads to improper healing. Despite several experimental studies and mathematical models exploring the signaling pathways behind tip cell selection, there is a noticeable gap regarding the effect of extracellular matrix (ECM) stiffness on this process. Given that alterations in stiffness occur in various physiological and pathological processes, comprehension of this effect is clinically relevant. This thesis aims to address the existing gap by investigating the specific influence of ECM stiffness on tip/stalk cell patterning. A computational model is created that simulates a vessel sprout under stimulation of growth factors. This model is able to predict the cell patterning over various ECM stiffness levels, and highlights the relevance of incorporating ECM stiffness in the investigation of angiogenic treatments. Enhancing the models’ accuracy and validating the ECM stiffness-dependent model predictions requires additional experimental data. However, further development of the model has great potential for deepening our understanding of angiogenesis dyna, Applied Mathematics

With a growing interest in carbon membranes for gas separation, understanding their performance and behaviour is essential for proper design of the membrane separation. Currently not many models exist that correctly describe transport through carbon membranes due to its complex nature. This work attempts to implement a general modelling approach which describes several key transport phenomena inside carbon membranes. The approach assumes a membrane wall to be a bundle of pores with parallel transport mechanisms using the pore size distribution as a weight factor to sum the different transport phenomena. This work adapts this approach specifically for carbon membranes, additionally accounting for molecular sieving and pore blocking effects. Imposing realistic boundary conditions, the model is solved using global optimization algorithms. For testing, four different CMSMs have been produced with hydroquinone and novolac precursors. Pure- and mixed gas permeation tests are done for these CMSMs with H2, N2, and CO2 and the model is fit to this permeation data. Fitting results with pure gas measurements show the model is able to predict the contributions of different mass transport mechanism for the different membranes. This is validated by comparing these results to gas-pair permselectivity data. The model is furthermore fit to mixed gas data. Existence of multi-component effects shows that the model could be further improved. Overall, the model presented in this work is shown to be able to describe complex mass transport behaviour for various different carbon membranes.

Mosquito-borne disease is a significant public health issue and within Australia Ross River virus (RRV) is the most reported. This study combines a mechanistic model of mosquito development for two mosquito vectors; Aedes vigilax and Aedes camptorhynchus, with climate projections from three climate models for two Representative Concentration Pathways (RCPs), to examine the possible effects of climate change and sea-level rise on a temperate tidal saltmarsh habitat in Perth, Western Australia. The projections were run under no accretion and accretion scenarios using a known mosquito habitat as a case study. This improves our understanding of the possible implications of sea-level rise, accretion and climate change for mosquito control programmes for similar habitats across temperate tidal areas found in Southwest Western Australia. The output of the model indicate that the proportion of the year mosquitoes are active increases. Population abundances of the two Aedes species increase markedly. The main drivers of changes in mosquito population abundances are increases in the frequency of inundation of the tidal wetland and size of the area inundated, increased minimum water temperature, and decreased daily temperature fluctuations as water depth increases due to sea level changes, particularly under the model with no accretion. The effects on mosquito populations are more marked for RCP 8.5 when compared to RCP 4.5 but were consistent among the three climate change models. The results indicate that Ae. vigilax is likely to be the most abundant species in 2030 and 2050, but that by 2070 Aedes camptorhynchus may become the more abundant species. This increase would put considerable pressure on existing mosquito control programmes and increase the risk of mosquito-borne disease and nuisance biting to the local community, and planning to mitigate these potential impacts should commence now.

[EN] In this work, we propose a new mathematical model for the description of the sterilization process of packaged food in steam retorts. The main advantage of such a model with respect to those existing in the literature is that it has been developed to be used in the framework of nolinear model predictive control (NMPC), which requires solving on-line dynamic optimization problems (periods shorter than 5 seconds). In addition, the proposed model describes a number of physical phenomena that had not been taken into account in previous models. In particular, it considers the possibility that: (i) air enters through the purge; (ii) gases exit through the drain; (iii) liquid water and steam in the autoclave are not in equilibrium. The main contribution is the use of the Fischer-Burmeister equation to model the discrete state changes derived from (iii) in an efficient way, [ES] En este trabajo proponemos un nuevo modelo matemático para la descripción del proceso de esterilización de alimentos envasados en autoclaves de vapor. La principal ventaja de dicho modelo con respecto a los existentes en la literatura es que ha sido desarrollado para ser usado en el marco del control predictivo no lineal basado en modelos (NMPC, por sus siglas en inglés), lo que requiere resolver problemas de optimización dinámica en línea (periodos inferiores a 5 segundos). Además, el modelo propuesto describe una serie de fenómenos físicos que no se habían tenido en cuenta en modelos anteriores. En particular, se considera la posibilidad de que: (i) el agua y el vapor en el autoclave no estén en equilibrio; (ii) haya entrada de aire por la purga; (iii) haya salida de gases por el drenaje. La principal contribución es la utilización de la ecuación de Fischer-Burmeister para modelar los cambios de estado discretos derivados de (i) de forma eficiente

Mathematical models within the Ross–Macdonald framework increasingly play a role in our understanding of vector-borne disease dynamics and as tools for assessing scenarios to respond to emerging threats. These threats are typically characterized by a high degree of heterogeneity, introducing a range of possible complexities in models and challenges to maintain the link with empirical evidence. We systematically identified and analysed a total of 77 published papers presenting compartmental West Nile virus (WNV) models that use parameter values derived from empirical studies. Using a set of 15 criteria, we measured the dissimilarity compared with the Ross–Macdonald framework. We also retrieved the purpose and type of models and traced the empirical sources of their parameters. Our review highlights the increasing refinements in WNV models. Models for prediction included the highest number of refinements. We found uneven distributions of refinements and of evidence for parameter values. We identified several challenges in parametrizing such increasingly complex models. For parameters common to most models, we also synthesize the empirical evidence for their values and ranges. The study highlights the potential to improve the quality of WNV models and their applicability for policy by establishing closer collaboration between mathematical modelling and empirical work.

Trichome patterning in Arabidopsis is regulated by R2R3MYB, bHLH and WDR (MBW) genes. These are considered to form a trimeric MBW protein complex that promotes trichome formation. The MBW proteins are engaged in a regulatory network to select trichome cells among epidermal cells through R3MYB proteins that can move between cells and repress the MBW complex by competitive binding with the R2R3MYB to the bHLHL protein. We use quantitative pull-down assays to determine the relative dissociation constants for the protein-protein interactions of the involved genes. We find similar binding strength between the trichome promoting genes and weaker binding of the R3MYB inhibitors. We used the dissociation constants to calculate the relative percentage of all possible complex combinations and found surprisingly low fractions of those complexes that are typically considered to be relevant for the regulation events. Finally, we predict an increased robustness in patterning as a consequence of higher ordered complexes mediated by GL3 dimerization.

Data is structured in the format provided by Nanion SyncroPatch software. The folder structure is named after each compound tested, inside there is one folder per each of the three protocols used. Data is stored in JSON files containing the information of the experiment., Background and Objective: Assessment of drug cardiotoxicity is critical in the development of new compounds and modeling of drug-binding dynamics to hERG can improve early cardiotoxicity assessment. We previously developed a methodology to generate Markovian models reproducing preferential state-dependent binding properties, trapping dynamics and the onset of IKr block using simple voltage clamp protocols. Here, we test this methodology with real IKr blockers and investigate the impact of drug dynamics on action potential prolongation. Methods: Experiments were performed on HEK cells stably transfected with hERG and using the Nanion SyncroPatch 384i. Three protocols, P-80, P0 and P40, were applied to obtain the experimental data from the drugs and the Markovian models were generated using our pipeline. The corresponding static models were also generated and a modified version of the O´Hara-Rudy action potential model was used to simulate the action potential duration. Results: The experimental Hill plots and the onset of IKr block of ten compounds were obtained using our voltage clamp protocols and the models generated successfully mimicked these experimental data, unlike the CiPA dynamic models. Marked differences in APD prolongation were observed when drug effects were simulated using the dynamic models and the static models. Conclusions: These new dynamic models of ten well-known IKr blockers constitute a validation of our methodology to model dynamic drug–hERG channel interactions and highlight the importance of state-dependent binding, trapping dynamics and the time-course of IKr block to assess drug effects even at the steady-state.

Data is structured in the format provided by Nanion SyncroPatch software. The folder structure is named after each compound tested, inside there is one folder per each of the three protocols used. Data is stored in JSON files containing the information of the experiment., Background and Objective: Assessment of drug cardiotoxicity is critical in the development of new compounds and modeling of drug-binding dynamics to hERG can improve early cardiotoxicity assessment. We previously developed a methodology to generate Markovian models reproducing preferential state-dependent binding properties, trapping dynamics and the onset of IKr block using simple voltage clamp protocols. Here, we test this methodology with real IKr blockers and investigate the impact of drug dynamics on action potential prolongation. Methods: Experiments were performed on HEK cells stably transfected with hERG and using the Nanion SyncroPatch 384i. Three protocols, P-80, P0 and P40, were applied to obtain the experimental data from the drugs and the Markovian models were generated using our pipeline. The corresponding static models were also generated and a modified version of the O´Hara-Rudy action potential model was used to simulate the action potential duration. Results: The experimental Hill plots and the onset of IKr block of ten compounds were obtained using our voltage clamp protocols and the models generated successfully mimicked these experimental data, unlike the CiPA dynamic models. Marked differences in APD prolongation were observed when drug effects were simulated using the dynamic models and the static models. Conclusions: These new dynamic models of ten well-known IKr blockers constitute a validation of our methodology to model dynamic drug–hERG channel interactions and highlight the importance of state-dependent binding, trapping dynamics and the time-course of IKr block to assess drug effects even at the steady-state.

Endotoxin administration is commonly used to study the inflammatory response, and though traditionally given as a bolus injection, it can be administered as a continuous infusion over multiple hours. Several studies hypothesize that the latter better represents the prolonged and pronounced inflammation observed in conditions like sepsis. Yet very few experimental studies have administered endotoxin using both strategies, leaving significant gaps in determining the underlying mechanisms responsible for their differing immune responses. We used mathematical modelling to analyse cytokine data from two studies administering a 2 ng kg−1 dose of endotoxin, one as a bolus and the other as a continuous infusion over 4 h. Using our model, we simulated the dynamics of mean and subject-specific cytokine responses as well as the response to long-term endotoxin administration. Cytokine measurements revealed that the bolus injection led to significantly higher peaks for interleukin (IL)-8, while IL-10 reaches higher peaks during continuous administration. Moreover, the peak timing of all measured cytokines occurred later with continuous infusion. We identified three model parameters that significantly differed between the two administration methods. Monocyte activation of IL-10 was greater during the continuous infusion, while tumour necrosis factor (Formula presented.) and IL-8 recovery rates were faster for the bolus injection. This suggests that a continuous infusion elicits a stronger, longer-lasting systemic reaction through increased stimulation of monocyte anti-inflammatory mediator production and decreased recovery of pro-inflammatory catalysts. Furthermore, the continuous infusion model exhibited prolonged inflammation with recurrent peaks resolving within 2 days during long-term (20–32 h) endotoxin administration.

The integration of microalgae cultivation in anaerobic digestion (AD) plants can take advantage of relevant nutrients (ammonium and ortho-phosphate) and CO2 loads. The proposed scheme of microalgae integration in existing biogas plants aims at producing approximately 250 ty(-1) of microalgal biomass, targeting the biostimulants market that is currently under rapid expansion. A full-scale biorefinery was designed to treat 50 kty(-1) of raw liquid digestate from AD and 0.45 kty(-1) of CO2 from biogas upgrading, and 0.40 kty(-1) of sugar-rich solid by-products from a local confectionery industry. An innovative three-stage cultivation process was designed, modelled, and verified, including: i) microalgae inoculation in tubular PBRs to select the desired algal strains, ii) microalgae cultivation in raceway ponds under greenhouses, and iii) heterotrophic microalgae cultivation in fermenters. A detailed economic assessment of the proposed biorefinery allowed to compute a biomass production cost of 2.8 +/- 0.3 kg DW-1, that is compatible with current downstream process costs to produce biostimulants, suggesting that the proposed nutrient recovery route is feasible from the technical and economic perspective. Based on the case study analysis, a discussion of process, bioproducts and policy barriers that currently hinder the development of microalgae-based biorefineries is presented.

La radiación ultravioleta es la región del espectro solar cuya longitud de onda está comprendida entre 100 y 400 nm. La importancia del conocimiento de esta radiación es debida a la gran influencia que tiene en distintos aspectos de la salud y la vida en la tierra. A pesar de la importancia de esta banda del espectro solar, muy pocas estaciones meteorológicas poseen sensores para su medición, por lo que es esencial poder determinar su valor a partir de otras variables que se miden de forma más habitual en estaciones terrestres. En este trabajo se ha realizado un estudio matemático completo de esta banda del espectro solar en sus componentes global y eritemática ambas sobre el plano horizontal, utilizando diferentes estrategias que combinan modelos de regresiones multilineales tradicionales, y novedosas técnicas de aprendizaje automático basadas en redes neuronales artificiales. También se ha abordado una aplicación práctica de los modelos de ecuaciones estructurales, que ha permitido la obtención de información latente en datos cualitativos procedentes de encuestas en un grupo de control. Los estudios realizados han permitido obtener modelos locales precisos de radiación UV y UV eritemática en función de las condiciones atmosféricas, determinadas según el tipo de cielo (todo tipo de cielo, cubierto, intermedio y claro) clasificados mediante la norma ISO/CIE. Además, se ha realizado un estudio, mediante modelos de ecuaciones estructurales, de la influencia de la percepción subjetiva de las personas al riesgo que supone para la salud la radiación UV, y su repercusión en hábitos de comportamiento, como es el uso de ropa de protección en sus actividades al aire libre., Ultraviolet irradiation is the region of the solar spectrum with wavelengths ranging from 100 to 400nm. Understanding ultraviolet irradiation is crucial due to its significant impact on various aspects of health and life on Earth. Despite the importance of this band of the solar spectrum, very few meteorological stations are equipped with sensors to measure it. Therefore, it is essential to determine its value from other variables that are more commonly measured at ground stations. In this study, a comprehensive mathematical analysis solar ultraviolet irradiation, including its global and erythemal components on the horizontal plane, was conducted using various strategies that combine traditional multiple linear regression models and innovative machine learning techniques based on artificial neural networks. Additionally, a practical application of structural equation models was employed to extract latent information from qualitative data obtained through surveys in a control group. The conducted studies have allowed for the development of accurate local models for UV irradiation and erythemal UV irradiation based on atmospheric conditions, categorized according to the type of sky (all sky types, overcast, intermediate, and clear) as defined by the ISO/CIE standard. Furthermore, through structural equation models, an analysis was conducted on the influence of people's subjective perception of the health risks associated with UV irradiation and its impact on behavioural habits, such as the use of protective clothing during outdoor activities., Esta tesis ha sido financiada en convocatorias competitivas, gracias a los siguientes proyectos de investigación: 1.- Valoración técnica de los niveles de exposición a radiación solar en trabajos de exterior: identificación de grupos de riesgo y medidas de prevención. (INVESTUN/19/BU/004). Junta de Castilla y León. Dirección General de Trabajo y Prevención de riesgos laborales. IP: Montserrat Díez Mediavilla. 01/01/2019-31/12/2021. 2.- Análisis Espectral de la Radiación Solar: Aplicaciones Climáticas, Energéticas y Biológicas (RTI-2018-098900-B-I00). Ministerio de Universidades e Investigación Programa Estatal De I+D+i Orientada a los Retos de la Sociedad. IP: Cristina Alonso Tristán y Montserrat Díez Mediavilla. 1/01/2019-30/09/2022. 3.- Modelado espectral de la radiación solar en entornos urbanos: una oportunidad para la sostenibilidad de las ciudades. (TED2021-131563B-I00). Agencia Estatal de Investigación. IP: Cristina Alonso Tristán. 1/12/2022-30/11/2024. 4.- Valoración técnica de los niveles óptimos de iluminación efectiva para la salud visual y psicológica en entornos laborales. (INVESTUN/22/BU/001). Junta de Castilla y León. Dirección General de Trabajo y Prevención de riesgos laborales. IP: Cristina Alonso Tristán. 1/01/2022-30/09/2024. 5.- Avances para un urbanismo de bajo consumo energético. (PID2022139477OB-I00). Agencia Estatal de Investigación. IP: Cristina Alonso Tristán y David González Peña. 1/09/2023-31/08/2026

Endotoxin administration is commonly used to study the inflammatory response, and though traditionally given as a bolus injection, it can be administered as a continuous infusion over multiple hours. Several studies hypothesize that the latter better represents the prolonged and pronounced inflammation observed in conditions like sepsis. Yet very few experimental studies have administered endotoxin using both strategies, leaving significant gaps in determining the underlying mechanisms responsible for their differing immune responses. We used mathematical modelling to analyse cytokine data from two studies administering a 2 ng kg−1 dose of endotoxin, one as a bolus and the other as a continuous infusion over 4 h. Using our model, we simulated the dynamics of mean and subject-specific cytokine responses as well as the response to long-term endotoxin administration. Cytokine measurements revealed that the bolus injection led to significantly higher peaks for interleukin (IL)-8, while IL-10 reaches higher peaks during continuous administration. Moreover, the peak timing of all measured cytokines occurred later with continuous infusion. We identified three model parameters that significantly differed between the two administration methods. Monocyte activation of IL-10 was greater during the continuous infusion, while tumour necrosis factor (Formula presented.) and IL-8 recovery rates were faster for the bolus injection. This suggests that a continuous infusion elicits a stronger, longer-lasting systemic reaction through increased stimulation of monocyte anti-inflammatory mediator production and decreased recovery of pro-inflammatory catalysts. Furthermore, the continuous infusion model exhibited prolonged inflammation with recurrent peaks resolving within 2 days during long-term (20–32 h) endotoxin administration.

Problem solving at the crossroads between chemistry and mathematics presents significant challenges for students at all levels of education. This licentiate thesis aims to enhance our understanding of such problem solving, with a focus on how university students approach problems in the context of chemical kinetics. The thesis is based on two papers. The video data analysed in these papers were collected from problem-solving sessions where second-year chemistry students worked in pairs to solve tasks centred around a key concept in chemical kinetics. The first paper aimed to develop a framework suitable for analysing problem solving at the interface of chemistry and mathematics. Deductive and inductive analysis of the collected video data resulted in the extended mathematical modelling cycle (MMC). This empirically derived framework offers a fine-grained picture of the processes and resources at play during problem solving in chemical kinetics, suggesting that students: (1) engage in a range of (sub)processes beyond those typically outlined in the classical MMC; and (2) employ extra-mathematical resources (EMRs) in all stages of the MMC. The EMRs can be divided into chemical and other resources. While chemical resources are essential in translating chemical information into mathematical relationships, they also play a crucial role during mathematical work, offering guidance to the mathematical operations. The purpose of the second paper was to further characterise the nature and roles of other resources. Findings suggest that other resources can be divided into: implicit models of results, explicit examples from experience, and superficial procedural resources. Analysing their roles in problem solving revealed that implicit models primarily influence students’ ideas of where they are going, while explicit examples and superficial procedural resources provide a basis of strategies for how to get there.

This thesis consists of four papers in the field of mathematical biology. All papers aim to advance our understanding of biological systems through the development and application of innovative mathematical models. These models cover a diverse range of biological scales, from the nuclei of unicellular organisms to the collective behaviours of animal populations, showcasing the broad applicability and potential of mathematical approaches in biology. While the first three papers study mathematical models of very different applications and at various scales, all models contribute to the understanding of how oscillations and/or feedback mechanisms on the individual level give rise to complex emergent patterns on the collective level. In Paper I, we propose a mathematical model of basal cognition, inspired by the true slime mould, Physarum polycephalum. The model demonstrates how a combination of oscillatory and current-based reinforcement processes can be used to couple resources in an efficient manner. In Paper II, we propose a model of social burst-and-glide motion in pairs of swimming fish by combining a well-studied model of neuronal dynamics, the FitzHugh-Nagumo model, with a model of fish motion. Our model, in which visual stimuli of the position of the other fish affect the internal burst or glide state of the fish, captures a rich set of swimming dynamics found in many species of fish. In Paper III, we study a class of spatially explicit individual-based models with contest competition. Based on measures of the spatial statistics, we develop two new approximate descriptions of the spatial population dynamics. Paper IV takes a reflective turn, advocating from a philosophical perspective the importance of developing new mathematical models in the face of current scientific challenges.

The performance of Photo-Fenton treatments is reported to heavily rely on how hydrogen peroxide is supplied. Rigorously optimizing the dosage profile of hydrogen profile is a challenge that has been hardly addressed. Although some model-based approaches have been explored, solutions of practical significance have not been produced. However, model-based approaches can be used to explore new dosage schemes and identify practical sub-optimal improvements. This work addressed the photo-Fenton degradation of Paracetamol (PCT) in an annular photoreactor, and used a kinetic model including variable H 2 O 2 dosage previously fit and reported for simulating new dosage schemes for unexplored operational conditions. Preliminary results allowed understanding trends and proposing new simulations, which in turn allowed identifying promising operation alternatives. Finally, experimental validation confirmed that significant reduction of TOC levels (20 percent points, beyond 80%) are possible. Furthermore, alternatives that could reach total mineralization were also identified for larger processing times (beyond 20 h). Thus, the work has once again demonstrated that model exploitation allows producing significant practical outcomes with a much-reduced experimental effort, and has produced unexplored hydrogen peroxide dosage schemes that increase the process performance reported previously and indicates the way to total mineralization., Peer Reviewed, Postprint (published version)

Every encountered pathogen leaves an imprint on the immune system. This is termed as immune memory. A significant part of this immune memory is stored in a subset of T cells called memory T cells. As memory T cells are experienced in pathogen control, they are of significant interest to immunologists in their search for better vaccine technologies. For example, if the condition and the time of when memory T cells are formed is known, then technologies can be developed that either increase the number of memory T cells produced to better fend off an infection or decrease the number of memory T cells created to limit self-harm in autoimmune diseases. Similarly, if the lifespan of both an individual memory T cell and the memory T-cell population is known, questions on the efficacy and longevity of vaccines can be addressed. Therefore, it is essential to detail the mechanisms underlying the generation and maintenance of memory T cells. This thesis presents experimental data, their mathematical analyses and theoretical simulations that 1) discuss the lifespan of memory T cells, 2) ways to accurately approximate these lifespans, 3) the events leading up to the generation of memory T cells during an immune response and 4) probable mechanisms that could sustain the immunity provided by memory T cells against a pathogen for longer.

The controlled modulation of the nozzle exit velocity acts as a disturbance source, superimposing the natural disturbances in axisymmetric turbulent air jets. The modulation controls the vortex rollup, and thus the overall vortex structure in the jet. The vortex structures have a significant influence on the heat transfer properties of the jet configurations. The jet can be modulated by an external source of low amplitude oscillations or by self-sustaining oscillations generated by the operation of the specially designed whistler nozzles. The aim of the experimental investigations, mathematical modelling and numerical simulations was to investigate the properties and vortex structures of acoustically modified and non-modified jets and to find an efficient way to control them. This study can serve as a basis for further development and optimisation of technological processes related to air nozzles. The paper presents the results of experimental research and mathematical modelling and numerical simulation of free and impinging turbulent axisymmetric modified and not modified air jets.

In reaction to the COVID-19 pandemic, the government of Luxembourg suspended in-school teaching and learning towards remote teaching. A survey conducted by the Ministry of Education after three weeks of confinement, showed that more than half of the parents faced difficulties when using remote teaching with their students. To tackle this new challenge, we adapted our research to the use of augmented reality, digital and physical mathematical modelling in remote mathematics education for elementary schools. The elementary school students (aged 5 to 12) created cultural artifacts (i.e., Easter egg cups) during the confinement. In this paper, we will describe mathematical modelling in remote teaching and further concentrate on parents’ perspectives, who played an essential role in assisting their children. Moreover, we will discuss different didactical principles that emerged from the task design during the study through parents’ eyes. Thus, understanding parents’ perspectives became highly important in enabling us to improve task designs and related pedagogical approaches in remote teaching. The data collected in this study included semi-structured interviews with students, parents, and teachers as well as questionnaires and field notes. We followed an exploratory stance with our data analyses, primarily utilizing grounded theory (Corbin & Strauss, 1990, 2014) approaches. Through the insights we gained from our findings, we aim to explain how the parents perceived teaching and learning mathematical modelling in our experiments, how they scaffolded the given tasks, and what support they required and would need in future remote teaching.

Cardiovascular diseases are the most common cause of death worldwide. There are known risk factorsfor cardiovascular diseases, such as high blood pressure, and it is also known that cardiovasculardiseases are associated with both the macrocirculation and the microcirculation. The macrocirculationis the term for the large vessels within the circulatory system, while microcirculation refersto the small vessels near the cells. In the clinics, the macrocirculation is more commonly examinedthan the microcirculation. Hypothetically indications of cardiovascular diseases could be foundearlier in the microcirculation than in the macrocirculation. If that is true, cardiovascular diseasescould be found earlier than as of today by microcirculatory examinations. The microcirculation hasbeen studied previous with mathematical models. However, there is no mathematical model on theoxygen transport in the skin microcirculation that constitute ordinary differential equations, has ahigh time resolution and where the impacts on the oxygen transport of risk factors of cardiovasculardiseases are studied.This thesis showcases that the microvascular oxygen transport is possible to study in high resolutionwith a mathematical model and that high blood pressure may have an impact on the abilityto recruit more vessels due to a perturbation of the blood system. The model shows the main principlesof the dynamics of the oxygen in skin microcirculation. Although the model is a simplificationof the real microcirculatory system, the model is able to describe experimental data. Further knowledgeabout the microcirculation and the impact of blood pressure has been drawn from the model.An improved model could be used to understand and learn even more about the microcirculationand the impact of more risk factors besides high blood pressure. That knowledge is important tofind and treat cardiovascular diseases earlier than as of today to worldwide decrease the morbidityand mortality of cardiovascular dise

A new modelling approach for dissolution of polydisperse powders is developed within the framework of the classical Noyes-Whitney/Nernst-Brunner analysis. Its distinguishing feature is that the underlying continuous particle-size distribution is retained. Two different but related dependencies of the diffusion-layer thickness on particle size are considered. First, a power-law dependence that interpolates between a thickness that is proportional to (or equals) the particle radius (obtained when the exponent equals 1) and a constant thickness (obtained when the exponent is 0). Second, a piecewise linear function such that the thickness equals the particle radius for sufficiently small particles and is constant for larger ones. The modelling approach is exemplified by consideration of a lognormal particle-size distribution. Highly accurate closed-form expressions for the fraction of dissolved drug are obtained for dissolution under sink conditions (which are exact if the diffusion-layer thickness is radius-independent). Moreover, it is demonstrated that any result derived under sink conditions can be reused to determine the fraction of dissolved/absorbed drug under non-sink conditions, using the concept of a retarded time. Comparison with literature data and experiments are used to validate the modelling approach and to demonstrate its usefulness in a practical context.

In reaction to the COVID-19 pandemic, the government of Luxembourg suspended in-school teaching and learning towards remote teaching. A survey conducted by the Ministry of Education after three weeks of confinement, showed that more than half of the parents faced difficulties when using remote teaching with their students. To tackle this new challenge, we adapted our research to the use of augmented reality, digital and physical mathematical modelling in remote mathematics education for elementary schools. The elementary school students (aged 5 to 12) created cultural artifacts (i.e., Easter egg cups) during the confinement. In this paper, we will describe mathematical modelling in remote teaching and further concentrate on parents’ perspectives, who played an essential role in assisting their children. Moreover, we will discuss different didactical principles that emerged from the task design during the study through parents’ eyes. Thus, understanding parents’ perspectives became highly important in enabling us to improve task designs and related pedagogical approaches in remote teaching. The data collected in this study included semi-structured interviews with students, parents, and teachers as well as questionnaires and field notes. We followed an exploratory stance with our data analyses, primarily utilizing grounded theory (Corbin & Strauss, 1990, 2014) approaches. Through the insights we gained from our findings, we aim to explain how the parents perceived teaching and learning mathematical modelling in our experiments, how they scaffolded the given tasks, and what support they required and would need in future remote teaching.

Cardiovascular diseases are the most common cause of death worldwide. There are known risk factorsfor cardiovascular diseases, such as high blood pressure, and it is also known that cardiovasculardiseases are associated with both the macrocirculation and the microcirculation. The macrocirculationis the term for the large vessels within the circulatory system, while microcirculation refersto the small vessels near the cells. In the clinics, the macrocirculation is more commonly examinedthan the microcirculation. Hypothetically indications of cardiovascular diseases could be foundearlier in the microcirculation than in the macrocirculation. If that is true, cardiovascular diseasescould be found earlier than as of today by microcirculatory examinations. The microcirculation hasbeen studied previous with mathematical models. However, there is no mathematical model on theoxygen transport in the skin microcirculation that constitute ordinary differential equations, has ahigh time resolution and where the impacts on the oxygen transport of risk factors of cardiovasculardiseases are studied.This thesis showcases that the microvascular oxygen transport is possible to study in high resolutionwith a mathematical model and that high blood pressure may have an impact on the abilityto recruit more vessels due to a perturbation of the blood system. The model shows the main principlesof the dynamics of the oxygen in skin microcirculation. Although the model is a simplificationof the real microcirculatory system, the model is able to describe experimental data. Further knowledgeabout the microcirculation and the impact of blood pressure has been drawn from the model.An improved model could be used to understand and learn even more about the microcirculationand the impact of more risk factors besides high blood pressure. That knowledge is important tofind and treat cardiovascular diseases earlier than as of today to worldwide decrease the morbidityand mortality of cardiovascular dise

In a digital world where algorithms and mathematical models impact students’ lives and society as a whole, it is important to learn critical thinking to understand and reflect upon what is happening. How will students perceive an inclusion of mathematical models that affect society in their mathematics lessons? Prior research shows that mathematical modelling is a valuable skill. However, critical thinking regarding models is currently not included in the curriculum. The theory in the study is based on critical mathematics and will include four different types of knowledge regarding mathematical modelling: pure mathematical knowledge, technical knowledge, reflective knowledge and extra-mathematical knowledge. In this study a field study was conducted in two Swedish upper secondary schools, together with a survey and focus group interviews. The study found that students’ experiences during the lessons show resemblance with critical mathematics while working with mathematical models and that the students are capable of evaluating the impact that the models have on society. The student’s experiences working with mathematical models that affect society alludes to a possibility to work towards including democracy in the mathematical classroom. This study focuses on the students’ perspective, further research regarding the teachers’ perspective could provide additional insight.

A new modelling approach for dissolution of polydisperse powders is developed within the framework of the classical Noyes-Whitney/Nernst-Brunner analysis. Its distinguishing feature is that the underlying continuous particle-size distribution is retained. Two different but related dependencies of the diffusion-layer thickness on particle size are considered. First, a power-law dependence that interpolates between a thickness that is proportional to (or equals) the particle radius (obtained when the exponent equals 1) and a constant thickness (obtained when the exponent is 0). Second, a piecewise linear function such that the thickness equals the particle radius for sufficiently small particles and is constant for larger ones. The modelling approach is exemplified by consideration of a lognormal particle-size distribution. Highly accurate closed-form expressions for the fraction of dissolved drug are obtained for dissolution under sink conditions (which are exact if the diffusion-layer thickness is radius-independent). Moreover, it is demonstrated that any result derived under sink conditions can be reused to determine the fraction of dissolved/absorbed drug under non-sink conditions, using the concept of a retarded time. Comparison with literature data and experiments are used to validate the modelling approach and to demonstrate its usefulness in a practical context.

In this work, a previously published model for the water up take of stormwater in sponge-like porous bodies by the group is further developed. This is done by investigating the highest-performing model and considering the water uptake from the surroundings of a pond and rain-infiltrated soil. This implies that water uptake from impermeable to partially permeable surfaces is examined. Hence, the following cases are considered: (1) impervious bottom surface and no precipitation, (2) impervious bottom surface with precipitation, (3) permeable soil with no precipitation, and (4) permeable soil with precipitation. A mathematical model covering all these cases is presented, where the governing equations are the mass conservation and Darcy’s law together with an assumption of a sharp wetting front being a first-order approximation of the complete Richard’s equation. Results for the water uptake height, pond depth, and wetting front are computed numerically and plotted against time. Analytical solutions are also presented in certain cases, and critical values are obtained. The parametric study includes variations in the ratio of the model- to the surrounding ground surface area, initial pond depth, precipitation, and soil characteristics. To exemplify, the time it takes to absorb the water from the pond after a precipitation period is presented. The results are related to the Swedish rainfall data of 1 h duration with a return period of 10 years. When evaluating efficiency, the focus is on the absorption time. Results vary considerably, demonstrating a general trend that with soil infiltration, the water absorption rate is higher. For most cases, the considered water amount is absorbed completely, although depending on the parameters and conditions. These results serve to optimize the model for each of the cases. The main focus of the research lies in the theoretical aspect., Validerad;2023;Nivå 2;2023-09-12 (joosat);CC BY 4.0 License

A new modelling approach for dissolution of polydisperse powders is developed within the framework of the classical Noyes-Whitney/Nernst-Brunner analysis. Its distinguishing feature is that the underlying continuous particle-size distribution is retained. Two different but related dependencies of the diffusion-layer thickness on particle size are considered. First, a power-law dependence that interpolates between a thickness that is proportional to (or equals) the particle radius (obtained when the exponent equals 1) and a constant thickness (obtained when the exponent is 0). Second, a piecewise linear function such that the thickness equals the particle radius for sufficiently small particles and is constant for larger ones. The modelling approach is exemplified by consideration of a lognormal particle-size distribution. Highly accurate closed-form expressions for the fraction of dissolved drug are obtained for dissolution under sink conditions (which are exact if the diffusion-layer thickness is radius-independent). Moreover, it is demonstrated that any result derived under sink conditions can be reused to determine the fraction of dissolved/absorbed drug under non-sink conditions, using the concept of a retarded time. Comparison with literature data and experiments are used to validate the modelling approach and to demonstrate its usefulness in a practical context.

In Northern Finland, the most significant land use challenges are related to bioenergy production from peat extraction and forest biomass. Increasing societal demand for bioenergy may increase production rates. However, environmental impacts of peat extraction are of increasing concern, which has led to a decline in production, thereby freeing up these areas for other uses. Using storylines for different societal futures and process-based models (PERSiST and INCA), we simulated the effect of simultaneous land use change and climate change on water quality (phosphorus, nitrogen and suspended sediments concentration). Conversion of peat extraction areas to arable land, together with climate change, may pose a risk for deterioration of ecological status. On the other hand, continuous forestry may have positive impacts on water quality. Suspended sediment concentrations in the river do not exceed water quality requirements for salmonids, but nitrogen concentrations may exceed threshold values especially during high flows. A storyline emphasizing sustainable development in energy production led to the best outcome in terms of water protection.

In this study, the drying kinetics of noni (Morinda citrifolia L.) was investigated in a laboratory tunnel dryer at air temperatures of 50, 60, and 70 degrees C and velocities of 1.0, 1.5, and 2.0 m/s. Noni showed only a falling drying rate period. Further, a non-linear regression procedure was used to determine the characteristic drying curve. The experimental drying data of noni were employed to fit thin-layer models. Under the evaluated experimental conditions, the Page model provided the best representation of thin -layer drying characteristics of noni. The effective moisture diffusivity ranged from 1.77 x 10-7 to 3.33 x 10-7 m2/s. The activation energy was found to be 3.34 kJ/mol., QC 20230404

In this work, a previously published model for the water up take of stormwater in sponge-like porous bodies by the group is further developed. This is done by investigating the highest-performing model and considering the water uptake from the surroundings of a pond and rain-infiltrated soil. This implies that water uptake from impermeable to partially permeable surfaces is examined. Hence, the following cases are considered: (1) impervious bottom surface and no precipitation, (2) impervious bottom surface with precipitation, (3) permeable soil with no precipitation, and (4) permeable soil with precipitation. A mathematical model covering all these cases is presented, where the governing equations are the mass conservation and Darcy’s law together with an assumption of a sharp wetting front being a first-order approximation of the complete Richard’s equation. Results for the water uptake height, pond depth, and wetting front are computed numerically and plotted against time. Analytical solutions are also presented in certain cases, and critical values are obtained. The parametric study includes variations in the ratio of the model- to the surrounding ground surface area, initial pond depth, precipitation, and soil characteristics. To exemplify, the time it takes to absorb the water from the pond after a precipitation period is presented. The results are related to the Swedish rainfall data of 1 h duration with a return period of 10 years. When evaluating efficiency, the focus is on the absorption time. Results vary considerably, demonstrating a general trend that with soil infiltration, the water absorption rate is higher. For most cases, the considered water amount is absorbed completely, although depending on the parameters and conditions. These results serve to optimize the model for each of the cases. The main focus of the research lies in the theoretical aspect., Validerad;2023;Nivå 2;2023-09-12 (joosat);CC BY 4.0 License

Solar photovoltaic (PV) parks have proliferated all over the world as a result of the growing demand for electricity, and especially electricity from renewables. As these parks become larger and complex, it becomes increasingly important to develop accurate and efficient mathematical models that can be used to predict their performance and optimize their design. The inverter is an essential component of a solar PV system that converts the DC power generated by the solar panels into AC power that can be used by the grid or by local loads. This research paper presents a comparative study between a pre-existing reference model and a mathematical model, developed specifically for predicting the AC power output of photovoltaic systems. In addition, a hybrid model is included for comparative analysis. The performance of each model was evaluated using real-world data installed at Glava Energy Centre in Hillringsberg, Sweden. The reference and hybrid models showed similar trends in their calculated versus actual values, but the hybrid model outperformed the reference model slightly. The actual power values were found to be similar to the simulated values in all three models. However, the mathematical model was more specific and sensitive to the inverter under consideration, resulting in a comprehensive and accurate representation of the inverter's behaviour. The models take into account the inverter's characteristics, as well as environmental elements like temperature and solar irradiance that affect its performance. The results showed that the mathematical model outperformed the other models in terms of accuracy and reliability, achieving an R2 score of 0.9226, 0.9936, 0.9789, and 0.9736 for the months of February, April, July, and October, respectively. The mathematical model also had the lowest root mean square error (RMSE) and mean absolute error (MAE) values compared to the other models. The results of this study demonstrate the value of mathematical modelling in the d

A new modelling approach for dissolution of polydisperse powders is developed within the framework of the classical Noyes-Whitney/Nernst-Brunner analysis. Its distinguishing feature is that the underlying continuous particle-size distribution is retained. Two different but related dependencies of the diffusion-layer thickness on particle size are considered. First, a power-law dependence that interpolates between a thickness that is proportional to (or equals) the particle radius (obtained when the exponent equals 1) and a constant thickness (obtained when the exponent is 0). Second, a piecewise linear function such that the thickness equals the particle radius for sufficiently small particles and is constant for larger ones. The modelling approach is exemplified by consideration of a lognormal particle-size distribution. Highly accurate closed-form expressions for the fraction of dissolved drug are obtained for dissolution under sink conditions (which are exact if the diffusion-layer thickness is radius-independent). Moreover, it is demonstrated that any result derived under sink conditions can be reused to determine the fraction of dissolved/absorbed drug under non-sink conditions, using the concept of a retarded time. Comparison with literature data and experiments are used to validate the modelling approach and to demonstrate its usefulness in a practical context.

Solar photovoltaic (PV) parks have proliferated all over the world as a result of the growing demand for electricity, and especially electricity from renewables. As these parks become larger and complex, it becomes increasingly important to develop accurate and efficient mathematical models that can be used to predict their performance and optimize their design. The inverter is an essential component of a solar PV system that converts the DC power generated by the solar panels into AC power that can be used by the grid or by local loads. This research paper presents a comparative study between a pre-existing reference model and a mathematical model, developed specifically for predicting the AC power output of photovoltaic systems. In addition, a hybrid model is included for comparative analysis. The performance of each model was evaluated using real-world data installed at Glava Energy Centre in Hillringsberg, Sweden. The reference and hybrid models showed similar trends in their calculated versus actual values, but the hybrid model outperformed the reference model slightly. The actual power values were found to be similar to the simulated values in all three models. However, the mathematical model was more specific and sensitive to the inverter under consideration, resulting in a comprehensive and accurate representation of the inverter's behaviour. The models take into account the inverter's characteristics, as well as environmental elements like temperature and solar irradiance that affect its performance. The results showed that the mathematical model outperformed the other models in terms of accuracy and reliability, achieving an R2 score of 0.9226, 0.9936, 0.9789, and 0.9736 for the months of February, April, July, and October, respectively. The mathematical model also had the lowest root mean square error (RMSE) and mean absolute error (MAE) values compared to the other models. The results of this study demonstrate the value of mathematical modelling in the d

In this work we succintly review the main features of bone formation in vertebrates. Out of the many aspects of this exceedingly complex process, some particular stages are selected for which mathematical modelling appears as both feasible and desirable. In this way, a number of open questions are formulated whose study seems to require interaction among mathematical analysis and biological experimentation, European Contract, Spanish Ministry of Science, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

In this work we present a comprehensive account of our current knowledge on vascular morphogenesis, both from a biological and a mathematical point of view. To this end, we first describe the basic steps in the known mechanisms of blood vessel morphogenesis, whose structure, function and unfolding properties are examined. We then provide a wide, although by no means exhaustive, account of mathematical models which are used to describe and discuss particular aspects of the overall biological process considered. We finally summarize the approaches presented, and suggest possible directions for future research. Details about some of the major signalling molecules involved are included in a first Appendix at the end of the paper. A second Appendix provides a brief overview of design principles for vascular nets, a subject that has deserved considerable attention over the years., Banco Santander Central Hispano, Universidad Complutense de Madrid, Ministerio de Ciencia e Innovacion, Spain, European Community's Sixth Framework Programme contract ("HeartRepair"), ISCIII cooperative and thematic research networks RECAVA and TERCEL, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

For the sake of energy and cost savings, it is sometimes necessary to maintain the indoor climate in a room at conditions that deviate from optimal thermal comfort. More important than thermal sensation is how a change in conditions will affect the thermal acceptability of a space and whether the percentage of people who are (dis)satisfied with the environment will change with regard of the acceptability. The aim of this technical note and arithmetic study is to find out to what extent the thermal indoor climate can be assessed on the basis of thermal acceptability, in addition to the thermal (dis)satisfied, by making use of research that has already been carried out. In addition to the relationship between the percentage of (dis)satisfied and acceptability, attention is paid to how this result relates to current Dutch government building regulations. The paper concerns a proposal for the assessment of thermal indoor climate based on the thermal acceptability, in addition to the thermal (dis)satisfied., Emerging Materials