This thesis project aims to model a quadcopter and design a linear quadratic regulator (LQR) by means of Matlab/Simulink. To this purpose, the LQR-based optimal control theory for controllinga quadcopter is first studied which includes state-space representation (SSR) of a dynamicprocess or system, cost function, LQR, quadcopter flight dynamics and system linearization. A quadcopter model is developed in Matlab/Simulink, followed by the implementation of a LQR-based control system. The LQR parameters are tuned and the system is tested under various flight conditions (wind disturbance, in the simulation, specific/simplified model, etc.). The simulation results show that the LQR is an effective controller for maintaining stable hover at a height straight up and compensating for wind disturbances. However, when the quadcopter moves to a new position, oscillations occur, highlighting the limitations of the LQR due to its reliance on a simplified and linearized model. Additionally, modifications to the model parameters, such as mass and inertia, impact the system performance, indicating potential robustness issues with the controller. It can be concluded that Matlab/Simulink is an effective tool for quadcopter modeling, LQR designing and LQR performance analyzing. In this thesis project, only the LQR method is used for controlling a quadcopter and the LQR tuning process is not efficient. In future work other techniques such as regional linearization and alternative non-linear controllers, like model predictive control (MPC) or sliding mode control (SMC), can be explored. Development of optimization algorithms for LQR tuning in the LQR method is highly recommended.

This study is about teachers in socially oriented subjects and their attitudes and experiences regarding working with controversial issues in teaching. Previous research has shown that there are shortcomings and major challenges in handling controversial subjects in the classroom. Therefore, I chose to investigate this by interviewing eight subject teachers in socially oriented subjects. The purpose of the study was to examine different teachers' work with controversial issues and their experiences of opportunities and challenges respectively in teaching controversial subjects. After conducting a qualitative interview study with eight teachers, the results were consistent with previous research. The results of the study indicate a lack of time and challenges associated with working on controversial issues, as they are difficult to handle and can lead to conflicts and disruptions in the classroom. Consequently, some teachers choose not to teach about controversial issues. However, on the other hand, the results of the study show that there were teachers who encouraged working with controversial issues as they considered it important to socialize students into society by addressing controversial topics. They believed that by doing so, students develop into democratic citizens with political tolerance. Another interesting finding from the interview study is that certain schools as a whole choose not to work with controversial issues to avoid negative consequences. This is interesting because other schools in the study, for example, those with UN profiles, focus on challenging students with controversial issues to develop them into democratic citizens of society. One can therefore conclude that working with controversial issues is a task that must involve the entire school, not just the teacher, as it requires efforts from management, colleagues, teachers, and students. Thus, in schools where only the teacher is responsible for addressing controversial issues without support from management or colleagues, it may lead to a reduction in teaching on controversial subjects.

The most prominent threats to epiphytic lichen funga are modern industrial forestry and air pollution. Macrolichens with cyanobacteria, cyanolichens, are particularly vulnerable. One of these is the lungwort lichen, Lobaria pulmonaria. The lungwort lichen is not among the most threatened species in Sweden, but the populations have nevertheless decreased significantly during the last 100 years. One area where the lungwort lichen still can be found is around lake Möckeln, in the south of Sweden. In earlier inventories 94 trees with Lobaria pulmonaria were identified. The aim of this study was to investigate the population changes of L. pulmonaria in this area as well as the ecology and management options for this species. My questions were: 1. Does the population of L. pulmonaria around the lake Möckeln decrease?  2. Is there a positive correlation between the circumference of the trees and the coverage of lichens? 3: Is there a positive correlation between the number of individuals and coverage? 4: Is there a positive correlation between the circumference of the trees and the number of thalli?  5: Is there a negative correlation between the size of the populations and the proximity to the lake? Between 2001 and 2024 the total population decrease was 23%. There was no correlation between circumference and coverage or number of individuals. No effect of nearby water bodies on population size could be detected. There was, however,  a strong correlation between coverage and the number of thalli. This result is not obvious since thalli can vary substantially in size. The results which suggest a decline are consistent with earlier studies in southern Sweden which also show a decrease of the L. pulmonaria populations in the south of Sweden. Since L. pulmonaria forests have high conservation values I propose that all the sites investigated in this study should receive protection as nature preserves.

Although gas and liquid chromatography have emerged as dominant separation techniques in environmental analytical chemistry, these methods do not allow for the concurrent analysis of chemically diverse groups of persistent organic pollutants (POPs). There are also a small number of compounds which are not easily amenable to either of these traditional separation techniques. The main objective of this thesis was to address these issues by demonstrating the applicability of packed column supercritical fluid chromatography (pSFC) coupled to mass spectrometry (MS) in various aspects of environmental chemistry. First, pSFC/MS analytical methods were developed for legacy POPs (PCDDs, PCDFs, and PCBs) as well as the emerging environmental contaminant Dechlorane Plus (DP), and issues relating to the ionization of target analytes when pSFC was coupled to MS were explored. Novel APPI and APCI reagents (fluorobenzene and triethylamine) were optimized and real samples (water and soil) were analyzed to demonstrate environmental applicability. The possibility of chiral and preparative scale pSFC separations was then demonstrated through the isolation and characterization of thermally labile hexabromocyclododecane (HBCDD) stereoisomers. The analytical pSFC separation of the α-, β-, and γ-HBCDD enantiomers as well as the δ and ε meso forms was shown to be superior to results obtained using a published LC method. Finally, technical mixtures of phosphorus flame retardants (RBDPP, BPA-BDPP, and DOPO; a group of related compounds which are challenging to analyze concurrently) were examined using multiple analytical techniques and pSFC was found to be the only method which facilitated the accurate determination of the components of all 3 mixtures. This thesis confirms the potential of pSFC/MS as a fast, green, and cost effective means of separating and analyzing environmental contaminants.

Since its isolation in 2004, that resulted in the Nobel Prize award in 2010, graphene has been the object of an intense interest, due to its novel physics and possible applications in electronic devices. Graphene has many properties that differ it from usual semiconductors, for example its low-energy electrons behave like massless particles. To exploit the full potential of this material, one first needs to investigate its fundamental properties that depend on shape, number of layers, defects and interaction. The goal of this thesis is to perform such an investigation. In paper I, we study electronic transport in monolayer and bilayer graphene nanoribbons with single and many short-range defects, focusing on the role of the edge termination (zigzag vs armchair). Within the discrete tight-binding model, we perform an-alytical analysis of the scattering on a single defect and combine it with the numerical calculations based on the Recursive Green's Function technique for many defects. We find that conductivity of zigzag nanoribbons is practically insensitive to defects situated close to the edges. In contrast, armchair nanoribbons are strongly affected by such defects, even in small concentration. When the concentration of the defects increases, the difference between different edge terminations disappears. This behaviour is related to the effective boundary condition at the edges, which respectively does not and does couple valleys for zigzag and armchair ribbons. We also study the Fano resonances. In the second paper we consider electron-electron interaction in graphene quantum dots defined by external electrostatic potential and a high magnetic field. The interaction is introduced on the semi-classical level within the Thomas Fermi approximation and results in compressible strips, visible in the potential profile. We numerically solve the Dirac equation for our quantum dot and demonstrate that compressible strips lead to the appearance of plateaus in the electron energies as a function of the magnetic field. This analysis is complemented by the last paper (VI) covering a general error estimation of eigenvalues for unbounded linear operators, which can be used for the energy spectrum of the quantum dot considered in paper II. We show that an error estimate for the approximate eigenvalues can be obtained by evaluating the residual for an approximate eigenpair. The interpolation scheme is selected in such a way that the residual can be evaluated analytically. In the papers III, IV and V, we focus on the scattering on ultra-low long-range potentials in graphene nanoribbons. Within the continuous Dirac model, we perform analytical analysis and show that, considering scattering of not only the propagating modes but also a few extended modes, we can predict the appearance of the trapped mode with an energy eigenvalue close to one of the thresholds in the continuous spectrum. We prove that trapped modes do not appear outside the threshold, provided the potential is sufficiently small. The approach to the problem is different for zigzag vs armchair nanoribbons as the related systems are non-elliptic and elliptic respectively; however the resulting condition for the existence of the trapped mode is analogous in both cases. / Sedan isoleringen av grafen 2004, vilket belönades med Nobelpriset 2010, har intresset för grafen varit väldigt stort på grund av dess nya fysikaliska egenskaper med möjliga tillämpningar i elektronisk apparatur. Grafen har många egenskaper som skiljer sig från vanliga halvledare, exempelvis dess lågenergi-elektroner som beter sig som masslösa partiklar. För att kunna utnyttja dess fulla potential måste vi först undersöka vissa grundläggande egenskaper vilka beror på dess form, antal lager, defekter och interaktion. Målet med denna avhandling är att genomföra sådana undersökningar. I den första artikeln studerar vi elektrontransporter i monolager- och multilagergrafennanoband med en eller flera kortdistansdefekter, och fokuserar på inverkan av randstrukturen (zigzag vs armchair), härefter kallade zigzag-nanomband respektive armchair-nanoband. Vi upptäcker att ledningsförmågan hos zigzag-nanoband är praktiskt taget okänslig för defekter som ligger nära kanten, i skarp kontrast till armchairnanoband som påverkas starkt av sådana defekter även i små koncentrationer. När defektkoncentrationen ökar så försvinner skillnaden mellan de två randstrukturerna. Vi studerar också Fanoresonanser. I den andra artikeln betraktar vi elektron-elektron interaktion i grafen-kvantprickar som definieras genom en extern elektrostatisk potential med ett starkt magnetfält. Interaktionen visar sig i kompressibla band (compressible strips) i potentialfunktionens profil. Vi visar att kompressibla band manifesteras i uppkomsten av platåer i elektronenergierna som en funktion av det magnetiska fältet. Denna analys kompletteras i den sista artikeln (VI), vilken presenterar en allmän feluppskattning för egenvärden till linjära operatorer, och kan användas för energispektrumav kvantprickar betraktade i artikel II. I artiklarna III, IV och V fokuserar vi på spridning på ultra-låg långdistanspotential i grafennanoband. Vi utför en teoretisk analys av spridningsproblemet och betraktar de framåtskridande vågor, och dessutom några utökade vågor. Vi visar att analysen låter oss förutsäga förekomsten av fångade tillstånd inom ett specifikt energiintervall förutsatt att potentialen är tillräckligt liten.

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Annotation: The thesis is entitled ,,The Possibilities of Movement from the Area of Drama in Education in Working out the Topics from Educational Plan." The theoretical part is divided and focused on four sections: Drama in Education, specification about children of early school age, movement and compare Drama in Education with Dance and Movement in Education. The practical part is focused on realization of seven the teaching lessons, which are worked up according to topics from Educational Plan and with utilization of Movement from the Area of Drama in Education. Key words: Movement Drama in Education Early school age Educational Plan Selection of the Topics Realization Reflection

La recherche en didactique menée dans le cadre de cette thèse vise à explorer les modes de formalisation du genre débat dans trois domaines disciplinaires à l’école élémentaire : lecture-littérature, sciences et philosophie. Plus précisément, cette recherche s’intéresse à l’actualisation disciplinaire de ce genre scolaire dans les différents espaces constitutifs de l’École au cycle 3 (CE2-CM1-CM2): les espaces de prescription, de recommandation, de pratiques déclarées et de pratiques effectives. L’étude des configurations disciplinaires du débat dans chacun de ces espaces est construite empiriquement au moyen d’un recueil et d’analyse de données spécifiques : les Instructions Officielles pour les trois disciplines de débat pour l’analyse des espaces de prescription, 25 éditions de manuels scolaires (18 en français et 7 en sciences) pour l’analyse des espaces de recommandation, les déclarations de 184 enseignants de cycle 3 sur leurs pratiques de débats pour l’analyse des espaces de pratiques déclarées et la retranscription de trois séries de débats en débat en lecture-littérature, en sciences et en philosophie menés respectivement par quatre enseignants de cycle 3 de la banlieue lilloise (deux enseignants de classes à pédagogie classique et deux enseignants de classes à pédagogie alternative). Cette approche méthodologique et les comparaisons disciplinaires qu’elle permet, nous conduisent à mettre en évidence les spécificités d'une formalisation disciplinaire du débat en fonction des différents espaces. On observe notamment comment les consignes formulées aux élèves dans les manuels scolaires orientent les débats disciplinaires, comment la gestion des débats par les enseignants révèle une tension entre l’aménagement d’une place conséquente laissée aux élèves au cours des débats et la construction de contenus disciplinaires, ou encore en quoi et comment la scénarisation des contenus par les enseignants durant les temps de débat permet aux élèves de s’instituer en tant que sujets didactiques. / Educational research conducted as part of this thesis aims to explore ways of formalizing gender debate in three subject areas in elementary school : literature, science and philosophy. More specifically, this research focuses on the update of this school disciplinary gender in different areas of the school building in cycle 3 (CE2 - CM1 - CM2): spaces prescription, advocacy, and reported practices actual practices. The study disciplinary configurations debate in each of these spaces is constructed empirically using a collection and analysis of specific data: Official Instructions for the three disciplines of debate for analyzing spaces prescription, 25 editions textbooks (18 French and 7 in science) for the analysis of spaces recommendation statements cycle 3, 184 teachers on their practice debates for analysis of areas reported practices and the transcript of three sets of debates in discussion literature , science and philosophy led respectively by four teachers from cycle 3 of the suburbs of Lille (two teachers teaching classes in classical and two teachers in alternative education classes). This methodological and disciplinary approach that allows comparisons lead us to highlight the specific disciplinary formalization of debate based on different spaces. We observe how particular instructions made to students in textbooks guide disciplinary debates how management discussions by teachers reveals a tension between the development of a consistent place left to students during debate and building contents disciplinary, or why and how the script content by teachers during times of debate allows students to establish as teaching subjects.

In this licentiate thesis, I present detailed case studies of students as they make use of simulated digital learning environments to engage with physics phenomena. In doing so, I reveal the moment-to-moment minutiae of physics students’ open-ended inquiry in the presence of two digital tools, namely the sandbox software Algodoo and the PhET simulation My Solar System (both running on an interactive whiteboard). As this is a topic which has yet to receive significant attention in the physics education research community, I employ an interpretivist, case-oriented methodology to illustrate, build, and refine several theoretical perspectives. Notably, I combine the notion of semi-formalisms with the notion of Newtonian modeling, I illustrate how Algodoo can be seen to function as a Papertian microworld, I meaningfully combine the theoretical perspectives of social semiotics and embodied cognition into a single analytic lens, and I reveal the need for a more nuanced taxonomy of students’ embodiment during physics learning activities. Each of the case studies presented in this thesis makes use of conversation analysis in a fine-grained examination of video-recorded, small-group student interactions. Of particular importance to this process is my attention to students’ non-verbal communication via gestures, gaze, body position, haptic-touch, and interactions with the environment. In this way, I bring into focus the multimodally-rich, often informal interactions of students as they deal with physics content. I make visible the ways in which the students (1) make the conceptual connection between the physical world and the formal/mathematical domain of disciplinary physics, (2) make informal and creative use of mathematical representations, and (3) incorporate their bodies to mechanistically reason about physical phenomena. Across each of the cases presented in this thesis, I show how, while using open-ended software on an interactive whiteboard, students can communicate and reason about physics phenomena in unexpectedly fruitful ways.

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