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Výdrž a účinnost multicopterů jsou z velké části ovlivněny výběrem pohonného systému, zejména pak vrtulí. Avšak u malých bezpilotních prostředků, které většinu času stráví ve visu (např. multicoptery), pracují vrtule při nízkých Reynoldsových číslech, případně i v režimu odtržení. Tyto problémy a efekty spojené s rotací jsou řešeny pomocí korekcí aerodynamických koeficientů a aplikovány na vírovou teorii. Tento přístup vede k významnému zvýšení přesnosti výpočtu leteckých vrtulí. Nicméně pro nulovou rychlost nabíhajícího proudu mají tyto korekce tendenci nadhodnocovat hodnoty tahu vrtule. Pro snížení výpočetní náročnosti a času nezbytného k získání potřebných aerodynamických vlastností pro různá Reynoldsova a Machova čísla jsou použity neuronové sítě. Celý proces je implementován do prostředí MATLAB (včetně grafického rozhraní, neuronových sítí a adaptivních algoritmů) a validován na pěti různých vrtulích k prokázání, že vypočtené výkony vrtulí se shodují s experimentálními daty. Variační počet byl vybrán jako metoda pro návrh optimalizované vrtule, jelikož s jeho využitím lze navrhnout vrtuli s maximálním tahem pro zadaný výkon. Pro ověření zvoleného přístupu byla navrhnuta optimalizovaná vrtule, jejíž koeficient tahu je vyšší než odpovídající vrtule, se kterou je srovnávána, při zachování stejné hodnoty koeficientu výkonu.

Optomechanical components are widely used in many optical experiments. This diploma thesis deals with design and manufacturing optomechanical components using 3D print technology. These are cheaper alternatives of commercial devices. In addition to 3D printed parts, minimum number of other components are used to assemble functional devices. Using simple experimental setups, the manufactured components are evaluated and compared with commercially available ones. The results show that they can be used in applications where high accuracy is not required. The second part is devoted to the design and manufacturing of a polarimeter as a mechanism combining electrical and mechanical components with 3D printed parts. The polarimeter is used to measure some properties of polarized light.

L'espace de Wasserstein est l'ensemble des mesures de probabilité définies sur un domaine fixé et muni de la distance de Wasserstein quadratique. Dans ce travail, nous étudions des problèmes variationnels dans lesquels les inconnues sont des applications à valeurs dans l'espace de Wasserstein.Quand l'espace de départ est un segment, c'est-à-dire quand les inconnues sont des courbes à valeurs dans l'espace de Wasserstein, nous nous intéressons à des modèles où, en plus de l'action des courbes, des termes pénalisant les configurations de congestion sont présents. Nous développons des techniques permettant d'extraire de la régularité à partir de l'interaction entre l'évolution optimale de la densité (minimisation de l'action) et la pénalisation de la congestion, et nous les appliquons à l'étude des jeux à champ moyen et de la formulation variationelle des équations d'Euler.Quand l'espace de départ n'est plus seulement un segment mais un domaine de l'espace euclidien, nous considérons seulement le problème de Dirichlet, c'est-à-dire la minimisation de l'action (qui peut être appelée l'énergie de Dirichlet) parmi toutes les applications dont les valeurs sur le bord du domaine de départ sont fixées. Les solutions sont appelées les applications harmoniques à valeurs dans l'espace de Wasserstein. Nous montrons que les différentes définitions de l'énergie de Dirichlet présentes dans la littérature sont en fait équivalentes; que le problème de Dirichlet est bien posé sous des hypothèses assez faibles; que le principe de superposition est mis en échec lorsque l'espace de départ n'est pas un segment; que l'on peut formuler une sorte de principe du maximum; et nous proposons une méthode numérique pour calculer ces applications harmoniques. / The Wasserstein space is the space of probability measures over a given domain endowed with the quadratic Wasserstein distance. In this work, we study variational problems where the unknowns are mappings valued in the Wasserstein space. When the source space is a segment, i.e. when the unknowns are curves valued in the Wasserstein space, we are interested in models where, in addition to the action of the curves, there are some terms which penalize congested configurations. We develop techniques to extract regularity from the minimizers thanks to the interplay between optimal density evolution (minimization of the action) and penalization of congestion, and we apply them to the study of Mean Field Games and the variational formulation of the Euler equations. When the source space is no longer a segment but a domain of a Euclidean space, we consider only the Dirichlet problem, i.e. the minimization of the action (which can be called the Dirichlet energy) among mappings sharing a fixed value on the boundary of the source space. The solutions are called harmonic mappings valued in the Wasserstein space. We prove that the different definitions of the Dirichlet energy in the literature turn out to be equivalent; that the Dirichlet problem is well-posed under mild assumptions; that the superposition principle fails if the source space is no longer a segment; that a sort of maximum principle holds; and we provide a numerical method to compute these harmonic mappings.

Orientador: Rubens de Figueiredo Camargo / Resumo: O presente trabalho apresenta a nova modelagem fracionária, que considera propriedades hereditárias e efeitos de memória, no modelo de Gompertz, para descrever a evolução do câncer causado pela infecção do HPV 16. Devido a variabilidade do desenvolvimento do câncer em humanos, utiliza-se o crescimento in vivo do tumor em camundongo transgênico que expressam os oncogenes E6 e E7 tratados com DMBA / TPA (inicializador e promotor do HPV 16) para capturar as características gerais dessa variabilidade. Resultados mostram que a inserção de um novo parâmetro na correção dimensional da modelagem fracionária, descreve, em comparação ao modelo clássico, o progresso do volume tumoral em maior conformidade com os conjuntos de dados reais. / Abstract: The present work presents the fractional modeling, which considers hereditary properties and memory effects, to describe through the Gompertz model, the evolution of cancer caused by HPV 16 infection. Due to the variability of the development of cancer in humans, we used the in vivo growth of the transgenic mouse tumor expressing DMBA / TPA-treated E6 and E7 oncogenes (HPV 16 initiator and promoter) to capture the general characteristics of this variability. Results show that the insertion of a new parameter in the dimensional correction of fractional modeling describes, compared to the classical model, the progress of tumor volume in greater concorda with the actual data sets. / Doutor

abstract: Computer science education is an increasingly vital area of study with various challenges that increase the difficulty level for new students resulting in higher attrition rates. As part of an effort to resolve this issue, a new visual programming language environment was developed for this research, the Visual IoT and Robotics Programming Language Environment (VIPLE). VIPLE is based on computational thinking and flowchart, which reduces the needs of memorization of detailed syntax in text-based programming languages. VIPLE has been used at Arizona State University (ASU) in multiple years and sections of FSE100 as well as in universities worldwide. Another major issue with teaching large programming classes is the potential lack of qualified teaching assistants to grade and offer insight to a student’s programs at a level beyond output analysis. In this dissertation, I propose a novel framework for performing semantic autograding, which analyzes student programs at a semantic level to help students learn with additional and systematic help. A general autograder is not practical for general programming languages, due to the flexibility of semantics. A practical autograder is possible in VIPLE, because of its simplified syntax and restricted options of semantics. The design of this autograder is based on the concept of theorem provers. To achieve this goal, I employ a modified version of Pi-Calculus to represent VIPLE programs and Hoare Logic to formalize program requirements. By building on the inference rules of Pi-Calculus and Hoare Logic, I am able to construct a theorem prover that can perform automated semantic analysis. Furthermore, building on this theorem prover enables me to develop a self-learning algorithm that can learn the conditions for a program’s correctness according to a given solution program. / Dissertation/Thesis / Doctoral Dissertation Computer Science 2020

In dieser Arbeit geben wir eine Einführung in das Diskrete Äußere Kalkül (engl.: Discrete Exterior Calculus, kurz: DEC), das sich mit der Diskretisierung von Differentialformen und -operatoren beschäftigt. Wir beschränken uns hierbei auf zweidimensionalen orientierten kompakten Riemannschen Mannigfaltigkeiten und zeigen auf, wie diese als wohlzentrierte Simplizialkomplexe zu approximieren sind. Dabei beschreiben wir die Implementierung der Methode und testen diese an Beispielen, wie Helmholtz-artige PDEs und die Berechnung von in- und extrinsischen Krümmungsgrößen.:0 Einführung 1 Diskrete Mannigfaltigkeiten 1.1 Primär- und Dualgitter 1.2 Kettenkomplexe 1.3 Gittergenerierung für Oberflächen 1.4 Implizit gegebene Oberflächen 2 Diskretes Äußeres Kalkül (DEC) 2.1 Diskrete Differentialformen 2.2 Äußere Ableitung 2.3 Hodge-Stern-Operator 2.4 Laplace-Operator 2.5 Primär-Dual-Gradient im Mittel 3 Anwendung: Oberflächenkrümmung 3.1 Weingartenabbildung 3.2 Krümmungsvektor 3.3 Gauß-Bonnet-Operator 3.4 Numerisches Experiment 4 Fazit und Ausblicke 5 Appendix 5.1 Häufige Bezeichner 5.2 Algorithmen 5.3 Krümmungen für impliziten Oberflächen 5.4 Ausgewählte Oberflächen Literaturverzeichnis

Geodätische Messabweichungen werden oft gut durch Wahrscheinlichkeitsverteilungen beschrieben, die steilgipfliger als die Gaußsche Normalverteilung sind. Das gilt besonders, wenn grobe Messabweichungen nicht völlig ausgeschlossen werden können. Neben einigen in der Geodäsie bisher verwendeten Verteilungen (verallgemeinerte Normalverteilung, Hubers Verteilung) diskutieren wir hier die skalenkontaminierte Normalverteilung, die für die praktische Rechnung einige Vorteile bietet. / Geodetic measurement errors are frequently well described by probability distributions, which are more peak-shaped than the Gaussian normal distribution. This is especially true when gross errors cannot be excluded. Besides some distributions used so far in geodesy (generalized normal distribution, Huber’s distribution) we discuss the scale contaminated normal distribution, which offers some advantages in practical calculations.

This thesis is concerned with two problems in the Calculus of Variations touching on two central aspects of Materials Science: the structure of solid matter and its dynamic behavior. The problem pertaining to the first aspect is the analysis of the rigidity properties of possibly branched microstructures formed by shape memory alloys undergoing cubic-to-tetragonal transformations. On the basis of a variational model in the framework of linearized elasticity, we derive a non-convex and non-discrete valued differential inclusion describing the local volume fractions of such structures. Our main result shows the inclusion to be rigid without additional regularity assumptions and provides a list of all possible solutions. We give constructions ensuring that the various types of solutions indeed arise from the variational model and quantitatively describe their rigidity via H-measures. Our contribution to the second aspect is a conditional result on the convergence of the Allen-Cahn Equations to multi-phase mean curvature flow, which is a popular model for grain growth in polychrystalline metals. The proof relies on the gradient flow structure of both models and borrows ideas from certain convergence proofs for minimizing movement schemes.:1 Introduction 1.1 Shape memory alloys 1.2 Multi-phase mean curvature flow 2 Branching microstructures in shape memory alloys: Rigidity due to macroscopic compatibility 2.1 The main rigidity theorem 2.2 Outline of the proof 2.3 Proofs 3 Branching microstructures in shape memory alloys: Constructions 3.1 Outline and setup 3.2 Branching in two linearly independent directions 3.3 Combining all mechanisms for varying the volume fractions 4 Branching microstructures in shape memory alloys: Quantitative aspects via H-measures 4.1 Preliminary considerations 4.2 Structure of the H-measures 4.3 The transport property and accuracy of the approximation 4.4 Applications of the transport property 5 Convergence of the Allen-Cahn Equation to multi-phase mean curvature flow 5.1 Main results 5.2 Compactness 5.3 Convergence 5.4 Forces and volume constraints

Detta examensarbete har gjorts i samarbete med JM Entreprenad som är ett helägt dotterbolag till JM AB. JM AB är ett av Sveriges största byggföretag. Arbetet har gått ut på att hjälpa JM Entreprenad Region Hus med att undersöka hur erfarenhetsåterföringen mellan Kalkylavdelningen och produktion ser ut samt att komma med förslag till förbättringar. Erfarenhetsåterföring handlar om att samla in och återanvända de erfarenheter och kunskaper som kommer från olika delar av organisationen för att sedan ha dessa som utgångspunkt för förbättringar av det framtida arbetet. Det finns i nuläget inga fastslagna rutiner för hur denna erfarenhetsåterföring skall genomföras vilket är en stor brist i organisationen. För att förändra detta bör företaget sträva efter att bli en lärande organisation och skapa tydliga rutiner för hur detta arbete skall läggas upp. / This thesis has been done in collaboration with JM Entreprenad, a wholly owned subsidiary of JM AB. JM AB is one of Sweden's largest construction companies. The task has been to assist JM Entreprenad Region Hus with an investigation concerning how the experience feedback between Calculus Department and Production is working and to make suggestions for improvements. Experience feedback comprises collecting and reusing the experience and knowledge which comes from different parts of the organization and to use this knowledge as a basis for improvement of future work. There is currently no established procedures for how this experience feedback shall be carried out which is a shortcoming in the organization. To change this, the company should strive to become a learning organization and establish clear procedures for how this work shall be organized.