This report aims to give an insight to the path integral formalism in quantum mechanics. After explaining the kernel's construction, some of its properties and ways to compute it, we see how it relates to the Schrödinger picture. Moreover, we see how its representation can change if it is defined in the space, momentum, time or energy space. Finally, we derive Born's expansion with the kernel showing how this formalism helps to understand perturbation theory and thus scattering. The path integral formalism is then used in quantum field theory with proofs and examples of simple correlation functions. Furthermore, supersymmetry in zero and one dimension are studied with use of the localization principle and the Witten index.

Quantum field theories are very good at describing the world around us but use complicated computations that cannot always be solved exactly. Introducing conformal symmetry to quantum field theory can reduce this complexity and allow for quite simple calculation in the best case. This report aims to describe the critical part of the Ising model in 2 dimensions using conformal field theory while assuming only some knowledge of quantum mechanics and complex analysis from the reader. This is done by using the book Conformal Field Theory as the source for information about conformal field theory. / Kvantfältteorier är mycket bra på att beskriva verkligheten runt om oss men de använder sig av avancerade beräkningar som inte alltid kan lösas exakt. Genom att ge systemet konform symmetri så kan dessa avancerade beräkningar förenklas och bli ganska enkla i de bästa fallen. Målet med denna rapport är att beskriva hur en modell som kallas för "Ising model" kan beskrivas i sitt kritiska tillstånd med hjälp utav konform fältteori. Läsaren antas kunna kvantmekanik samt komplex analys. Informationen om konform fältteori hämtas ifrån boken Conformal Field Theory

Motivated by the successes in the field of deep learning, the scientific community has been increasingly interested in neural networks that are able to reason about physics. As neural networks are universal approximators, they could in theory learn representations that are more efficient than traditional methods whenever improvements are theoretically possible. This thesis, done in collaboration with Algoryx, serves both as a review of the current research in this area and as an experimental investigation of a subset of the proposed methods. We focus on how useful these methods are as \textit{learnable simulators} of mechanical systems that are possibly constrained and multiscale. The experimental investigation considers low-dimensional problems with training data generated by either custom numerical integration or by use of the physics engine AGX Dynamics. A good learnable simulator should express some important properties such as being stable, accurate, generalizable, and fast. Importantly, a generalizable simulator must be able to represent reconfigurable environments, requiring a model known as a graph neural network (GNN). The experimental results show that black-box neural networks are limited to approximate physics in the states it has been trained on. The results also suggest that traditional message-passing GNNs have a limited ability to represent more challenging multiscale systems. This is currently the most widely used method to realize GNNs and thus raises concern as there is not much to be gained by investing time into a method with fundamental limitations.

Forest biotechnology is a fast emerging field of research. The application of biotechnological tools will enhance the quality of the forest products. The resultant value added and environmentally sustainable products are an absolute necessity in the future. The study of wood biosynthesis and degradation will result in enormous knowledge resources, which can be used for exploiting wood properties. This thesis addresses questions representing both wood degradation and biosynthesis. The wood degrading fungus Phanerochaete chrysosporium is expression profiled with the microarray technology. The objective is to understand the expression pattern of the extracellular carbohydrate active enzymes (CAZymes) secreted by the organism. The data obtained increases our understanding of gene expression upon growth on cellulose. Wood biosynthesis is studied with the model wood forming tree species, Populus. The plentiful data resources from the expression profiling during wood formation in Populus are used as the platform of this work. One of the wood specific genes, PttMAP20, previously with an unknown function is studied in this thesis. The immunolocalisation of PttMAP20 with specific antibodies is demonstrated. The putative microtubule-targeting domain of the protein is demonstrated microscopically and by using a biochemical binding assay. / QC 20101217

The test production of a simulated nuclear fuel, possible to use as a calibration standard was donethru dissolving the preferred dopant-metals in a nitric-salt into weak acid. This solution wasmixed with dissolved uranium-salt to aimed concentration. This was precipitated by rising pHforming metallic-hydroxide.The precipitated salt was dried in an reduction gas, pressed to pellets and sintered in oven. Thequality of the pellets and its content was evaluated thru comparing theoretical and measureddensity, ICP-MS for which ground elements and which concentration of these forming thepellets. XRD was used to evaluate formed associated ground-elements and the lattice parameters.Finally, SEM was used to evaluate how homogenous the distribution of the doped elementsturned out.There are still a variety of tests yet to perform in order to create a high quality calibrationstandard. Our preparation of dissolved metallic salts will hopefully be usable for any furtherexperimentalist in this field. The single-doped calibration-standards are aimed to be used byStudsvik to calibrate their Lazer Ablation Inductivity coupled Plasma Mass Spectrometryinstrument.

I den svenska skolan ges undervisningen i sexualitet, samtycke och relationer (SSR) under både högstadiet och i gymnasiet. På skolan där undersökningen genomfördes har eleverna haft SSR-undervisning i årskurs 8 på högstadiet och på skolan ges SSR-undervisningen först i årskurs 3. Denna undervisning kan verka tillräcklig för många men på en gymnasieskola i södra Sverige finns det några ungdomar som tycker annorlunda. I och med att kunskapsområdet innefattar aspekter som många tycker är jobbiga att prata om kan det vara tabu för vissa, men det är också centralt i människans liv. Detta gör att det är ett område som borde tas upp mer under skolgången. Detta arbete undersöker vilka uppfattningar några ungdomar på en gymnasieskola har om undervisningen i sexualitet, samtycke och relationer som ges under skolgången. Denna undersökning genomfördes med hjälp av intervjuer tillsammans med 8 elever. Eleverna som genomförde intervjuerna var uppdelade i fyra olika grupper där det var två elever i varje grupp. Resultatet i denna undersökning visade att elevgruppen på gymnasieskolan tyckte att undervisningen i sexualitet, samtycke och relationer inte är fullt tillräcklig. Eleverna hade alltså velat ha en mer omfattande undervisning i SSR. Eleverna vill generellt ha mer undervisning i SSR eftersom de inte tycker att undervisningen är tillräcklig. Exempelvis vill eleverna ha mer undervisning i pornografi och normer eftersom de inte tycker att detta har varit prioriterat i undervisningen som de blivit tilldelade. Dock stämde inte alla elevernas uppfattningar om undervisningen överens, en elev tyckte att undervisningen var bra som den var. Efter detta genomfördes en tematisk analys på resultaten i förhållande till en del av styrdokumenten, det centrala innehållet. Elevernas uppfattningar om undervisningen jämfördes med det egentliga centrala innehållet och förslag på förbättringar framfördes. Skolverket har nyligen uppdaterat sina styrdokument, men denna uppsats kommer inte lägga en större vikt på revideringarna, dock kommer delar som är intressanta för uppsatsen nämnas.

The Bose-Hubbard Model, a tight binding model within solid state theory can be solved exactly using a number theoretical approach. From this approach, in the two sited Bose-Hubbard model, the hopping term in the model takes the form of a Pauli x matrix. The hopping term can be interpreted as a two energy level system or a dimer with k+1 particles. The statistical properties of this dimer is investigated assuming Boltzmann distribution. The partition function and particle density on each site in the dimer is calculated for spin 1/2 system. The entropy and average energy is also calculated. The particle density is calculated and plotted as a function of temperature for the spin 1/2,1,3/2 and 2 system. At low temperature the particles are more likely to be found in the lower energy site and at high temperatures the particles is equally distributed at the both sites. / Bose-Hubbard modellen är en tight binding modell inom fasta tillstånd- ets fysik som kan lösas exakt genom att använda en talteoretisk lösning- smetod. Genom att göra detta med bara två interagerande platser i modellen tar hoppingtermen i modellen formen av en Pauli x-matris. Hopping modellen kan tolkas som ett system med två energinivåer eller en så kallad dimer med k+1 partiklar. Dimerens statistiska egenskaper undersöks utifrån Boltzmannfördelningen. Partitionsfunktionen och partikeldensiteten på varje plats i dimeren beräkn- as för ett spin 1/2 system, tillsammans med entropin och medelenergin. Vidare är partikeldensiteten  beräknad och plottad som funktion av temperaturen för spinn 1/2, 1, 3/2 och 2 system. Vid låg temperatur befinner sig partiklarna i dimeren i den lägre energinivån och vid hög temperatur är partiklarna jämt fördelade i de två energinivåerna

This is a project with the ambition of demonstrating the possibilities and applications of the quantum approximation optimization algorithm (QAOA). Throughout the paper discussions on the theoretical background and fundamentals of the algorithm will be done by examining the relevant nomenclature. Then a set of possible application problems will be considered where it will be discussed why this specific algorithm is of interest for each individual problem. In the fourth section these problems will concretely be tested via simulations of the QAOA and lastly an analysis of the outcomes will be done.

The focus of this thesis is to introduce the path integral and some of its applications. One interpretation of quantum mechanics is that a microscopic system which moves from an initial- to a final state moves through each possible intermediate state. The path integral uses the principle of least action to sum over all such intermediate states to find the evolution of a quantum mechanical system. We compare the path integral approach to that of the Schrödinger equation and show that the two give an equivalent description of quantum mechanics. To demonstrate the usefulness of the path integral, we introduce low-dimensional quantum field theory (QFT). In particular, we discuss Feynman diagrams. The idea behind Feynman diagrams is to sum over all possible weak interactions between fields to evaluate the properties of a system through the path integral. We also carry out a computation of a low energy effective action in a 0-dimensional model. The result of the computation shows that there is free energy also in a vacuum. Finally, we briefly generalize some of the previous discussion to 1-dimensional QFT. To give an example of a practical application, we give a qualitative discussion of how the path integral can be applied to statistical mechanics to predict the behaviour of superfluids. / Målet med den här rapporten är att introducera konceptet vägintegral och några av dess applikationer. En tolkning av kvantmekanik är att ett mikroskopiskt system som går från ett initialt- till ett slutgiltigt tillstånd kommer att passera genom alla möjliga mellanliggande tillstånd. Vägintegralen använder sig av principen om minsta verkan för att summera över alla sådana mellanliggande tillstånd för att hitta utvecklingen hos ett system. Vi kommer att jämföra vägintegralen med Schrödingers ekvation och visa att de två ger en ekvivalent beskrivning av kvantmekaniken. För att demonstrera vägintegralens användbarhet introducerar vi lågdimensionell kvantfältteori. Vi diskuterar speciellt Feynmandiagram. Idén bakom Feynmandiagram är att summera över alla möjliga svaga interaktioner mellan fält för att utvärdera fysikaliska egenskaper hos system med hjälp av vägintegraler. Vi kommer också att utvärdera en effektiv verkan i 0-dimensionell kvantfältteori. Resultatet visar att det finns fri energi även i ett vakuum. Slutligen generaliserar vi delar av vår tidigare diskussion till 1-dimensionell kvantfältteori. Som ett exempel på praktiska applikationer för vi en kvalitativ diskussion kring hur vägintegraler kan användas inom statistisk mekanik för att förutsäga egenskaper hos superfluider.

The cardiovascular systems in ectothermic reptiles have long been studied and its development represent a transition state between a single- and a double circulation. This literature review focus on the typical-reptilian heart and therefore distinguishes between orders within the class of Reptilia. The typical-reptilian heart is found in the non-crocodilian reptiles referring to the orders Chelonia and Squamata. The heart is composed of two atria and one common ventricle, compartmentalized into three interconnected ventricular cava. However, there is some species-specific variation in gross anatomy where the monitor lizard Varanus and Python pose a striking exception to the typical-reptilian heart. The cardiac building plan exhibits variation in size and relative dimensions, in particular the relationship between cava and the degree of ventricular septation. Varanus and Python have a larger and more muscular systemic side of the ventricle, a highly developed vertical septum and muscular ridge. Today, it is known that a ventricle with a less developed muscular ridge acts as a single pressure source, subsequently allowing admixture of oxygenated- and deoxygenated blood within the ventricle. In contrast, a ventricle with a more developed muscular ridge and vertical septum may function as a dual pressure source during parts of systole, temporarily separating the ventricle in a high-pressure systemic side and a low-pressure pulmonary side. Septal development provides different haemodynamic conditions and yield diverse functions. This literature review is a combination of practical laboratory work and a literature study. Dissections of the typical-reptilian hearts provide information about exterior and interior morphology, and findings are then compared to existing literature.