<p>Our group aims to develop a dedicated PET/MR system for breast cancer imaging. In order to evaluate and optimize the performance of the PET component, Monte Carlo simulation was made to help us choose the configuration parameters for hardware design. A resolution modeling method was also proposed and implemented on the GPU device to not only improve the spatial resolution of the reconstructed images but also accelerate the reconstruction speed. The PET component is configured with a ring shape composed of LYSO+SiPM detectors. Such design is compatible to MRI, and feasible for time of flight PET. Several aspects are included to be investigated in the simulation which are geometry configuration, counting performance and image quality. From the simulation result, the system configured using 2x2x20mm3 LYSO crystal with two DOI layers and 3 detector rings results in 6.2% photon sensitivity. The Noise equivalent count rate is improved with better time resolution, the peak NEC is found to be 7886 cps with 250 ps time resolution. The system is able to achieve 2.0 mm spatial resolution which is found to be more uniform with the addition of DOI layers. With the help of TOF, the lesion is visualizable with shorter scan time than the non-TOF system. The resolution modeling method is based on the coincidence detection response function modeling and multiray projection. It is found to improve the spatial resolution uniformity and contrast recovery. At the same time it reduces the position offset and background noise. The speed and accuracy improvement for this model is also discussed.</p> / Master of Science (MSc)

This study explores the application of GPU-based algorithms in radiowave propagation modeling, specifically through the scope of solving parabolic wave equations. Radiowave propagation models are crucial in the field of wireless communications, where they help predict how radio waves travel through different environments, which is vital for planning and optimization. The research specifically examines the implementation of two numerical methods: the Split Step Method and the Finite Difference Method. Both methods are adapted to utilize the parallel processing capabilities of modern GPUs, harnessing a parallel computing framework known as CUDA to achieve considerable speed enhancements compared to traditional CPU-based methods.Our findings reveal that the Split Step method generally achieves higher speedup factors, especially in scenarios involving large system sizes and high-frequency simulations, making it particularly effective for expansive and complex models. In contrast, the Finite Difference Method shows more consistent speedup across various domain sizes and frequencies, suggesting its robustness across a diverse range of simulation conditions. Both methods maintained high accuracy levels, with differences in computed norms remaining low when comparing GPU implementations against their CPU counterparts.

The use of non-ionizing radiation in the magnetic resonance imaging (MRI) made it a safer diagnostic technique in comparison to the X-ray imaging method. MRI can also produce soft tissue images with a very high contrast without contrast agent which is another advantage that made MRI an important imaging technique for studying the mechanism of the deep brain stimulation (DBS) and for targeting the desired regions in the brain that should be stimulated. For these and other advantages, the number of MRI examinations have increased hugely around the world including Sweden. Despite the consideration that MRI is a safe modality, it is not free from risks and hazards. The radiofrequency (RF)-induced heating of the tissues and the metallic implants is one of the safety concerns in MRI which certainly includes patients with DBS implant.The purpose of this project, motivated by the dangers accompanying the RF-induced heating in implantable DBS lead, is to investigate the effect of the exposure to the RF fields in MRI on these leads. After temperature measurements were made, the observations were focused on the amount of temperature increase, and the time required for the temperature to increase and then to decrease to its initial value. Some factors that could affect the lead temperature were studied and that includes the effect of the lead configuration, the lead surrounding medium, the exposure level, and the orientation of the lead coil with respect to the RF field.The result showed that the temperature of the lead (placed in air) increased more but slower when the lead was formed as a coil than when it was randomly configured. It was also showed that the lead coil temperature rise was higher and faster when the coil was placed in air than when it was immersed in deionized water or in saline. The lead coil temperature rise was higher, but slower when the coil was immersed in saline compared to deionized water. Also, exposure level affected the temperature rise such that the higher exposure level showed higher and faster temperature rise of the lead coil. When the lead coil was placed in air and oriented perpendicular to the strongest magnetic field component, its temperature increased higher and faster. On the other hand, the results when the lead coil was immersed in deionized water or in saline showed a deviation from when it was placed in air such that two magnetic field components had the same effect on the lead coil temperature. The time required for the temperature to decrease to its initial value, after the end of the exposure, depended on the magnitude of the RF magnetic flux density, orientation of the lead coil with respect to the RF magnetic field, and the lead surrounding medium. The stronger RF magnetic field is, the longer time is for the temperature to decrease. Consequently, when the lead coil was directed perpendicularly to the strongest component of the RF magnetic field, it took longer time for the temperature to decrease. The time for the temperature to decrease was longer when the lead coil was immersed in water (deionized or saline) than when the lead coil was placed in air. It also took longer time for the temperature to decrease when the lead coil was immersed in saline than in deionized water.

Granular matter is defined as a collection of particle grains, such as sand.This type of matter have different characteristics (solid, liquid and gas) depending on the energy level per grain. There are several approaches to modeling and numerical simulations of granular matter. They are used by different groups for different purposes, and the choice between the approaches is based on knowledge and tradition rather than what might be best for the purpose. The key questions are when to use what method and what physical quality is lost depending on the choice.Two regimes of discrete element granular simulations emerge: smooth and non-smooth. To compare the efficiency and physical quality of the two approaches, four physics softwares are examined including Bullet Physics, LMGC90, AgX and LIGGGHTS. Test scenes are setup in each software and the results are compared to each other or to the results of other work.The thesis is performed at UMIT Research Lab at Umeå University.

Denna studie utforskar användningen av undersökande arbetssätt inom fysikundervisning utifrån ett lärarperspektiv. Förankrad inom lärarprogrammet vid Karlstads universitet, strävar denna forskning efter att noggrant undersöka användningen av systematiska undersökningar i grundskolans fysikundervisning och att tydliggöra lärarnas åsikter kring dessa. Genom att använda den kvalitativa forskningsmetoden fenomenografi får vi fram resultat som framhäver en allmänt förekommande positiv inställning bland lärarna till användningen av undersökande arbetssätt i fysik-klassrummet. I korthet visar denna undersökning att lärarna möter olika utmaningar när de implementerar undersökande arbetssätt i fysikundervisningen. De flestalärarna i denna studie är entusiastiska över att integrera detta arbetssätt och ser den som en chans för eleverna att aktivt utforska vetenskapliga koncept. De framhäver att elevernas engagemang fördjupar deras förståelse och stärker deras förmåga att tänka kritiskt och lösa problem. Samtidigt står vissa inför hinder som brist på tid, resurser och osäkerhet kring genomförandet av undersökande arbetssätt. Det är viktigt att betona att lärarnas behov av resurser inte får bli en anledning till att undvika praktiskt arbete. Skolledningen bör stödja lärarna genom att tillhandahålla de nödvändiga resurserna. Genom att hantera dessa utmaningar kan skolor skapa en miljö där elevernas lärande främjas på bästa sätt.

In the 1970s, the tandem shaped charge was developed to overcome countermeasures like active armor and thicker armor. It uses a leading charge to clear a path for the main trailing charge, theoretically improving penetration. However, disturbances from shock waves can cause under-performance. To address this, the leading charge's shock waves must be minimized to protect the main charge. Designing a part with shock wave attenuating properties can help achieve this.There is limited information on grenade structures that reduce shock wave stresses from impact and detonation. Most studies on shock wave attenuation focus on protecting buildings and humans, with few addressing structures designed to withstand and then halt the transmission of shock waves. Here we report on simulations in IMPETUS Afea where an explicit FEM solver approach have been made to compare four different concepts to an original structure. Physical theories about attenuation of shock waves in solids has been applied. The first concept utilize a mass with different area increases in the propagation path of the shock wave. The second concept use the characteristics of interfaces between two different materials, with different shock wave impedance which will reflect and transmit the incoming wave. The third concept incorporate a brittle ceramic which should shatter when a shock wave propagates to it, if the brittle structure fracture, no more shock waves can be transmitted. The fourth concept utilize the properties of porous metals. All concepts shows shock wave attenuating effects, but only the third concept which totally disconnects the leading shaped charge to the main charge might be a full solution. The fourth concept compared to the third has other advantages, it attenuate the shock wave to more than 90%, not halt the transmission. Configuration of the porosity in the structural part can be made to have characteristics that can solve the problem. Concept three and four are the main recommendations for a feasibility study. / På 1970-talet utvecklades tandem-RSV laddningar för att övervinna motmedel som aktivt pansar och tjockare pansar. De använder en förladdning för att skapa en väg för den efterföljande huvudladdningen, vilket teoretiskt sett förbättrar prestandan. Störningar från tryckvågor från olika källor orsaka prestandaförluster. För att hantera detta måste islagets och förladdningens tryckvågor minimeras för att skydda huvudladdningen. Att designa en mellandel med egenskaper som dämpar tryckvågor kan hjälpa till att uppnå detta. Information om granatstrukturer som minskar tryckvågsbelastningar från islag och detonation är begränsad. De flesta studier om dämpning av tryckvågor fokuserar på att skydda byggnader och människor, med få som behandlar strukturer designade för att motstå och sedan stoppa överföringen av tryckvågor. Här rapporterar vi om simuleringar genomförda i IMPETUS Afea med en explicit FEM-lösare för att jämföra fyra olika koncept mot en originalstruktur. Fysiska teorier om dämpning av tryckvågor i fasta material har tillämpats. Det första konceptet utnyttjar en massa med olika areaökningar i tryckvågens propagationsväg. Det andra konceptet använder egenskaperna hos gränsytor mellan två olika material med olika tryckvågsimpedanser som kommer att reflektera och transmittera den inkommande tryckvågen. I det tredje konceptet appliceras en spröd keram som bör splittras när en tryckvåg fortplantas till den. Om den spröda strukturen spricker kan då inga fler tryckvågor överföras genom strukturen. Det fjärde konceptet utnyttjar egenskaperna hos porösa metaller. Alla koncept visar tryckvågsdämpande effekter. Men endast det tredje konceptet som helt kopplar bort förladdningen från huvudladdningen kan vara en fullständig lösning. Det fjärde konceptet jämfört med det tredje har andra fördelar; det dämpar tryckvågen till mer än 90%, men stoppar inte överföringen helt. Konfigurationen av porositeten i den strukturella delen kan utformas för att ha egenskaper som kan lösa problemet. Koncept tre och fyra är de huvudsakliga rekommendationerna för en genomförbarhetsstudie.

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.

In this thesis, there is a presentation of the isometries from the Lorentz-Minkowski Plane and a solution to the Frieze Patterns. There is a suggestion for a solution for the Tiling Patterns. Since the construction of these mathematical structures is well understood in the Euclidean plane, one can follow a similar approach to the construction of such objects to find the unique number of groups that describe all possible frieze patterns while there is a suggestion of the number for the tiling case. There is a reflection of these results in a computational and cosmological context.

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.

Deformable image registration (DIR) is an essential tool in medical image processing. It provides a means to combine image datasets, allowing for intra-subject, inter-subject, multi-modality, and multi-instance analysis, as well as motion detection and compensation. One of the most popular DIR algorithms models the displacement vector field (DVF) as B-splines, a sum of piecewise polynomials with coefficients that enable local shape control. B-splines have many advantageous properties in the context of DIR, but they often struggle to adequately model steep local gradients and discontinuities. This dissertation addresses that limitation by proposing the replacement of conventional B-splines with a generalized formulation known as a Non-Uniform Rational B-Splines (NURBS). Beginning with the 1D fitting, heuristic rules are developed to determine the values of the additional free parameters introduced by NURBS. These rules are subsequently modified and extended to the 2D and 3D fitting of anonymized and publicly available patient DVFs. Based on the lessons learned from these increasingly complex test cases, a 2D DIR scheme is developed and tested on slices from a thoracic computed tomography (CT) scan. Finally, an automatic, non-uniform scheme is presented, and its registration performance is compared to the conventional uniform methods.