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Background & Purpose: The current standard dosimetry in brachytherapy treatment planning, the TG-43 formalism, ignore the presence of non-water media and finite patient dimensions. This can cause clinically relevant errors in dose estimates. To over- come the limitations of the TG-43 formalism, Model-Based Dose Calculation Algorithms (MBDCAs) have evolved. One of the commercial available MBDCAs is the Advanced Collapsed cone Engine (ACE) by Elekta. In ACE, the total dose is divided into three components, the primary, the first-scattered and the multiple-scattered dose, where the two last mentioned are calculated by the means of the Collapsed Cone Algorithm. In this study the performance of ACE has been investigated. The study has been di- vided into 2 parts, where the aim of part 1 was to analyze the relationship between the so called discretization artifacts, caused by the collapsed cone approximation, and the number of dwell positions. The severeness of the artifact is thought to decrease as the number of dwell positions are increased. The second part focus on ACE’s behavior in cortical bone, with the aim to form a hypothesis (explanation and solution) to the previously observed dose underestimation of the dose to bone made by ACE. Materials and Methods: The generic 192Ir source, the Oncentra Brachy (OcB) treatment planning system (TPS) and the Monte Carlo (MC) platform ALGEBRA have been utilized. In the first part of the study, six source configurations, all with a different number of dwell positions, were created and placed in the center of large water phantoms, i.e. under TG-43 conditions in which the TG-43 formalism can be assumed to yield a high accuracy of the estimated dose. The accuracy of ACE has been judged by its’ deviation from TG-43. In the second part of the study, a cubic source configuration, of 27 dwell positions, was positioned at the center of a cubic water phantom. Three cases where constructed, with a small cortical bone heterogeneity positioned at different distances from the source configu- ration. The ACE calculated dose distribution has been divided into its’ three constituents. The accuracy of ACE and TG-43 has been judged by its’ deviation from MC. Results: Part 1 showed that increasing the number of dwell positions does not guar- antee an improved accuracy of ACE. Local dose difference ratios of > 2%, caused by the artifacts, were mainly located outside the 5% isodose line. A general dose underestima- tion was observed in ACE, with an increased magnitude as the dose level decreased. The majority of local dose difference ratios below -4% were found where the multi-resolution voxelization grid of ACE has a voxel size of ≥23 mm3, that is at a distance of ≥8 cm from the closest dwell position when using the ACE standard accuracy level. In part 2, ACE underestimated the dose to cortical bone, with an increased magnitude as the bone was positioned farther away from the source configuration. The TG-43 formalism gave slightly better estimates of the mean dose to bone than ACE, especially at higher dose levels. For a mean dose to the cortical bone heterogeneity equal to 45% of the prescribed dose, TG-43 and ACE underestimated the mean dose with 1% and 4%, respectively. The estimated mean dose to a volume located directly behind the heterogeneity agreed within 1% between ACE and MC. However, an increased amount of positive local dose difference ratios were observed in this volume. Conclusions: Increasing the number of dwell positions cause a ”blurring” effect of the artifact, but may also increase the fluence gradient. In such situations the severeness of the artifact may not be improved. In patient cases the dwell positions are usually added in a more random manner which may favor the ”blurring effect”. The underestimations observed in ACE are thought to be caused by both the multiple- resolution voxelization grid of ACE and the relationship between the dimensions of the phantom in which the multiple-scattered kernel has been generated and the current calcu- lation volume. ACE was unsuccessful to predict the dose to cortical bone, and should hence be used with caution when cortical bone is an organ at risk, as long as the problem remains. The results indicates that the error in ACE is located in the scatter dose calculations and that the heterogeneity cause ACE to displace the dose. The error is thought to be located in the multiple-scattered dose component, which was also shown by Terribilni et al.. A hypothesis is that the problem is caused by the neglected effect of media dependent absorption coefficients in the multiple-scattered dose calculation. A suggested solution, left to be proven, is to use effective attenuation scaling factors.

We present the supersymmetry and localization of an N=2 theory on S3b along with that of an N=(2,2) theory on S2. Performing the dimensional reduction of the theory on S3b produces a theory on S2 with no flux-sectors. A re-evaluated version of twisted reduction is applied on the level of the S3b partition function, arguing for a splitting of the partition function into pieces. The splitting produces flux-like sectors correspondent to the S2 theory but holds the potential for superfluous sectors. An argument interpreting these sectors as true flux is given and utilized to remove superfluous sectors due to topological restrictions on S2. The final result is a method which gives a bijective mapping ZS3b to ZS2 . / Vi utför konstruktionen av två supersymmetriska teorier på en deformerad 3-sfär samt en 2-sfär. Den utökade symmetrin tillåter oss att använda en lokaliseringsmetod för att reducera partitionsfunktionerna till ändligt-dimensionella integraler. På 2-sfären finner vi diskreta konfigurationer vars tolkning vi vill finna i konstruktionen på 3-sfären. Vi utför en dimensionell reduktion ifrån 3-sfären till 2-sfären och finner en ekvivalens som saknar dessa konfigurationer. Som substitut presenteras en metod där integralen delas upp i delar som kan tolkas att vara ekvivalenta med de avsaknade diskreta konfigurationerna. Slutligen framförs ett argument för vilka delar av integralen som kan existera på 2-sfären och resterande delar avfärdas. Resultatet är en exakt avbilding mellan partitionsfunktionerna.

Ground Penetrating Radar is a tool for mapping the subsurface in a noninvasive way. The radar instrument transmits electromagnetic waves and records the resulting scattered field. Unfortunately, the data from a survey can be hard to interpret, and this holds extra true for non-experts in the field. The data are also usually in 2.5D, or pseudo 3D, meaning that the vast majority of the scanned volume is missing data. Interpolation algorithms can, however, approximate the missing data, and the result can be visualized in an application and in this way ease the interpretation. This report has focused on comparing different interpolation algorithms, with extra focus on behaviour when the data get sparse. The compared methods were: Linear, inverse distance weighting, ordinary kriging, thin plate splines and fk domain zone-pass POCS. They were all found to have some strengths and weaknesses in different aspects, although ordinary kriging was found to be the most accurate and created the least artefacts. Inverse distance weighting performed surprisingly well considering its simplicity and low computational cost. A web-based, easy-to-use visualization application was developed in order to view the results from the interpolations. Some of the tools implemented include time slice, crop of a 3D cube, and iso surface.

Two different definitions of cluster-size heterogeneity are investigated as well as correlation time of different quantities using the Metropolis algorithm and the Wolff algorithm. It is confirmed that the correlation time multiplied by the computation time is lower for the Wolff algorithm in an area around the critical temperature. It is also confirmed that one definition of the heterogeneity has a local maximum at the critical temperature where as the other has an abrupt change in derivative. The local maximum appears with L ≥ 64 and it is predicted but not verified that systems with L > 43 have such a maximum. The relationship between the number of distinct cluster sizes for clusters with spin-up and spin-down is investigated and it is observed that these transition from being significantly different at lower temperatures to being mostly similar at higher temperatures. The point of transition appears to be near the critical temperature.

The quantum Hall effect occurs when a conductor carrying a current is placed in a perpendicular magnetic field. If certain conditions are met, such as strong magnetic field and low temperature, the resistivity becomes quantised, taking values of integer or fractional multiples of h/e2. By analysing the movement of electrons in a magnetic field classically and quantum mechanically information about the integer quantum Hall effect and the fractional quantum Hall effect can be gathered, using the two different gauge potentials of Landau gauge and Symmetric gauge. Resistance Metrology is one field of study that the quantum Hall effect has greatly impacted by providing a way to universally maintain the ohm, with significantly less uncertainty than previously. / Den kvantmekaniska hall-effekten uppstår när en strömbärande ledare placeras i ett vinkelrätt magnetfält. Om vissa villkor är uppfyllda, såsom starkt magnetfält och låg temperatur, blir resistiviteten kvantiserad. Given av heltal (integer) eller fraktions-(fractional) multiplar av h/e2. Genom att analysera elektroners rörelse i ett magnetfält klassiskt och kvantmekaniskt fås information om Hall-effekterna; integer quantum Hall effect och fractional quantum Hall effect, med hjälp av de två gauge potentialerna Landau gauge och Symmetrisk gauge. Resistansmetrologi är ett forskningsområde som kvant Hall-effekten har starkt påverkat genom att tillhandahålla ett sätt att universellt upprätthålla ohm-enheten med betydligt mindre osäkerhet än tidigare.

Först ges en beskrivning av undervsiningsfilosofin Investigative Science Learning Environment (ISLE) och research-based assessment instruments (RBAIerna) CLASS och ECLASS, följt av en översättning till svenska av RBAIerna. En analys skedde sedan av hur svaren till påståendena i RBAIerna (pre- vs post-) förväntas ändras om en ISLE-baserad undervisning ges. I analysen försökte jag koppla påståendena till någon eller några av de sex vetenskapliga förmågorna och deras tillhörande bedömningsmatriser, vilka nu är en integrerad komponent i ISLE filosofin, men som ursprungligen utvecklades av Rutgers Physics and Astronomy Education (PAER) group. Jag använde även litteratur om ISLE och textboken "College Physics: Explore and Apply", vilken används i ISLEbaserade kurser, för att analysera påståendena. Resultatet blev att en majoritet av alla påståenden - 72\% av CLASS- och 77\% av ECLASSpåståendena - bör besvaras mer expertlikt efter en ISLE-baserad undervisning än innan. Ett påstående i CLASS, vilket motsvarar 3\% av påståendena i enkäten bedömdes även besvaras mindre expertlikt och resterande kunde jag inte, utifrån min analysmetod förutsäga om de skulle besvaras mindre, lika eller mer expertlikt. Efter analysen och undersökningar av tidigare studier om studenters prestationer på CLASS- och ECLASSenkäterna, formulerades en förutsägelse att en ISLE-baserad undervisning bör leda till att elever svarar mer expertlikt än om de undervisas traditionellt. En pilotstudie av den svenska översättningen genomfördes sedan på elever inom olika utbildningsnivåer mellan gymnasie- och doktorandnivå. Resultatet analyserades och jämfördes med tidigare forskning i andra länder, även om både skillnader och likheter kunde hittas var det svårt att dra några generella slutsatser på grund av få svarande i min studie. / A description of the teaching philosophy Investigative Science Learning Environment (ISLE) and the research-based assessment instruments (RBAIs) CLASS and ECLASS are given, followed by a translation of the RBAIs into Swedish. An analysis is then made of how the answers to the RBAIs (pre- vs. post-) are expected to change if students take an ISLE-based physics course. In the analysis, I tried to connect the statements to one or more of the six scientific abilities and their associated rubrics, which are now a component of the ISLE philosophy but are originally developed by the Rutgers Physics and Astronomy Education (PAER) group. I did also use literature about ISLE and the textbook “College Physics: Explore and Apply” which is used in ISLE based courses, to analyze the statements. I found that that the majority of the statements - 72 \% in CLASS and 77 \% in ECLASS – are expected to be answered in a more expert-like way after an ISLE-based course. One statement in CLASS, which corresponds to 3 \% of the statements in the survey, is expected to be answered in a less expert-like way. For the rest of the statements I could not predict, using my method of analysis, if they would be answered less, equally or more expert-like.  After performing the analysis and examining the existing research literature on student performance on CLASS and ECLASS surveys, a prediction that ISLE-based teaching should lead to more expert-like answers than traditional teaching is formulated. Results from a recent empirical study done in the US, published after my analysis was complete, appear to be in agreement with the prediction that follows from my analysis. A pilot study of the Swedish translations of CLASS and ECLASS was also performed on students at different educational levels, ranging from upper secondary to doctoral level. The results were analyzed and compared to previous research in other countries. Although both differences and similarities could be found, it was not possible to draw any general conclusions due to the small number of respondents in my study.

Diskrepansen mellan inställningen gentemot fysik hos elever på gymnasiet i Europa och Nordamerika och arbetsmarknadens krav på kompetens inom naturvetenskapliga ämnen skapar utmaningar inför framtiden. Inställningen gentemot fysik har visat sig förbättras genom användandet av kollaborativt lärande och representationer. Rapporten syftar till att analysera svenska gymnasieelevers kommunikation i relation till deras identitet som fysiker samt hur de använder olika fysikaliska representationer i en kollaborativ kontext. Datan har insamlats genom gruppdiskussioner där elever tre och tre tillsammans löser kontextrika problem. Det visar sig att den matematiska representationen används frekvent och har en stark ställning i samtalen medan andra representationer som grafer och figurer snarare ses som hjälpmedel för lösningen. Den matematiska representationen ger även upphov till att respondenterna positionerar sig i samtalen som experter. Resultaten stärker tidigare forskningsresultat som påvisar matematikrepresentationens frekventa användning. / The discrepancy between the attitudes that students in upper secondary school has towards physics as a subject in Europe and North America and the labor market requirements of competence in science and technology creates challenges for future generations. The attitudes towards physics have shown to improve when different educational approaches of teaching, such as collaboration and the use of multiple representations have been applied. This report aims to analyse students in Swedish upper secondary schools communication in relation to their physics identity, as well as how they use multiple representations in a collaborative context. To analyse these relations, data has been gathered through group discussionss where students are encouraged to solve context-rich problems collaboratively. My findings shows that the mathematical representation is the most frequently used and also have a dominant position in relation to other representations such as graphs and figures, which are seen predominantly as an aid in forming the solution. When the students in the study utilize the mathematical representation they also tend to position themselves as experts. The findings are in line with previous research which have studied how students use multiple representations.

Tsirelson's bound is the upper bound for a Bell inequality which is valid for all quantum mechanical systems. We discuss why Tsirelson's bound was developed by looking at some historical arguments in quantum physics, such as the Einstein-Podolsky-Rosen (EPR) paradox, an argument for the quantum mechanical description of physical reality being incomplete, and local hidden variables. We present the counterargument to those theories, Bell's inequality, which later expanded to include any inequality that a local system fulfills, but that an entangled quantum system can violate. We present the proof of two specific Bell inequalities: the Clauser-Horne-Shimony-Holt (CHSH) inequality and the I3322 inequality. Then the Tsirelson's bound for the CHSH inequality is proven with a simple system of two entangled spin-1/2 particles and with a general argument that is valid for all entangled systems. We give the upper quantum bound for the generalized CHSH inequality, which describes the situation that we have more than two measurement options, by using semidefinite programming. We prove the Tsirelson's bound for the I3322 inequality by using maximally entangled systems and semidefinite programming. Finally, we discuss the upper bounds that are obtained from these different methods. / Tsirelson's gräns är den övre gränsen till en Bell olikhet som är giltig för alla kvantmekaniska system. Vi diskuterar varför Tsirelson's gräns togs fram genom att titta på histroiska argument i kvantfysik, så som Einstein-Podolsky-Rosen (EPR) paradoxen, ett argument som säger att den kvantmekaniska beskrivningen av den fysikaliska verkligheten är offulständig, och lokala gömda variabler. Vi presenterar motargumentet till dessa teorier, Bell's olikheter, som senare generaliserades för att betyda alla olikheter som lokala system uppfyller, men som ett system i kvantsammanflättning kan bryta. Vi presenterar beviset för två specifika Bell olikheter: CHSH olikheten och I3322 olikheten. Sedan bevisas Tsirelson's gräns för CHSH olikheten med ett enkelt system av två sammanflättade spin-1/2 partiklar och ett generellt argument som stämmer för alla sammanflättade system. Vi ger den övre kvant gränsen för den generaliserade Clauser-Horne-Shimony-Holt (CHSH) olikheten, som beskriver situationen då vi har flera valmöjligheter för mätningar, genom att använda semidefinit programmering. Vi bevisar Tsirelson's gräns för I3322 olikheten genom att använda maximalt sammanflättade system och semidefinit programmering. Till slut diskuterar vi de övre gränserna som har erhållits ifrån de olika metoderna.

The purpose of the present thesis is to study the influence of Proton Exchange on Electric Field assisted Poling of congruent Lithium Niobate and its applications on periodically pat-terned structures. Moreover, the possibility of using Proton Exchange to avoid neighbours domains merging is studied and successfully demonstrated for period shorter than 10μm. Before approaching the poling of periodically patterned LiNbO3 samples, the main charac-teristics of the evolution of the poling of uniform samples in different masking conditions are investigated. It is well known that the kinetics of domains switching is highly dependent on the poling setup and on the quality/type of electrode employed to contact the crystal to the high voltage. We used a thin layer of Titanium both as mask for proton diffusion and as metal electrode for poling experiments. Moreover different masking configurations are pre-sented and characterized. The second part of this work deals with the periodic poling of 0.5mm-thick congruent lith-ium niobate. 9x4 mm2 1-D Ti gratings with 8.66μm and 8.03μm period were first fabricated on the +z side of the crystal and a superficial chemical pattern was reproduced via acid bath. Three different types of samples were obtained and before the poling the metallic mask was removed whereas in one configuration it was left assuring better homogeneity of the in-verted areas. The results we obtained suggest it could be possible to achieve periodically poled congruent lithium niobate gratings with period shorter than 4μm in ~500μm thick samples and hence obtain aspect ratios of more than 250.