We consider a series of problems regarding quantum Hall edges, focusing on both dynamics and the mathematical structure of edge states. We begin in Chapter 3 with a limiting case of the Laughlin state placed in a very steep confining potential, but which is weak compared to the interactions. We find that the eigenstates have a Jack polynomial structure and an energy spectrum which is extremely different from the well-known Luttinger liquid edge. In Chapter 5 we analyse the inner products of edge state wavefunctions, using an effective description given by a large-N expansion ansatz proposed by J. Dubail, N. Read and E. Rezayi, PRB 86, 245310 (2012). As noted by these authors, the terms in this ansatz can be constrained using symmetry, a procedure we perform to high orders. We then check the conjecture by calculating overlaps exactly for small system sizes and comparing the numerics with our high-order expansion to find excellent agreement. Finally, Chapter 6 considers the behaviour of quantum Hall edges close to the Luttinger liquid fixed point that occurs in the low energy, large system limit. We construct effective Hamiltonians using a local field theory description and then consider the effect of bulk symmetries on this edge. The symmetry analysis produces remarkable simplifications which allow for very accurate descriptions of the low-energy edge physics even relatively far away from the Luttinger liquid fixed point.

Neste trabalho apresentamos alguns resultados da invariância conforme e da teoria de escala para sistemas finitos. Estudamos, usando tais técnicas, dois modelos estatísticos (modelos 1 e 2). Para cada modelo obtivemos a anomalia conforme e as dimensões dos operadores energia e magnetização bem como seus respectivos descendentes / In this work we show some results of conformal invariance theory and finite-size scaling. We study by using these theories two statistical mechanics models (models 1 and 2). To each model we obtained the conformal anomaly, the dimensions of energy and magnetization operators as well their respective descendents

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Space curves have a variety of uses within mathematics, and much attention has been paid to calculating quantities related to such objects. The quantities of curvature and energy are of particular interest to us. While the notion of curvature is well-known, the Mobius energy is a much newer concept, having been first defined by Jun O'Hara in the early 1990s. Foundational work on this energy was completed by Freedman, He, and Wang in 1994, with their most important result being the proof of the energy's conformal invariance. While a variety of results have built those of Freedman, He, and Wang, two topics remain largely unexplored: the interaction of curvature and Mobius energy and the generalization of the Mobius energy to curves with a varying thickness. In this thesis, we investigate both of these subjects. We show two fundamental results related to curvature and energy. First, we show that any simple, closed, twice-differentiable curve can be transformed in an energy-preserving and length-preserving way that allows us to make the pointwise curvature arbitrarily large at a point. Next, we prove that the total absolute curvature of a twice-differentiable curve is uniformly bounded with respect to conformal transformations. This is accomplished mainly via an analytic investigation of the effect of inversions on total absolute curvature. In the second half of the thesis, we define a generalization of the Mobius energy for simple curves of varying thickness that we call the "nonuniform energy." We call such curves "weighted knots," and they are defined as the pairing of a curve parametrization and positive, continuous weight function on the same domain. We then calculate the first variation formulas for several different variations of the nonuniform energy. Variations preserving the curve shape and total weight are shown to have no minimizers. Variations that "slide" the weight along the curve are shown to preserve energy is special cases.

In this thesis we accomplish two goals: We construct a two dimensional conformal field theory (CFT), in the form of a Liouville theory, in the near horizon limit for three and four dimensions black holes. The near horizon CFT assumes the two dimensional black hole solutions that were first introduced by Christensen and Fulling (1977 Phys. Rev. D 15 2088-104) and later expanded to a greater class of black holes via Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303). The two dimensions black holes admit a $Diff(S^1)$ or Witt subalgebra, which upon quantization in the horizon limit becomes Virasoro with calculable central charge. These charges and lowest Virasoro eigen-modes reproduce the correct Bekenstein-Hawking entropy of the four and three dimensions black holes via the Cardy formula (Bl"ote et al 1986 Phys. Rev. Lett. 56 742; Cardy 1986 Nucl. Phys. B 270 186). Furthermore, the two dimensions CFT's energy momentum tensor is anomalous, i.e. its trace is nonzero. However, In the horizon limit the energy momentum tensor becomes holomorphic equaling the Hawking flux of the four and three dimensions black holes. This encoding of both entropy and temperature provides a uniformity in the calculation of black hole thermodynamics and statistical quantities for the non local effective action approach. We also show that the near horizon regime of a Kerr-Newman-$AdS$ ($KNAdS$) black hole, given by its two dimensional analogue a la Robinson and Wilczek, is asymptotically $AdS_2$ and dual to a one dimensional quantum conformal field theory (CFT). The $s$-wave contribution of the resulting CFT's energy-momentum-tensor together with the asymptotic symmetries, generate a centrally extended Virasoro algebra, whose central charge reproduces the Bekenstein-Hawking entropy via Cardy's Formula. Our derived central charge also agrees with the near extremal Kerr/CFT Correspondence in the appropriate limits. We also compute the Hawking temperature of the $KNAdS$ black hole by coupling its Robinson and Wilczek two dimensional analogue (RW2DA) to conformal matter.

This summer Herman Gluck and Weiqing Gu proved the last step in a process that took conformal maps between two complex spaces and related them to Volume Preserving Great Circle Fibrations of S3. These fibrations, which are non-intersecting flows, break down under certain conditions. We obtained the fibrations by applying the process to different conformal maps then calculated the angles where they intersect. This paper centers around the developments in the method for converting the conformal maps and finding the critical angles. Finally, the examples are included in their various stages of completeness.

Conformal antennas have widespread applications in communication systems for vehicular bodies, aircrafts, and spacecrafts etc. They are non-protruding and can arbitrarily take any shape on the surface where they are etched. This thesis is a summary of two main projects. The first project employs a conformal array of four S-band and four GPS-band antennas for sub-payload of a sounding rocket. The sub-payload is a small cylinder and therefore the eight conformal antennas are based on curved patch geometry. The second project employs a conformal antenna for a CubeSat. The antenna is based on a cavitybacked slot and therefore can be conveniently integrated around the surface-mount solar cells of the CubeSat. Such an integration has enormous merits for CubeSat because there is no competition between the antennas and solar cells for the limited surface real estate. The antenna design operates UHF band with circular polarization, making it the first UHF nondeployed antenna for CubeSats. For both projects, problems such as isolation, impedance bandwidth, axial ratio bandwidth, and EMI shielding have been analyzed and resolved. This thesis work yields a prototype-ready design for the first project, and a final prototype and measurements for the second project.

Two-dimensional transmission dosimetry in radiotherapy has been discussed in the literature for some time as being a potential method for in vivo dosimetry. However, it still remains to become a wide spread practice in radiotherapy clinics. This is most likely due to the variety in radiotherapy treatment sites and the challenges they would present in terms of detection and interpretation at the transmitted dose level. Thus, the full potential and limitations of applying transmission dosimetry in the presence of dosimetry errors still need to be demonstrated. This thesis is a theoretical evaluation of transmission dosimetry using the Pinnacle3 treatment planning system. The accuracy of predicting reliable and accurate absolute transmitted dose maps using the planning system dose algorithm for comparison with measured transmitted dose maps was initially investigated. The resolution in the dose calculations at the transmitted level was then evaluated for rectilinear and curved homogeneous phantoms and rectilinear inhomogeneous phantoms, followed by studies combining both surface curvature and heterogeneities using anthropomorphic phantoms. In order to perform transmitted dose calculations at clinically relevant beam focus-to-transmitted dose plane distances using clinical patient CT data it was first necessary to extend the CT volume. Finally, the thesis explored the efficacy of applying transmission dosimetry in the clinic by simulating realistic dosimetry errors in the planning system using patient treatment plans for a prostate, head and neck, and breast CRT (Conformal Radiotherapy) treatment. Any differences at the transmitted dose level were interpreted and quantified using the gamma formalism. To determine whether the transmitted dose alone was a sufficient indicator of the dosimetry errors, the magnitude in transmission dose differences were compared with those predicted at the midplane of the patient. Dose-Volume Histograms (DVHs) were also used to evaluate the clinical significance of the dose delivery errors on the target volume and surrounding healthy tissue structures. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1339807 / Thesis (Ph.D.) - University of Adelaide, School of Chemistry and Physics, 2008

BACKGROUND : Radiation oncology was these 20 last years revolutionized by the 3-dimensional conformal radiotherapy (3D-CRT) and its technical evolution, the intensity modulated radiotherapy (IMRT). Thanks to steep dose gradient dose distribution, these techniques allow to conform the prescribed dose to the Planning Target Volume (PTV) while significantly decreasing the dose delivered to the Organs at Risk (OAR). One critical step remains the accurate definition of the Gross Tumor Volume (GTV). If the GTV is underestimated, there is a risk of missing part of the target. If the GTV is overestimated, the risk is to overirradiate normal tissues. Today's gold standard for GTV definition is the Computed Tomography (CT) scanner. We though know that its poor soft tissues contrast is a factor of variability for target definition purpose. AIMS : It can be hypothesized that, for Head and Neck Squamous Cell Carcinomas located in the oropharynx or the laryngo-hypopharynx, the use of other anatomical (like Magnetic Resonance Imaging – MRI) or functional (like positron emission tomography with either 11C-methionine – MET-PET- or 18F-fluorol-deoxy-glucose – FDG-PET) imaging modalities could complement CT for GTV delineation, and have an impact on subsequent CTV and PTV delineation and dose distribution to the non target tissues outside the PTV. RESULTS : We could demonstrate that, providing an adequate and controlled methodology concerning image coregistration and tumor volume delineation on functional images, differences were observed for the delineation of primary tumor volume or GTV according to the modality used. Moreover, the trends were the same for both locations studied (oropharyngeal and laryngo-hypopharyngeal) : CT, MRI and MET-PET volumes were not significantly different in absolute volumes, but there was no total overlap, each imaging modality having the tendency to visualize different types and relatively specific pathways of tumor extension (e.g. : cartilages in MRI). What was very interesting was the significantly smaller FDG-PET volume which could have a real impact on radiation oncology practice by (1) allowing to reduce dose distribution and (2) providing fast and reproducible GTV delineation based on its functional characteristic. Furthermore, we could demonstrate on the subset of operated patients that these smaller FDG-PET volumes were not the fact of a volume underestimating delineation algorithm but well the reflection of true tumor extension. But one must keep in mind that because of spatial resolution limitations, there was still a significant overestimate of this true GTV. Also, none of the imaging modalities was able to visualize very small tumor extensions. This last fact put in the light the need for strict guidelines for CTV prediction based on GTV extension. This is what was done with the help of both anatomical and histo-pathological literature data. These guidelines were used to delineate CTVs on our images, allowing to perform comparative planning on primary tumor. It could be concluded that differences in GTV had not only an impact on CTV and subsequent PTV, but also on dose distribution, either on total irradiated volume or -perhaps more important- on mean dose to parotid glands. No significant effect could be observed on maximal dose to spinal cord. Compared to planning performed on macroscopy-based volumes, no significant difference could be found with what was done on PET-derived planning. CONCLUSION : This research paves the way for the use of FDG-PET for GTV delineation in planning the patients with oropharyngeal and laryngo-hypopharyngeal squamous cell carcinomas. / INTRODUCTION : La radiothérapie moderne a terriblement évolué ces 20 dernières années grâce au développement de la radiothérapie conformationnelle tridimensionnelle (3D-CRT) et de son évolution technique, la radiothérapie par modulation d'intensité (IMRT). Grâce à la création de gradients de dose très raides, ces techniques permettent de conformer au mieux la distribution de la dose au “Planning Target Volume” (PTV) tout en diminuant de manière significative la dose délivrée aux Organes à Risque (OAR). La précision de la définition du “Gross Tumor Volume” (GTV) ou volume tumoral macroscopique reste une étape cruciale dans le sens où une sous-estimation du volume augmente le risque de sous-doser la dose délivrée à la tumeur. Dans l'autre sens, la surestimation du volume tumoral conduit immanquablement à une surirradiation des tissus sains. La tomographie computée par scanner (CT) est l'imagerie de référence pour la définition du GTV. Cependant, le manque de constraste entre tissus mous – à fortiori entre la tumeur et les tissus environnants- constitue un facteur de variabilité reconnu quant à la précision de délimitation du GTV. BUTS : Pour les cancers de la sphère cervico-maxillo-faciale, en particulier pour les tumeurs épithéliales oropharyngées et laryngo-hypopharyngées, démontrer que l'usage complémentaire d'une autre imagerie anatomique comme la résonance magnétique (IRM) ou fonctionnelle comme la tomographie par émission de positrons utilisant soit la méthionine marquée au carbone 11 (MET-TEP), soit le fluoro-déoxy-glucose marqué au fluor 18 (FDG-TEP) peut améliorer la précision de la délimitation GTV. Dans ce cas, démontrer également que cela a un impact sur la délimitation des CTV et PTV sous-jacents et, in fine, sur la distribution de la dose aux tissus sains extérieurs au PTV. RESULTATS : Moyennant l'utilisation adéquate et contrôlée de méthodes de corégistration des images et de délimitation automatique des volumes en imagerie fonctionnelle, nous avons pu démontrer des différences en terme de GTV délimité selon les différentes modalités d'imagerie, avec une tendance identique que l'on se situe au niveau oropharyngé ou laryngo-hypopharyngé. Les GTV délimités sur CT, IRM et MET-TEP n'étaient pas significativement différents en valeurs absolues, mais chaque modalité avait tendance, au-delà d'une zone de congruence s'élevant en moyenne à 50% du volume total, à visualiser des extensions vers des zones anatomiques lui étant propre (ex. : les cartilages en IRM). Les volumes délimités en FDG-TEP étaient significativement plus petits que ceux délimités sur les autres modalités d'imagerie. Nous pûmes de plus démontrer sur un ensemble de patients opérés par laryngectomie totale que le FDG-TEP était aussi la plus précise des modalités d'imagerie. Cependant, par manque de résolution spatiale, aucune des modalités d'imagerie ne fut en mesure de couvrir totalement le GTV. Ce fait met en lumière le besoin de recommendations claires pour la prédiction du CTV sur base de l'extension du GTV. Ce travail fut réalisé sur base des données de la littérature anatomique (normale et pathologique). Ces recommendations furent utilisées pour délimiter les CTV sur les images CT, FDG-TEP et du spécimen chirurgical (les imageries IRM et MET-TEP ne furent pas analysées puisque n'apportant rien en regard du CT). Les PTV furent ensuite générés et une planification tridimensionnelle réalisée. Tant les CTV que les PTV délimités sur le FDG-TEP restaient significativement plus petits que leurs homologues délimités sur CT. Cette réduction permettait une réduction de la dose délivrée aux glandes parotides en particulier, aux tissus hors PTV de manière plus générale. CONCLUSION : Cette recherche ouvre la voie à l'utilisation du FDG-TEP pour la délimitation du GTV chez les patients atteints de tumeurs épithéliales des sphères oropharyngée et laryngo-hypopharyngée.

No description available.