Dans ce travail nous abordons deux problèmes non résolus en Probabilité appliquée. Nous les approchons tous deux sous un angle nouveau, en utilisant des outils aussi variés que les chaînes de Markov, les mouvements Browniens, les transformations de Schwarz-Christoffel, les processus de Poisson et la théorie des temps d'arrêts optimaux. Problème de la ruine pour N joueurs Le problème de la ruine pour $N$ joueurs est un problème célèbre dont la solution pour $N=2$ est connue depuis longtemps. Nous l'abordons premièrement en toute généralité, en le modélisant comme un problème d'absorption pour une chaîne de Markov. Nous obtenons les distributions associées à ce problème et nous décrivons un algorithme (appelé {it folding algorithm}) permettant de diminuer considérablement le nombre d'opérations nécessaires à une résolution complète. Cette étude nous permet de mettre en avant un certain nombres de relations de récurrence satisfaites par les probabilités de ruines associées à chaque état de la chaîne de Markov. Nous étudions ensuite une version asymptotique du problème de la ruine pour 3 joueurs. Nous utilisons les propriétés d'invariance des mouvements Browniens par transformations conformes pour décrire une résolution de ce problème via les transformations de Schwarz-Christoffel. Cette méthode dépasse le cadre strict du problème de la ruine pour 3 joueurs et s'applique à d'autres problèmes de temps d'atteinte d'un bord par un mouvement Brownien. Problème de Robbins Ce problème s'inscrit dans le cadre de la théorie des temps d'arrêts optimaux. C'est un problème d'analyse séquentielle dans lequel un observateur examine $n$ variables aléatoires indépendantes de manière séquentielle et doit en sélectionner exactement une sans rappel. L'objectif est de déterminer une stratégie qui permette de minimiser le rang moyen de l'observation sélectionnée. Nous décrivons un modèle alternatif de ce problème, dans lequel le décideur observe un nombre aléatoire d'arrivées distribuées suivant un processus de Poisson homogène sur un horizon fixe $t$. Nous prouvons l'existence d'une stratégie optimale pour chaque horizon, et nous montrons que la fonction de perte associée à cette stratégie est uniformément continue sur $R$. Nous décrivons une fonction de perte restreinte qui permet d'obtenir une estimation de la valeur asymptotique du problème, et nous obtenons la valeur asymptotique associée à des stratégies spécifiques. Nous obtenons ensuite une équation intégro-diffférentielle sur la fonction de perte associée à la stratégie optimale. Finalement nous étudions les valeurs asymptotiques du problème et nous les comparons à celles du problème en temps discret. Nous concluons cette thèse en décrivant des stratégies spécifiques qui permettent d'obtenir des estimations sur le comportement asymptotique de la fonction de perte.

No description available.

Cobalt-60 (Co-60) units played an integral role in radiation therapy from the mid-1950s to the 1970s. Although they continue to be used to treat cancer in some parts of the world, their role has been significantly reduced due to the invention of medical linear accelerators. A number of groups have indicated a strong potential for Co-60 units in modern radiation therapy. The Medical Physics group at the Cancer Center of the Southeastern Ontario and Queen’s University has shown the feasibility of Intensity Modulated Radiation Therapy (IMRT) via simple conformal treatment planning and dose delivery using a Co-60 unit. In this thesis, initial Co-60 tomotherapy planning investigations on simple uniform phantoms are extended to actual clinical cases based on patient CT data. The planning is based on radiation dose data from a clinical Co-60 unit fitted with a multileaf collimator (MLC) and modeled in the EGSnrc Monte Carlo system. An in house treatment planning program is used to calculate IMRT dose distributions. Conformal delivery in a single slice on a uniform phantom based on sequentially delivered pencil beams is verified by Gafchromic film. Volumetric dose distributions for Co-60 serial tomotherapy are then generated for typical clinical sites that had been treated at our clinic by conventional 6MV IMRT using Varian Eclipse treatment plans. The Co-60 treatment plans are compared with the clinical IMRT plans using conventional matrices such as dose volume histograms (DVH). Dose delivery based on simultaneously opened MLC leaves is also explored and a novel MLC segmentation method is proposed. In order to increase efficiency of dose calculations, a novel convolution based fluence model for treatment planning is also proposed. The ion chamber measurements showed that the Monte Carlo modeling of the beam data under the MIMiC MLC is accurate. The film measurements from the uniform phantom irradiations confirm that IMRT plans from our in-house treatment planning system are deliverable. Comparing the Co-60 dose distributions and DVHs to the IMRT plans from the clinic indicates that Co-60 is able to provide similar dose conformality to targets and dose sparing to critical organs. The results of the novel MLC segmentation algorithm and the photon fluence model proposed in this work compared well with the Monte Carlo calculations. In summary, the investigations presented in this thesis confirm that Co-60 tomotherapy is indeed capable of providing state-of-the-art conformal dose delivery. We have shown that the perceived beam limitations often identified with Co 60 (e.g., lower penetration, source size artifacts under small field collimation, and larger penumbra) are negligible when using intensity modulated techniques. / Thesis (Ph.D, Physics, Engineering Physics and Astronomy) -- Queen's University, 2013-08-22 11:34:14.861

Cobalt-60 (Co-60) units played an integral role in radiation therapy from the mid-1950s to the 1970s. Although they continue to be used to treat cancer in some parts of the world, their role has been significantly reduced due to the invention of medical linear accelerators. A number of groups have indicated a strong potential for Co-60 units in modern radiation therapy. The Medical Physics group at the Cancer Center of the Southeastern Ontario and Queen’s University has shown the feasibility of Intensity Modulated Radiation Therapy (IMRT) via simple conformal treatment planning and dose delivery using a Co-60 unit. In this thesis, initial Co-60 tomotherapy planning investigations on simple uniform phantoms are extended to actual clinical cases based on patient CT data. The planning is based on radiation dose data from a clinical Co-60 unit fitted with a multileaf collimator (MLC) and modeled in the EGSnrc Monte Carlo system. An in house treatment planning program is used to calculate IMRT dose distributions. Conformal delivery in a single slice on a uniform phantom based on sequentially delivered pencil beams is verified by Gafchromic film. Volumetric dose distributions for Co-60 serial tomotherapy are then generated for typical clinical sites that had been treated at our clinic by conventional 6MV IMRT using Varian Eclipse treatment plans. The Co-60 treatment plans are compared with the clinical IMRT plans using conventional matrices such as dose volume histograms (DVH). Dose delivery based on simultaneously opened MLC leaves is also explored and a novel MLC segmentation method is proposed. In order to increase efficiency of dose calculations, a novel convolution based fluence model for treatment planning is also proposed. The ion chamber measurements showed that the Monte Carlo modeling of the beam data under the MIMiC MLC is accurate. The film measurements from the uniform phantom irradiations confirm that IMRT plans from our in-house treatment planning system are deliverable. Comparing the Co-60 dose distributions and DVHs to the IMRT plans from the clinic indicates that Co-60 is able to provide similar dose conformality to targets and dose sparing to critical organs. The results of the novel MLC segmentation algorithm and the photon fluence model proposed in this work compared well with the Monte Carlo calculations. In summary, the investigations presented in this thesis confirm that Co-60 tomotherapy is indeed capable of providing state-of-the-art conformal dose delivery. We have shown that the perceived beam limitations often identified with Co 60 (e.g., lower penetration, source size artifacts under small field collimation, and larger penumbra) are negligible when using intensity modulated techniques. / Thesis (Ph.D, Physics, Engineering Physics and Astronomy) -- Queen's University, 2013-08-22 11:34:14.861

No description available.

In this thesis we are concerned with the existence of infrared fixed points and the conformal window for gauge theories with fermions. We are particularly interested in those theories that are candidates for walking technicolor. We discuss the background of technicolor and the techniques relevant to a theoretical understanding of the conformal window. Following this we extend the ideas of metric confinement and causal analyticity to theories with fermions in non-fundamental representations. We use these techniques to, respectively, provide a lower bound on the lower end of the conformal window and to provide a measure of perturbativity. As well as analytic calculations we use lattice techniques to investigate two particular candidate theories for walking technicolor - SU(2) with two adjoint fermions and with six fundamental fermions. We use Schrodinger Functional techniques to investigate the running of the theory across a wide range of scales. We measure both the running of the coupling and an estimator for the fermion mass anomalous dimension, $gamma$. We find that both theories are consistent with an infrared fixed-point. However, paying particular attention to our error estimates, we are unable to absolutely confirm their existence. This is a not unexpected result for SU(2) with two adjoint fermions but is rather surprising for SU(2) with only six fundamental fermions. In the region where we are consistent with a fixed point we find $0.05<gamma<0.56$ for $SU(2)$ with two adjoint fermions and $0.135<gamma<1.03$ for $SU(2)$ with six fundamental fermions. The measurement of $gamma$ for $SU(2)$ with two adjoint fermions is the first determination of $gamma$ for any candidate theory of walking technicolor.

This thesis comes in three main parts. In the first of these (comprising chapters 2 - 6), the basic theory of Riemannian and conformal submersions is described and the relevant geometric machinery explained. The necessary Clifford algebra is established and applied to understand the relationship between the spinor bundles of the base, the fibres and the total space of a submersion. O'Neill-type formulae relating the covariant derivatives of spinor fields on the base and fibres to the corresponding spinor field on the total space are derived. From these, formulae for the Dirac operators are obtained and applied to prove results on Dirac morphisms in cases so far unpublished. The second part (comprising chapters 7-9) contains the basic theory and known classifications of G2-structures and Spin+ 7 -structures in seven and eight dimensions. Formulae relating the covariant derivatives of the canonical forms and spinor fields are derived in each case. These are used to confirm the expected result that the form and spinorial classifications coincide. The mean curvature vector of associative and Cayley submanifolds of these spaces is calculated in terms of naturally-occurring tensor fields given by the structures. The final part of the thesis (comprising chapter 10) is an attempt to unify the first two parts. A certain `7-complex' quotient is described, which is analogous to the well-known hyper-Kahler quotient construction. This leads to insight into other possible interesting quotients which are correspondingly analogous to quaternionic-Kahler quotients, and these are speculated upon with a view to further research.

This thesis presents a method to obtain the per-unit-length electrical parameters of a given overhead transmission line or underground cable in an unbounded space considering the effect of the ground. This is achieved using a two-dimensional conformal mapping technique, which consists of a modified bilinear transformation to map a semi-open half-space problem into a unit circle. The Helmholtz equations describing the quasi-stationary approximation for the electromagnetic field behaviour are solved using finite element method, with the aid of commonly used commercial software program, COMSOL Multiphysics. The per-unit-length resistance, inductance and capacitance are calculated using the proposed mapping method, the truncation of the original space method and then compared with the analytical solution obtained from Carson's approximation for the overhead lines and Wedepohl's formulation for the underground cables. / October 2016

Abstract The collective field theory technique provides a method of tackling problems with two N × N matrices in the large N limit. The collective field background from one matrix is first found, then the second matrix is introduced into this background as an impurity. Within the context of the AdS/CFT correspondence, this technique can be used to describe gauge theory states in the BMN limit. This dissertation starts by developing the collective field theory technique, firstly in general variables, then for one matrix, and subsequently for two matrices. It goes on to introduce a Yang-Mills interaction term, where two variable identifications are considered. The first is the more traditional angular momentum eigenstate model. The second is a model that directly uses two of the Higgs scalars. This model has been mentioned in the literature, but has not been considered in great depth. The exact two impurity spectrum is found, and the multi-impurity spectrum is found to first order. The resulting energy values match a spectrum that has been found for giant magnons.

Cette thèse a pour objet principal l'étude des structures pseudo-riemanniennes et de leurs groupes de transformations conformes, locales et globales. On cherche à obtenir des informations générales sur la structure du groupe conforme d'une variété pseudo-riemannienne compacte de dimension au moins 3, et on s'intéresse également à la géométrie et la dynamique des actions conformes de groupes de Lie sur de telles structures. L'essentiel des résultats présentés en géométrie conforme se situe en signature lorentzienne (1,n-1).Le point de vue qui est adopté ici est d'interpréter une structure conforme de dimension au moins 3 comme étant la donnée d'une géométrie de Cartan modelée sur l'univers d'Einstein de même signature. Ces structures géométriques, introduites par Élie Cartan, sont rigides et leurs symétries locales ont des propriétés remarquables. Nous retrouvons dans ce contexte des résultats formulés par Mikhaïl Gromov à la fin des années 1980, et les mettons en œuvre sur le cas particulier de la géométrie de Cartan définie par une structure conforme. / The main object of this thesis is the study of pseudo-Riemannian structures and their local and global conformal transformation groups. The purpose is to obtain general informations about the conformal group of a compact pseudo-Riemannian manifold of dimension greater than or equal to 3, and we also study dynamical and geometrical properties of conformal Lie group actions on such structures. The largest part of the result that are presented in this work are formulated in the (1,n-1) Lorentz signature.The approach we have chosen here to study a conformal structure is to work with its associated normal Cartan geometry modeled on the Einstein universe with same signature. These geometric structures, introduced by Élie Cartan, are rigid and their local automorphisms have nice behaviours. We formulate in this context results of Mikhaïl Gromov, that go back to the late 1980', and use them in the particular case of the normal Cartan geometry associated to a conformal structure.