Establishing the resonance spectrum of the nucleon with accuracy would provide important new information about the dynamics and degrees of freedom of its constituents. The spectrum and properties of nucleon resonances are a fundamental test of the emerging predictions from Lattice QCD calculations and will guide re finements to QCD-based phenomenological models. Pion photoproduction is an excellent tool to study the nucleon resonance spectrum, as this channel is expected to couple strongly to most resonances. The new generation of measurements for this reaction, of which the measurement presented in this thesis forms a crucial part, will provide a great improvement in the quality of available experimental data. For the photoproduction process in particular, the use of photon beams and targets with high degrees of polarisation, coupled with large acceptance particle detectors is essential for disentangling the spectrum of excited states. There are many nucleon resonances predicted by recent Lattice QCD calculations and by phenomenological nucleon models which are only observed inconsistently by different analyses of the same experimental data or which are not observed at all. It is of upmost importance to establish if this means that the resonances do not exist in nature, reflecting inappropriate degrees of freedom in the theoretical description of the nucleon or if the current experimental measurements have not been sensitive enough. As such, there is a current world effort at modern tagged photon facilities to measure the \complete set" of photoproduction observables necessary to fully constrain the partial wave analyses used to extract the experimental excitation spectrum from the data. This thesis will present the first detailed measurement to date of positive pion photoproduction in the 730-2300 MeV photon energy (1400-2280 MeV centre-of-mass energy) region with a linearly polarised photon beam and a longitudinally polarised proton target with a close-to-complete angular coverage in detection of the reaction products. This unique set up allows for the extraction of the double-polarisation observable, G. The data were taken as part of the g9 experiment at the Thomas Jefferson National Accelerator Facility in Virginia, using a tagged, polarised photon beam and the Frozen Proton Spin Target, FROST, in conjunction with the CEBAF Large Acceptance Spectrometer, CLAS. The results of the study presented here are compared to the sparse existing data set for the G double-polarisation observable along with the current solutions of the the three main partial wave analyses: MAID, SAID and Bonn-Gatchina. Some agreement is obtained with the expectations of these PWA at lower energies, while disagreement at higher energies is clearly evident. This is the energy region where many of the missing resonances are expected to lie. Once incorporated into the MAID, SAID and Bonn-Gatchina models, these new data will provide an important contribution to constraining the amplitudes and therefore the resonance spectrum and properties of the nucleon. The new data will form a central part of the world effort to accurately establish the nucleon excitation spectrum for the first time by achieving the first complete measurement of experimental observables in meson photoproduction.

The composite structure of the nucleon leads to a spectrum of excited states, or resonances, which contain important constraints on the dynamics and interactions of its constituents. A major world programme measuring meson photoproduction from the nucleon is currently under way to improve our knowledge of this fundamental spectrum. These new generation of measurements exploit polarisation degrees of freedom of the incident photon along with spin degrees of freedom in the target and recoiling nucleons. The meson photoproduction process can be described by 16 independent experimental observables. To fully constrain the four underlying complex photoproduction amplitudes requires the measurement of a least 8 of these. Measurements of double polarisation observables, where the photon beam and nucleon target are polarised are crucial to achieve this requirement. This thesis will present the analysis and extraction of the first preliminary measurement of the double polarisation observable. F in the single pion photoproduction reaction γ→ + p →n + π+ was undertaken to measure both F and T. The resulting measurement of polarisation observables from this reaction in conjunction with with those from the Pπ0 channel will provide stringent constraints on partial wave analyses aiming to extract precision information on the properties of the low lying nucleon resonances.

Establishing the excitation spectrum of the nucleon would be a key advance to further our understanding of nucleon structure and Quantum Chromodynamics (QCD). Recent theoretical advances allow predictions of the excitation spectrum of the nucleon and other nucleon properties directly from QCD in the non-perturbative regime, via numerical methods (such as Lattice QCD), complementing existing constituent quark models. There is an ongoing world programme in meson photoproduction from the nucleon, which has already led to a number of nucleon resonances being discovered and established. This advance has largely been made possible by the first accurate measurement of polarisation observables. Available data has been obtained for proton targets, whereas for a complete picture of meson photoproduction, data from the neutron must also be obtained. This is important, as nucleon resonances can have very different photo-couplings to the proton and neutron. This thesis presents the first measurement of the E double-polarisation observable for the exclusive γn → K+Ʃ- reaction using a polarised hydrogen-deuterium target from the g14 run period at CLAS. Circularly polarised photons of energies between 1:1 and 2:3 GeV were used, with results shown in 200 MeV bins in Eγ and bins of 0:4 in cos θC.M./K+. Further to this, CLAS has undergone a detector upgrade in order to facilitate electrons of up to 12 GeV from Jefferson Lab's upgraded accelerator. Essential to this, is a new system for tagging quasi-real photons by detecting electrons scattered at very small angles. My work includes significant contributions to the design, realisation and construction of a hodoscope for this forward photon tagging apparatus. Presented in this thesis is a comprehensive overview of my work in developing and constructing the scintillating hodoscope for the CLAS12 Forward Tagger.

This thesis describes the research I did during my Master's study. I investigated the stau-neutralino coannihilation region of the Mirage Mediation Model at the Large Hadron Collider (LHC). By constructing five kinematic observables at the LHC, the masses of supersymmetric particles (sparticles) were determined. The Mirage Mediation Model parameters were determined from the sparticles' masses. This is the first time to establish the Mirage Mediation Model at the LHC. All these techniques can be applied to other coannihilation regions of the Mirage Mediation Model and other supersymmetry (SUSY) models.

The Monte Carlo forward Euler method with uniform time stepping is the standard technique to compute an approximation of the expected payoff of a solution of an Itô SDE. For a given accuracy requirement TOL, the complexity of this technique for well behaved problems, that is the amount of computational work to solve the problem, is O(TOL-3). A new hybrid adaptive Monte Carlo forward Euler algorithm for SDEs with non-smooth coefficients and low regular observables is developed in this thesis. This adaptive method is based on the derivation of a new error expansion with computable leading-order terms. The basic idea of the new expansion is the use of a mixture of prior information to determine the weight functions and posterior information to compute the local error. In a number of numerical examples the superior efficiency of the hybrid adaptive algorithm over the standard uniform time stepping technique is verified. When a non-smooth binary payoff with either GBM or drift singularity type of SDEs is considered, the new adaptive method achieves the same complexity as the uniform discretization with smooth problems. Moreover, the new developed algorithm is extended to the MLMC forward Euler setting which reduces the complexity from O(TOL-3) to O(TOL-2(log(TOL))2). For the binary option case with the same type of Itô SDEs, the hybrid adaptive MLMC forward Euler recovers the standard multilevel computational cost O(TOL-2(log(TOL))2). When considering a higher order Milstein scheme, a similar complexity result was obtained by Giles using the uniform time stepping for one dimensional SDEs. The difficulty to extend Giles' Milstein MLMC method to the multidimensional case is an argument for the flexibility of our new constructed adaptive MLMC forward Euler method which can be easily adapted to this setting. Similarly, the expected complexity O(TOL-2(log(TOL))2) is reached for the multidimensional case and verified numerically.

No description available.

Dans cette thèse, nous étudions les propriétés d’un mouvement de diffusion intermittent dans un milieu confiné.Dans ce but, nous considérons un modèle minimal de catalyse hétérogène, mettant en jeu une particule soumise à un mouvement de diffusion “surface-mediated”, alternant des phases de diffusion volumique à l’intérieur d’un disque, et des phases de diffusion surfacique sur le pourtour du disque. Pour un tel mouvement, nous obtenons des résultats pour plusieurs observables de premier passage (i) le temps moyen de premier passage d'atteindre une cible, (ii) la probabilité de splitting d’atteindre une cible spécifique, (iii) le territoire exploré avant de sortir du disque (iv) la probabilité de réaction avec des sites catalytiques. Selon la position relative de départ de de ces quantités vis-à-vis du temps d'adsorption moyen sur la surface. Nous avons montré que des excursions volumiques peuvent minimiser le temps de recherche d’une cible, même si celle-ci est située sur la surface. Nous présentons également un modèle simple de milieu poreux ordonné, constitué d’un réseau hypercubique de cavités identiques. Nous présentons deux modèles : (i) pour un mouvement brownien simple, (ii) pour un mouvement intermittent, en introduisant un paramètre de persistance. Nous montrons que ces deux modèles, dans la limite de non-persistance, converge vers le même résultat. Nous avons aussi etudié le comportement et l’optimisation du coefficient de diffusion vis-à-vis du temps moyen d’adsorption. Pour évaluer nos résultats théoriques, nous utilisons des simulations de Monte-Carlo et des résolutions numériques par le méthode des éléments finis. / In this thesis, we study first-passage properties for an intermittent Brownian motion inside a confining domain. We consider a minimal model of heterogenous catalysis in which a molecule performs surface-mediated diffusion inside a confining domain whose boundary contains catalytic sites. We obtain results for several observables : (i) the mean first-passage time to reach a target, (ii) the splitting probabilities that the molecule reach a specific target, (iii) the covered territory on the confining surface before the molecule exits the domain, (iv) the probability of reacting with catalytic sites. These results are exact for point like-targets, and are shown to be accurate also for extended targets, located on the surface or inside the bulk. Depending of the relative positions of the entrance and exit points, very different behaviors with respect to the mean adsorption time of the molecule on the surface are found. Although non-intuitive for bulk targets, it is found that boundary excursions, can minimize the search time. We also present a simple model of an ordered porous media. We present two models : (i) for a simple Brownian motion, (ii) for a surface-mediated diffusion with a parameter of persistence b. This model leads to a less simple result for the efficient diffusion coefficient. Our main result shows that in the limit of non persistence (b=0), both results are the same. We also provide an analysis of the behaviors of the efficient diffusion coefficient with respect to the mean adsorption time, showing optimisation possibilities. Numericals Monte-Carlo simulations and finite element solver have been used to evaluate our theoretical results.

No description available.

This paper will examine observables in the bc system, a two-dimensional free conformal field theory. We begin by encoding the bc system into the BV formalism following procedures of Costello and Gwilliam. This will allow us to construct the factorization algebra of observables for the bc system. The cohomology of the factorization algebra recovers the observables themselves. In cohomology, we will compute the commutation relations and factorization algebra structure maps for observables supported on disks and annuli. These structure maps will be used to prove the equivalence of the factorization algebra and vertex algebra structures for the bc system. This proof provides a rigorous derivation of the free fermionic vertex algebra starting from the action functional of the bc system. Using this equivalence, we will provide a dictionary to translate the action of the Virasoro algebra to the language of factorization algebras. Also in this paper, we examine the bc system in four-dimensions. We construct its factorization algebra and show that its observables are anti-commutative. Lastly, we prove that the global observables of the bc system are one-dimensional on a compact manifold of complex dimension one or two.

Contracts are legally enforceable agreements between two or more parties. The agreements can contain temporally based conditions, such as actions taken by the contract parties or events that happen, that trigger changes to the state of the contract when the conditions become true. Since the structure of these conditions can be very complex, it can be difficult to write contracts in a natural language in a clear and unambiguous way. A better approach is to have a formal language with a precise semantics to represent contracts. Contracts expressed in such a language have a mathematically precise meaning and can be written, analyzed, and manipulated by software. This thesis presents FCL, a formal language with a precise semantics for writing general contracts that may depend on temporally based conditions. Motivated by carefully selected examples of contracts, we derive a set of desirable requirements that a formal language of contracts should support. Based on the requirements, we clearly de ne the notion of contract and address what it means to fulfill or breach a contract. We present the formal syntax and semantics of FCL. We also successfully formalize different kinds of contracts in FCL and develop a reasoning system for FCL. / Thesis / Doctor of Philosophy (PhD)