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Krylov subspace iterative methods provide an effective tool for reducing the solution of large linear systems to a size for which a direct solver may be applied. However, the problems of limited storage and speed are still a concern. Therefore, in this dissertation work, we present iterative Krylov subspace algorithms for non-Hermitian systems which do have fixed memory requirements and have favorable convergence characteristics. This dissertation describes three projects. The first project concerns short-term recurrence Krylov subspace methods for nearly-Hermitian linear systems. In 2008, Beckermann and Reichel introduced a short-term recurrence progressive GMRES algorithm for nearly-Hermitian linear systems. However, we have found this method to be unstable. We document the instabilities and introduce a different fixed-memory algorithm to treat nearly-Hermitian problems. We present numerical experiments demonstrating that the performance of this algorithm is competitive. The other two projects involve extending a strategy called Krylov subspace recycling, introduced by Parks and colleagues in 2005. This method requires more overhead than other subspace augmentation methods but offers the ability to recycle subspace information between cycles for a single linear system and recycle information between related linear systems. In the first project, we extend subspace recycling to the block Krylov subspace setting. A block Krylov subspace is a generalization of Krylov subspace where a single starting vector is replaced with a block of linearly independent starting vectors. We then apply our method to a sequence of matrices arising in a Newton iteration applied to fluid density functional theory and present some numerical experiments. In the second project, we extend the methods of subspace recycling to a family of linear systems differing only by multiples of the identity. These problems arise in the theory of quantum chromodynamics, a theory of the behavior of subatomic particles. We wish to build on the class of Krylov methods which allow the simultaneous solution of all shifted linear systems while generating only one subspace. However, the mechanics of subspace recycling complicates this situation and interferes with our ability to simultaneously solve all systems using these techniques. Therefore, we introduce an algorithm which avoids this complication and present some numerical experiments demonstrating its effectiveness. / Mathematics

We present results from Fermilab MPS experiment E580 on the reactions π⁻N->V°X where V° is K°_S, A or A̅ and X are charged particles. Transverse and longitudinal momentum distributions for the V° and for K*^±(892), Σ^±(1385), Ξ⁻(1321) and Ξ⁺(1321) are presented. A comparison is made with the prediction of QCD quark counting rules. Evidence for A⁺_C; is presented. / Ph. D.

Ultra-relativisitic heavy ion collisions produce quark gluon plasma-a hot and dense soup of deconfined quarks and gluons akin to the early universe. We study two models in the context of these collisions namely, Polyakov Quark Meson Model (PQM) and Hadron Resonance Gas Model (HRGM).The PQM Model provides us with a simple and intuitive understanding of the QCD equation of state and thermodynamics at non zero temperature and baryon density while the HRGM is the principle model to analyse the hadron yields measured in these experiments across the entire range of beam energies. We study the effect of including the commonly neglected fermionic vacuum fluctuations to the (2+1) flavor PQM model. The conventional PQM model suffers from a rapid phase transition contrary to what is found through lattice simulations. Addition of the vacuum term tames the rapid transition and significantly improves the model’s agreement to lattice data. We further investigate the role of the vacuum term on the phase diagram. The smoothening effect of the vacuum term persists even at non zero . Depending on the value of the mass of the sigma meson, including the vacuum term results in either pushing the critical end point into higher values of the chemical potential or excluding the possibility of a critical end point altogether. We compute the fluctuations(correlations) of conserved charges up to sixth(fourth) order. Comparison is made with lattice data wherever available and overall good qualitative agreement is found, more so for the case of the normalised susceptibilities. The model predictions for the ratio of susceptibilities approach to that of an ideal gas of hadrons as in HRGM at low temperatures while at high temperature the values are close to that of an ideal gas of massless quarks. We examine the stability of HRGMs by extending them to take care of undiscovered resonances through the Hagedorn formula. We find that the influence of unknown resonances on thermodynamics is large but bounded. We model the decays of resonances and investigate the ratios of particle yields in heavy-ion collisions. We find that extending these models do not have much effect on hydrodynamics but the hadron yield ratios show better agreement with experiment. In principle HRGMs are internally consistent up to a temperature higher than the cross over temperature in QCD; but by examining quark number susceptibilities we find that their region of applicability seems to end even below the QCD cross over.

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Cette thèse décrit la recherche de nouvelles particules scalaires octets de couleur dans les données de l'expérience ATLAS auprès du Grand Collisionneur de Hadrons (LHC). Pour une large gamme de masse, la désintégration de ces scalaires en deux partons du MS domine. Cela motive la recherche de ces nouveaux scalaires dans des états finaux multijet, où ils se signaleraient comme des résonances dijet. Comme les nouveaux scalaires sont produits par paires, un état final contenant au moins quatre jets est utilisé comme environnement de recherche. Une méthode est développée pour extraire une possible résonance multijet scalaire du grand fond QCD et est utilisée pour chercher de tels scalaires dans les données de l'expérience ATLAS collectées en 2010 et 2011. Les données sont en accord avec l'estimation du fond et des limites sont posées sur la section efficace de production des scalaires en fonction de leur masse. En interprétant ces limites dans des modèles de supersymétrie, le gluon scalaire du MRSSM et du modèle hybride N=1/N=2 est exclu à 95 % CL entre 100 et 287 GeV. Les limites sont aussi interprétées dans un modèle de symétrie de jauge à la QCD, où le sgluon est remplacé par l'hyperpion qui est exclu dans une gamme de masse légèrement plus restreinte de part sa section efficace plus faible. / This thesis describes the search for new color-octet scalar particles in the ATLAS experiment data at the Large Hadron Collider (LHC). For a wide range of mass, the decay of the scalar to two SM partons dominates. This motivates the search for these new scalars in multijet final states, where they would manifest as dijet resonances. As the new scalars are products in pairs, a final state containing at least four jets is used as a search environment. A method is developed to extract a possible scalar resonance from the multijet QCD background and is used to search for such scalar in the data from the ATLAS experiment collected in 2010 and 2011. The data are in agreement with the estimation of the background and limits are set on the scalar production cross section as a function of the scalar mass. Interpreting these limits in models of supersymmetry, the scalar gluon of the MRSSM and of the hybrid N=1/N=2 model is excluded at the 95 % CL between 100 and 287 GeV. Limits are also interpreted in a model of gauge symmetry à la QCD, where the sgluon is replaced by the hyperpion excluded in a mass range slightly smaller because of its smaller cross section.

Le sujet de cette thèse est le calcul ab initio de masses en QCD sur réseau.Dans la première partie on reconstruit le spectre des hadrons légers de la QCD. En utilisant une action de jauge de Lüscher-Weisz et une action fermionique de Wilson clover qui couplent par le biais de liens ayant subi six étapes de smearing stout, on extrait les masses de hadrons légers dans simulations à $N_f=2+1$ saveurs. Ces masses sont en accord avec l'expérience avec une précision de l'ordre de quelques pourcents et tous les erreurs systématiques sont contrôlées.Dans la seconde partie, on détermine les masses de quarks légers. L'action est la même que précédement mais on utilise deux étapes de smearing hex. Les simulations sont réalisées à la masse du pion et on utilise cinq réseaux pour prendre la limite du continu, éliminant de ce fait une grande source d'erreur systématique. La renormalisation est effectuée à la Rome-Southampton pour ne pas induire d'incertitudes dues à la théorie des perturbations. On obtient ainsi les premiers résultats au point physique atteignant une précision inférieure à 5%. / The main topic of this thesis is the computation ab initio of masses from lattice QCD.In the first part, the light hadron spectrum is computed. Thanks to a Lüscher-Weisz gauge action and a clover Wilson action describing with the quarks with six levels of stout-smearing, light hadron masses are extracted from simulations with $N_f=2+1$ flavors. These masses agree with experiment with a few percent accuracy and all the systematic errors are under control.In the second part, the light quark masses are determined. We use the same action as previously but with two levels of hex smearing. The simulations are done at the physical point mass and five lattice spacings are used to take a safe conitnuum limit, thus eliminating a higher source of systematice incertitude. Renormalization is perfo,rmed non perturbatively à la Rome-Southampton, thereby suppressing perturbative errors. We obtain in this work the first full non perturbative resultats at the physical point with a high accuracy since we obtain an error of about 5%.

Nesta dissertação nós revisamos aspectos gerais de teorias de gauge, os princípios da formulação de rede da cromodinâmica quântica (QCD) e algumas propriedades de quarkônios pesados, i.e. estados ligados de um quark pesado e seu antiquark. Como um exemplo de simulações de Monte Carlo de modelos de rede, apresentamos aplicações nos casos do oscilador harmônico e teorias de gauge SU(2). Nós estudamos o efeito de incorporar o propagador de gluon de simulações na rede em um modelo de potencial para a descrição do quarkônio, no caso do botômomio e do charmônio. Nós usamos em ambos os casos uma abordagem numérica para calcular as massas dos estados de quarkônio. O espectro resultante é comparado em ambos os casos com cálculos usando o potencial de Coulomb mais linear (ou potencial Cornell). / In this dissertation we review general aspects of gauge theories, the principles of the lattice formulation of quantum chromodynamics (QCD) and some properties of heavy quarkonia, i.e. bound states of a heavy quark and its antiquark. As an illustration of Monte Carlo simulations of lattice models, we present applications in the case of the harmonic oscillator and SU(2) gauge theory. We study the effect of incorporating the gluon propagator from lattice simulations into a potential model for the description of quarkonium, in the case of bottomonium and charmonium. We use a numerical approach to evaluate masses of quarkonium states. The resulting spectrum is compared in both cases to calculations using the Coulomb plus linear (or Cornell) potential.