This thesis presents a first study of the continuum limit of light hadronic physics using a lattice gauge theory simulation with good chiral symmetry. The results are interpreted and extrapolated using both the chiral effective theory and analytic models. Matrix elements of operators of the effective weak Hamiltonian are calculated. The thesis details a combined chiral and continuum extrapolation of two ensemble sets of 2+1 flavour Domain Wall QCD data with inverse lattice spacings around 1.73 and 2.32 GeV. A novel procedure of matching lattice data at unphysical quark masses is used to define the scaling trajectory to the continuum limit. Quantities studied include the pion and kaon masses and decay constants, the average up/down quark mass, the strange quark mass, and the neutral kaon mixing parameter BK. The latter is an important theoretical input to the K band in the unitarity triangle of the CKM matrix. A subset of recent results of ref. [1] in the chiral effective theory needed to perform our fits are re-derived. New methods for the improved determination of the BK matrix element (and other correlation functions), and also for the renormalisation of the relevant four-quark operator for BK are presented.

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The motion of microorganisms presents interesting and diffcult problems ranging from mechanisms of propulsion to collective effects. Experimentally, some of the complicating factors, such as death, reproduction, chemotaxis, etc., can be suppressed through genetic manipulation or environmental control. Nonequilibrium statistical mechanics has been used to study simple models, however proceeding analytically is extremely challenging. Thus simulations, where one has total control over and knowledge of the system, are a compelling method for examining models of their behaviour. In this work I present simulations of minimal, self-propelled particles, while ensuring realistic hydrodynamic behaviour using the lattice Boltzmann method (LBM), a well-studied method for simulating fluid flows that scales linearly in computational effort with the system volume. The derivation of the LBM is reviewed, including the addition of forces in a consistent, accurate manner as well as thermal fluctuations that satisfy the fluctuation-dissipation theorem. It is extended to include singular forces via a regularization of the Dirac δ-function. This is implemented and extensively tested for agreement with low Reynolds number hydrodynamics. The regularized singularities are used to develop an effcient algorithm for pointlike particles which move under the influence of an external force, such as gravity, or thermal fluctuations of the fluid. The method is compared to theoretical results and simulations using a well-studied algorithm that resolves the particle, finding good agreement in the dilute limit and significantly reduced computational requirements. Using the singular forces, we then construct a minimal model for self-propelled particles, that may also experience forces or undergo random changes of orientation (modelling the “run-and-tumble” dynamics observed in swimming bacteria such as E. coli). The collective behaviour of these model swimmers is studied in three situations: sedimentation under gravity; in a central, harmonic trap; and in a Poiseuille flow between parallel plates. For sedimentation, the behaviour is not very different from that expected of non-interacting run-and-tumble particles, except that total collapse to the container bottomwhen the weight of the particles equals the propelling force is prevented by the velocity fluctuations caused by the particles’ activity. The trapped particles, for runlengths comparable to the trap size, self-assemble into a pump-like structure, while for short run-lengths an approximately Gaussian distribution seenwithout hydrodynamic interactions, is maintained. In Poiseuille flows we find the particles orient upstream; forweak flows this results in a net upstreamcurrent. We find significant hydrodynamic effects, in the dilute limit, only when there is some mechanism that causes alignment of the particles.

The Large Hadron Collider (LHC) and the four major experiments set up along its 27 kilometers of circumference (ATLAS, CMS, ALICE and LHCb), have recently started to explore the high–energy frontier at √s = 8 TeV, and will move to even higher energy in just about 2 years. The aim of physics searches at LHC experiments was to complete the picture of the Standard Model (SM) of elementary particles with the discovery of the Higgs boson and to look for specific signatures of models extending the current understanding of particle interactions, at zero and non–zero temperature. In 2012, the official discovery of the Higgs boson, the only missing particle of the StandardModel, was announced by ATLAS and CMS. Other important results include the measurement of rare decay modes in heavy quarks systems, and indications of CP violation in charm decays by LHCb. Signatures of beyond the Standard Model (BSM) physics are currently being looked for in the experimental data, and this often requires the knowledge of quantities that can be computed only with non–perturbative methods. This thesis focuses on some possible extensions of the SM and the analysis of interesting physical observables, like masses or decay rates, calculated using non– perturbative lattice methods. The approach followed for the main part of this work is to model BSM theories as effective field theories defined on a lattice. This lattice approach has a twofold advantage: it allows us to explore non– renormalizable gauge theories by imposing an explicit gauge–invariant cutoff and it allows us to go beyond perturbative results in the study of strongly interacting systems. Some of the issues of the SM that we will try to address include, for example, the hierarchy problem and the origin of dynamical electroweak symmetry breaking (DEWSB). We investigate non–perturbatively the possibility that the lightness of the mass for an elementary scalar field in a four–dimensional quantum field theory might be due to a higher–dimensional gauge symmetry principle. This idea fits in the Gauge–Higgs unification approach to the hierarchy problem and the results we present extend what is known from perturbative expectations. Extra dimensional models are also often used to approach DEWSB. Another approach to DEWSB implies a new strongly interacting gauge sector that extends the SM at high energies and it is usually referred to as Technicolor. The phenomenological consequences of Technicolor can only be studied by non– perturbative methods at low energy since the theory is strongly coupled at large distances. We perform a comprehensive lattice study of fermionic and gluonic scalar bound states in one of the candidate theories for Technicolor BSM physics. We relate our findings to the nature of the newly discovered Higgs boson. New physics is also commonly believed to be hidden in the flavour sector of the SM. In this sector, lattice calculations of non–perturbative input parameters are needed in order to make precise predictions and extract signals of possible new physics. In particular, heavy quark physics on the lattice is still in development and it is important to understand the relevant discretisation errors. We describe a preliminary study of the mixing parameter of heavy–light mesons oscillations in a partially–quenched scenario, using staggered dynamical fermions and domain wall valence fermions.

This paper is a contribution to the study of countable Borel equivalence relations on standard Borel spaces. We concentrate here on the study of the nature of translation equivalence. We study these known hyperfinite spaces in order to gain insight into the approach necessary to classify certain variables as either being hyperfinite or not. In Chapter 1, we will give the basic definitions and examples of spaces used in this work. The general construction of marker sets is developed in this work. These marker sets are used to develop several invariant tilings of the equivalence classes of specific variables . Some properties that are equivalent to hyperfiniteness in the certain space are also developed. Lastly, we will give the new result that there is a continuous injective embedding from certain defined variables.

Liquid water management in the cathode of polymer electrolyte membrane fuel cells (PEMFC) is crucial to efficient transport of gases and to maintaining electrochemical activity in the catalyst layer. Cracks and interfacial voids are typical of catalyst layers in operating cells, and are thought to affect water management and other transport properties such as gas diffusion and conductivity. This thesis investigates the effect of such morphological imperfections on liquid water transport using a combination of numerical techniques. Both the catalyst layer and microporous layer parts of the cathode are considered. The layers are first numerically reconstructed using data from advanced microscopy, and cracks, perforations and interfacial voids are created. Lattice Boltzmann simulations of the dynamics liquid water imbibition process are performed to study the effect of characterizing features of the cracks and interfacial voids such as aperture area, degree of protrusion, and tortuosity. The resulting liquid water distributions were then input into a pore scale model to characterize the effect of the morphological features on other transport properties, such as effective diffusivities and conductivities. Larger crack apertures were found to increase liquid water uptake, and elongated cracks allowed for faster breakthrough at lower saturation levels. A notable observation is that short and large interfacial cracks have a higher liquid water uptake potential due to the lower effective capillary pressures. It was also found that elongated cracks aligned with the pressure gradient provide preferential pathway, and a capillary pressure increase that favours liquid water transport towards the membrane and mitigates flooding. The effective diffusivity increased for all crack protrusion depths, even for the wet catalyst layer, likely due to low liquid water saturation. The geometry with the most elongated crack showed a significant increase in gas diffusion under wet conditions, indicating that enhanced gas transport is achievable when liquid water removal is effective. Protonic and electrical conductivities decreased for all crack shapes due to higher contact resistance. / Graduate / 0548 / vlosier@uvic.ca

The past decade has shown distinct advances in the theory of multiple input multi output techniques for wireless communication systems. Now, the time has come to demonstrate this progress in terms of applications. This thesis introduces implementation of Schnorr- Euchner strategy based decoding algorithm applied on Altera system-on-chip (Stratix EP1S10F780C6) with Nios embedded processor. The lattice decoder is developed on FPGA using VHDL. The preprocessing part of algorithm is targeted for Nios embedded processor using C language. A controller is also designed to interface and communicate between the Nios embedded processor and lattice decoder.