We calculate the strange quark content of the nucleon, <N|ss|N> − <0|ss|0> using a novel method with the MILC lattice QCD gauge ensembles. The strangeness of the nucleon is related to the interaction cross section between dark matter and ordinary nuclear matter (e.g. in detectors) in many models. Previous results for this quantity suffered from uncontrolled systematic errors and/or large statistical uncertainties. The first result using our methods was the first modern calculation of the strangeness of the nucleon[76] with good control of systematic errors and reasonably small statistical errors, greatly reducing the uncertainty in dark matter detection cross sections. A refinement of this method allows for further reduction of statistical error. On the MILC Asqtad data, we obtain <N|ss|N> = 0.637(55)(stat)(74)(sys). The results obtained from this method are consistent with those obtained from other commonly-used methods applied to the MILC data. We also calculate the disconnected part of the pion-nucleon sigma term and the intrinsic charm of the nucleon using this method. The intrinsic charm has large statistical errors but is consistent with a perturbative calculation.

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Zirconium and its alloys are used extensively in the nuclear industry. In the Canadian Deuterium Uranium reactor, the primary containment in the primary coolant system is composed of Zr-2.5wt%Nb in the form of a pressure tube. The permissible chemical composition of Zr-2.5wt%Nb for use in the pressure tube in nuclear reactors is dictated by ASTMB353. Oxygen and iron are the highest content controlled elements in the standard alloy, after zirconium and niobium. Oxygen is an alpha-stabilizer, and diffuses preferentially to the alpha phase, leading to a well established increase in the yield strength of the alpha phase. Iron is a beta-stabilizer, and is concentrated in the beta phase, as well as near alpha-beta grain boundaries. While the mechanical properties of standard Zr-2.5wt%Nb alloy are well understood, there is a dearth of knowledge on the individual effect of these alloying additions, especially at non-standard concentrations. Additionally, the experimental evidence that does exist does not directly take into account the two-phase nature of the alloy, or the effect of impurities on specific deformation modes. Notably absent is experimental evidence on the effect of interstitial impurities on twinning in the hexagonal close-packed alpha phase. This work seeks to complement the present understanding of these phenomena. Mechanical tests have been performed on three specially prepared Zr-2.5wt%Nb alloys to clarify the contributions of oxygen and iron to Zr-2.5wt%Nb deformation properties. Traditional mechanical measurements were complemented by in situ and ex situ diffraction measurements. Tests were performed at a range of temperatures (77K - 673K) and strain rates (quasi-static to 10^-2/s). Increasing oxygen content from 1176wppm to 3300wppm increases the macroscopic yield stress at room temperature, and results in a transition in work hardening behaviour at low strain rates. Increasing iron content from 547wppm to 1080wppm has no effect on the macroscopic yield stress, but increases the work hardening rate at room temperature. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2013-10-11 20:06:57.655

Neutron diffraction is a widely used technique for measuring internal stresses inside polycrystalline materials. By examining the diffraction patterns collected during in situ uniaxial deformation, the lattice strains along various crystallographic directions can be calculated. These lattice strains give insight into the active deformation mechanisms active within the material during plastic deformation. This is most commonly done by fitting model results to the experimentally measured lattice strains through an iterative process of refining the model parameters. A numerical optimization technique was successfully applied to the problem of refining the input parameters of an elastoplastic self-consistent (EPSC) model. The results were found to be comparable to those obtained by a past researcher manually refining the model parameters and subjectively judging the fit to the experimental data. The numerical optimization method was able to reach an acceptable result much faster than is possible by a human being (days as opposed to weeks or months), meaning that it has the potential to reduce the turn-around time from data collection to interpretation/publication significantly. At the same time, common experimental techniques for conducting diffraction experiments during uniaxial deformation tests were examined. It is common to use an interrupted loading scheme where the sample is brought to a certain loading condition and then held steady while the neutron data is collected, a processes that often takes several minutes. This interrupted loading may be done such that the sample is held at constant stress, strain, or simply by having the load frame stay in a constant position. Each of these different loading modes results in a particular type of relaxation within the sample as it is being held, so a series of experiments were conducted to investigate any impact these different relaxation types may have on the measured values of the lattice strains. Overall it was found that both qualitative and quantitative differences in the recorded data can arise as a result of the different loading modes, and that such differences tend to manifest themselves at or near the point at which the material begins to yield macroscopically. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2013-03-05 19:37:19.995

This dissertation focuses on two areas of garnet porphyroblast crystallization that have until now remained largely uninvestigated: epitaxial nucleation of garnet porphyroblasts and yttrium and rare earth (Y+REE) uptake in metamorphic garnet. The mechanism of epitaxial nucleation is explored as a step towards determining which aspects of interfaces are significant to interfacial energies and nucleation rates. Garnet from the aureole of the Vedrette di Ries tonalite, Eastern Alps, shows a clear case of epitaxial nucleation in which garnet nucleated on biotite with (110)grt || (001)bt with [100]grt || [100]bt. The occurrence is remarkable for the clear genetic relationships revealed by the microstructures and for its preservation of the mica substrate, which allows unambiguous determination of the coincident lattice planes and directions involved in the epitaxy. Not all epitaxial nucleation is conspicuous; to increase the ability to document epitaxial relationships between garnet and micas, I develop and apply a method for determining whether evidence for epitaxial nucleation of garnet is present in porphyroblasts containing an included fabric. Although the magnitude of uncertainties in orientation measurements for garnets from Passo del Sole (Switzerland), the Nevado Filabride Complex (Spain), and Harpswell Neck (USA) preclude definitive identification of epitaxial relationships, the method has potential to become a viable technique for creating an inventory of instances and orientations of epitaxial nucleation with appropriate sample selection. Using lattice-dynamics simulations, I explore the most commonly documented epitaxial relationship, (110)grt || (001)ms. The range of interfacial energies resulting from variations in the intracrystalline layer within garnet at the interface, the initial atomic arrangement at the interface, and the rotational orientation of the garnet structure relative to the muscovite structure shows that the intracrystalline layer within garnet has the greatest effect on interfacial energy. A complete understanding of the role of intergranular diffusion for yttrium and rare-earth-element uptake in porphyroblastic garnet is critical because the complexities of Y+REE zoning in garnets and the mechanisms of Y+REE uptake have implications for petrologic interpretations and garnet-based geochronology. Y+REE distributions in garnets from the Picuris Mountains (USA), Passo del Sole (USA), and the Franciscan Complex (USA) imply diverse origins linked to differing degrees of mobility of these elements through the intergranular medium during garnet growth.

This dissertation focuses on two areas of garnet porphyroblast crystallization that have until now remained largely uninvestigated: epitaxial nucleation of garnet porphyroblasts and yttrium and rare earth (Y+REE) uptake in metamorphic garnet. The mechanism of epitaxial nucleation is explored as a step towards determining which aspects of interfaces are significant to interfacial energies and nucleation rates. Garnet from the aureole of the Vedrette di Ries tonalite, Eastern Alps, shows a clear case of epitaxial nucleation in which garnet nucleated on biotite with (110)grt || (001)bt with [100]grt || [100]bt. The occurrence is remarkable for the clear genetic relationships revealed by the microstructures and for its preservation of the mica substrate, which allows unambiguous determination of the coincident lattice planes and directions involved in the epitaxy. Not all epitaxial nucleation is conspicuous; to increase the ability to document epitaxial relationships between garnet and micas, I develop and apply a method for determining whether evidence for epitaxial nucleation of garnet is present in porphyroblasts containing an included fabric. Although the magnitude of uncertainties in orientation measurements for garnets from Passo del Sole (Switzerland), the Nevado Filabride Complex (Spain), and Harpswell Neck (USA) preclude definitive identification of epitaxial relationships, the method has potential to become a viable technique for creating an inventory of instances and orientations of epitaxial nucleation with appropriate sample selection. Using lattice-dynamics simulations, I explore the most commonly documented epitaxial relationship, (110)grt || (001)ms. The range of interfacial energies resulting from variations in the intracrystalline layer within garnet at the interface, the initial atomic arrangement at the interface, and the rotational orientation of the garnet structure relative to the muscovite structure shows that the intracrystalline layer within garnet has the greatest effect on interfacial energy. A complete understanding of the role of intergranular diffusion for yttrium and rare-earth-element uptake in porphyroblastic garnet is critical because the complexities of Y+REE zoning in garnets and the mechanisms of Y+REE uptake have implications for petrologic interpretations and garnet-based geochronology. Y+REE distributions in garnets from the Picuris Mountains (USA), Passo del Sole (USA), and the Franciscan Complex (USA) imply diverse origins linked to differing degrees of mobility of these elements through the intergranular medium during garnet growth.

The problem of two-dimensional acoustic scattering of an incident plane wave by a semi-infinite lattice is solved. The problem is first considered for sound-soft cylinders whose size is small compared to the wavelength of the incident field. In this case the formulation leads to a scalar Wiener--Hopf equation, and this in turn is solved via the discrete Wiener--Hopf technique. We then deal with a more complex case which arises either by imposing Neumann boundary condition on the cylinders' surface or by increasing their radii. This gives rise to a matrix Wiener--Hopf equation, and we present a method of solution that does not require the explicit factorisation of the kernel. In both situations, a complete description of the far field is given and a conservation of energy condition is obtained. For certain sets of parameters (`pass bands'), a portion of the incident energy propagates through the lattice in the form of a Bloch wave. For other parameters (`stop bands' or `band gaps'), no such transmission is possible, and all of the incident field energy is reflected away from the lattice.

This thesis describes the design of novel magnetic lattices for the transport line and gantry of a charged particle therapy complex. The designs use non-scaling Fixed Field Alternating Gradient (ns-FFAG) magnets and were made as part of the PAMELA project. The main contributions in this thesis are the near-perfect FFAG dispersion suppression design process and the designs of the transport line and the gantry lattices. The primary challenge when designing an FFAG gantry is that particles with different momenta take up different lateral positions within the magnets. This is called dispersion and causes problems at three points: the entrance to the gantry, which must be rotated without distortion of the beam; at the end of the gantry where reduced dispersion is required for entry to the scanning system; and a third of the way through the gantry, where a switch in curvature of the magnets is required. Due to their non-linear fields, dispersion suppression in conventional FFAGs is never perfect. However, as this thesis shows, a solution can be found through manipulation of the field components, meaning near-perfect dispersion suppression can be achieved using ns-FFAG magnets (although at a cost of irregular optics). The design process for an FFAG dispersion suppressor shown in this thesis is a novel solution to a previously unsolved problem. Other challenges in the gantry lattice design, such as height and the control of the optics, are tackled and a final gantry design presented and discussed. The starting point for the transport line is a straight FFAG lattice design. This is optimised and matched to a 45o bend. Fixed field solutions to the problem of extracting to the treatment room are discussed, but a time variable field solution is decided on for practical and patient safety reasons. A matching scheme into the gantry room is then designed and presented.

We consider the purity-based entanglement detection scheme introduced in [C. Moura Alves and D. Jaksch, Phys. Rev. Lett. 93, 110501 (2004)]. We describe how it could be implemented in an optical lattice using two-atom loss, and prove that in this form it detects all pure entangled states even without any spatial resolution. We then prove that correcting for certain reasonable types of experimental error is possible, and practical for error rates up to the order of one over the number of lattice sites considered. Limited spatial resolution similarly becomes a significant improvement over no spatial resolution only at nearly single site level. We also show how to use this process for state parameter estimation and collapse-revival evidence of entanglement, for which it remains useful even when the error rate is too high to permit unambiguous entanglement detection. We also consider an optical lattice bosonic analogue of the fractional quantum Hall (FQH) effect. This system can reach high “magnetic fields” very difficult to attain in the solid state FQH system, where the discrete nature of the lattice becomes important. Near simple rational numbers l/n of flux quanta per lattice cell, we find that the single particle states become nearly periodic with period n lattice sites, and have an n fold degeneracy which leads to FQH states resembling those of n-internal-state particles. Standard time of flight expansion would reveal this periodicity and be able to distinguish FQH states from vortex lattice or Mott insulator states. Shot noise correlation would provide further information on the nature of the FQH states.