Hadronic matrix elements in lattice QCD

The lattice formulation of Quantum ChromoDynamics (QCD) has become a reliable tool providing an ab initio calculation of low-energy quantities. Despite numerous successes, systematic uncertainties, such as discretisation effects, finite-size effects, and contaminations from excited states, are inherent in any lattice calculation. Simulations with controlled systematic uncertainties and close to the physical pion mass have become state-of-the-art. We present such a calculation for various hadronic matrix elements using non-perturbatively O(a)-improved Wilson fermions with two dynamical light quark flavours. The main topics covered in this thesis are the axial charge of the nucleon, the electro-magnetic form factors of the nucleon, and the leading hadronic contributions to the anomalous magnetic moment of the muon. Lattice simulations typically tend to underestimate the axial charge of the nucleon by 5 − 10%. We show that including excited state contaminations using the summed operator insertion method leads to agreement with the experimentally determined value. Further studies of systematic uncertainties reveal only small discretisation effects. For the electro-magnetic form factors of the nucleon, we see a similar contamination from excited states as for the axial charge. The electro-magnetic radii, extracted from a dipole fit to the momentum dependence of the form factors, show no indication of finite-size or cutoff effects. If we include excited states using the summed operator insertion method, we achieve better agreement with the radii from phenomenology. The anomalous magnetic moment of the muon can be measured and predicted to very high precision. The theoretical prediction of the anomalous magnetic moment receives contribution from strong, weak, and electro-magnetic interactions, where the hadronic contributions dominate the uncertainties. A persistent 3σ tension between the experimental determination and the theoretical calculation is found, which is considered to be an indication for physics beyond the Standard Model. We present a calculation of the connected part of the hadronic vacuum polarisation using lattice QCD. Partially twisted boundary conditions lead to a significant improvement of the vacuum polarisation in the region of small momentum transfer, which is crucial in the extraction of the hadronic vacuum polarisation.

Study of the Compressive Strength of Aluminum Curved Elements

Currently, the Specification for Aluminum Structures (Aluminum Association, 2010) shows thin-walled aluminum plate sections with radii greater than eight inches have a lower compressive strength capacity than a flat plate with the same width and thickness. This inconsistency with intuition, which suggests any degree of folding a plate should increase its elastic buckling strength, inspired this study. A wide range of curvatures are studied—from a nearly flat plate to semi-circular. To quantify the curvature, a single non-dimensional parameter is used to represent all combinations of width, thickness and radius. Using the finite strip method (CU-FSM), elastic local buckling stresses are investigated. Using the ratio of stress values of curved plates compared to flat plates of the same size, equivalent plate-buckling coefficients are calculated. Using this data, nonlinear regression analyses are performed to develop closed form equations for five different edge support conditions. These equations can be used to calculate the elastic critical buckling stress for any curved aluminum section when the geometric properties (width, thickness, and radius) and the material properties (elastic modulus and Poisson’s ratio) are known. This procedure is illustrated in examples, each showing the applicability of the derived equations to geometries other than those investigated in this study and also providing comparisons with theoretically exact numerical analysis results.

Muffler characterization with implementation of the finite element method and experimental techniques

Determining how an exhaust system will perform acoustically before a prototype muffler is built can save the designer both a substantial amount of time and resources. In order to effectively use the simulation tools available it is important to understand what is the most effective tool for the intended purpose of analysis as well as how typical elements in an exhaust system affect muffler performance. An in-depth look at the available tools and their most beneficial uses are presented in this thesis. A full parametric study was conducted using the FEM method for typical muffler elements which was also correlated to experimental results. This thesis lays out the overall ground work on how to accurately predict sound pressure levels in the free field for an exhaust system with the engine properties included. The accuracy of the model is heavily dependent on the correct temperature profile of the model in addition to the accuracy of the source properties. These factors will be discussed in detail and methods for determining them will be presented. The secondary effects of mean flow, which affects both the acoustical wave propagation and the flow noise generation, will be discussed. Effective ways for predicting these secondary effects will be described. Experimental models will be tested on a flow rig that showcases these phenomena.

Concentration of trace elements in samples of sea water determined by use of two methods of concentrating

A device and a specific procedure for simultaneous concentration of trace ele¬ments from sea water by co-precipitating them in precipitate of magnesium hydroxide obtained by electrolytic alkalization of samples in a two-chamber electrolyzer are described. Analyses of sea water samples for zinc, iron, copper, nickel and lead demonstrate that the method produces a thousand-fold concentration and gives results that agree well with those obtained by extractive concentration using diethyldithiocarbamate and 8-hydroxyquinoline in chloroform. Extracts were analyzed by flame atomic absorption. Correlation coefficients of results obtained with use of these two methods of concentration were 0.76-0.87 for zinc, iron, and copper at confidence levels of 0.05-0.07. Average zinc and iron concentrations determined by the method differed by less than 10%.

Platinum group elements and geochemistry of altered oceanic crust of ODP Hole 140-504B

Primary chemical heterogeneity in the sheeted dike complex in Deep Sea Drilling Project Hole 504B makes these rocks unsuitable for conventional mass balance calculations in determining element mobility associated with hydrothermal alteration. Due to the original heterogeneity and variable degrees of fractionation in the dikes, an appropriate reference sample on which calculations can be based is difficult to find. Therefore, the use of incompatible element ratios is developed to evaluate geochemical changes during alteration(s). For example, on a Zr/Yb-La/Yb plot, scatter along a straight line suggests tapping of a variably depleted mantle source and deviation from the line suggests element mobility (gain or loss). Using this method, our data indicates that the hydrothermal evolution of the sheeted dike complex was accompanied by significant loss of Cu, Zn, and Ti and some loss of La. The sheeted dike complex has low platinum group element (PGE) concentrations and steep PGE patterns, typical of mid-ocean ridge basalts (MORBs) on the global scale. We propose that the unusual PGE patterns of MORBs cannot be entirely generated by a partial melting and sulfide segregation model; instead, these patterns in part must have been inherited from their mantle source. The Au data show no evidence for mobilization during hydrothermal alteration of the dikes.

Elements and mineralogical compostions from different sediment cores off the southern China Sea

The mineralogy, major and trace elements, and neodymium and strontium isotopes of surface sediments in the South China Sea (SCS) are documented with the aim of investigating their applicability in provenance tracing. The results indicate that mineralogical compositions alone do not clearly identify the sources for the bulk sediments in the SCS. The Nd isotopic compositions of the SCS sediments show a clear zonal distribution. The most negative epsilon-Neodymium values were obtained for sediments from offshore South China (-13.0 to -10.7), while those from offshore Indochina are slightly more positive (-10.7 to -9.4). The Nd isotopic compositions of the sediments from offshore Borneo are even higher, with epsilon-Neodymium ranging from -8.8 to -7.0, and the sediments offshore from the southern Philippine Arc have the most positive epsilon-Neodymium values, from -3.7 to +5.3. This zonal distribution in epsilon-Neodymium is in good agreement with the Nd isotopic compositions of the sediments supplied by river systems that drain into the corresponding regions, indicating that Nd isotopic compositions are an adequate proxy for provenance tracing of SCS sediments. Sr isotopic compositions, in contrast, can only be used to identify the sediments from offshore South China and offshore from the southern Philippine Arc, as the 87Sr/86Sr ratios of sediments from other regions overlapped. Similar zonal distributions are also apparent in a La-Th-Sc discrimination diagram. Sediments fromthewestmargin of the SCS, such as those fromBeibuwan Bay, offshore fromHainan Island, offshore from Indochina, and from the Sunda Shelf plot in the same field, while those offshore from the northeastern SCS, offshore from Borneo, and offshore from the southern Philippine Arc plot in distinct fields. Thus, the La-Th-Sc discrimination diagram, coupledwith Nd isotopes, can be used to trace the provenance of SCS sediments. Using this method, we re-assessed the provenance changes of sediments at Ocean Drilling Program (ODP) Site 1148 since the late Oligocene. The results indicate that sediments deposited after 23.8 Ma (above 455 mcd: meters composite depth) were supplied mainly from the eastern South China Block, with a negligible contribution from the interior of the South China Block. Sediments deposited before 26 Ma (beneath 477 mcd) were supplied mainly from the North Palawan Continental Terrane, which may retain the geochemical characteristics of the materials covered on the late Mesozoic granitoids along the coastal South China. For that the North Palawan Continental Terrane is presently located within the southern Philippine Arc but was located close to ODP Site 1148 in the late Oligocene. The weathering products of volcanic material associated with the extension of the SCS ocean crust also contributed to these sediments. The rapid change in sediment source at 26-23.8 Ma probably resulted from a sudden cessation of sediment supply from the North Palawan Continental Terrane. Wesuggest that the North Palawan Continental Terrane drifted southwards alongwith the extension of the SCS ocean crust during that time, and when the basin was large enough, the supply of sediment from the south to ODP Site 1148 at the north slope may have ceased.