Cluster Approach Applied to the One-Dimensional Anderson-Hubbard Model
S. Johri and R. Bhatt developed a real-space renormalization group approach aimed at extracting the localized single-particle eigenstates of the Anderson model from a large system by identifying clusters of resonant site potentials. E. Campbell generalized this real-space renormalization group approach using standard perturbation theory. Both approaches were intended to approximate the single-particle density of states of the Anderson model. In this thesis, we aimed to test the potential of applying a similar real-space renormalization group approach to calculate the density of states of the interacting Anderson-Hubbard model. Our interest in the density of states of this model is due to a V-shaped zero-bias anomaly in two-dimensional systems. A real-space renormalization group approach is best applied to a one-dimensional system. We found that the zero-bias anomaly is not V-shaped in one-dimension. To test the potential of a real-space renormalization group approach, we used the cluster approach which is the same as the non-interacting renormalization group approach but without the perturbation theory and found that for strong disorder this technique could accurately calculate the density of states over a wide range of energies but deviated from exact results at the band edge, at $\omega=\pm U$ and near $\omega=0$. The first two inaccuracies will be reduced with a proper real-space renormalization group approach. We suspect that the last inaccuracy is associated with long range physics and may be difficult to recover. We also developed a technique that adjusts the identification of clusters in the cluster approach to improve the computation time of the density of states with minimal loss of accuracy in a tunable range around the Fermi level. We found that this technique significantly reduced the computation time and was able to preserve the density of states near the Fermi level, except at the smallest energies near $\omega=0$. Author Keywords: Anderson-Hubbard model, renormalization group, Strong electron correlations, Zero-bias anomaly
Phosphoric Acid Chemically Activated Waste Wood
Activated Carbon (AC) is commonly produced by gasification, but there has been increasing interest in chemical activation due to its lower activation temperatures and higher yields. Phosphoric acid, in particular, succeeds in both these areas. Phosphoric acid activated carbon (PAC) can be environmentally sustainable, and economically favourable, when the phosphoric acid used in the activation is recycled. This thesis describes the digestion and activation of waste wood using phosphoric acid, as well as methods used to recover phosphoric acid, functionalize the produced activated carbon with iron salts and then test their efficacy on the adsorption of target analytes, selenite and selenate. In order to achieve an efficient phosphoric acid based chemical activation, further understanding of the activation process is needed. A two-step phosphoric acid activation process with waste wood feed stock was examined. The filtrate washes of the crude product and the surface composition of the produced PAC were characterized using X-ray Photoelectron Spectroscopy (XPS), Fourier Transform-Infrared spectroscopy (FT-IR), Ion Chromatography (IC), and 31P Nuclear Magnetic Resonance (NMR). XPS of the unwashed PAC contained 13.3 atomic percent phosphorous, as phosphoric acid, while the washed sample contained 1.4 atomic percent phosphorous as PO43-, and P2O74-. Using 31P NMR, phosphoric acid was identified as the primary phosphorous species in the acidic 0.1 M HCl washings, with pyrophosphates also appearing in the second 0.1 M NaOH neutralizing wash, and finally a weak signal from phosphates with an alkyl component also appearing in the DI wash. IC showed high concentrations of phosphoric acid in the 0.1 M HCl wash with progressively lower concentrations in both the NaOH and DI washes. Total phosphoric acid recovery was 96.7 % for waste wood activated with 25 % phosphoric acid, which is higher than previous literature findings for phosphoric acid activation. The surface areas of the PAC were in the 1500-1900 m2g-1 range. Both pre and post activation impregnation of iron salts resulted in iron uptake. Pre-activation resulted in only iron(III) speciation while post-activation impregnation of iron(II)chloride did result in iron(II) forming on the PAC surface. The pre-activated impregnated PAC showed little to no adsorption of selenite and selenate. The post-activation impregnated iron(II)chloride removed up to 12.45 ± 0.025 mg selenium per g Iron-PAC. Competitive ions such as sulfate and nitrate had little effect on selenium adsorption. Phosphate concentration did affect the uptake. At 250 ppm approximately 75 % of adsorption capacity of both the selenate and the selenite solutions was lost, although selenium was still preferentially adsorbed. Peak adsorption occurred between a pH of 4 and 11, with a complete loss of adsorption at a pH of 13. Author Keywords: Activated Carbon, doping, Iron, phosphoric acid, selenium
Investigation of Using Phase Change Materials for Thermal Energy Storage in Adiabatic Compressed Air Energy Storage
There is an increasing global need for grid scale electrical energy storage to handle the implementation of intermittent renewable energy sources. Adiabatic compressed air energy storage is an emerging technology with similar performance to pumped hydro except it has the issue of heat loss during the compression stage. Previously, it has been considered to use sensible heat storage materials to store the heat created by compression in a thermal energy storage unit until energy is required, and then transfer the heat back to the air. This research proposes to instead use phase change materials to store the heat of compression, as this will reduce entropy generation and maximize roundtrip exergy efficiency. Different configurations and placements of the phase change materials are considered and exergy analyses are presented. The thermodynamic equations are derived and optimal setup conditions including amount of latent heat and melting temperatures are calculated. Author Keywords: Compressed Air Energy Storage, Energy Storage, Exergy, Phase Change Materials
Correlating density of states features with localization strength in disordered interacting systems
Johri and Bhatt found singular behavior near the band edge in the density of states as well as in the inverse participation ratio of the Anderson model. These singularities mark a transition to an energy range dominated by resonant states. We study the interacting case using an ensemble of two-site Anderson-Hubbard systems. We find the ensemble-averaged density of states and generalized inverse participation ratio have more structure than in the non-interacting case because there are more transitions and in particular the transitions depend on the ground state. Nonetheless, there are regions of sharp decline in the generalized inverse participation ratio associated with specific density of state features. Moreover these features move closer to the Fermi level with the addition of interactions making them more experimentally accessible. Unfortunately resonances unique to interacting systems cannot be specifically identified. Author Keywords: Correlated electrons, Disorder, Localization
Model for the Differential Susceptibility of Strontium Titanate
The appearance of a two-dimensional electron gas (2DEG) in oxide interfaces between strontium titanate (STO) and other materials has become a major area of study. The behaviour of the 2DEG in STO is not well understood in part because the dielectric properties of STO are not well characterized. The differential susceptibility has a major impact on the electric fields within strontium titanate, and therefore to understand the 2DEG a better understanding of the susceptibility is needed. An expression for the soft mode phonon frequency of bulk strontium titanate is derived and used to model the susceptibility as a function of spatially homogeneous electric field, temperature and wavevector. This model is used to discuss the effect of spatially inhomogeneous electric fields and the local vs. nonlocal nature of the susceptibility. The critical exponents and the free energy are determined and discussed. Author Keywords: critical exponents, differential susceptibility, quantum paraelectric, strontium titanate
Heavy Rydberg Photo-dissociation Cross-section Calculations and Experimental Progress Towards Cold Collisions in Lithium
This thesis is divided into two parts, each of which supports constructing and using a lithium magneto-optical trap for cold collision studies: Part I One outgoing channel of interest from cold collisions is the production of ion pairs. We describe an effective method for calculating bound-to-continuum cross-sections for charged binary systems by examining transitions to states above the binding energy that become bound when the system is placed within an infinite spherical well. This approach is verified for ionization of a hydrogen atom, and is then applied to the heavy Rydberg system Li+...I-. Part II A wavemeter previously built in the lab is redesigned for increased reliability and ease of use by replacing the optical hardware with a rocker system, which can be aligned in mere minutes rather than half a day as was previously the case. The new wavemeter has been tested through saturated absorption spectroscopy of lithium. Author Keywords: cross-section, dissociation, lithium, magneto-optical trap, Michelson, wavemeter
"Multimodal Contrast" from the Multivariate Analysis of Hyperspectral CARS Images
The typical contrast mechanism employed in multimodal CARS microscopy involves the use of other nonlinear imaging modalities such as two-photon excitation fluorescence (TPEF) microscopy and second harmonic generation (SHG) microscopy to produce a molecule-specific pseudocolor image. In this work, I explore the use of unsupervised multivariate statistical analysis tools such as Principal Component Analysis (PCA) and Vertex Component Analysis (VCA) to provide better contrast using the hyperspectral CARS data alone. Using simulated CARS images, I investigate the effects of the quadratic dependence of CARS signal on concentration on the pixel clustering and classification and I find that a normalization step is necessary to improve pixel color assignment. Using an atherosclerotic rabbit aorta test image, I show that the VCA algorithm provides pseudocolor contrast that is comparable to multimodal imaging, thus showing that much of the information gleaned from a multimodal approach can be sufficiently extracted from the CARS hyperspectral stack itself. Author Keywords: Coherent Anti-Stokes Raman Scattering Microscopy, Hyperspectral Imaging, Multimodal Imaging, Multivariate Analysis, Principal Component Analysis, Vertex Component Analysis

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