Principal component and second generation wavelet analysis of Treasury yield curve evolution

Prices of U.S. Treasury securities vary over time and across maturities. When the market in Treasurys is sufficiently complete and frictionless, these prices may be modeled by a function time and maturity. A cross-section of this function for time held fixed is called the yield curve; the aggregate of these sections is the evolution of the yield curve. This dissertation studies aspects of this evolution. ^ There are two complementary approaches to the study of yield curve evolution here. The first is principal components analysis; the second is wavelet analysis. In both approaches both the time and maturity variables are discretized. In principal components analysis the vectors of yield curve shifts are viewed as observations of a multivariate normal distribution. The resulting covariance matrix is diagonalized; the resulting eigenvalues and eigenvectors (the principal components) are used to draw inferences about the yield curve evolution. ^ In wavelet analysis, the vectors of shifts are resolved into hierarchies of localized fundamental shifts (wavelets) that leave specified global properties invariant (average change and duration change). The hierarchies relate to the degree of localization with movements restricted to a single maturity at the base and general movements at the apex. Second generation wavelet techniques allow better adaptation of the model to economic observables. Statistically, the wavelet approach is inherently nonparametric while the wavelets themselves are better adapted to describing a complete market. ^ Principal components analysis provides information on the dimension of the yield curve process. While there is no clear demarkation between operative factors and noise, the top six principal components pick up 99% of total interest rate variation 95% of the time. An economically justified basis of this process is hard to find; for example a simple linear model will not suffice for the first principal component and the shape of this component is nonstationary. ^ Wavelet analysis works more directly with yield curve observations than principal components analysis. In fact the complete process from bond data to multiresolution is presented, including the dedicated Perl programs and the details of the portfolio metrics and specially adapted wavelet construction. The result is more robust statistics which provide balance to the more fragile principal components analysis. ^

Role of carbon nanotube dispersion in fracture toughening of plasma sprayed aluminum oxide-carbon nanotube nanocomposite coating

Aluminum oxide (Al2O3, or alumina) is a conventional ceramic known for applications such as wear resistant coatings, thermal liners, heaters, crucibles, dielectric systems, etc. However applications of Al 2O3 are limited owing to its inherent brittleness. Due to its excellent mechanical properties and bending strength, carbon nanotubes (CNT) is an ideal reinforcement for Al2O3 matrix to improve its fracture toughness. The role of CNT dispersion in the fracture toughening of the plasma sprayed Al2O3-CNT nanocomposite coating is discussed in the current work. Pretreatment of powder feedstock is required for dispersing CNTs in the matrix. Four coatings namely spray dried Al2O 3 (A-SD), Al2O3 blended with 4wt.% CNT (A4C-B), composite spray dried Al2O3-4wt.% CNT (A4C-SD) and composite spray dried A1203-8wt.% CNT (A8C-SD), are synthesized by plasma spraying. Owing to extreme temperatures and velocities involved in the plasma spraying of ceramics, retention of CNTs in the resulting coatings necessitates optimizing plasma processing parameters using an inflight particle diagnostic sensor. A bimodal microstructure was obtained in the matrix that consists of fully melted and resolidified structure and solid state sintered structure. CNTs are retained both in the fully melted region and solid-state sintered regions of processed coatings. Fracture toughness of A-SD, A4C-B, A4C-SD and A8C-SD coatings was 3.22, 3.86, 4.60 and 5.04 MPa m1/2 respectively. This affirms the improvement of fracture toughness from 20% (in A4C-B coating) to 43% (in A4C-SD coating) when compared to the A-SD coating because of the CNT dispersion. Fracture toughness improvement from 43% (in A4C-SD) to 57% (in A8C-SD) coating is evinced because of the CNT content. Reinforcement by CNTs is described by its bridging, anchoring, hook formation, impact alignment, fusion with splat, and mesh formation. The Al2O3/CNT interface is critical in assisting the stress transfer and utilizing excellent mechanical properties of CNTs. Mathematical and computational modeling using ab-initio principle is applied to understand the wetting behavior at the Al2O 3/CNT interface. Contrasting storage modulus was obtained by nanoindentation (∼210, 250, 250-350 and 325-420 GPa in A-SD, A4C-B, A4C-SD, and A8C-SD coatings respectively) depicting the toughening associated with CNT content and dispersion.

Lattice Boltzmann modeling of fluid flow and solute transport in karst aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Lattice Boltzmann Modeling of Fluid Flow and Solute Transport in Karst Aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Role of carbon nanotube dispersion in fracture toughening of plasma sprayed aluminum oxide - carbon nanotube nanocomposite coating

Aluminum oxide (A1203, or alumina) is a conventional ceramic known for applications such as wear resistant coatings, thermal liners, heaters, crucibles, dielectric systems, etc. However applications of A1203 are limited owing to its inherent brittleness. Due to its excellent mechanical properties and bending strength, carbon nanotubes (CNT) is an ideal reinforcement for A1203 matrix to improve its fracture toughness. The role of CNT dispersion in the fracture toughening of the plasma sprayed A1203-CNT nanocomposite coating is discussed in the current work. Pretreatment of powder feedstock is required for dispersing CNTs in the matrix. Four coatings namely spray dried A1203 (A-SD), A1203 blended with 4wt.% CNT (A4C-B), composite spray dried A1203-4wt.% CNT (A4C-SD) and composite spray dried A1203-8wt.% CNT (A8CSD), are synthesized by plasma spraying. Owing to extreme temperatures and velocities involved in the plasma spraying of ceramics, retention of CNTs in the resulting coatings necessitates optimizing plasma processing parameters using an inflight particle diagnostic sensor. A bimodal microstructure was obtained in the matrix that consists of fully melted and resolidified structure and solid state sintered structure. CNTs are retained both in the fully melted region and solid-state sintered regions of processed coatings. Fracture toughness of A-SD, A4C-B, A4C-SD and A8C-SD coatings was 3.22, 3.86, 4.60 and 5.04 MPa m1/2 respectively. This affirms the improvement of fracture toughness from 20 % (in A4C-B coating) to 43% (in A4C-SD coating) when compared to the A-SD coating because of the CNT dispersion. Fracture toughness improvement from 43 % (in A4C-SD) to 57% (in A8C-SD) coating is evinced because of the CNT content. Reinforcement by CNTs is described by its bridging, anchoring, hook formation, impact alignment, fusion with splat, and mesh formation. The A1203/CNT interface is critical in assisting the stress transfer and utilizing excellent mechanical properties of CNTs. Mathematical and computational modeling using ab-initio principle is applied to understand the wetting behavior at the A1203/CNTinterface. Contrasting storage modulus was obtained by nanoindentation (~ 210, 250, 250-350 and 325-420 GPa in A-SD, A4C-B, A4C-SD, and A8C-SD coatings respectively) depicting the toughening associated with CNT content and dispersion.

The effect of weathering processes on the vertical turbulent dispersion characteristics of crude oil spilled on the sea

Since the Exxon Valdez accident in 1987, renewed interest has come forth to better understand and predict the fate and transport of crude oil lost to marine environments. The short-term fate of an Arabian Crude oil was simulated in laboratory experiments using artificial seawater. The time-dependent changes in the rheological and chemical properties of the oil under the influence of natural weathering processes were characterized, including dispersion behavior of the oil under simulated ocean turbulence. Methodology included monitoring the changes in the chemical composition of the oil by Gas Chromatography/Mass Spectrometry (GCMS), toxicity evaluations for the oil dispersions by Microtox analysis, and quantification of dispersed soluble aromatics by fluorescence spectrometry. Results for this oil show a sharp initial increase in viscosity, due to evaporative losses of lower molecular weight hydrocarbons, with the formation of stable water-in-oil emulsions occurring within one week. Toxicity evaluations indicate a decreased EC-50 value (higher toxicity) occurring after the oil has weathered eight hours, with maximum toxicity being observed after weathering seven days. Particle charge distributions, determined by electrophoretic techniques using a Coulter DELSA 440, reveal that an unstable oil dispersion exists within the size range of 1.5 to 2.5 um, with recombination processes being observed between sequential laser runs of a single sample.