A dimensionally compatible system of equations for stand basal area, volume, and basal area and volume growth was derived using dimensional analysis. These equations are analytically and numerically consistent with dimensionally compatible individual tree volume and taper equations and share parameters with them. Parameters for the system can be estimated by fitting individual tree taper and volume equations or by fitting stand level basal area and volume equations. In either case the parameters are nearly identical. Therefore, parameters for the system can be estimated at the tree or stand level without changing the results. Data from a thinning study in loblolly pine (Pinus taeda L.) plantations established on cutover site-prepared lands were used to estimate the parameters. However, the developed system of equations is general and can be applied to other tree species in other locales. / Ph. D.

Digital Particle Image Velocimetry (DPIV) is a planar measurement technique to measure the velocity within a fluid by correlating the motion of flow tracers over a sequence of images recorded with a camera-laser system. Sophisticated digital processing algorithms are required to provide a high enough accuracy for quantitative DPIV results. This study explores the potential of a variety of cross-correlation filters to improve the accuracy and robustness of the DPIV estimation. These techniques incorporate the use of the Phase Transform (PHAT) Generalized Cross Correlation (GCC) filter applied to the image cross-correlation. The use of spatial windowing is subsequently examined and shown to be ideally suited for the use of phase correlation estimators, due to their invariance to the loss of correlation effects. The Robust Phase Correlation (RPC) estimator is introduced, with the coupled use of the phase correlation and spatial windowing. The RPC estimator additionally incorporates the use of a spectral filter designed from an analytical decomposition of the DPIV Signal-to-Noise Ratio (SNR). This estimator is validated in a variety of artificial image simulations, the JPIV standard image project, and experimental images, which indicate reductions in error on the order of 50% when correlating low SNR images. Two variations of the RPC estimator are also introduced, the Gaussian Transformed Phase Correlation (GTPC): designed to optimize the subpixel interpolation, and the Spectral Phase Correlation (SPC): estimates the image shift directly from the phase content of the correlation. While these estimators are designed for DPIV, the methodology described here provides a universal framework for digital signal correlation analysis, which could be extended to a variety of other systems. / Master of Science

Fischer-Tropsch Synthesis (FTS) is a promising technology for the production of ultra-clean fuels and chemical feedstocks from biomass, coal, or natural gas. Iron catalysts are ideal for conversion of coal and biomass. However, precipitated iron catalysts used in slurry-bubble column reactors suffer from high attrition resulting in difficulty separating catalysts from product and increased slurry viscosity. Thus, development of an active and selective-supported iron catalyst to manage attrition is needed. This thesis focuses on the development of a supported iron catalyst and kinetic models of FTS on the catalyst using advanced statistical methods for experimental design and analysis. A high surface area alumina, modified by the addition of approximately 2 wt% lanthanum, was impregnated with approximately 20 wt% Fe and 1% Pt in a two step procedure. Approximately 10 wt% Fe and 0.5 wt% Pt was added in each step. The catalyst had a CO uptake of 702 μmol/g, extent of reduction of 69%, and was reduced at 450°C. The catalyst was stable over H2 partial pressures of 4-10 atm, CO partial pressures of 1-4 atm, and temperatures of 220-260°C. Weisz modulus values were less than 0.15. A Langmuir-Hinshelwood type rate expression, derived from a proposed FTS mechanism, was used with D-optimal criterion to develop experiments sequentially at 220°C and 239°C. Joint likelihood confidence regions for the rate expression parameters with respect to run number indicate rapid convergence to precise-parameter estimates. Difficulty controlling the process at the designed conditions and steep gradients around the D-optimal criterion resulted in consecutive runs having the same optimal condition. In these situations another process condition was chosen to avoid consecutive replication of the same process condition. A kinetic model which incorporated temperature effects was also regressed. Likelihood and bootstrap confidence intervals suggested that the model parameters were precise. Histograms and skewness statistics calculated from Bootstrap resampling show parameter-effect nonlinearities were small.