On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .

The Terroir of Winter Hardiness: Investigation of Winter Hardiness, Water Metrics, and Yield of Riesling and Cabernet Franc in the Niagara Region Using Geomatic Technologies

Grapevine winter hardiness is a key factor in vineyard success in many cool climate wine regions. Winter hardiness may be governed by a myriad of factors in addition to extreme weather conditions – e.g. soil factors (texture, chemical composition, moisture, drainage), vine water status, and yield– that are unique to each site. It was hypothesized that winter hardiness would be influenced by certain terroir factors , specifically that vines with low water status [more negative leaf water potential (leaf ψ)] would be more winter hardy than vines with high water status (more positive leaf ψ). Twelve different vineyard blocks (six each of Riesling and Cabernet franc) throughout the Niagara Region in Ontario, Canada were chosen. Data were collected during the growing season (soil moisture, leaf ψ), at harvest (yield components, berry composition), and during the winter (bud LT50, bud survival). Interpolation and mapping of the variables was completed using ArcGIS 10.1 (ESRI, Redlands, CA) and statistical analyses (Pearson’s correlation, principal component analysis, multilinear regression) were performed using XLSTAT. Clear spatial trends were observed in each vineyard for soil moisture, leaf ψ, yield components, berry composition, and LT50. Both leaf ψ and berry weight could predict the LT50 value, with strong positive correlations being observed between LT50 and leaf ψ values in eight of the 12 vineyard blocks. In addition, vineyards in different appellations showed many similarities (Niagara Lakeshore, Lincoln Lakeshore, Four Mile Creek, Beamsville Bench). These results suggest that there is a spatial component to winter injury, as with other aspects of terroir, in the Niagara region.

APPLICATION OF GEOMATICS TECHNOLOGIES TO CHARACTERIZE SPATIAL VARIABILITY AT STRATUS VINEYARDS

Vineyards vary over space and time, making geomatics technologies ideally suited to study terroir. This study applied geomatics technologies - GPS, remote sensing and GIS - to characterize the spatial variability at Stratus Vineyards in the Niagara Region. The concept of spatial terroir was used to visualize, monitor and analyze the spatial and temporal variability of variables that influence grape quality. Spatial interpolation and spatial autocorrelation were used to measure the pattern demonstrated by soil moisture, leaf water potential, vine vigour, soil composition and grape composition on two Cabernet Franc blocks and one Chardonnay block. All variables demonstrated some spatial variability within and between the vineyard block and over time. Soil moisture exhibited the most significant spatial clustering and was temporally stable. Geomatics technologies provided valuable spatial information related to the natural spatial variability at Stratus Vineyards and can be used to inform and influence vineyard management decisions.