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) .

Landscape geochemical investigations in the vicinity of a lead deposit near Snertingdal, southern Norway

Landscape geochemical investigations were conducted upon portions of a natural uniform landscape in southern Norway. This consisted of sampling both soil profile samples and spruce tree twigs for the analysis of twelve chemical elements. These elements were cobalt, copper, nickel, lead, zinc, manganese, magnesium, iron, calcium, sodium, potassium and aluminum which were determined by atomic absorption analysis on standardized extraction techniques for both organic and inorganic materials. Two "landscape traverses" were chosen for a comparative study of the effects of varying landscape parameters upon the trace element distribution patterns throughout the landscape traverses. The object of this study was to test this method of investigation and the concept of an ideal uniform landscape under Norwegian conditions. A "control traverse" was established to represent uniform landscape conditions typical of the study area and was used to determine "normal" or average trace element distribution patterns. A "signal traverse" was selected nearby over an area of lead mineralization where the depth to bedrock is very small. The signal traverse provided an area of similar landscape conditions to those of the control traverse with significant differences in the bedrock configuration and composition. This study was also to determine the effect of the bedrock mineralization upon the distribution patterns of the twelve chemical elements within the major components of the two landscape traverses (i.e. soil profiles and tree branches). The lead distribution within the soils of the signal traverse showed localized accumulations of lead within the overburden with maximum values occurring within the organic A horizon of soil profile #10. Above average concentrations of lead were common within the signal traverse, however, the other elements studied were not significantly different from those averages determined throughout the soils of the control traverse. The spruce twig samples did not have corresponding accumulations of lead near the soil lead anomaly. This is attributable to the very localized nature of the lead dispersion pattern within the soils. This approach to the study of the geochemistry of a natural landscape was effective in establishing: a) average or "normal" trace element distribution patterns b) local variations in the landscape morphology and c) the effect of unusually high lead concentrations upon the geochemistry of the landscape (i.e. within the soil profiles and tree branches). This type of study provides the basis for further more intensive studies and serves only as a first approximation of the behaviour of elements within a natural landscape.

The effects of altered heat stress on voluntary pacing strategies during prolonged cycling

Central Governor Model (CGM) suggests that perturbations in the rate of heat storage (AS) are centrally integrated to regulate exercise intensity in a feed-forward fashion to prevent excessive thermal strain. We directly tested the CGM by manipulating ambient temperature (Tam) at 20-minute intervals from 20°C to 35°C, and returning to 20°C, while cycling at a set rate of perceived exertion (RPE). The synchronicity of power output (PO) with changes in HS and Tam were quantified using Auto-Regressive Integrated Moving Averages analysis. PO fluctuated irregularly but was not significantly correlated to changes in thermo physiological status. Repeated measures indicated no changes in lactate accumulation. In conclusion, real time dynamic sensation of Tam and integration of HS does not directly influence voluntary pacing strategies during sub-maximal cycling at a constant RPE while non-significant changes in blood lactate suggest an absence of peripheral fatigue.

Ontario Winter Games records, 1984-1985.

The Ontario Winter Games began in 1970. This four day sporting event features amateur athletes from across the province, with the majority of the athletes being between the ages of 14-18. The event is held every two years and averages 3,500 participants, including athletes, coaches and officials. It provides an opportunity for young athletes to showcase and develop their skills, often preparing them for sports competitions at the national and international level. The 1985 Ontario Winter Games were held in St. Catharines, Ontario, from March 14-17.