On the anharmonic, multi-phonon, Debye-Waller contributions to the phonon-limited resistivity of metals : applications to Na and K

The anharmonic, multi-phonon (MP), and Oebye-Waller factor (OW) contributions to the phonon limited resistivity (;0) of metals derived by Shukla and Muller (1979) by the doubletime temperature dependent Green function method have been numerically evaluated for Na and K in the high temperature limit. The anharmonic contributions arise from the cubic and quartic shift of phonons (CS, QS), and phonon width (W) and the interference term (1). The QS, MP and OW contributions to I' are also derived by the matrix element method and the results are in agreement with those of Shukla and Muller (1979). In the high temperature limit, the contributions to;O from each of the above mentioned terms are of the type BT2 For numerical calculations suitable expressions are derived for the anharmonic contributions to ~ in terms of the third and fourth rank tensors obtained by the Ewald procedure. The numerical calculation of the contributions to;O from the OW, MP term and the QS have been done exactly and from the CS, Wand I terms only approximately in the partial and total Einstein approximations (PEA, TEA), using a first principle approach (Shukla and Taylor (1976)). The results obtained indicate that there is a strong pairwise cancellation between the: OW and MP terms, the QS and CS and the Wand I terms. The sum total of these contributions to;O for Na and K amounts to 4 to 11% and 2 to 7%, respectively, in the PEA while in the TEA they amount to 3 to 7% and 1 to 4%, respectively, in the temperature range.

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 interpretation of environmental sustainability (ES) by the IOC/Olympic Games 1994-2008

The purpose of this qualitative multi-case study was to examine the interpretation of environmental sustainability (ES) within the Olympic 11 Movement. Two research questions guided the inquiry - first, how has the concept of ES been defined by the International Olympic Committee (lOC), and second, how has the concept of ES been defined and enacted by the Organizing Committees ofthe Olympic Games (OCOGs)? During the past two decades, the International Olympic Committee (lOC) established several policies and programs related to ES. Its actions reflect a broader trend of environmentalism within economic and social spheres around the world (Milton-Smith, 2002). Despite the numerous initiatives, the Olympic Games continue to cause significant environmental damage. Frey, et al. (2007) argued that the Olympic Movement contradicts the fundamental premises of ES because the Games are hosted in a two week time period, are situated in a confined area, and accumulate operating and infrastructure costs in the billions of dollars. Further, Etzion (2007) stated "there is positive and significant correlation between firm siz~ and environmental performance" (p. 642) and in the context of the Olympics the sizeimpact relation is striking. Since 1972, the year the UN launched its international environmental awareness efforts, the Summer Olympics grew to 201 nations (39% increase), 10,500 athletes (32% increase), 28 sports (30% increase), and 302 events (43% increase) (Johnson, 2004; Girginov & Parry, 2005; Upegui, 2008). The proliferation of Games activities counters the ES principles that exist within many of the IOC declarations, policies and programs.