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) .

Thermodynamic properties and Debye-Waller factor of fee materials

We have calculated the equation of state and the various thermodynamic properties of monatomic fcc crystals by minimizing the Helmholtz free energy derived in the high temperature limit for the quasiharmonic theory, QH, and the lowest-order (cubic and quartic), 'A2, anharmonic terms of the perturbation theory, PT. The total energy in each case is obtained by adding the static energy. The calculation of the thermal properties was carried out for a nearest-neighbour central-force model of the fcc lattice by means of the appropriate thermodynamic relations. We have calculated the lattice constant, the thermal expansion, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the isothermal and adiabatic bulk moduli, and the Griineisen parameter, for the rare-gas solids Kr and Xe, and gold. Morse potential and modified Morse potential were each used to represent the atomic interaction for the three fcc materials. For most of the calculated thermodynamic properties from the QH theory, the results for Kr and Xe with the modified Morse potential show an improvement over the results for the Morse potential when compared with the experimental data. However, the results of the 'A 2 equation of state with the modified Morse potential are in good agreement with experiment only in the case of the specific heat at constant volume and at constant pressure. For Au we have calculated the lattice contribution from the QH and 'A 2 PT and the electronic contribution to the thermal properties. The electronic contribution was taken into account by using the free electron model. The results of the thermodynamic properties calculated with the modified Morse potential were similar to those obtained with the Morse potential. U sing the minimized equation of state we also calculated the Mossbauer recoilless fraction for Kr and Xe and the Debye-Waller factor (DWF) for Pb, AI, eu, Ag, and Au. The Mossbauer recoilless fraction was obtained for the above two potentials and Lennard-Jones potential. The L-J potential gives the best agreement with experiment for Kr. No experimental data exists for Xe. At low temperature the calculated DWF results for Pb, AI, and eu show a good agreement with experimental values, but at high temperature the experimental DWF results increase very rapidly. For Ag the computed values were below the expected results at all temperatures. The DWF results of the modified Morse potential for Pb, AI, eu and Ag were slightly better than those of the Morse potential. In the case of Au the calculated values were in poor agreement with experimental results. We have calculated the quasiharmonic phonon dispersion curves for Kr, Xe, eu, Ag, and Au. The calculated and experimental results of the frequencies agree quite well for all the materials except for Au where the longitudinal modes show serious discrepancies with the experimental results. In addition, the two lowest-order anharmonic contributions to the phonon frequency were derived using the Green's function method. The A 2 phonon dispersion curves have been calculated only for eu, and the results were similar to those of the QH dispersion curves. Finally, an expression for the Griineisen parameter "( has been derived from the anharmonic frequencies, and calculated for these materials. The "( results are comparable with those obtained from the thermodynamic definition.

The effects of plants(Typha Latifolia)and root-bed medium on the treatment of domestic sewage within a vertical flow constructed wetland /

The effect that plants {Typha latifolia) as well as root-bed medium physical and chemical characteristics have on the treatment of primary treated domestic wastewater within a vertical flow constructed wetland system was investigated. Five sets of cells, with two cells in each set, were used. Each cell was made of concrete and measured 1 .0 m X 1 .0 m and was 1.3 m deep. Four different root-bed media were tested : Queenston Shale, Fonthill Sand, Niagara Shale and a Michigan Sand. Four of the sets contained plants and a single type of root-bed medium. The influence of plants was tested by operating a Queenston Shale set without plants. Due to budget constraints no replicates were constructed. All of the sets were operated independently and identically for twenty-eight months. Twelve months of data are presented here, collected after 16 months of continuous operation. Root-bed medium type did not influence BOD5 removal. All of the sets consistently met Ontario Ministry of Environment (MOE) requirements (<25 mg/L) for BOD5 throughout the year. The 12 month average BOD5 concentration from all sets with plants was below 2.36 mg/L. All of the sets were within MOE discharge requirements (< 25 mg/L) for suspended solids with set effluent concentrations ranging from 1.53 to 14.80 mg/L. The Queenston Shale and Fonthill Sand media removed the most suspended solids while the Niagara Shale set produced suspended solids. The set containing Fonthill Sand was the only series to meet MOE discharge requirements (< Img/L) for total phosphorus year-round with a twelve month mean effluent concentration of 0.23 mg/L. Year-round all of the root-bed media were well below MOE discharge requirements (< 20mg/L in winter and < 10 mg/L in sumnner) for ammonium. The Queenston Shale and Fonthill Sand sets removed the most total nitrogen. Plants had no effect on total nitrogen removal, but did influence how nitrogen was cycled within the system. Plants increased the removal of suspended solids by 14%, BOD5 by 10% and total phosphorus by 22%. Plants also increased the amount of dissolved oxygen that entered the system. During the plant growing season removal of total phosphorus was better in all sets with plants regardless of media type. The sets containing Queenston Shale and Fonthill Sand media achieved the best results and plants in the Queenston Shale set increased treatment efficiency for every parameter except nitrogen. Vertical flow wetland sewage treatment systems can be designed and built to consistently meet MOE discharge requirements year-round for BOD5, suspended solids, total phosphorus and ammonium. This system Is generally superior to the free water systems and sub-surface horizontal flow systems in cold climate situations.

Free Niagara.--

6 leaves of advertisements at end.

How Niagara was made free : The passage of Niagara Reservation Act in 1885 /

Reprinted from the Buffalo Historical Society Publications.

An anharmonic contribution to the Helmholtz free energy O(lambda 6)

The anharmonic contributions of order A6 to the Helmholtz free energy for a crystal in which every atom is on a site of inversion symmetry, have been evaluated The cor~esponding diagrams in the various orders of the perturbation theory have been presented The validity of the expressions given is for high temperatures. Numerical calculations for the diagrams which contribute to the free energy have been worked out for a nearest-n~ighbour central-force model of a facecentered cubic lattice in the high-temperature limit and in the leading term and the Ludwig approximations. The accuracy of the Ludwig approximation in evaluating the Brillouin-zone sums has been investigated. Expansion for all diagrams in the high-temperature limit has been carried out The contribution to the specific heat involves a linear as well as cubic term~ We have applied Lennard-Jones, Morse and Exponential 6 types of potentials. A comparison between the contribution to the free energy of order A6 to that of order A4 has been made.

"Man of science, man of faith" : Lost, consumer agency and the fate/free will binary in the post-9/11 context

In 2004, Lost debuted on ABC and quickly became a cultural phenomenon. Its postmodem take on the classic Robinson Crusoe desert island scenario gestures to a variety of different issues circulating within the post-9II1 cultural consciousness, such as terrorism, leadership, anxieties involving air travel, torture, and globalization. Lost's complex interwoven flashback and flash-forward narrative structure encourages spectators to creatively hypothesize solutions to the central mysteries of the narrative, while also thematically addressing archetypal questions of freedom of choice versus fate. Through an examination of the narrative structure, the significance of technological shifts in television, and fan cultures in Lost, this thesis discusses the tenuous notion of consumer agency within the current cultural context. Furthermore, I also explore these issues in relation to the wider historical post-9/II context.

The true history regarding alleged connection of the order of ancient, free and accepted Masons: with the abduction and murder of William Morgan in western New York, in 1826... (1886)

Cover title: Masonic light on the abduction and murder of Wm. Morgan.

Planar Topological Defects in Unconventional Superconductors

In this work, we consider the properties of planar topological defects in unconventional superconductors. Specifically, we calculate microscopically the interaction energy of domain walls separating degenerate ground states in a chiral p-wave fermionic superfluid. The interaction is mediated by the quasiparticles experiencing Andreev scattering at the domain walls. As a by-product, we derive a useful general expression for the free energy of an arbitrary nonuniform texture of the order parameter in terms of the quasiparticle scattering matrix. The thesis is structured as follows. We begin with a historical review of the theories of superconductivity (Sec. 1.1), which led the way to the celebrated Bardeen-Cooper- Schrieffer (BCS) theory (Sec. 1.3). Then we proceed to the treatment of superconductors with so-called "unconventional pairing" in Sec. 1.4, and in Sec. 1.5 we introduce the specific case of chiral p-wave superconductivity. After introducing in Sec. 2 the domain wall (DW) model that will be considered throughout the work, we derive the Bogoliubov-de Gennes (BdG) equations in Sec. 3.1, which determine the quasiparticle excitation spectrum for a nonuniform superconductor. In this work, we use the semiclassical (Andreev) approximation, and solve the Andreev equations (which are a particular case of the BdG equations) in Sec. 4 to determine the quasiparticle spectrum for both the single- and two-DW textures. The Andreev equations are derived in Sec. 3.2, and the formal properties of the Andreev scattering coefficients are discussed in the following subsection. In Sec. 5, we use the transfer matrix method to relate the interaction energy of the DWs to the scattering matrix of the Bogoliubov quasiparticles. This facilitates the derivation of an analytical expression for the interaction energy between the two DWs in Sec. 5.3. Finally, to illustrate the general applicability our method, we apply it in Sec. 6 to the interaction between phase solitons in a two-band s-wave superconductor.

Youth, Global Citizenship and Help: A Critical Rhetorical Analysis of Free The Children

Since 1995 Free The Children (FTC) has grown to be one of the largest and most recognized youth-focused and youth-led non-governmental organizations (NGOs) in Canada. FTC has distinguished itself by developing slick marketing campaigns, promising youth that they will become agents of change who can make a significant contribution towards eradicating poverty and promoting global social justice. The organization has utilized the Internet, creating an engaging and dynamic web page used to promote its development initiatives and celebrate the altruistic actions of its young participants. FTC uses a variety of strategies including text, video and images to persuade the viewer to engage with and elicit support for the organization. FTC attracts viewers by highlighting the successes of its overseas initiatives and the contributions made by young Northern volunteers in the global South. The organization also uses celebrity ambassadors, and cultural events such as We Day to raise its profile. Using a critical rhetorical analysis, this thesis interrogates FTC’s online promotional materials, exploring how the organization uses rhetorical strategies to persuade young people to take an interest in social justice activities. More specifically, an examination of FTC web-based promotional materials identifies and problematizes the organization’s rhetorical emphasis on youth empowerment, global citizenship and direct forms of helping the global South. This thesis argues that FTC does not direct adequate attention to fostering critical awareness among it participants. Further, the organization fails to provide its online participants with the appropriate tools or opportunities to critically engage with the structural issues related to global inequities. This thesis also examines how the organization uses rhetoric that promotes simplistic, feel-good projects that avoid exposing young people to an analysis of global social injustices.

Phonon spectra and temperature variation of thermodynamic properties of fcc metals via Finnis-Sinclair type many body potentials: Sutton-Chen and improved Sutton-Chen models

Volume(density)-independent pair-potentials cannot describe metallic cohesion adequately as the presence of the free electron gas renders the total energy strongly dependent on the electron density. The embedded atom method (EAM) addresses this issue by replacing part of the total energy with an explicitly density-dependent term called the embedding function. Finnis and Sinclair proposed a model where the embedding function is taken to be proportional to the square root of the electron density. Models of this type are known as Finnis-Sinclair many body potentials. In this work we study a particular parametrization of the Finnis-Sinclair type potential, called the "Sutton-Chen" model, and a later version, called the "Quantum Sutton-Chen" model, to study the phonon spectra and the temperature variation thermodynamic properties of fcc metals. Both models give poor results for thermal expansion, which can be traced to rapid softening of transverse phonon frequencies with increasing lattice parameter. We identify the power law decay of the electron density with distance assumed by the model as the main cause of this behaviour and show that an exponentially decaying form of charge density improves the results significantly. Results for Sutton-Chen and our improved version of Sutton-Chen models are compared for four fcc metals: Cu, Ag, Au and Pt. The calculated properties are the phonon spectra, thermal expansion coefficient, isobaric heat capacity, adiabatic and isothermal bulk moduli, atomic root-mean-square displacement and Gr\"{u}neisen parameter. For the sake of comparison we have also considered two other models where the distance-dependence of the charge density is an exponential multiplied by polynomials. None of these models exhibits the instability against thermal expansion (premature melting) as shown by the Sutton-Chen model. We also present results obtained via pure pair potential models, in order to identify advantages and disadvantages of methods used to obtain the parameters of these potentials.

Totals of free goods up – class 3 and class 4

Totals of free goods up – class 3 and class 4 (1 page, handwritten), n.d.

Unsigned letter to A. Jeffrey written on an envelope stating that the glass was free from breakage, therefore there would be a deduction of 10 percent

Unsigned letter to A. Jeffrey written on an envelope stating that the glass was free from breakage, therefore there would be a deduction of 10 percent, June 28, 1875.