Thesis (M.S.) B.Y.U. Dept. of History.

Thesis (M.S.) B.Y.U. Dept. of History. / Electronic thesis. Also available in print ed.

This thesis presents a study of the applications of the variational principle to periodic lattices. A calculation of the conduction Knight Shift in the Alkali Meals is chosen as an example of the calculations possible with this method. The Knight Shift is discussed with reference to the contributions of both the core and conduction electrons. The approximation of neglect of the effect of the core electrons as found in previous calculations is discussed and its validity questioned. / Thesis / Master of Science (MS)

Th. : Lett. : Paris : 1932. / Bibliogr. : p. 127-199.

Habilitationsschrift--Karlsruhe. / Bibliography: p. 584-589.

This dissertation is the beginning of the development of a microscopic theory of the Knight shift. The Knight shift experiment has been used in superconductivity research throughout history, however, a complete understanding of the Knight shift in conventional as well as unconventional superconductors does not yet exist. Motivated by the results of a literature review, which discusses Knight shift anomalies in multiple superconducting materials, this research studies a new model of the Knight shift, which involves the processes involved in nuclear magnetic resonance measurements in metals. The result of this study is a microscopic model of nuclear magnetic resonance in metals. The spins of the spin-1/2 local nucleus and its surrounding orbital electrons interact with the arbitrary constant ${\bf B}_0$ and perpendicular time-oscillatory magnetic inductions ${\bf B}_1(t)$ and with each other via an anisotropic hyperfine interaction. An Anderson-like Hamiltonian describes the excitations of the relevant occupied local orbital electrons into the conduction bands, each described by an anisotropic effective mass with corresponding Landau orbits and an anisotropic spin ${\bf g}$ tensor. Local orbital electron correlation effects are included using the mean-field decoupling procedure of Lacroix. The metallic contributions to the Knight shift resonance frequency and linewidth shifts are evaluated to leading orders in the hyperfine and Anderson excitation interactions. While respectively proportional to $(B_1/B_0)^2$ and a constant for weak $B_0 > > B_1$, both shifts are shown to depend strongly upon ${\bf B}_0$ when a Landau level is near the Fermi energy.

This thesis seeks to answer the question "how much of the internal tide propagating up Knight Inlet, B.C. is reflected by a right-angled bend ?" The internal tide in Knight Inlet is generated by the interaction of the barotropic tide with a shallow sill seaward of the bend. It then propagates in both directions as a travelling Kelvin wave. The up-inlet propagating wave then encounters the bend, where some of it may be reflected. This question is looked at with both theory (Chapter 2) and observations (Chapter 3). The theoretical study investigates the propagation of a Kelvin wave around a bend in a channel. The solution of the linearised long wave equations is expressed as a truncated series of cross-channel modes in each of three regions. The solution is matched across the two common boundaries by a least squares point matching process. The "rectangular bend" gives unsatisfactory results because of a singularity in the velocity field at the sharp inside corner. However, the "annular bend" gives good results. The bend acts as a diffraction grating, with total transmission for certain bend angles and "lobes" of high reflection for intermediate angles. Bends to the left give rise to the same reflection as bends to the right of the same angle, even if the incident Kelvin wave has a small cross-channel decay scale. For the parameters corresponding to the M₂ internal tide in Knight Inlet, the energy flux reflection coefficient is very small, much less than 1%. The method of solution breaks down inexplicably for diurnal tides. The observational study is based upon 2⅓ months of cyclesonde current meter data from four stations in Knight Inlet taken during the summers of 1981 and 1983. The vertical profiles of amplitude and phase of the M₂ constituent of longitudinal velocity and density fluctuations are found to be the same from month to month at a particular station, but different from station to station. These complex amplitude profiles are decomposed into a truncated series of normal modes for waves propagating both up-inlet and down-inlet. The phase speeds and zero-crossing depths of the normal modes do not agree with those calculated by Farmer and Smith (1980a) using 1977 data. Two simple models of the stratification are used to explain the differences in the normal modes in terms of differences in the Brunt-Väisälä frequency profile used to calculate them. At the two stations up-inlet of the sill, acceptable fits can be obtained using only two up-inlet propagating waves, indicating that the data are compatible with the low reflection found in the theoretical study. When down-inlet waves are included in the fit, their amplitudes are found to be small, although care must be taken to avoid trying to fit too many modes since some of them are highly correlated in the depth range for which data are available. At the two stations seaward of the sill, the up-inlet energy flux is of the same order of magnitude as the down-inlet flux, indicating a second source of internal tide seaward of those two stations. The results indicate that only 30-50% of the power removed from the barotropic tide is being fed into the internal tide in the summer. This conclusion is at variance with that of Stacey (1985), whose model shows that most of the power lost from the barotropic tide is being fed into the internal tide. A consistent interpretation of these results is that most of the power lost from the barotropic tide initially goes into the internal tide, but that 50-70% of it is rapidly dissipated through turbulence within a couple of kilometers of the sill. The low frequency component of the velocity signals from the cyclesonde data is also presented (Chapter 4), with a brief analysis . The monthly averaged residual velocity profiles are also found to be fairly repeatable from month to month at a particular station, but different from station to station. These profiles could be useful in validating general circulation models. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

In the first part of this thesis I investigated the surface layer dynamics of Knight Inlet to see which of the governing forces: inertial accelerations, pressure gradient, or stress, dominated the momentum balance for a steady two-layer flow. I estimated the inertial terms and pressure term in the momentum equation, which had been integrated over the surface layer, from conductivity, temperature, and depth data measured in Knight Inlet in the springs of 1986 and 1987. I solved for the coefficient of interfacial friction, k, so that an estimate of the interfacial stress, Tί = pkΔu², could be made. I obtained the idea of the Knight Inlet analysis from an earlier attempt I had made at resolving the balance of forces in the Fraser River plume. I found an estimate of the friction coefficient at the interface for the plume; k = 1.55 x 10¯⁴, which was much smaller than an assumed value used by Cordes, et al. (1980). The results of the Knight Inlet study showed that within the inlet (inside the sill), the pressure gradient, and the stress dominated the balance for high runoff conditions. Estimates of the coefficient of friction were on the order of 10⁻² and 10⁻³. The depth of the interface appeared to be constant inland of the sill. The second part of this thesis was a qualitative study of fine structure in Knight Inlet. I processed the CTD data measured in 1986 and 1987 to find the first differences of temperature and salinity. I used the profiles of ΔT and ΔS to describe features present in the upper and lower water. Later, data that had been measured with a special microprofiler at the same time as the 1987 CTD data were sampled, were compared to the CTD data. For this comparison, I studied profiles of [formula omitted] (calculated as a centered first difference), and the log of the variance of [formula omitted]. Results of this study were that the upper water (< 30 m) appeared more highly active than the deeper water (> 30 m), especially at the head of the inlet, at the sill, and in the region of the interface. The deeper water contained fluctuations of temperature and salinity that were concentrated in patches which were several meters thick. For the year, 1987, the microprofiler revealed the existence of temperature variations that were more significant than I had originally judged from the profiles of ΔT and ΔS. Values of the variance of the temperature gradient, [formula omitted] in some areas of the deeper water were almost as large as values in the upper water. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

No description available.

Integrating chivalric romance narrative with complicated instances of pre-modern exchange, Sir Gawain and the Green Knight reveals the binding power of pledging one?s trawþe and the transformative power of exchanged objects in a gift economy. By reading the Exchange of Blows and the Exchange of Winnings according to the social demands of a gift economy and of a pledged trawþe, this thesis delineates the nature of Gawain?s failure to keep his word to his host. I offer my analysis of gift theory to suggest how the poem reveals the tensions between chivalric pledges of loyalty and nascent capitalist exchanges. R. A. Shoaf demonstrates the presence in the text of an emerging commercial economy, claiming the poem ?involves the transformation of Gawain?into a consumer and?into a merchant? (3-4). While Gawain behaves as a nascent capitalist, as evident by his passive reception of the exchanged items and his lack of generosity, the other residents of Hautdesert do not. The workings of gift exchange were first postulated by social anthropologists: Marcel Mauss focused on reciprocity, while Branislaw Malinowski, and later, Annette Weiner, argued that gift exchanges operate in a circular system, with repayment not necessarily directed toward the original donor. The exchanges between Bertilak and Gawain show elements of the requisite reciprocity of Mauss? formulation, yet the presence of Morgan le Fey and Lady Bertilak complicates the exchanges and suggests an economy of circularity. While Geraldine Heng and Sheila Fischer have argued that the women of the text exhibit agency?Morgan initiates the Exchange of Blows and Lady Bertilak gives kisses and the girdle?this project argues that it is the performative presence of the trawþe between Gawain and Bertilak that creates a male bond, ultimately denying the women authority. The trawþe circumscribes Morgan?s control and allows for the exchange of Lady Bertilak as an object. Richard Firth Green addresses the late medieval tensions in the semantic definitions of ?truth,? arguing that ?in an oral society the precise words of the oath?bind the speaker and listener by virtue of an inherent performative power? (60). While Gawain functions as a self-interested capitalist, keeping the girdle for its value to save his life, the chivalric trawþe ensures that failure to adhere to the terms of the agreement results not only in contractual liability but knightly disgrace. Gawain?s failure to reciprocate the gift leads to his dishonor, for the medieval gift that is not reciprocated ?would make the recipient dependent on the donor,? endangering ?his honour, freedom and even his life? (Gurevich 180). In medieval gift systems the values of exchanged objects are determined not only by their function within a competitive game about prestige and power, but also by their identification with the donors themselves. Annette Weiner?s articulation of the inalienability of certain objects?the possibility that some objects are ?kept? despite apparent exchange?is useful in explaining the significance of the girdle in Gawain?s failure. Weiner explains that what ?makes a possession inalienable is its exclusive and cumulative identity with a particular series of owners through time? (Weiner 33). The girdle presents just such an inalienable possession; Bertilak ?keeps? the girdle despite Gawain?s physical possession of it. Gawain remains indebted to his adversary, and although he is released from his trawþe, he will continue to wear the girdle as a sign of his failure and the bond with the Green Knight. Ultimately, the court of Camelot assumes the sign of the green girdle, a subtle warning by the Gawain-poet of the inevitable spread of un-trawþe in prioritizing the values of self-interested capitalist exchange.