The problem of classifying variations according to technical plan and stylistic treatment centers on the determination of which elements of the theme (melody, harmonic scheme, structure) are retained in each component variation and the compositional methods (elaboration, embellishment, motivic fragmentation) which are applied.

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published_or_final_version / Physics / Master / Master of Philosophy

Molecular nitrogen is a highly abundant element in the atmosphere; it is stable and not very reactive. Anthropogenic activities have caused greater concentrations of nitrogen-containing compounds that are highly reactive and ultimately toxic. Reactive nitrogen concentrations have become a growing concern on the South African Highveld, with satellite images indicating very high nitrogen dioxide concentrations in the region. This study investigates the nitrogen budget on the Highveld through the analysis of the nitrogen species emitted into the atmosphere on a temporal scale as well as the atmospheric conversion, transport and removal of these species. Data was collected at Elandsfontein monitoring site, which is centrally located on the industrialised Highveld. The formation and interaction of nitric oxide (NO), nitrogen dioxide (NO2), and nitrate (NO3) are a major focus in the study. NOx concentrations are higher in winter (6.5 to 8.5 μg.m-3) as a result of stable atmospheric conditions. NO3 concentrations also peak during winter (3.5 to 5.5 μg.m-3), with a distinct biomass burning peak during July and August. Diurnally, NOx concentrations indicate a tall-stack industrial source, with concentrations peaking at midday. NO3 concentrations are higher at night and lower during the day, as during the day the NO3 radical is rapidly photolysed and nitrates cannot be produced. Case studies indicate that the conversion rate of NO to NO2 is highly variable as a result of varying atmospheric factors. These rates range from 11% to 59% per hour. Rates of dry deposition of NO, NO2 and NO3 are generally higher during winter as a result of higher concentrations and increased atmospheric stability, which prevents transport out of the region. Nitrogen is predominantly deposited as NO2 throughout the year, except during spring when NO3 deposition dominates. The total amount of nitrogen deposited to the Mpumalanga Highveld region is in the range of 6.7 to 13.1 kg ha-1 yr-1, which is well below the stipulated critical load value. Such deposition therefore does not pose significant threats to the natural environment on the Highveld. Between 4% and 14% of the total emitted nitrogen on the Highveld is deposited to the surface via wet and dry deposition. The remainder stays in the atmosphere and is advected out of the region.

This project presents the homogenization analysis for a static contact problem with slip dependent friction between an elastic body and a rigid foundation. The homogenization for the static eigenvalue problem associated to this model is studied. We prove that the eigenvalues are of order epsilon. We obtain the limit problem for the contact model. The analysis is carried out by using the Gamma-convergence theory.

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Aaron Copland has been in the forefront of the American musical scene since the 1920s. He has been called an "American composer" for his ability to formulate the essence of American folk music into a wide variety of mediums. The variety and scope of his compositions encompass a diverse array of styles and techniques. From the jazz influenced works that dominated his early period to the works for Hollywood films, from the chamber music that was directly influenced by his Jewish background to the partial acceptance of serial technique, Copland has managed to delve equally into all these styles. Yet, one could arguably rank his works for the stage as his most popular and generally most successful compositions of his career. The extent to which the American public has accepted these works as being "folk" is a case for the genius and adaptability of Copland's talent. Although works like Appalachian Spring, Rodeo, and Lincoln Portrait command the attention of the general public, of whom Aaron Copland was constantly aware, there are works for the piano that deserve and demand close study by pianists. One such work is the Piano Variations. Written in 1930, it has been acknowledged as a twentieth century masterpiece in publications for piano and piano literature as well as by pianists since its premiere in 1931. It is a brutal and sparse work that encompasses a quasi-serial technique in which the motto of four notes transforms itself through the course of twenty variations and a coda. The demands of learning a work such as this can be overwhelming for the pianist not accustomed to the rigors of a non-diatonic piece. However, a careful analysis precipitated by specific questions directed not only at learning the piece but also with the goal of performance in mind, can shape the interpretational issues that will eventually face the pianist. The questions that I pose are directly pulled from Michael Remson's article, "Copland's Piano Variations: A Forgotten Masterpiece." Although it is considered by this writer as an introduction to the technique of serialism, largely because of the classical practices among which are tonal center, period structure and interruptions of the motto, Copland's Piano Variations is a classic example of a twentieth century work that will be heard as avant-garde and studied in the style of late Romanticism.

The Khan Variations is the first work for solo marimba by Argentinean composer Alejandro Viñao (b.1951). Since publication in 2001, Khan Variations has been performed at many international percussion festivals and is often a repertoire choice for performers in the final round of numerous marimba competitions. This thesis and accompanying lecture recital provide a supplemental guide to Alejandro Viñao's Khan Variations, focusing on analytical and structural theory, as well as performance practice, thus filling the void of information on this piece in the percussion community. Khan Variations was jointly commissioned by twelve of the world's prominent marimba performers and educators, including: Michael Burritt, Jack Van Geem, William Moersch, Robert Van Sice, and Nancy Zeltsman. The project organizer of the Khan Variations commission was Nancy Zeltsman, Chair of the Percussion Department at the Boston Conservatory and a leader in the field of commissioning new marimba works. Utilizing William Moersch's organization New Music Marimba as the financial conduit, Zeltsman and her group issued this commission in 1999. Alejandro Viñao studied composition with the Russian composer Jacobo Ficher in Buenos Aires, and Viñao later went on to complete his doctorate in composition from City University in London. His works span the genres of opera, choir, orchestra, electroacoustic chamber music, and more than twenty film scores. Viñao's composing style is influenced by Mexican-American composer Conlon Nancarrow and Islamic religious music known as Qawwali. Alejandro Viñao's works typically contain complex rhythmic structures and use rhythm as the main element for musical form and development. The impetus for this thesis is to provide a musical analysis and performance guide for The Khan Variations by Alejandro Viñao. This thesis also illuminates the significance of the joint commission led by Nancy Zeltsman, and highlights the influences and inspirations of Alejandro Viñao as a rising composer of international renown.

Forest fires occur frequently in the boreal forest of North America and greatly affect vegetation dynamics, biogeochemical cycles and resident human populations. Estimates of the frequency of boreal forest fires would be useful for understanding boreal ecosystems and managing the affects of fires on human populations. The objectives of this work were to investigate relations between fire frequency and climate change, vegetation)n type and waterbreaks in Wood Buffalo National Park (WBNP), located in northern Alberta. To address these objectives, four hypotheses were tested: 1) tree ring-width records from the boreal forest can provide a proxy climate record; 2) annual area burned in the boreal forest varies in response to climate changes; 3) boreal fores: fire frequency varies with differences in forest type and the proximity to waterbreaks and 4) fossil pollen and macroscopic charcoal records from massive lake sediments can provide meaningful estimates of local fire frequency. The first hypothesis was tested by constructing tree ring chronologies from 3 white spruce and two jack pine sites in WBNP. All five chronologies were significantly positively correlated with June precipitation in the growth year or the previous year, and were significantly negatively correlated with historical records of fire weather and annual area burned. The second hypothesis was tested by analyzing historical records of annual area burned and climate. and tree ring records of fire history and climate. Annual area burned was significantly negatively correlated with seasonal means of fire weather indices. The time since last fire was estimated using tree ring records from 166 sites located throughout WBNP. These records exhibited decadal and centennial scale variations in fire frequency. Comparisons with tree ring other proxy climate records suggest that the~e variations are related to climatic changes. The third hypothesis was tested using survival analysis of the time since last fire records, disaggregated by dominant vegetation and the mean distance to waterbreaks. Sites dominated by jack pine (Pinus banksiana) and aspen (Populus tremuloides) exhibited significantly higher fire frequencies than did sites dominated by black spruce (Picea mariana) or white spruce (Picea glauca). Fire frequency increased with increased mean distance to waterbreaks. The fourth hypothesis was tested by analyzing fossil pollen and charcoal records from two lakes at -5 year resolution for 600 years. I compared their fire history records with local tree ring records of fire, and their mean fire intervals with regional fire frequency estimates for sites with similar vegetation and mean distances to waterbreaks. One lake exhibited a meaningful fire frequency estimate and the other lake did not. The poor fire frequency estimate was related to high sediment mixing and the lack of homogenous vegetation around the lake. The results indicate that: 1) area burned and fire frequency in the boreal forest of northern Alberta varies temporally at the annual, decadal and centennial scales; 2) fire frequency varies spatially in relation to vegetation type and mean waterbreak distance; and 3) lakes with massive sediments can provide meaningful estimates of local fire frequency. / Thesis / Doctor of Philosophy (PhD)

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