Computational Aspects of the Calculation of Isometry Groups in General Relativity

We describe the ideas behind the package 'isometry', implemented in Maple to calculate isometry groups of dimensions 2, 3 and 4 in General Relativity. The package extends the functionality of previous programs written to perform invariant classification of space-times in General Relativity. Programming solutions used to surmount problems encountered with the calculation of eigenvectors and the determination of the signs of expressions are described. We also show how the package can be used to find the Killing vectors of a space-time.

Ensaio sobre o fluxo de Ricci e os buracos negros: fundamentação e estudo computacional

Pós-graduação em Ciência da Computação - IBILCE

Aplicativo computacional para utilização de componentes principais em experimentação agronômica

Pós-graduação em Agronomia (Energia na Agricultura) - FCA

Compreensões de conceitos de cálculo diferencial no primeiro ano de matemática: uma abordagem integrando oralidade, escrita e informática

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Abordagem geométrica: possibilidades para o ensino e aprendizagem de Introdução às Equações Diferenciais Ordinárias

Pós-graduação em Educação Matemática - IGCE

Aprendizagem de eletromagnetismo via programação e computação simbólica

Relatamos a experiência de utilizar programação em Maple como ferramenta de aprendizagem do estudante num curso básico de teoria eletromagnética. Acreditamos que este relato possa ser útil a quem desejar utilizar o computador como instrumento pedagógico no ensino de Física.

Aplicação da computação simbólica na resolução de problemas de condução de calor em cilindros vazados com condições de contorno convectivas

Pós-graduação em Engenharia Mecânica - FEG

Limit cycles of cubic polynomial differential systems with rational first integrals of degree 2

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Algorithmische Methoden zur Berechnung von Vierbeinfunktionen

Die vorliegende Arbeit beschäftigt sich mit derAutomatisierung von Berechnungen virtuellerStrahlungskorrekturen in perturbativen Quantenfeldtheorien.Die Berücksichtigung solcher Korrekturen aufMehrschleifen-Ebene in der Störungsreihenentwicklung istheute unabdingbar, um mit der wachsenden Präzisionexperimenteller Resultate Schritt zu halten. Im allgemeinen kinematischen Fall können heute nur dieEinschleifen-Korrekturen als theoretisch gelöst angesehenwerden -- für höhere Ordnungen liegen nur Teilergebnissevor. In Mainz sind in den letzten Jahren einige neuartigeMethoden zur Integration von Zweischleifen-Feynmandiagrammenentwickelt und im xloops-Paket in algorithmischer Formteilweise erfolgreich implementiert worden. Die verwendetenVerfahren sind eine Kombination exakter symbolischerRechenmethoden mit numerischen. DieZweischleifen-Vierbeinfunktionen stellen in diesem Rahmenein neues Kapitel dar, das durch seine große Anzahl vonfreien kinematischen Parametern einerseits leichtunüberschaubar wird und andererseits auch auf symbolischerEbene die bisherigen Anforderungen übersteigt. Sie sind ausexperimenteller Sicht aber für manche Streuprozesse vongroßem Interesse. In dieser Arbeit wurde, basierend auf einer Idee von DirkKreimer, ein Verfahren untersucht, welches die skalarenVierbeinfunktionen auf Zweischleifen-Niveau ganz ohneRandbedingungen an den Parameterraum zu integrierenversucht. Die Struktur der nach vier Residuenintegrationenauftretenden Terme konnte dabei weitgehend geklärt und dieKomplexität der auftretenden Ausdrücke soweit verkleinertwerden, dass sie von heutigen Rechnern darstellbar sind.Allerdings ist man noch nicht bei einer vollständigautomatisierten Implementierung angelangt. All dies ist dasThema von Kapitel 2. Die Weiterentwicklung von xloops über Zweibeinfunktionenhinaus erschien aus vielfältigen Gründen allerdings nichtmehr sinnvoll. Im Rahmen dieser Arbeit wurde daher einradikaler Bruch vollzogen und zusammen mit C. Bauer und A.Frink eine Programmbibliothek entworfen, die als Vehikel fürsymbolische Manipulationen dient und es uns ermöglicht,übliche symbolische Sprachen wie Maple durch C++ zuersetzen. Im dritten Kapitel wird auf die Gründeeingegangen, warum diese Umstellung sinnvoll ist, und dabeidie Bibliothek GiNaC vorgestellt. Im vierten Kapitel werdenDetails der Implementierung dann im Einzelnen vorgestelltund im fünften wird sie auf ihre Praxistauglichkeituntersucht. Anhang A bietet eine Übersicht über dieverwendeten Hilfsmittel komplexer Analysis und Anhang Bbeschreibt ein bewährtes numerisches Instrument.

Abandoned Coal Mine Drainage and Its Remediation: Impacts on Stream Ecosystem Structure and Function

The effects of abandoned mine drainage (AMD) on streams and responses to remediation efforts were studied using three streams (AMD-impacted, remediated, reference) in both the anthracite and the bituminous coal mining regions of Pennsylvania (USA). Response variables included ecosystem function as well as water chemistry and macroinvertebrate community composition. The bituminous AMD stream was extremely acidic with high dissolved metals concentrations, a prolific mid-summer growth of the filamentous alga, Mougeotia, and .10-fold more chlorophyll than the reference stream. The anthracite AMD stream had a higher pH, substrata coated with iron hydroxide(s), and negligible chlorophyll. Macroinvertebrate communities in the AMD streams were different from the reference streams, the remediated streams, and each other. Relative to the reference stream, the AMD stream(s) had (1) greater gross primary productivity (GPP) in the bituminous region and undetectable GPP in the anthracite region, (2) greater ecosystem respiration in both regions, (3) greatly reduced ammonium uptake and nitrification in both regions, (4) lower nitrate uptake in the bituminous (but not the anthracite) region, (5) more rapid phosphorus removal from the water column in both regions, (6) activities of phosphorus-acquiring, nitrogenacquiring, and hydrolytic-carbon-acquiring enzymes that indicated extreme phosphorus limitation in both regions, and (7) slower oak and maple leaf decomposition in the bituminous region and slower oak decomposition in the anthracite region. Remediation brought chlorophyll concentrations and GPP nearer to values for respective reference streams, depressed ecosystem respiration, restored ammonium uptake, and partially restored nitrification in the bituminous (but not the anthracite) region, reduced nitrate uptake to an undetectable level, restored phosphorus uptake to near normal rates, and brought enzyme activities more in line with the reference stream in the bituminous (but not the anthracite) region. Denitrification was not detected in any stream. Water chemistry and macroinvertebrate community structure analyses capture the impact of AMD at the local reach scale, but functional measures revealed that AMD has ramifications that can cascade to downstream reaches and perhaps to receiving estuaries.

A VEGETATION RECONSTRUCTION OF UNION COUNTY, PENNSYLVANIA DURING THE EARLY HISTORICAL PERIOD (1755-1855)

This thesis assesses relationships between vegetation and topography and the impact of human tree-cutting on the vegetation of Union County during the early historical era (1755-1855). I use early warrant maps and forestry maps from the Pennsylvania historical archives and a warrantee map from the Union County courthouse depicting the distribution of witness trees and non-tree surveyed markers (posts and stones) in early European settlement land surveys to reconstruct the vegetation and compare vegetation by broad scale (mountains and valleys) and local scale (topographic classes with mountains and valleys) topography. I calculated marker density based on 2 km x 2 km grid cells to assess tree-cutting impacts. Valleys were mostly forests dominated by white oak (Quercus alba) with abundant hickory (Carya spp.), pine (Pinus spp.), and black oak (Quercus velutina), while pine dominated what were mostly pine-oak forests in the mountains. Within the valleys, pine was strongly associated with hilltops, eastern hemlock (Tsuga canadensis) was abundant on north slopes, hickory was associated with south slopes, and riparian zones had high frequencies of ash (Fraxinus spp.) and hickory. In the mountains, white oak was infrequent on south slopes, chestnut (Castanea dentata) was more abundant on south slopes and ridgetops than north slopes and mountain coves, and white oak and maple (Acer spp.) were common in riparian zones. Marker density analysis suggests that trees were still common over most of the landscape by 1855. The findings suggest there were large differences in vegetation between valleys and mountains due in part to differences in elevation, and vegetation differed more by topographic classes in the valleys than in the mountains. Possible areas of tree-cutting were evenly distributed by topographic classes, suggesting Europeans settlers were clearing land and harvesting timber in most areas of Union County.

Effects of elevated atmospheric CO2 and O3 on wood density, antomical proerties and decomposition of Northern Hardwoods

Anthropogenic activities continue to drive atmospheric CO2 and O3 concentrations to levels higher than during the pre-industrial era. Accumulating evidence indicates that both elevated CO2 and elevated O3 could modify the quantity and biochemistry of woody plant biomass. Anatomical properties of woody plants are largely influenced by the activity of the cambium and the growth characteristics of wood cells, which are in turn influenced by a range of environmental factors. Hence, alterations in the concentrations of atmospheric CO2 and / or O3 could also impact wood anatomical properties. Many fungi derive their metabolic resources for growth from plant litter, including woody tissue, and therefore modifications in the quantity, biochemistry and anatomical properties of woody plants in response to elevated CO2 and / or O3 could impact the community of wood-decaying fungi and rates of wood decomposition. Consequently carbon and nutrient cycling and productivity of terrestrial ecosystem could also be impacted. Alterations in wood structure and biochemistry of woody plants could also impact wood density and subsequently impact wood quality. This dissertation examined the long term effects of elevated CO2 and / or O3 on wood anatomical properties, wood density, wood-decaying fungi and wood decomposition of northern hardwood tree species at the Aspen Free-Air CO2 and O3 Enrichment (Aspen FACE) project, near Rhinelander, WI, USA. Anatomical properties of wood varied significantly with species and aspen genotypes and radial position within the stem. Elevated CO2 did not have significant effects on wood anatomical properties in trembling aspen, paper birch or sugar maple, except for marginally increasing (P < 0.1) the number of vessels per square millimeter. Elevated O3 marginally or significantly altered vessel lumen diameter, cell wall area and vessel lumen area proportions depending on species and radial position. In line with the modifications in the anatomical properties, elevated CO2 and O3, alone, significantly modified wood density but effects were species and / or genotype specific. However, the effects of elevated CO2 and O3, alone, on wood anatomical properties and density were ameliorated when in combination. Wood species had a much greater impact on the wood-decaying fungal community and initial wood decomposition rate than did growth or decomposition of wood in elevated CO2 and / or O3. Polyporales, Agaricales, and Russulales were the dominant orders of fungi isolated. Based on the current results, future higher levels of CO2 and O3 may have moderate effects on wood quality of northern hardwoods, but for utilization purposes these may not be considered significant. However, wood-decaying fungal community composition and decomposition of northern hardwoods may be altered via shifts in species and / or genotype composition under future higher levels of CO2 and O3.

Patch selection by wintering white-tailed deer : consequences for eastern hemlock regeneration at local and landscape scales

Tsuga canadensis (eastern hemlock) is a highly shade-tolerant, late-successional, and long-lived conifer species found throughout eastern North America. It is most often found in pure or nearly pure stands, because highly acidic and nutrient poor forest floor conditions are thought to favor T. canadensis regeneration while simultaneously limiting the establishment of some hardwood species with greater nutrient requirements. Once a common species, T. canadensis is currently experiencing widescale declines across its range. The hemlock woolly adelgid (Adelges tsugae) is decimating the population across its eastern distribution. Across the Upper Great Lakes region, where the adelgid is currently being held at bay by cold winter temperatures, T. canadensis has been experiencing failures in regeneration attributed, in part, to herbivory by white-tailed deer (Odocoileus virginianus). Deer utilize T. canadensis stands as winter habitat in areas of high snow depth. Tsuga canadensis, once a major component of these forests, currently exists at just a fraction of its pre-settlement abundance due to historic logging and contemporary forest management practices, and what remains is found in small remnant patches surrounded by second- and third-growth deciduous forests. The deer population across the region, however, is likely double that of pre-European settlement times. In this dissertation I explore the relationship between white-tailed deer use of T. canadensis as winter habitat and the effect this use is having on regeneration and forest succession. For this research I quantified stand composition and structure and abiotic variables of elevation and snow depth in 39 randomly selected T. canadensis stands from across the western Upper Peninsula of Michigan. I also quantified composition and the configuration of the landscapes surrounding these stands. I measured relative deer use of T. canadensis stands as pellet group piles deposited in each stand during each of three consecutive winters, 2005-06, 2006-07, and 2007-08. The results of this research suggest that deer use of T. canadensis stands as winter habitat is influenced primarily by snow depth, elevation, and the composition and configuration of the greater landscapes surrounding these stands. Specifically, stands with more heterogeneous landscapes surrounding them (i.e., a patchy mosaic of conifer, deciduous, and open cover) had higher relative deer use than stands surrounded by homogenous deciduous forest cover. Additionally, the intensity of use and the number of stands used was greater in years with higher average snow depth. Tsuga canadensis regeneration in these stands was negatively associated with deer use and Acer saccharum (sugar maple) basal area. Of the 39 stands, 17 and 22 stands had no T. canadensis regeneration in small and large sapling categories, respectively. Acer saccharum was the most common understory tree species, and the importance of A. saccharum in the understory (stems < 10 cm dbh) of the stands was positively associated with overstory A. saccharum dominance. Tsuga canadensis establishment was associated with high-decay coarse woody debris and moss, and deciduous leaf litter inputs in these stands may be limiting access to these important microsites. Furthermore, A. saccharum is more tolerant to the effects of deer herbivory than T. canadensis, giving A. saccharum a competitive advantage in stands being utilized as winter habitat by deer. My research suggests that limited microsite availability, in conjunction with deer herbivory, may be leading to an erosion in T. canadensis patch stability and an altered successional trajectory toward one of A. saccharum dominance, an alternately stable climax species.

Effects of conifer sawdust, hardwood sawdust, and peat on soil properties and a barefoot conifer seedling development

Organic amendments are commonly used to improve tree nursery soil conditions for increased seedling growth. However, few studies compare organic amendments effects on soil conditions, and fewer compare subsequent effects on seedling growth. The effects of three organic amendments on soil properties and seedling growth were investigated at the USDA Forest Service J.W. Toumey Nursery in Watersmeet, MI. Pine sawdust (red pine, Pinus resinosa), hardwood sawdust (maple, Acer spp. and aspen, Populus spp.), and peat were individually incorporated into a loamy sand nursery soil in August, 2006, and soil properties were sampled periodically for the next 14 months. Jack (Pinus banksiana), red, and white pine (Pinus strobus) were sown into test plots in June, 2007 and sampled for growth responses at the end of the growing season. It is hypothesized; pine sawdust and peat can be used as a satisfactory soil amendment to improve soil conditions and produce high quality seedlings, when compared to hardwood sawdust in bareroot nursery soils. This study has the potential to reduce nursery costs while broadening soil amendment options. The addition of peat and pine sawdust increased soil organic matter above control soil conditions after 14 months. However, hardwood sawdust-amended soils did not differ from control soils after same time period. High N concentrations in peat increased total soil N over the other treatments. Similarly, the addition of peat increased soil matric potential and available water over all other treatments. Seedlings grew tallest with the largest stem diameter, and had the largest biomass in both control soil and soil amended with peat, compared to either sawdust treatment. Seedlings grown in peat-amended soils had higher N concentrations than those grown in soils treated with pine sawdust, though neither was different from seedlings grown in control or hardwood sawdust-amended soils. Overall, peat is a well suited organic soil amendment for the enhancement of soil properties, but no amendments were able to increase one-year seedling growth over control soils.

The influence of concurrent disturbances on plant community dynamics in northern hemlock-hardwood forests

Throughout the Upper Great Lakes region, alterations to historic disturbance regimes have influenced plant community dynamics in hemlock-hardwood forests. Several important mesic forest species, eastern hemlock (Tsuga canadensis), yellow birch (Betula alleghaniensis), eastern white pine (Pinus strobus), and Canada yew (Taxus canadensis), are in decline due to exploitive logging practices used at the turn of the 20th century and the wave of intense fires that followed. Continued regeneration and recruitment failure is attributed to contemporary forest management practices and overbrowsing by white-tailed deer (Odocoileus virginianus). Therefore, I examined the influence of two concurrent disturbances, overstory removal and herbivory, on plant community dynamics in two hemlock-hardwood forests. I measured the post-disturbance regeneration response (herbaceous and woody species) inside and outside of deer exclosures in 20 artificial canopy gaps (50 – 450 m2) and monitored survival and growth for hundreds of planted seedlings. The results of this research show that interacting disturbances can play a large role in shaping plant community composition and structure in hemlock-hardwood forests. White-tailed deer herbivory homogenized the post-disturbance plant communities across the experimental gradient of gap areas, essentially making species compositions in small gaps “look like” those in large gaps. Deer browsing also influenced probability of survival for planted Canada yew cuttings; all else being equal an individual was nearly seven times more likely to survive if protected from herbivory (P < 0.001). In contrast, the ability of sugar maple (Acer saccharum) to persist under high levels of herbivory and respond rapidly to overstory release appears to be related to the presence of stem layering(i.e., portions of below-ground prostrate stem). Layering occurred in 52% of excavated saplings (n = 100) and was significantly associated with increased post-disturbance height growth. Understory light was also important to planted seedling establishment and height growth. Higher levels of direct under-canopy light negatively impacted survival for shade-tolerant hemlock and Canada yew, while an increase in diffuse light was linked to a higher probability of survival for yellow birch and height growth for hemlock and Canada yew. Increases in white pine height growth were also significantly associated with a decrease in canopy cover.