In this section, we will consider two methods for computing an eigenvector and in addition the associated eigenvalue of a matrix A.

Huanglongbing (HLB) é considerada a doença mais devastadora dos citros. O HLB é causado pela bactéria \'Candidatus Liberibacter spp.\' e transmitido pelo inseto vetor, o psilídeo Diaphorina citri. Não existem ainda métodos curativos para essa doença, ou variedades resistentes, e seu manejo é baseado na aquisição de mudas sadias, monitoramento e controle químico frequente do vetor e inspeção e erradicação de plantas sintomáticas. Devido à dificuldade de manejo da doença, muitos produtores acabam por abandonar a atividade citrícola. O objetivo desse trabalho foi determinar o modelo de gradiente de dispersão da doença que melhor se ajusta aos dados de proporção de plantas sintomáticas erradicadas, a fim de propor medidas mais eficientes de manejo. Para isso, foram ajustados os modelos potência inversa e exponencial negativo à dados de proporção de plantas sintomáticas erradicadas em relação a borda dos lotes, para 21 lotes retangulares de pomares comerciais de laranja doce. Foram utilizadas duas abordagens para a análise dos gradientes, denominadas de \"concêntrica\" e \"direcional\". Para ambas utilizou-se a proporção de plantas erradicadas para faixas de 20 em 20 metros de distância em relação a todas as bordas do pomar para a primeira (concêntrica), e em relação a cada borda dos lotes (direcional). Em ambas as abordagens analisadas, houve melhor ajuste do modelo potência inversa. No entanto, a abordagem concêntrica obteve 15 ajustes de um total de 21 lotes, enquanto que para a abordagem direcional, houve ajuste do modelo para apenas seis lotes. Esses resultados demonstram que há um gradiente de doença da borda para o interior dos lotes, e que ocorre um influxo de insetos vetores de todas as direções. Além disso, o ajuste do modelo da potência inversa sugere que os lotes sofreram influência de fontes de inóculo externas, ou seja, psilídeos bacterilíferos pousam preferencialmente na borda dos pomares e uma pequena parte adentra o interior do lote levando a doença. O gradiente de dispersão em relação da borda dos lotes é consequência da disseminação primária, a qual só poderá ser evitada com o manejo regional, sendo indispensável para um manejo eficiente do HLB a curto e médio prazo.Huanglongbing (HLB) é considerada a doença mais devastadora dos citros. O HLB é causado pela bactéria \'Candidatus Liberibacter spp.\' e transmitido pelo inseto vetor, o psilídeo Diaphorina citri. Não existem ainda métodos curativos para essa doença, ou variedades resistentes, e seu manejo é baseado na aquisição de mudas sadias, monitoramento e controle químico frequente do vetor e inspeção e erradicação de plantas sintomáticas. Devido à dificuldade de manejo da doença, muitos produtores acabam por abandonar a atividade citrícola. O objetivo desse trabalho foi determinar o modelo de gradiente de dispersão da doença que melhor se ajusta aos dados de proporção de plantas sintomáticas erradicadas, a fim de propor medidas mais eficientes de manejo. Para isso, foram ajustados os modelos potência inversa e exponencial negativo à dados de proporção de plantas sintomáticas erradicadas em relação a borda dos lotes, para 21 lotes retangulares de pomares comerciais de laranja doce. Foram utilizadas duas abordagens para a análise dos gradientes, denominadas de \"concêntrica\" e \"direcional\". Para ambas utilizou-se a proporção de plantas erradicadas para faixas de 20 em 20 metros de distância em relação a todas as bordas do pomar para a primeira (concêntrica), e em relação a cada borda dos lotes (direcional). Em ambas as abordagens analisadas, houve melhor ajuste do modelo potência inversa. No entanto, a abordagem concêntrica obteve 15 ajustes de um total de 21 lotes, enquanto que para a abordagem direcional, houve ajuste do modelo para apenas seis lotes. Esses resultados demonstram que há um gradiente de doença da borda para o interior dos lotes, e que ocorre um influxo de insetos vetores de todas as direções. Além disso, o ajuste do modelo da potência inversa sugere que os lotes sofreram influência de fontes de inóculo externas, ou seja, psilídeos bacterilíferos pousam preferencialmente na borda dos pomares e uma pequena parte adentra o interior do lote levando a doença. O gradiente de dispersão em relação da borda dos lotes é consequência da disseminação primária, a qual só poderá ser evitada com o manejo regional, sendo indispensável para um manejo eficiente do HLB a curto e médio prazo. / Huanglongbing (HLB) is considered the most devastating disease of citrus. HLB is caused by the bacterium \'Candidatus Liberibacter spp.\' and transmitted by the insect vector, the psyllid Diaphorina citri. There are no curative methods for this disease, or resistant varieties, and its management is based on the acquisition of healthy seedlings, monitoring and frequent chemical control of the vector and inspection and eradication of symptomatic plants. Due to the difficulty of managing the disease, many producers end up abandoning citrus activity. The objective of this work was to determine the disease dispersion gradient model that best fits the proportion of symptomatic eradicated plants, in order to propose more efficient management measures. For this, inverse power and negative exponential models were adjusted to the proportion of symptomatic plants eradicated in relation to batch border for 21 rectangular plots of commercial sweet orange orchards. Two approaches were used for the analysis of gradients, of \"concentric\" and \"directional\". For both, the proportion of eradicated plants for strips 20-by-20-m apart from all orchard edges was used for the first (concentric), and for each lot border (directional). In both approaches analyzed, there was better fit of the inverse power model. However, the concentric approach obtained 15 adjustments of a total of 21 batches, whereas for the directional approach, there was adjustment of the model to only six batches. These results demonstrate that there is a disease gradient from the edge to the interior of the batches, and that an influx of vector insects from all directions occurs. In addition, the adjustment of the inverse potency model suggests that the lots were influenced by external inoculum sources, that is, bacterial insects preferentially land on the edge of the orchards and a small part enters the interior of the lot leading to illness. The dispersion gradient in relation to the edge of the lots is a consequence of the primary dissemination, which can only be avoided with the regional management, being indispensable for an efficient management of the HLB in the short and medium term.

Invasive exotic species threaten the biodiversity and function of native ecosystems. Existing models, attempting to predict and control successful invaders, often emphasize isolated stages of in their life history and fail to formalize interactions between exotic species and recipient environments. In order to elucidate key mechanisms in the success of select invaders, I investigated the role of dispersal, establishment, proliferation, and persistence in their threat to natural areas. Focusing on Riding Mountain National Park, Manitoba, Canada, I integrated the native climatic range and biological traits of 251 exotic vascular plants reported inside and outside the park. Based on their climatic range in Europe, 155 among 174 exotic plant species absent from the Park were predicted to establish within its boundaries; among these, 40 clonal perennials were considered the highest threat to the Park’s biodiversity. Focusing on smooth brome (Bromus inermis Leyss.), a Eurasian perennial, threatening the structure and function of native prairies throughout the Great Plains, I extended my research to investigate the role of dispersal, establishment, proliferation, and persistence in characterizing its threat to the endemic diversity of northern fescue prairies, protected within Riding Mountain National Park. Patterns of smooth brome invasions were contingent on the type of propagules dispersed. The shallow dispersal gradient of individual florets combined with the steeper gradient of panicles and spikelets suggested that smooth brome is capable of simultaneously invading along dense fronts as well as by establishing isolated foci. While low correlations between the number of dispersed seeds and their recruitment suggested post-dispersal transport, seedling establishment remained contingent on prairie diversity. Seedling biomass increased with declining plant diversity, however, its impact depended on the availability of soil nitrogen. As a result, disturbed areas, preserving the root function of native plants, resisted smooth brome establishment. Even though low nitrogen contributed to a decline in seedling biomass, physiological integration between ramets facilitated their vegetative proliferation in low resource environments. Despite its rapid establishment and proliferation, smooth brome productivity declined at the center of invading clones. Although field and greenhouse observations failed to implicate soilborne pathogens, reasons for the observed decline remain unresolved. My research demonstrates that while Riding Mountain National Park and other natural areas in western Canada will continue to be impacted by exotic plants, integrating key stages in their life history provides an important conceptual framework in predicting their threat to natural areas and prioritizing management. / October 2008

Invasive exotic species threaten the biodiversity and function of native ecosystems. Existing models, attempting to predict and control successful invaders, often emphasize isolated stages of in their life history and fail to formalize interactions between exotic species and recipient environments. In order to elucidate key mechanisms in the success of select invaders, I investigated the role of dispersal, establishment, proliferation, and persistence in their threat to natural areas. Focusing on Riding Mountain National Park, Manitoba, Canada, I integrated the native climatic range and biological traits of 251 exotic vascular plants reported inside and outside the park. Based on their climatic range in Europe, 155 among 174 exotic plant species absent from the Park were predicted to establish within its boundaries; among these, 40 clonal perennials were considered the highest threat to the Park’s biodiversity. Focusing on smooth brome (Bromus inermis Leyss.), a Eurasian perennial, threatening the structure and function of native prairies throughout the Great Plains, I extended my research to investigate the role of dispersal, establishment, proliferation, and persistence in characterizing its threat to the endemic diversity of northern fescue prairies, protected within Riding Mountain National Park. Patterns of smooth brome invasions were contingent on the type of propagules dispersed. The shallow dispersal gradient of individual florets combined with the steeper gradient of panicles and spikelets suggested that smooth brome is capable of simultaneously invading along dense fronts as well as by establishing isolated foci. While low correlations between the number of dispersed seeds and their recruitment suggested post-dispersal transport, seedling establishment remained contingent on prairie diversity. Seedling biomass increased with declining plant diversity, however, its impact depended on the availability of soil nitrogen. As a result, disturbed areas, preserving the root function of native plants, resisted smooth brome establishment. Even though low nitrogen contributed to a decline in seedling biomass, physiological integration between ramets facilitated their vegetative proliferation in low resource environments. Despite its rapid establishment and proliferation, smooth brome productivity declined at the center of invading clones. Although field and greenhouse observations failed to implicate soilborne pathogens, reasons for the observed decline remain unresolved. My research demonstrates that while Riding Mountain National Park and other natural areas in western Canada will continue to be impacted by exotic plants, integrating key stages in their life history provides an important conceptual framework in predicting their threat to natural areas and prioritizing management.

Invasive exotic species threaten the biodiversity and function of native ecosystems. Existing models, attempting to predict and control successful invaders, often emphasize isolated stages of in their life history and fail to formalize interactions between exotic species and recipient environments. In order to elucidate key mechanisms in the success of select invaders, I investigated the role of dispersal, establishment, proliferation, and persistence in their threat to natural areas. Focusing on Riding Mountain National Park, Manitoba, Canada, I integrated the native climatic range and biological traits of 251 exotic vascular plants reported inside and outside the park. Based on their climatic range in Europe, 155 among 174 exotic plant species absent from the Park were predicted to establish within its boundaries; among these, 40 clonal perennials were considered the highest threat to the Park’s biodiversity. Focusing on smooth brome (Bromus inermis Leyss.), a Eurasian perennial, threatening the structure and function of native prairies throughout the Great Plains, I extended my research to investigate the role of dispersal, establishment, proliferation, and persistence in characterizing its threat to the endemic diversity of northern fescue prairies, protected within Riding Mountain National Park. Patterns of smooth brome invasions were contingent on the type of propagules dispersed. The shallow dispersal gradient of individual florets combined with the steeper gradient of panicles and spikelets suggested that smooth brome is capable of simultaneously invading along dense fronts as well as by establishing isolated foci. While low correlations between the number of dispersed seeds and their recruitment suggested post-dispersal transport, seedling establishment remained contingent on prairie diversity. Seedling biomass increased with declining plant diversity, however, its impact depended on the availability of soil nitrogen. As a result, disturbed areas, preserving the root function of native plants, resisted smooth brome establishment. Even though low nitrogen contributed to a decline in seedling biomass, physiological integration between ramets facilitated their vegetative proliferation in low resource environments. Despite its rapid establishment and proliferation, smooth brome productivity declined at the center of invading clones. Although field and greenhouse observations failed to implicate soilborne pathogens, reasons for the observed decline remain unresolved. My research demonstrates that while Riding Mountain National Park and other natural areas in western Canada will continue to be impacted by exotic plants, integrating key stages in their life history provides an important conceptual framework in predicting their threat to natural areas and prioritizing management.

Le but est d’explorer l’interaction entre les particules quantiques et la gravitation. On utilisera la quantification de Landau, l’effet Hall quantique et on examinera la relation entre la gravitation et l’effet Josephson. On propose une version de l’expérience "COW" (Colella-Overhauser-Werner) pour examiner les déviations de la loi du carré inverse de type Yukawa et de puissance inverse. Il est question de montages permettant d’investiguer la possibilité de mesurer le gravitomagnétisme et la constante de la gravitation G. On a examiné les transitions quantiques pour des neutrons ultra-froids (Ultra-Cold Neutron : UCN). Les résultats étaient satisfaisants pour 105 UCN. On a imaginé un effet laser avec ces neutrons émetteurs de gravitons : le phénomène est cependant très faible. Pour les corrections des niveaux de Landau : on a utilisé trois types d’espace-temps. Pour Schwarzschild, en utilisant une masse perturbatrice, les corrections d’ordres 1 et 2 dépendent du niveau n et du nombre quantique `. Cela enlève la dégénérescence des niveaux conventionnels. On obtient des résultats similaires pour les espaces-temps de Kerr et de Levi-Civita. On a proposé une expérience analogue à l’expérience COW. On a des déphasages malgré de faibles valeurs anticipées : de 10^−18 rad à 10^−4 rad pour le type Yukawa et de 10^−3 rad à 10^−9 rad pour puissance inverse. On a proposé des mesures possibles pour le gravitomagnétisme. On a aussi repris l’étude de l’influence de la gravitation sur l’effet Hall quantique. On obtient de faibles corrections pour un champ gravitationnel. On ne peut toutefois pas conclure à des quantités mesurables pour les déviations de type Yukawa et de puissance inverse. Par contre, on peut utiliser l’effet pour mesurer G avec grande précision. On a examiné l’effet Josephson sous l’effet de la gravitation en imaginant un montage simple. On a d’excellents résultats : des corrections de 10^−7 à 10^−9 Hz pour des déviations de type Yukawa et 10^−6 Hz pour des déviations en puissance inverse. Surtout, le lien entre la gravitation et la fréquence du courant de Josephson est clairement établit et mesurable. / The goal is to explore the interaction between quantum particles and gravitation. We will use Landau quantization, the quantum Hall effect and we will examine the relationship between gravity and Josephson’s effect. We propose a version of "COW" experience (Colella-Overhauser-Werner) to examine the Yukawa and inverse power deviations. We propose setups to investigate the possibility to measure gravitomagnetism and the gravitational constant G. Quantum transitions for ultra-cold neutrons (UCN) have been examined. The results were satisfactory for 105 UCN. We imagined a laser effect with these graviton emitting neutrons: the phenomenon is however very weak. For Landau level corrections: we proceeded with three types of space-times. For Schwarzschild, using a disturbing mass, the corrections of orders 1 and 2 depend on the level n and the quantum number "`". This removes the degeneracy of conventional levels. Similar results are obtained for the Kerr and the Levi-Civita spacetimes. We took over an analog of the COW experiment. We have phase shifts despite low expected values: from 10^−18 rad to 10^−4 rad for Yukawa and from 10^−3 rad to 10^−9 rad for inverse power laws. The same setup has been proposed for testing gravitomagnetism. We have also resumed the study of the influence of gravity on the quantum Hall effect. Small corrections are obtained for a gravitational field. We cannot however conclude with measurable quantities for Yukawa and inverse power laws. On the other hand, one can use the effect to measure G with great precision. We examined the Josephson effect under the effect of gravity by imagining a simple setup. We have excellent results: corrections from 10^−7 to 10^−9 Hz for Yukawa and 10^−6 Hz for inverse power law. Above all, the link between gravity and the frequency of Josephson’s current is clearly established and measurable.

This thesis considers the hydrodynamic instability and optimal forcing of a number of incompressible flow cases. In the first part, the instabilities of three problems that are of great interest in energy and aerospace applications are studied, namely a Blasius boundary layer subject to localized wall-suction, a Falkner–Skan–Cooke boundary layer with a localized surface roughness, and a pair of helical vortices. The two boundary layer flows are studied through spectral element simulations and eigenvalue computations, which enable their long-term behavior as well as the mechanisms causing transition to be determined. The emergence of transition in these cases is found to originate from a linear flow instability, but whereas the onset of this instability in the Blasius flow can be associated with a localized region in the vicinity of the suction orifice, the instability in the Falkner–Skan–Cooke flow involves the entire flow field. Due to this difference, the results of the eigenvalue analysis in the former case are found to be robust with respect to numerical parameters and domain size, whereas the results in the latter case exhibit an extreme sensitivity that prevents domain independent critical parameters from being determined. The instability of the two helices is primarily addressed through experiments and analytic theory. It is shown that the well known pairing instability of neighboring vortex filaments is responsible for transition, and careful measurements enable growth rates of the instabilities to be obtained that are in close agreement with theoretical predictions. Using the experimental baseflow data, a successful attempt is subsequently also made to reproduce this experiment numerically. In the second part of the thesis, a novel method for computing the optimal forcing of a dynamical system is developed. The method is based on an application of the inverse power method preconditioned by the Laplace preconditioner to the direct and adjoint resolvent operators. The method is analyzed for the Ginzburg–Landau equation and afterwards the Navier–Stokes equations, where it is implemented in the spectral element method and validated on the two-dimensional lid-driven cavity flow and the flow around a cylinder. / <p>QC 20171124</p>