The onset of flowering time in a plant is extremely significant when evaluating population success. Floral growth, seed production, and dispersal are all dependent upon flowering time. Flowering early (and hence longer) increases the prospect of pollination but typically reduces vegetative growth and yields fewer/smaller flowers. Flowering late (and hence shorter) guarantees more/bigger flowers but carries the risk of insufficient pollination. This fundamental trade-off between growth and flowering time suggests that there may be an optimal time to initiate flowering. In this thesis, we consider a deterministic hybrid integrodifferential model where we represent the growing season in continuous time and the time between seasons as a discrete map. We track the evolution of flowering time, as a phenotype, by explicitly considering it as a variable in our model. The model is analyzed from two different viewpoints: (1) by mutual invasion analysis in the sense of adaptive dynamics; and (2) by deriving equations for the mean trait value and total population density when flowering time is considered to be Gamma-distributed. In both cases evolution to an intermediary flowering time was observed.

This work is a numerical study of the 2-D heat equation with Dirichlet boundary conditions over a polygonal domain. The motivation for this study is a chemical vapor deposition (CVD) reactor in which a substrate is heated while being exposed to a gas containing precursor molecules. The interaction between the gas and the substrate results in the deposition of a compound thin film on the substrate. Two different numerical approximations are implemented to produce numerical solutions describing the conduction of thermal energy in the reactor. The first method used is a Crank-Nicholson finite difference technique which tranforms the 2-D heat equation into an algebraic system of equations. For the second method, a semi-discrete method is used which transforms the partial differential equation into a system of ordinary differential equations. The goal of this work is to investigate the influence of boundary conditions, domain geometry, and initial condition on thermal conduction throughout the reactor. Once insight is gained with respect to the aforementioned conditions, optimal design and control can be investigated. This work represents a first step in our long term goal of developing optimal design and control of such CVD systems. This work has been funded through Partnerships in Research Excellence and Transition (PRET) grant number F49620-96-1-0329. / Master of Science

While moment matching can effectively reduce the dimension of a linear, time-invariant system, it can simultaneously fail to improve the stable time-step for the forward Euler scheme. In the context of a semi-discrete heat equation with spatially smooth forcing, the high frequency modes are virtually insignificant. Eliminating such modes dramatically improves the stable time-step without sacrificing output accuracy. This is accomplished by modal filtration, whose computational cost is relatively palatable when applied following an initial reduction stage by moment matching. A bound on the norm of the difference between the transfer functions of the moment-matched system and its modally-filtered counterpart yields an intelligent choice for the mode of truncation. The dual-stage algorithm disappoints in the context of highly nonnormal semi-discrete convection-diffusion equations. There, moment matching can be ineffective in dimension reduction, precluding a cost-effective modal filtering step.

Orientadores: Maicon Ribeiro Correa, Eduardo Cardoso de Abreu / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-27T11:41:21Z (GMT). No. of bitstreams: 1 Silva_FelipeAugustoGuedesda_M.pdf: 1119470 bytes, checksum: eeabeb98750e53492e778b99174c0887 (MD5) Previous issue date: 2015 / Resumo: O foco do presente trabalho consiste no estudo computacional de métodos de Galerkin Descontínuo para aproximação numérica de problemas diferenciais de natureza hiperbólica, com enfoque em esquemas explícitos e no uso de aproximações do tipo Runge-Kutta no tempo para aproximação de problemas lineares e não-lineares. Especificamente, serão exploradas as boas propriedades de estabilidade local, no tempo, dos métodos da classe Runge-Kutta em conjunto com funções de fluxo numérico estáveis e com o uso de limitadores de inclinação, com o objetivo de desenvolver métodos Galerkin Descontínuo de alta ordem capazes de obter uma boa resolução de gradientes abruptos e de soluções descontínuas, sem oscilações espúrias, em problemas hiperbólicos. Uma breve discussão sobre esquemas de volumes finitos centrais de alta ordem é apresentada, onde são introduzidos importantes conceitos a serem utilizados na construção dos métodos de Galerkin Descontínuo. Um conjunto representativo de simulações numéricas de modelos hiperbólicos lineares e não-lineares é apresentado e discutido para avaliar a qualidade das aproximações obtidas em uma comparação direta com outras aproximações precisas de volumes finitos ou com soluções exatas, sempre que possível / Abstract: The focus of this work is the computational study of some Discontinuous Galerkin methods for the numerical approximation of first order hyperbolic differential problems, focusing on explicit schemes with discretization based on Runge-Kutta type methods in time, in problems with linear and nonlinear fluxes. Specifically, the good local stability properties of Runge-Kutta methods are combined with stable numerical flux functions and slope limiters in order to propose new higher-order Discontinuous Galerkin methods that achieve high resolution of abrupt gradients and of discontinuous solutions, without spurious oscillations in numerical solutions. Furthermore, a brief discussion about higher-order finite volume central schemes is presented in order to introduce some important concepts to be used in the construction of the DG methods. A representative set of numerical simulations for linear and nonlinear hyperbolic models is presented and discussed, in order to check the accuracy of the obtained Discontinuous Galerkin solutions by comparing their results with those of existing well-established finite volume numerical methods and exact solutions / Mestrado / Matematica Aplicada / Mestre em Matemática Aplicada

Cette thèse s'intéresse à l'étude des stratégies d'introduction de populations dans l'environnement. Les deux principaux contextes présentés sont la lutte biologique et la réintroduction d'espèces. Si ces deux types d'introduction diffèrent, des processus biotiques et abiotiques les influencent de manière similaire. En particulier les populations introduites, souvent de petite taille, peuvent être sensibles à diverses formes de stochasticité, voire subir une baisse de leur taux de croissance à faible effectif, ce qu'on appelle « effet Allee ». Ces processus peuvent interagir avec les stratégies d'introduction des organismes et moduler leur efficacité. Dans un premier temps, nous modélisons le processus d'introduction à l'aide de systèmes dynamiques impulsionnels : la dynamique de la population est décrite par des équations différentielles ordinaires qui, à des instants donnés, sont perturbées par des augmentations soudaines de la taille de la population. Cette approche se concentre sur l'influence des effets Allee sur les populations isolées (réintroduction) ou dans un cadre proie-prédateur (lutte biologique). Dans un second temps, en nous concentrant sur l'aspect réintroduction, nous étendons ce cadre de modélisation pour prendre en compte des aspects stochastiques liés à l'environnement ou aux introductions elles-mêmes. Finalement, nous considérons un modèle individu centré pour étudier l'effet de la stochasticité démographique inhérente aux petites populations. Ces différentes approches permettent d'analyser l'influence de la distribution temporelle des introductions et ainsi déterminer les stratégies qui maximisent les chances de succès des introductions. / This thesis investigates introduction strategies of populations in the environment. Two main situations are considered: biological control and species reintroduction. Although these two kinds of introductions are different, many biotic and abiotic processes influence them in a similar way. Introduced populations are often small and may be sensitive to various stochastic factors. Further, small populations may suffer from a decrease of their growth rate when the population is small, a feature called "Allee effect". These processes may interact with introduction strategies and modulate their efficiency. First, we represent the introduction process using impulsive dynamical systems: population dynamics are described by ordinary differential equations that are disrupted at some instants by instantaneous increases of the population size. This approach focuses on the influence of Allee effects on single-species (reintroduction) or predator-prey interactions (biological control). Then, we concentrate on the reintroduction approach and extend the previous deterministic framework to take into consideration stochastic factors arising from the environment or from introductions themselves. Finally, we consider an individual-based model to study the effects of demographic stochasticity which is inherent to small populations. These different approaches allow to investigate the temporal distribution of introductions and determine which introduction strategies maximize the probability of success of introductions.

The probability density function (PDF) approach is a powerful technique for large eddy simulation (LES) based modeling of turbulent reacting flows. In this approach, the joint-PDF of all reacting scalars is estimated by solving a PDF transport equation, thus providing detailed information about small-scale correlations between these quantities. The objective of this work is to further develop the LES/PDF approach for studying flame stabilization in supersonic combustors, and for soot modeling in turbulent flames. Supersonic combustors are characterized by strong shock-turbulence interactions which preclude the application of conventional Lagrangian stochastic methods for solving the PDF transport equation. A viable alternative is provided by quadrature based methods which are deterministic and Eulerian. In this work, it is first demonstrated that the numerical errors associated with LES require special care in the development of PDF solution algorithms. The direct quadrature method of moments (DQMOM) is one quadrature-based approach developed for supersonic combustion modeling. This approach is shown to generate inconsistent evolution of the scalar moments. Further, gradient-based source terms that appear in the DQMOM transport equations are severely underpredicted in LES leading to artificial mixing of fuel and oxidizer. To overcome these numerical issues, a new approach called semi-discrete quadrature method of moments (SeQMOM) is formulated. The performance of the new technique is compared with the DQMOM approach in canonical flow configurations as well as a three-dimensional supersonic cavity stabilized flame configuration. The SeQMOM approach is shown to predict subfilter statistics accurately compared to the DQMOM approach. For soot modeling in turbulent flows, an LES/PDF approach is integrated with detailed models for soot formation and growth. The PDF approach directly evolves the joint statistics of the gas-phase scalars and a set of moments of the soot number density function. This LES/PDF approach is then used to simulate a turbulent natural gas flame. A Lagrangian method formulated in cylindrical coordinates solves the high dimensional PDF transport equation and is coupled to an Eulerian LES solver. The LES/PDF simulations show that soot formation is highly intermittent and is always restricted to the fuel-rich region of the flow. The PDF of soot moments has a wide spread leading to a large subfilter variance. Further, the conditional statistics of soot moments conditioned on mixture fraction and reaction progress variable show strong correlation between the gas phase composition and soot moments. / text