Orientador: João Frederico da Costa Azevedo Meyer / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T22:20:05Z (GMT). No. of bitstreams: 1 CajasGuaca_Denis_M.pdf: 6132685 bytes, checksum: 5e3780d261cb1b925daf089e42c326af (MD5) Previous issue date: 2015 / Resumo: Esta pesquisa visa descrever e ilustrar mediante a modelagem matemática e simulação computacional a poluição por esgoto que ocorre na Baía de Buenaventura no sudoeste do Pacífico Colombiano, e a influência do poluente no convívio de duas espécies de peixes. Para a dispersão de poluente usaremos o modelo que envolve a equação de Difusão-Advecção, a qual descreve as principais caraterísticas a considerar para o estudo do nosso problema, com suas respectivas condições de fronteira do entorno natural, considerando absorção de poluente nas margens da baía. Para a dinâmica populacional entre as espécies de peixes será usado um sistema não linear clássico do tipo Lotka-Volterra para modelar este problema, com condições de contorno de Neumann. A solução aproximada do modelo é obtida numericamente usando um método de segunda ordem no espaço e no tempo. Para a discretização da variável espacial usamos um método de diferenças finitas de segunda ordem e o método de Crank Nicolson para a discretização da variável temporal. Os resultados mostrados nas simulações computacionais para a concentração de poluente, e para a dinâmica populacional nos permitem julgar melhor o que está acontecendo ou o que pode acontecer, refletindo a necessidade de que os orgãos governamentais implementem mecanismos de mitigação ao problema ambiental para tentar diminuir os efeitos adversos do despejo direto no mar de águas residuais sem tratamento / Abstract: The propose of this research is to describe and illustrate the water pollution by sewage which occurs in Buenaventura Bay, in the southwest of the Colombian Pacific, and the influence of the pollutant in the interaction of two fish species, using mathematical modeling and computer simulation. Pollutant dispersion will be obtain using the model that involves the Diffusion - Advection equation, which describes the main features to be considered for the study of our problem with its respective boundary conditions of the natural environment, considering pollutant absorption in bayside. In order to describe the population dynamics between the fish species the classic Lotka -Volterra nonlinear system with Neumann boundary conditions will be used. The approximate solution of the model is obtained numerically using a second order method on the space and time. In order to discretize the spatial variable we use a second order finite difference method and the Crank Nicolson method for the time discretization. The results obtained in the computer simulations for the pollutant concentration, and the population dynamics allow us to judge what happening or what might happen. Reflecting in this way the necessity for the government agencies to implement mitigation mechanisms of the environmental problem in order to try reduce the adverse effects of dumping untreated sewage water directly into the sea / Mestrado / Matematica Aplicada / Mestra em Matemática Aplicada

Neste trabalho foi analisado o comportamento de um solo argiloso compactado (CCL) da Fm. Corumbataí e de um geocomposto bentonítico (GCL) composto por bentonita \'NA\', frente a gradientes hidráulicos e químicos. As propriedades físicas e mineralógicas dos solos foram avaliadas, bem como determinados em ensaios de adsorção em lote os parâmetros das isotermas de Freundlich e Langmuir. Foi desenvolvido um equipamento para avaliar o comportamento membrana e poder calcular o coeficiente de eficiência químico-osmótico (\'ômega\') em ensaio de difusão-membrana. Os ensaios de advecção foram executados com o equipamento já existente no departamento de Geotecnia. Em todos os ensaios foram utilizadas soluções monoiônicas de \'KCL\' e \'CU\'CL IND.2\' 2\'H IND.2\'O\'. O valor do factor de retardamento Rd determinado no ensaio em lote (batch test) foi maior que o Rd medido no ensaio de advecção, enquanto que, no ensaio de difusão-membrana, obteve-se o menor valor de Rd. Tanto o GCL quanto o CCL apresentaram comportamento membrana e geração de pressão osmótica para as soluções utilizadas. No entanto, com a solução de \'K POT.+\' as diferenças de pressão se mantiveram durante o ensaio, enquanto que no caso da solução de \'CU POT.+2\' a pressão induzida no corpo de prova do CCL e do GCL tem um pico e logo diminue até zero. O GCL teve um aumento na condutividade hidráulica, no ensaio de advecção, quando permeado com solução de \'CU POT.+2\'. Este comportamento é atribuído ao colapso da dupla camada difusa das partículas de argila. O CCL não apresentou este comportamento. Os resultados deste trabalho sugerem que o CCL da Fm. Corumbataí tem melhor desempenho como barreira que o GCL, nas condições de laboratório e para as soluções usadas. / In this research the behavior of a compacted clayey liner (CCL) of Corumbataí Fm. and a geosynthetic clay liner (GCL) containing \'NA\'-bentonite, was evaluated in presence of hydraulic and chemical gradients. Physical and mineralogical properties of the soils were determined and batch tests were executed to obtain the adsorption parameters of the Freundlich and Langmuir models. A laboratory apparatus was developed for assessment of the membrane behavior allowing determining the chemico-osmotic efficiency coefficient (\'ômega\') in diffusion-membrane test. The advection test was carried out with existent equipment in geotechnical department. Both tests were performed with single salt \'KCL\' and \'CU\'CL IND.2\' 2\'H IND.2\'O\' solutions. The measured value of the retardation factor (Rd) for the batch test is bigger than the Rd measured in advection test while in the diffusion-membrane test, the Rd obtained is the smallest. Both GCL and the CCL exhibit membrane behavior and they generate osmotic pressure with both solutions. However with \'KCL\' solution the difference of pressure are maintained during the test, while in the case of \'CU POT.+2\' solution the induced pressure across the specimen of CCL and GCL have a peak to after decrease to zero. The GCL had an increase in the hydraulic conductivity for a \'CU POT.+2\' solution in the advection test. This behavior is attributed to the collapse of the diffuse double layers of clay particles. The CCL did not exhibit this behavior. The results of this study suggest that the CCL of Corumbataí Fm. has a better performance as clay barrier tha the GCL, considering the solutions used and in the laboratory conditions.

Zlomkový kalkulus je matematická disciplína zabývající se vlastnostmi derivací a integrálů neceločíselných řádů (nazývaných zlomkové derivace a integrály, zkráceně diferintegrály) a metodami řešení diferenciálních rovnic obsahujících zlomkové derivace neznámé funkce (tzv. zlomkovými diferenciálními rovnicemi). V této práci představujeme standardní přístupy k definicím zlomkového kalkulu a důkazy některých základních vlastností diferintegrálů. Dále uvádíme krátký přehled metod řešení některých lineárních zlomkových diferenciálních rovnic a vymezujeme hranice jejich použitelnosti. Na závěr si všímáme některých fyzikálních aplikací zlomkového kalkulu.

No description available.

Transport codes are beginning to be parallelized in order to allow more complex add-ons, such as geochemical packages, to utilize finer, more accurate grids, and to reduce solution times making stochastic and Monte Carlo simulations more feasible. Most codes parallelized via MPI (message passing interface) offer good results, but require the development of a new parallel code. OpenMP, the shared-memory standard, offers incremental parallelization, allowing sequential codes to remain relatively intact with minimal changes or additions. OpenMP allows speedup to be seen on personal computers with dual processors or greater, unlike some other parallelization approaches that require a supercomputer. An operator-split strategy creates an environment for easy parallelization by decoupling the transport and reactions of species. The transport, when decoupled from the reactions, is dependent on surrounding nodes and not on species. Therefore, each species transport can be solved on a different processor. The reactions, when decoupled from the transport, are dependant on the other species concentrations and not on the surrounding nodes, allowing the concentrations for all species to be solve for at a given node as if in a batch reactor. This allows a parallelization of the nodes. Two codes are parallelized in this work. The first is a 100-species 1D theoretical problem. The second is RT3D, a modular computer code for simulating reactive multi-species transport in 3-dimensional groundwater systems written and developed by Dr. T. Prabhakar Clement. RT3D is a sub-component of a parent code, MT3DMS, which utilizes RT3D to solve reaction terms. A speedup factor of 3.91 is seen on four processors, accomplishing a processor efficiency of approximately 98% while spent in RT3D itself.

No description available.

Concrete is a popular construction material for bridges, due to its high durability and energy efficiency. An important concern for concrete bridges is the possible occurrence of chloride- induced corrosion in prestressing strands and reinforcing bars, which may substantially impact the service life of such structures. Chloride- induced corrosion is a complicated electrochemical process which is affected by heat transfer, moisture flow and transport of chemical species through the concrete pore network. Reliable and robust analytical tools are required to allow multi-physics simulations of steel corrosion. This study has developed a nonlinear finite element analysis program, called VT-MultiPhys, to enable multi-physics simulations, including analyses of chloride-induced corrosion. The program includes constitutive laws, element formulations and global solution schemes to allow the analysis of steady-state (static) and time-dependent (dynamic) problems, involving multiple, coupled processes such as mechanical deformation, heat transfer, mass flow and chemical reactions combined with advective/diffusive transport of the various species. Special analysis schemes, based on the streamline-upwind Petrov-Galerkin (SUPG) method, have also been implemented to address the spatial instabilities which characterize analyses of advection-dominated transport. The finite element modeling scheme, constitutive laws and boundary conditions for analysis of chloride-induced corrosion are described in detail. The constitutive laws can be combined with inelastic material models to capture the damage (e.g., cracking) due to chloride-induced corrosion. A set of verification analyses is presented, to demonstrate the capabilities of VT-MultiPhys to conduct different types of simulations and reproduce the closed-form analytical solutions of simple cases. Validation analyses for heat conduction, moisture flow and chloride transport, using data from experimental tests in the literature, are also presented. / Master of Science / The deterioration of concrete structures and infrastructures due to the chloride-induced corrosion in prestressing strands and reinforcing bars may substantially impact the service life of such structures. Chloride-induced corrosion is a complicated electrochemical process which is initiated and proceeds due to the chloride attacks at the surfaces of concrete structures and ends in the volume expansion, cracking and spalling of concrete. Due to the lack of comprehensive modeling tool, which can simultaneously comprise the influential factors in chloride-induced corrosion, the realistic estimation of the service life of reinforced concrete structures is still challenging. Reliable and robust analytical tools are required to allow multi-physics simulations of steel corrosion. This study has developed a comprehensive finite element analysis program, called VT-MultiPhys, for calculating and monitoring the contribution of chloride ions to chloride-induced corrosion during service life of concrete structures. The present analysis program enables modeling of the coupled physical process including heat transfer, moisture flow and transport of chemical species through the concrete pore network. Also, by modeling the influence of flexural cracks on chloride transport in concrete, the analysis program is able to predict the rate of steel corrosion in cracked concrete structures. A set of verification analyses is presented, to demonstrate the capabilities of VT-MultiPhys to conduct different types of simulations of heat conduction, moisture flow and chloride transport and the comparison is found to be satisfactory. The element formulations and solution algorithms in VT-MultiPhys also allow the investigation of other long-term deterioration mechanisms, such as carbonation-induced corrosion, alkali-silika reaction (ASR) and sulfate attack. The present contribution will hopefully enable and facilitate future research in these topics, through the formulation and implementation of proper constitutive laws and chemical reaction equations.

L’étude des processus physiques d’un système d’upwelling est essentielle pour comprendre sa variabilité actuelle et ses changements passés et futurs. Cette thèse présente une étude interdisciplinaire du système d’upwelling côtier à partir de différentes données acquises par satellite, l’accent étant mis principalement sur le système d’upwelling d’Afrique du Nord-Ouest (NWA). Cette étude interdisciplinaire aborde (1) le problème de l’identification et de l’extraction automatiques du phénomène d’upwelling à partir d’observations satellitaires biologiques et physiques. (2) Une étude statistique de la variation spatio-temporelle de l’upwelling de la NWA tout au long de son extension et de ses différents indices d’upwelling. (3) Une étude des relations non linéaires entre le mélange de surface et l’activité biologique dans les régions d’upwelling. (4) études lagrangiennes de tourbillons cohérents; leurs propriétés physiques et identification automatique. (5) L’étude des transports effectués par les tourbillons lagrangiens de la NWA Upwelling et leur impact sur l’océan. / Studying physical processes of an upwelling system is essential to understand its present variability and its past and future changes. This thesis presents an interdisciplinary study of the coastal upwelling system from different satellite acquired data, with the main focus placed on the North West African (NWA) upwelling system. This interdisciplinary study covers (1) the problem of the automatic identification and extraction of the upwelling phenomenon from biological and physical satellite observations. (2) A statistical study of the spatio-temporal variation of the NWA upwelling throughout its extension and different upwelling indices. (3) A Study of the nonlinear relationships between the surface mixing and biological activity in the upwelling regions. (4) Lagrangian studies of coherent eddies; their physical properties and automatic identification. (5) The study of transport made by Lagrangian eddies off the NWA Upwelling and their impact on the open ocean. [...]

Les infrastructures de transport est essentielle au maintien et à l'expansion des activités sociales et économiques dans les régions circumpolaires. À mesure que le climat se réchauffe, la dégradation du pergélisol sous les remblais a entraîné de graves dommages structuraux à la route, entraînant une augmentation importante des coûts d'entretien et une réduction de la durée de vie des infrastructures. Pendant ce temps, l'advection de chaleur déclenchée par les écoulements d’eau souterrains peut altérer le bilan énergétique du remblai et du pergélisol sous-jacent et modifier le régime thermique des remblais routiers. Cependant, peu de recherches ont été effectuées pour comprendre la synergie entre les processus thermiques de surface et souterrains des remblais routiers des régions froides. L'objectif de cette recherche était de comprendre les interactions thermiques entre l'atmosphère, le remblai routier, les écoulements d’eau et le pergélisol dans le contexte du changement climatique. Cette base, de connaissances est nécessaire pour la conception technique, l'entretien des routes et l'évaluation de la vulnérabilité des infrastructures. Les travaux de recherche ont permis de développer de nouvelles méthodes d'analyse thermique pour caractériser et identifier le rôle de l'advection thermique sur le changement de température d'un remblai routier expérimental au Yukon (Canada) en termes d’intensité, de vitesse et de profondeur de l'impact thermique. Les résultats montrent que l'augmentation de la température due aux flux de chaleur advectifs déclenchés par l’écoulement d'eau peut être jusqu'à deux ordres de grandeur plus rapide qu'en raison du seul réchauffement atmosphérique. La recherche a ensuite présenté un bilan énergétique de surface pour quantifier la quantité d'énergie entrant dans le centre et la pente du remblai avec des épaisseurs et des propriétés de neige variables. Le tout a été appuyé par des observations géothermique de plusieurs années et une grande quantité de données météorologiques. Les résultats illustrent que le bilan énergétique de surface est principalement contrôlé par le rayonnement net et moins par le flux de chaleur sensible. Le flux de chaleur transmis à la pente du remblai diminue de façon exponentielle avec l'augmentation de l'épaisseur de la neige et diminue de façon linéaire avec l’installation du couvert de neige et la longueur de la période d’enneigement. De plus, un modèle de bilan énergétique de surface et un modèle cryohydrologique entièrement couplé ont été développés pour étudier l'impact thermique de l'advection de chaleur associée à l'écoulement de l'eau souterraine sur le dégel du pergélisol et le développement de taliks (c.-à-d. zone perpétuellement non gelée dans les zones de pergélisol). Le modèle couplé a réussi à reproduire la tendance à la hausse du plafond du pergélisol (erreur absolue moyenne <0,2 m) au cours de la période 1997-2018. Les résultats montrent que l'advection de chaleur a fourni une source d'énergie supplémentaire pour accélérer le dégel du pergélisol et a doublé le taux d’augmentation de l’épaisseur de la couche active 0,1 m·a-1 à 0,19 m·a-1, par rapport au scénario où aucun écoulement d'eau ne se produit. Le talik s'est initialement formé et développé en fonction du temps sous l’effet combiné des écoulement d’eau, de l'isolation de la neige, de la construction de la route et du réchauffement climatique. Le débit d'eau souterraine a relié des corps isolés de talik et a amené le remblai de la route dans un état thermique irréversible, en raison de la rétroaction de l'eau liquide (effet de chaleur latente) piégée dans le talik. Ces résultats montrent l'importance de l'advection de chaleur induite par l'écoulement d'eau sur le régime thermique de la sous-couche (c.-à-d. la couche de matériau de remblai) et du sous-sol (c.-à-d. le matériau natif sous un remblai) du remblai lorsque le remblai routier intercepte le drainage local. De plus, les résultats obtenus soulignent la nécessité de coupler les processus thermiques de surface et souterrains dans le but d'évaluer la stabilité thermique des routes subarctiques. / Transportation infrastructure is crucial to maintaining and expanding the social and economic activities in circumpolar regions. As the climate warms, degradation of the permafrost causes severe structural damages to the road embankment, leading to large increases in maintenance costs and reductions in its lifespan. Meanwhile, heat advection triggered by mobile water flow can alter energy balance of the embankment and underlying permafrost and modify the thermal regime of road embankments. However, little research has been done to understand the synergy between surface and subsurface thermal processes of cold region road embankments. The overall goal of this research was to elucidate thermal interactions between the atmosphere, the road embankment, mobile water flow, and permafrost within the context of climate change. This knowledge is needed for engineered design, road maintenance, and infrastructure vulnerability assessment. The research first used new thermal analysis to characterize and identify the role of heat advection on temperature change of an experimental road embankment, Yukon, Canada in terms of magnitude, rate and thermal impact depth. It shows that soil temperature increase due to advective heat fluxes triggered by mobile water flow can be up to two orders of magnitude faster than due to atmospheric warming only. The research then presented a novel surface energy balance to quantify the amount of ground heat flux entering the embankment center and slope with varying snow depth and properties, supported by multi-year thermal and meteorological observations. My results illustrate that the surface energy budget is mainly controlled by net radiation, and less by the sensible heat flux. The ground heat flux released at embankment slope exponentially decreased with the increase of snow depth, and was linearly reduced with earlier snow cover and longer snow-covered period. A fully integrated surface energy balance and cryohydrogeological model was implemented to investigate the thermal impact of heat advection associated with subsurface water flow on permafrost thaw and talik (i.e., perennially unfrozen zone in permafrost areas) development. The integrated model successfully reproduced the observed increasing trend of the active layer depth (mean absolute error < 0.2 m) over the 1997-2018 period. The results show that heat advection provided an additional energy source to expedite permafrost thaw, doubling the increasing rate of permafrost table depth from 0.1 m·a-1 to 0.19 m·a-1, compared with the scenario where no water flow occurs. Talik formation and development occurred over time under the combined effect of subsurface water flow, snow insulation, road construction and climate warming. Subsurface water flow connected isolated talik bodies and triggered an irreversible thermal state for the road embankment, due to a local feedback mechanism (latent heat effect) of trapped, unfrozen water in talik. These findings elucidate the importance of heat advection induced by mobile water flow on the thermal regime of embankment subbase (i.e., a layer of fill material) and subgrade (i.e., the native material under an embankment) when the road embankment intercepts the local drainage. Furthermore, the obtained results emphasize the need to couple surface and subsurface thermal processes to evaluate the thermal stability of sub-Arctic roads.

Les besoins grandissants de prévisions robustes pour des systèmes complexes conduisent à introduire des modèles mathématiques considérant un nombre croissant de paramètres. Au temps s'ajoutent l'espace, l'aléa, les échelles de dynamiques, donnant lieu à des modèles stochastiques multi-échelles avec dépendance spatiale (modèles spatiaux). Cependant, l'explosion du temps de simulation de tels modèles complique leur utilisation. Leur analyse difficile a néanmoins permis, pour les modèles à une échelle, de développer des outils puissants: loi des grands nombres (LGN), théorème central limite (TCL), ..., puis d'en dériver des modèles simplifiés et algorithmes accélérés. Dans le processus de dérivation, des modèles et algorithmes dits hybrides ont vu le jour dans le cas multi-échelle, mais sans analyse rigoureuse préalable, soulevant ainsi la question d'approximation hybride dont la consistance constitue l'une des motivations principales de cette thèse.En 2012, Crudu, Debussche, Muller et Radulescu établissent des critères d'approximation hybride pour des modèles homogènes en espace de réseaux de régulation de gènes. Le but de cette thèse est de compléter leur travail et le généraliser à un cadre spatial.Nous avons développé et simplifié différents modèles, tous des processus de Markov de sauts pures à temps continu. La démarche met en avant, d'une part, des conditions d'approximations déterministes par des solutions d'équations d'évolution (type réaction-advection-diffusion), et, d'autre part, des conditions d'approximations hybrides par des processus stochastiques hybrides. Dans le cadre des réseaux de réactions biochimiques, un TCL est établi. Il correspond à une approximation hybride d'un modèle homogène simplifié à deux échelles de temps (suivant Crudu et al.). Puis, une LGN est obtenue pour un modèle spatial à deux échelles de temps. Ensuite, une approximation hybride est établie pour un modèle spatial à deux échelles de dynamique en temps et en espace. Enfin, des comportements asymptotiques en grandes populations et en temps long sont présentés pour un modèle d'épidémie de choléra, via une LGN suivie d'une borne supérieure pour les sous-ensembles compacts, dans le cadre d'un principe de grande déviation (PGD) correspondant.À l'avenir, il serait intéressant, entre autres, de varier la géométrie spatiale, de généraliser le TCL, de compléter les estimations du PGD, et d'explorer des systèmes complexes issus d'autres domaines. / The growing needs of precise predictions for complex systems lead to introducing stronger mathematical models, taking into account an increasing number of parameters added to time: space, stochasticity, scales of dynamics. Combining these parameters gives rise to spatial --or spatially inhomogeneous-- multiscale stochastic models. However, such models are difficult to study and their simulation is extremely time consuming, making their use not easy. Still, their analysis has allowed one to develop powerful tools for one scale models, among which are the law of large numbers (LLN) and the central limit theorem (CLT), and, afterward, to derive simpler models and accelrated algorithms. In that deduction process, the so-called hybrid models and algorithms have arisen in the multiscale case, but without any prior rigorous analysis. The question of hybrid approximation then shows up, and its consistency is a particularly important motivation of this PhD thesis.In 2012, criteria for hybrid approximations of some homogeneous regulation gene network models were established by Crudu, Debussche, Muller and Radulescu. The aim of this PhD thesis is to complete their work and generalize it afterward to a spatial framework.We have developed and simplified different models. They all are time continuous pure jump Markov processes. The approach points out the conditions allowing on the the one hand deterministic approximations by solutions of evolution equations of type reaction-advection-diffusion, and, on the other hand, hybrid approximations by hybrid stochastic processes. In the field of biochemical reaction networks, we establish a CLT. It corresponds to a hybrid approximation of a simplified homogeneous model (due to Crudu et al.). Then a LLN is obtained for a spatial model with two time scales. Afterward, a hybrid approximation is established, for a two time-space scales spatial model. Finally, the asymptotic behaviour in large population and long time are respectively presented for a model of cholera epidemic, through a LLN followed by the upper bound for compact sets, in the context of a corresponding large deviation principle (LDP).Interesting future works would be, among others, to study other spatial geometries, to generalize the CLT, to complete the LDP estimates, and to study complex systems from other fields.