Boundary feedback controller over a bluff body for prescribed drag and lift coefficients

This paper presents an improved boundary feedback controller for the two and three-dimensional Navier-Stokes equations, in a bounded domain Ω, for prescribed drag and lift coefficients. In order to determine the feedback control law, we consider an extended system coupling the equations governing the Navier-Stokes problem with an equation satisfied by the control on the bluff body, which is a part of the domain boundary. By using the Faedo-Galerkin method and a priori estimation techniques, a stabilizing boundary control is built. This control law ensures the stability of the controlled discrete system. A compactness result then allows us to pass to the limit in the non linear system satisfied by the approximated solutions

Global analysis of a shistosomiasis infection with biological control

In this paper, the analysis of a schistosomiasis infection model that involves human and intermediate snail hosts as well as an additional mammalian host and a competitor snail species is studied by constructing Lyapunov functions and using a Krasnoselkii sublinearity trick. We derive the basic reproduction number R0 for the deterministic model, and establish that the global dynamics are completely determined by the values of R0. We obtain the global stability of the disease-free equilibrium E0 when R0 ≤ 1 and we prove the existence and local stability of the endemic equilibrium E∗ when R0 > 1.On considère un modèle d'infection de la bilharziose qui prend en compte les humains et les hôtes intermédiaires d'escargots aussi bien des hôtes mammifères supplémentaires et une espèce d'escargot résistant . L'analyse de stabilité est étudié en construisant des fonctions de Lyapunov et une manie de Krasnoselskii de sous-linéarité. Nous établirons le taux de reproduction de base R0 pour le modèle posé et nous montrerons que la dynamique globale est complétement determinée par R0. Nous obtenons la stabilté globale du point d'équilibre sans maladie E0 lorsque R0 ≤ 1 et quand R0 > 1 nous prouvons l'éxistence et la stabilité du point d'équilibre endémique E∗

Modélisation asymptotique de plaques : contrôlabilité exacte frontière, piézoélectricité

autre_universite:Université Gaston Berger - SénégalThis dissertation deals with various aspects of plate modelling : boundary exact controllability of 2D structures, construction of models for piezoelectric plates, and analysis of singularities. The first chapter presents a result of boundary exact controllability for a 2D elastic plate. First, we solve an exact controllability problem for a plate with thickness h, by controlling only its interior and its lateral boundary. We choose interior controls that vanish as h tends to 0. In Chapters 2, 3, 4, we study the behavior of a piezoelectric plate when its thickness tends to 0. Particularly, in the dynamic case where the magnetic contribution is taken into account in the Maxwell equations. So, in one hand, we justify the thin plate models which assume that the electric potential is a second order polynomial in the thickness direction. On the other hand, we prove that in 2D models, the equilibrium equations depend on the electric potential only through the difference of potential between the horizontal faces. Moreover, we obtain the very contribution of the piezoelectric constants in the bending operator.Le mémoire est consacré à divers aspects de la modélisation de plaques : contrôlabilité frontière de structures bidimensionnelles et construction de modèles de plaques piézoélectriques, en relation avec des situations technologiques d'actualité, puis étude de singularités. Dans le premier chapitre on obtient un résultat de contrôlabilité exacte frontière pour une plaque élastique bidimensionnelle. On résout d'abord le problème de contrôlabilité exacte pour une plaque tridimensionnelle d'épaisseur h en controlant uniquement l'intérieur et la frontière latérale de la plaque ; le choix effectué des contrôles tridimensionnels permet de faire disparaitre les contrôles intérieurs lorsque h tend vers 0. On étudie, dans les chapitres 2, 3 et 4, le comportement d'une plaque piézoélectrique lorsque son épaisseur tend vers 0, notamment, dans le cas complet ou la contribution magnétique dans les équations de Maxwell n'est pas négligeable. Ainsi, d'une part, on justifie les modèles qui supposent que dans une plaque mince le potentiel électrique peut être assimilé à un polynome du second degré en la coordonnée d'espace suivant l'épaisseur. Et, d'autre part, on explique pourquoi dans les modèles bidimensionnels les équations d'équilibre mécanique, ou les équations d'évolution, sont liées au potentiel électrique uniquement par la différence de potentiel entre les deux faces horizontales. De plus, on exhibe de manière précise la contribution des termes piézoélectriques dans l'opérateur de flexion. Le chapitre 5 est consacré au calcul de coefficients de singularité sur un ouvert bidimensionnel polygonal non convexe

Modélisation asymptotique de plaques : contrôlabilité exacte frontière, piézoélectricité

autre_universite:Université Gaston Berger - SénégalThis dissertation deals with various aspects of plate modelling : boundary exact controllability of 2D structures, construction of models for piezoelectric plates, and analysis of singularities. The first chapter presents a result of boundary exact controllability for a 2D elastic plate. First, we solve an exact controllability problem for a plate with thickness h, by controlling only its interior and its lateral boundary. We choose interior controls that vanish as h tends to 0. In Chapters 2, 3, 4, we study the behavior of a piezoelectric plate when its thickness tends to 0. Particularly, in the dynamic case where the magnetic contribution is taken into account in the Maxwell equations. So, in one hand, we justify the thin plate models which assume that the electric potential is a second order polynomial in the thickness direction. On the other hand, we prove that in 2D models, the equilibrium equations depend on the electric potential only through the difference of potential between the horizontal faces. Moreover, we obtain the very contribution of the piezoelectric constants in the bending operator.Le mémoire est consacré à divers aspects de la modélisation de plaques : contrôlabilité frontière de structures bidimensionnelles et construction de modèles de plaques piézoélectriques, en relation avec des situations technologiques d'actualité, puis étude de singularités. Dans le premier chapitre on obtient un résultat de contrôlabilité exacte frontière pour une plaque élastique bidimensionnelle. On résout d'abord le problème de contrôlabilité exacte pour une plaque tridimensionnelle d'épaisseur h en controlant uniquement l'intérieur et la frontière latérale de la plaque ; le choix effectué des contrôles tridimensionnels permet de faire disparaitre les contrôles intérieurs lorsque h tend vers 0. On étudie, dans les chapitres 2, 3 et 4, le comportement d'une plaque piézoélectrique lorsque son épaisseur tend vers 0, notamment, dans le cas complet ou la contribution magnétique dans les équations de Maxwell n'est pas négligeable. Ainsi, d'une part, on justifie les modèles qui supposent que dans une plaque mince le potentiel électrique peut être assimilé à un polynome du second degré en la coordonnée d'espace suivant l'épaisseur. Et, d'autre part, on explique pourquoi dans les modèles bidimensionnels les équations d'équilibre mécanique, ou les équations d'évolution, sont liées au potentiel électrique uniquement par la différence de potentiel entre les deux faces horizontales. De plus, on exhibe de manière précise la contribution des termes piézoélectriques dans l'opérateur de flexion. Le chapitre 5 est consacré au calcul de coefficients de singularité sur un ouvert bidimensionnel polygonal non convexe

GLOBAL STABILIZATION OF THE NAVIER-STOKES EQUATIONS AROUND AN UNSTABLE EQUILIBRIUM STATE WITH A BOUNDARY FEEDBACK CONTROLLER

International audienceThis paper presents a global stabilization for the two and three-dimensional Navier-Stokes equations in a bounded domain Ω around a given unstable equilibrium state, by means of a boundary normal feedback control. The control is expressed in terms of the velocity field by using a non-linear feedback law. In order to determine the feedback control law, we consider an extended system coupling the equations governing the perturbation with an equation satisfied by the control on the domain boundary. By using the Faedo-Galerkin method and a priori estimation techniques, a stabilizing boundary control is built. This control law ensures a decrease of the energy of the controlled discrete system. A compactness result then allows us to pass to the limit in the system satisfied by the approximated solutions

BOUNDARY STABILIZATION OF THE NAVIER-STOKES EQUATIONS WITH FEEDBACK CONTROLLER VIA A GALERKIN METHOD

International audienceIn this work we study the exponential stabilization of the two and three-dimensional Navier-Stokes equations in a bounded domain Ω, around a given steady-state flow, by means of a boundary control. In order to determine a feedback law, we consider an extended system coupling the Navier-Stokes equations with an equation satisfied by the control on the domain boundary. While most traditional approaches apply a feedback controller via an algebraic Riccati equation, the Stokes-Oseen operator or extension operators, a Galerkin method is proposed instead in this study. The Galerkin method permits to construct a stabilizing boundary control and by using energy a priori estimation technics, the exponential decay is obtained. A compactness result then allows us to pass to the limit in the system satisfied by the approximated solutions. The resulting feedback control is proven to be globally exponentially stabilizing the steady states of the two and three-dimensional Navier-Stokes equations

Sequestration of organic carbon in West African soils by Aménagement en Courbes de Niveau

A recent Intergovernmental Panel on Climate Change (IPPC) report concludes that global warming, while already a global crisis, is likely to become even more devastating. The scientific consensus is that global warming is caused by increases in greenhouse gases including carbon dioxide. The Sahel of West Africa seems to be more adversely affected by such climate changes, leading to reduced and more sporadic rainfall. In addition, food security in the region is tenuous and fragile, due to adverse climate change, but also due to the historical mining of nutrients and carbon. With the adoption of the Kyoto accords, at least by some countries, sequestered carbon (C) has become a tradable commodity. This provides a double incentive to increase soil organic carbon in the C-depleted and degraded soils of West Africa – return C to improve soil quality and assist in removing CO$_{2}$ from the atmosphere to assist in mitigating climate change. A challenge, however, remains to determine which agricultural systems can actually sequester C. The technology called Aménagement en courbes de niveau (ACN), which can be roughly translated as `Ridge-tillage', has given crop yield increases of 30 to 50%. To date, there has only been anecdotal evidence suggesting that Aménagement en courbes de niveau leads to increased soil organic C. The objectives of the study reported here were to determine whether the technology has the potential to sequester C in West African soils, and, if so, how much. In this study, soil organic C was measured by combustion methods in soils sampled at 0–20 and 20–40 cm depths in a series of experiments in Mali, Senegal and The Gambia. Soil organic C was measured in three very different types of experiments, all including Aménagement en courbes de niveau technology, resulting in three methods of measuring C sequestration. Our results indicate that the Aménagement en courbes de niveau technology significantly increased maize yields by 24% by weight in the Gambia experiment while soil organic C was increased by 26% in The Gambia, by 12% in Siguidolo, Mali, and by 14% in peanut systems of Nioro, Senegal. These increases in soil organic C are likely due to three factors: (1) reduced erosion and movement of soil, (2) increased crop growth resulting from the greater capture of rainfall, and (3) increased growth and density of shrubs and trees resulting from the increased subsoil water, resulting in turn from the increased capture of rainfall, and reduced runoff. Measuring soil C on fields that were successively placed under Aménagement en courbes de niveau management and the use of replicated experimental plots appear to be the best methods to quantify the C sequestration potential of the practice. These results indicate that this soil and water conservation technology not only harvests water and increases food production, but also increases soil organic carbon. This technology thus is a successful technique to sequester C in soils and if carried out in a large region may both offset CO$_{2}$ emissions and help mitigate climate change