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In several types of coating processes a solid substrate is removed at a controlled velocity U from a liquid bath. The shape of the liquid meniscus and the thickness of the coating layer depend on U. These dependencies have to be understood in detail for non-volatile liquids to control the deposition of such a liquid and to lay the basis for the control in more complicated cases (volatile pure liquid, solution with volatile solvent). We study the case of non-volatile liquids employing a precursor film model that describes partial wettability with a Derjaguin (or disjoining) pressure. In particular, we focus on the relation of the deposition of (i) an ultrathin precursor film at small velocities and (ii) a macroscopic film of thickness h ∝ U^(2/3) (corresponding to the classical Landau Levich film). Depending on the plate inclination, four regimes are found for the change from case (i) to (ii). The different regimes and the transitions between them are analysed employing numerical continuation of steady states and saddle-node bifurcations and simulations in time. We discuss the relation of our results to results obtained with a slip model. In connection with evaporative processes, we will study the pinning of a droplet due to a sharp corner. The approach employs an evolution equation for the height profile of an evaporating thin film (small contact angle droplet) on a substrate with a rounded edge, and enables one to predict the dependence of the apparent contact angle on the position of the contact line. The calculations confirm experimental observations, namely that there exists a dynamically produced critical angle for depinning that increases with the evaporation rate. This suggests that one may introduce a simple modification of the Gibbs criterion for pinning that accounts for the non-equilibrium effect of evaporation.

Dans ce mémoire, nous étudions un système prédateur-proie de Gause généralisé avec une récolte de proie contrôlée et une fonction de réponse de Holling de type III généralisée. Nous introduisons une fonction de récolte contrôlée sur les proies tenant compte du nombre de proies et dépendant d'un seuil de récolte. Ceci permet de rendre le système réaliste, d'optimiser la récolte, et de prévenir la possibilité d'extinction des espèces que le système avec récolte constante pouvait avoir pour toutes valeurs de paramètres. Ce type de fonction de récolte implique a priori la manipulation d'un système discontinu: nous étudions donc des techniques de lissage de ces discontinuités par régularisation. Nous faisons d'abord un retour sur les systèmes sans et avec récolte de proie constante en traçant les diagrammes de bifurcations exacts et les portraits de phase de ces systèmes. Ensuite, nous étudions le système discontinu et les méthodes de régularisation afin de choisir la plus optimale. Finalement, nous assemblons le tout avec l'étude du système avec récolte de proie régularisé, en passant par l'étude complète du système avec approvisionnement de proie, et donnons les différents effets sur les portraits de phase selon les conditions initiales. / In this master thesis, we study a generalized Gause predator-prey system with controlled prey harvest and a generalized Holling response function of type III. We introduce a controlled prey harvesting function taking into account the number of preys with a harvesting threshold. This makes the system realistic, it optimizes the harvesting, and it prevents the possibility of species' extinction which exists in the system with constant harvest for all parameters. This type of harvesting function a priori implies handling a discontinuous system : therefore we study smoothing techniques of such discontinuities by regularization. We first return on systems without and with constant harvest by drawing the exact bifurcation diagrams and phase portraits of those systems. Then, we study the discontinuous system and the regularization methods in order to choose the optimal one. Finally, we put together everything by studying the regularized prey harvesting system through a complete study of the prey stocking system, and we highlight the different effects on the phase portraits under the initial conditions.

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In light of increasing harmful algal blooms and the need to protect human health and aquatic resources, proactive management approaches merit further study. For this purpose I conducted field samplings to characterize plankton community composition and laboratory experiments to test some approaches to new management schemes in the lower Rincon Delta. On site measurements and microscopic analysis showed that environmental parameters and plankton community composition varied considerably among sampling stations and sampling dates. A recent modeling study suggested that manipulation of freshwater inflow to estuaries might prevent phytoplankton blooms and enhance secondary productivity. To test this theory I conducted three semi-continuous design and flow-through incubation design experiments using natural plankton assemblages. I investigated the effect of two different pulsing regimes of inflow and nutrient loading on zooplankton densities, and phytoplankton biomass and diversity. Despite differences in zooplankton structure and phytoplankton community composition between the two experiment designs, the results confirmed that pulsed inflows might alter plankton dynamics. My findings showed that 3-day pulse treatments consistently supported greater zooplankton densities and higher phytoplankton species diversity when compared to 1-day pulse treatments. In addition, accumulation of phytoplankton biovolume remained low during 3-day pulse treatments. Differences in zooplankton performance between 3-day pulse and 1-day pulse inflow treatments were likely due to the ability of phytoplankton to uptake and store greater amounts of nutrients under conditions of 3-day pulse inflow. This resulted in food of higher quality for zooplankton, and might have supported greater zooplankton population growth rates. Additionally, in an attempt to understand the mechanisms leading to high biodiversity in aquatic ecosystems, I built a resource-storage model and studied the effects of resource-storage on competition of multiple phytoplankton species on multiple abiotic resources. I compared this model with a well-established multi-species competition model. My results showed that for certain species combinations a resource-storage-based model can generate dissimilar outcomes when compared to a model without resource-storage.

In light of increasing harmful algal blooms and the need to protect human health and aquatic resources, proactive management approaches merit further study. For this purpose I conducted field samplings to characterize plankton community composition and laboratory experiments to test some approaches to new management schemes in the lower Rincon Delta. On site measurements and microscopic analysis showed that environmental parameters and plankton community composition varied considerably among sampling stations and sampling dates. A recent modeling study suggested that manipulation of freshwater inflow to estuaries might prevent phytoplankton blooms and enhance secondary productivity. To test this theory I conducted three semi-continuous design and flow-through incubation design experiments using natural plankton assemblages. I investigated the effect of two different pulsing regimes of inflow and nutrient loading on zooplankton densities, and phytoplankton biomass and diversity. Despite differences in zooplankton structure and phytoplankton community composition between the two experiment designs, the results confirmed that pulsed inflows might alter plankton dynamics. My findings showed that 3-day pulse treatments consistently supported greater zooplankton densities and higher phytoplankton species diversity when compared to 1-day pulse treatments. In addition, accumulation of phytoplankton biovolume remained low during 3-day pulse treatments. Differences in zooplankton performance between 3-day pulse and 1-day pulse inflow treatments were likely due to the ability of phytoplankton to uptake and store greater amounts of nutrients under conditions of 3-day pulse inflow. This resulted in food of higher quality for zooplankton, and might have supported greater zooplankton population growth rates. Additionally, in an attempt to understand the mechanisms leading to high biodiversity in aquatic ecosystems, I built a resource-storage model and studied the effects of resource-storage on competition of multiple phytoplankton species on multiple abiotic resources. I compared this model with a well-established multi-species competition model. My results showed that for certain species combinations a resource-storage-based model can generate dissimilar outcomes when compared to a model without resource-storage.

No description available.

The escape of trajectories is a ubiquitous phenomenon in open dynamical systems and stochastic processes. If escape occurs repetitively for a statistical ensemble of trajectories, the population of remaining trajectories often undergoes an exponential decay characterised by the so-called escape rate. Its inverse defines the lifetime of the decaying state, which represents an intrinsic property of the system. This paradigm is fundamental to nucleation theory and reaction-rate theory in chemistry, physics, and biology.<p><p>In many circumstances, escape is activated by the presence of noise, which may be of internal or external origin. This is the case for thermally activated escape over a potential energy barrier and, more generally, for noise-induced escape in continuous-time or discrete-time dynamics. <p><p>In the weak-noise limit, the escape rate is often observed to decrease exponentially with the inverse of the noise amplitude, a behaviour which is given by the van't Hoff-Arrhenius law of chemical kinetics. In particular, the two important quantities to determine in this case are the exponential dependence (the ``activation energy') and its prefactor.<p><p>The purpose of the present thesis is to develop an analytical method to determine these two quantities. We consider in particular one-dimensional continuous and discrete-time systems perturbed by Gaussian white noise and we focus on the escape from the basin of attraction of an attracting fixed point.<p><p>In both classes of systems, using path-integral methods, a formula is deduced for the noise-induced escape rate from the attracting fixed point across an unstable fixed point, which forms the boundary of the basin of attraction. The calculation starts from the trace formula for the eigenvalues of the operator ruling the time evolution of the probability density in noisy maps. The escape rate is determined by the loop formed by two heteroclinic orbits connecting back and forth the two fixed points in a two-dimensional auxiliary deterministic dynamical system. The escape rate is obtained, including the expression of the prefactor to van't Hoff-Arrhenius exponential factor./L'échappement des trajectoires est un phénomène omniprésent dans les systèmes dynamiques ouverts et les processus stochastiques. Si l'échappement se produit de façon répétitive pour un ensemble statistique de trajectoires, la population des trajectoires restantes subit souvent une décroissance exponentielle caractérisée par le taux d'échappement. L'inverse du taux d'échappement définit alors la durée de vie de l'état transitoire associé, ce qui représente une propriété intrinsèque du système. Ce paradigme est fondamental pour la théorie de la nucléation et, de manière générale, pour la théorie des taux de transitions en chimie, en physique et en biologie.<p><p>Dans de nombreux cas, l'échappement est induit par la présence de bruit, qui peut être d'origine interne ou externe. Ceci concerne en particulier l'échappement activé thermiquement à travers une barrière d'énergie potentielle, et plus généralement, l'échappement dû au bruit dans les systèmes dynamiques à temps continu ou à temps discret.<p><p>Dans la limite de faible bruit, on observe souvent une décroissance exponentielle du taux d'échappement en fonction de l'inverse de l'amplitude du bruit, un comportement qui est régi par la loi de van't Hoff-Arrhenius de la cinétique chimique. En particulier, les deux quantités importantes de cette loi sont le coefficient de la dépendance exponentielle (c'est-à-dire ``l'énergie d'activation') et son préfacteur.<p><p>L'objectif de cette thèse est de développer une théorie analytique pour déterminer ces deux quantités. La théorie que nous présentons concerne les systèmes unidimensionnels à temps continu ou discret perturbés par un bruit blanc gaussien et nous considérons le problème de l'échappement du bassin d'attraction d'un point fixe attractif. Pour s'échapper, les trajectoires du système bruité initialement contenues dans ce bassin d'attraction doivent alors traverser un point fixe instable qui forme la limite du bassin.<p><p>Dans le présent travail, et pour les deux types de systèmes, une formule est dérivée pour le taux d'échappement du point fixe attractif en utilisant des méthodes d'intégrales de chemin. Le calcul utilise la formule de trace pour les valeurs propres de l'opérateur gouvernant l'évolution temporelle de la densité de probabilité dans le système bruité. Le taux d'échappement est déterminé en considérant la boucle formée par deux orbites hétéroclines liant dans les deux sens les deux points fixes dans un système dynamique auxiliaire symplectique et bidimensionnel. On obtient alors le taux d'échappement, comprenant l'expression du préfacteur de l'exponentielle de la loi de van't Hoff-Arrhenius. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished