5 resultados para kink solutions in finite volume

em CORA - Cork Open Research Archive - University College Cork - Ireland


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This thesis is concerned with uniformly convergent finite element methods for numerically solving singularly perturbed parabolic partial differential equations in one space variable. First, we use Petrov-Galerkin finite element methods to generate three schemes for such problems, each of these schemes uses exponentially fitted elements in space. Two of them are lumped and the other is non-lumped. On meshes which are either arbitrary or slightly restricted, we derive global energy norm and L2 norm error bounds, uniformly in the diffusion parameter. Under some reasonable global assumptions together with realistic local assumptions on the solution and its derivatives, we prove that these exponentially fitted schemes are locally uniformly convergent, with order one, in a discrete L∞norm both outside and inside the boundary layer. We next analyse a streamline diffusion scheme on a Shishkin mesh for a model singularly perturbed parabolic partial differential equation. The method with piecewise linear space-time elements is shown, under reasonable assumptions on the solution, to be convergent, independently of the diffusion parameter, with a pointwise accuracy of almost order 5/4 outside layers and almost order 3/4 inside the boundary layer. Numerical results for the above schemes are presented. Finally, we examine a cell vertex finite volume method which is applied to a model time-dependent convection-diffusion problem. Local errors away from all layers are obtained in the l2 seminorm by using techniques from finite element analysis.

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This thesis deals with the evaporation of non-ideal liquid mixtures using a multicomponent mass transfer approach. It develops the concept of evaporation maps as a convenient way of representing the dynamic composition changes of ternary mixtures during an evaporation process. Evaporation maps represent the residual composition of evaporating ternary non-ideal mixtures over the full range of composition, and are analogous to the commonly-used residue curve maps of simple distillation processes. The evaporation process initially considered in this work involves gas-phase limited evaporation from a liquid or wetted-solid surface, over which a gas flows at known conditions. Evaporation may occur into a pure inert gas, or into one pre-loaded with a known fraction of one of the ternary components. To explore multicomponent masstransfer effects, a model is developed that uses an exact solution to the Maxwell-Stefan equations for mass transfer in the gas film, with a lumped approach applied to the liquid phase. Solutions to the evaporation model take the form of trajectories in temperaturecomposition space, which are then projected onto a ternary diagram to form the map. Novel algorithms are developed for computation of pseudo-azeotropes in the evaporating mixture, and for calculation of the multicomponent wet-bulb temperature at a given liquid composition. A numerical continuation method is used to track the bifurcations which occur in the evaporation maps, where the composition of one component of the pre-loaded gas is the bifurcation parameter. The bifurcation diagrams can in principle be used to determine the required gas composition to produce a specific terminal composition in the liquid. A simple homotopy method is developed to track the locations of the various possible pseudo-azeotropes in the mixture. The stability of pseudo-azeotropes in the gas-phase limited case is examined using a linearized analysis of the governing equations. Algorithms for the calculation of separation boundaries in the evaporation maps are developed using an optimization-based method, as well as a method employing eigenvectors derived from the linearized analysis. The flexure of the wet-bulb temperature surface is explored, and it is shown how evaporation trajectories cross ridges and valleys, so that ridges and valleys of the surface do not coincide with separation boundaries. Finally, the assumption of gas-phase limited mass transfer is relaxed, by employing a model that includes diffusion in the liquid phase. A finite-volume method is used to solve the system of partial differential equations that results. The evaporation trajectories for the distributed model reduce to those of the lumped (gas-phase limited) model as the diffusivity in the liquid increases; under the same gas-phase conditions the permissible terminal compositions of the distributed and lumped models are the same.

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The past two decades has seen a dramatic upheaval in the international world order: the end of the Cold War, the 9/11 attacks and the subsequent 'War on Terror', increased Jihadist activities, the accelerated pace of globalization, climate change and the 2008 global financial crisis have contributed to fear, uncertainty, poverty, conflict, massive displacements of populations of asylum seekers and refugees globally and a proliferation of Protracted Refugee Situations (PRS), defined as situations in which refugees have been in exile 'for 5 years or more after their initial displacement, without immediate prospects for implementation of durable solutions. In the past two decades there has been a huge proliferation of these with more than 7.2 million refugees now trapped in these PRS, with a further 16 million internally displaced persons (IDPs) trapped in camps within their own countries. The Dadaab refugee complex in Kenya, which of as March 2012, holds over 463,000 refugees, is the most significant and extreme example in recent times of a PRS. It was established in 1991 following the collapse of the Somali Government of Dictator Siad Barre, and the disintegration of Somalia into the chaos that still exists today. PRS such as Dadaab raise particular issues about humanitarianism in terms of aid, protection, security, human rights and the actions (or inaction) of the various stakeholders on an international, national and local level. This thesis investigates these issues by the use of a case study methodology on Dadaab as a PRS, framed in the context of humanitarianism and in particular the issues that arise in terms of how the international community, the UN system and individual states provide assistance and protection to vulnerable populations. Although the refugee camps have been in existence (as of 2012) for over 20 years, there has never been such a detailed study of Dadaab (or any other PRS) undertaken to date and would be of interest to academics in the areas of international relations, refugee/migration studies and global Governance as well as practitioners in both humanitarian response and development

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The response of Lactococcus lactis subsp. cremoris NCDO 712 to low water activity (aw) was investigated, both in relation to growth following moderate reductions in the aw and in terms of survival following substantial reduction of the aw with NaCI. Lc.lactis NCDO 712 was capable of growth in the presence of ≤ 4% w/v NaCI and concentrations in excess of 4% w/v were lethal to the cells. The presence of magnesium ions significantly increased the resistance of NCDO 712 to challenge with NaCI and also to challenge with high temperature or low pH. Survival of Lc.lactis NCDO 712 exposed to high NaCI concentrations was growth phase dependent and cells were most sensitive in the early exponential phase of growth. Pre-exposure to 3% w/v NaCI induced limited protection against subsequent challenge with higher NaCI concentrations. The induction was inhibited by chloramphenicol and even when induced, the response did not protect against NaCI concentrations> 10% w/v. When growing at low aw, potassium was accumulated by Lc. lactis NCDO 712 growing at low aw, if the aw was reduced by glucose or fructose, but not by NaCI. Reducing the potassium concentration of chemically defined medium from 20 to 0.5 mM) produced a substantial reduction in the growth rate, if the aw was reduced with NaCI, but not with glucose or fructose. The reduction of the growth rate correlated strongly with a reduction in the cytoplasmic potassium concentration and in cell volume. Addition of the compatible solute glycine betaine, partially reversed the inhibition of growth rate and partially restored the cell volume. The potassium transport system was characterised in cells grown in medium at both high and low aw. It appeared that a single system was present, which was induced approximately two-fold by growth at low aw. Potassium transport was assayed in vitro using cells depleted of potassium; the assay was competitively inhibited by Na+ and by the other monovalent cations NH4+, Li+, and Cs+. There was a strong correlation between the ability of strains of Lc. lactis subsp. lactis and subsp. cremoris to grow at low aw and their ability to accumulate the compatible solute glycine betaine. The Lc. lactis subsp. cremoris strains incapable of growth at NaCI concentrations> 2% w/v did not accumulate glycine betaine when growing at low aw, whereas strains capable of growth at NaCI concentrations up to 4% w/v did. A mutant, extremely sensitive to low aw was isolated from the parent strain Lc. lactis subsp. cremoris MG 1363, a plasmid free derivative of NCDO 712. The parent strain tolerated up to 4% w/v NaCI and actively accumulated glycine betaine when challenged at low aw. The mutant had lost the ability to accumulate glycine betaine and was incapable of growth at NaCI concentrations >2% w/v or the equivalent concentration of glucose. As no other compatible solute seemed capable of substitution for glycine betaine, the data suggest that the traditional; phenotypic speciation of strains on the basis of tolerance to 4% w/v NaCI can be explained as possession or lack of a glycine betaine transport system.