The work presented in this thesis studies acoustic perturbations in slowly varying pipes. The slow variation is introduced in the form of a small parameter ${\epsilon}$ and through this in turn gives rise to a slow axial scale $X$ such that $X = {\epsilon}x$ where $x$ is the normal axial coordinate. This allows an asymptotic approach and the WKB method is used to solve the subsequent mathematical problems. The first deals with the existence of a trapped mode in a hard-walled pipe of varying radius conveying fluid. For the derived leading order propagating mode solution, its amplitude becomes singular at transition points $X_{t}$ and $X_{t'}$ where $X_{t} > 0$ and $X_{t'} < 0$ and thus is unable to propagate past these points. Because of the break down in the solution, this leads to the theory that in the neighbourhood of these points there exists a boundary layer in which the original assumption about having slow variation does not hold. By first seeking the thickness of the layer, valid solutions can then be derived and then matched to the outer solutions in order to produce a uniform solution which holds for the entire axial domain. Once this is achieved, it is then used to derive trapped mode solutions. In this case, the theory used is that of two single turning points which are then combined to obtain the full solution. It is illustrated through consideration of examples and the dependence on ${\epsilon}$ is also shown through various plots. This problem will be considered for a symmetric and asymmetric duct and for differing duct parameters. Problems may arise when the two turning points lie close together and so we seek to improve on the method used by deriving a solution to trapped modes encompassing both turning points, which will be proposed together with some illustrations in order to justify its use and reliability. Next, the case of mode propagations on a thin elastic shell of varying radius conveying fluid is studied. The acoustic solutions of a straight shell in vacuo are first briefly reviewed and then built up by the addition of radius variation and the presence of a stationary fluid. The work presented first outlines the analysis for wave propagation in a slowly-varying thin elastic shell in vacuo. It is found that the shell and the fluid terms are coupled through the fluid pressure term, which is added to the equation governing the radial shell displacements since the pressure is assumed to affect radial motion only. Once the newly corrected equation for the radial shell displacements has been obtained, together with the axial and azimuthal displacements equations, this new system of governing equations is then separated into leading order ${\epsilon}^{0}$ and first order ${\epsilon}^{1}$ systems. In order to simplify the calculations, only the zeroth azimuthal order $m = 0$ will be studied here. With this simplification, a notable result is that the solutions of the torsional motion is decoupled from the axial and radial solutions. Once the dispersion equation is extracted from the leading order system, it can be seen that the axial and radial solutions are in fact coupled. The solution to the in vacuo with varying radius problem is first briefly presented and it is then followed by the solution to the fluid inclusion problem with varying radius, which makes up the main part of this section. The solution is studied for various frequencies and at various points along the shell. In addition, the axial and radial components of the first three modes are examined along with their amplitudes and energy distributions. Finally, mean flow is added and the same analysis is carried out, paying particular attention to the differences which arise in comparison to the stationary flow case.

Contamination of soil/groundwater supplies by gasoline and other petroleum-derived hydrocarbons released from underground storage tanks (USTs) is a serious and widespread environmental problem. Corrosion, ground movement, and poor sealing can cause leaks in tanks and associated piping. Petroleum hydrocarbons contain methyl tertiary-butyl ether (MTBE) (a fuel oxygenate), benzene, toluene, ethylbenzene, and xylene isomers (BTEX), the major components of gasoline, which are hazardous substances regulated by many nations.The objective of this proposed study is to assess the potential of using a passive in situ oxidation barrier system. This passive active barrier system has advantages over conventional systems including less maintenance, cost-effectiveness, no above-ground facilities, no groundwater pumping and reinjection, and groundwater remediation in situ. The oxidation barrier system included a persulfate-releasing barrier, which contains persulfate-releasing materials. The slow-released persulfate would oxidize MTBE and benzene in aquifer. The persulfate-releasing materials would release persulfate when contacts with groundwater, thus oxidizes the MTBE and benzene. In the first part of this study, bench scale experiment was also performed to produce the persulfate-releasing materials high persulfate-releasing rate. The components of the persulfate-releasing materials and optimal concentrations of those components were determined in this study. Results indicate that the highest persulfate releasing rate can be obtained when the mass ratio of cement/sand/water was 1.4/0/0.7. Result obtained from the persulfate-releasing materials test and bench-scale were used for the design and operation of the following column experiments. Results from the column experiment indicate that approximately 98% of MTBE and 99% of benzene could be removed during the early persulfate-releasing stage. Results also reveal that the produced oxidation byproducts of MTBE, tert-butyl formate (TBF) and tert-butyl alcohol (TBA), can also be produce an acetone. Results from this study suggest that extra Fe(II) would cause the decrease in oxidation rates due to the reaction of sulfate with Fe(II). Results show that the parameters, which would affect the oxidation rate include persulfate concentration, oxidant reduction potential (ORP), conductivity, sulfate concentration, and contaminant concentration. The proposed treatment scheme would be expected to provide a more cost-effective alternative to remediate MTBE and other petroleum-hydrocarbon contaminated aquifers. Knowledge obtained from this study will aid in designing a persulfate oxidation system for site remediation.

This thesis concerns the use of labelled infinite trees to solve families of nested recursions of the form $R(n)=\sum_{i=1}^kR(n-a_i-\sum_{j=1}^{p_i}R(n-b_{ij}))+w$, where $a_i$ is a nonnegative integer, $w$ is any integer, and $b_{ij},k,$ and $p_i$ are natural numbers. We show that the solutions to many families of such nested recursions have an intriguing combinatorial interpretation, namely, they count nodes on the bottom level of labelled infinite trees that correspond to the recursion. Furthermore, we show how the parameters defining these recursion families relate in a natural way to specific structural properties of the corresponding tree families. We introduce a general tree ``pruning" methodology that we use to establish all the required tree-sequence correspondences.

This thesis concerns the use of labelled infinite trees to solve families of nested recursions of the form $R(n)=\sum_{i=1}^kR(n-a_i-\sum_{j=1}^{p_i}R(n-b_{ij}))+w$, where $a_i$ is a nonnegative integer, $w$ is any integer, and $b_{ij},k,$ and $p_i$ are natural numbers. We show that the solutions to many families of such nested recursions have an intriguing combinatorial interpretation, namely, they count nodes on the bottom level of labelled infinite trees that correspond to the recursion. Furthermore, we show how the parameters defining these recursion families relate in a natural way to specific structural properties of the corresponding tree families. We introduce a general tree ``pruning" methodology that we use to establish all the required tree-sequence correspondences.

<p>As obesity has become one of the most prevalent metabolic diseases, and diabetes mellitus has become the seventh leading causes of death in the United States, alternative food/nutrition-based approaches to tackle obesity that are both efficacious and cost effective are in high demand. Since starch and its derived products are the principal dietary supply of glucose, strategies of using slowly digestible starch to achieve moderated glycemic response and prolonged glucose delivery, as well as to locationally digest starch into the ileum, have shown successful results such as moderation of insulinemia and reducing food intake in obese animals. An important regulator of appetite suppression is the neuroendocrine system of the gut-brain axis. Glucagon-like peptide-1 (GLP-1), oxyntomodulin (OXM), and peptide YY (PYY) are the main anorexigenic peptide products of the intestinal enterendocrine L-cells that regulate postprandial insulin levels as well as satiety signals. The stimulation of the enteroendocrine L-cells throughout the gastrointestinal tract through glucose, fatty acids and proteins has been extensively studied and confirmed. However, the stimulatory effect of complex dietary carbohydrates on L-cells is not described. In this dissertation, we investigated the <i>in vitro</i> intestinal cell chemosensation of L-cells to α-amylase starch digestion products, named maltooligosaccharides (MOS), and in the possible application of using slowly digestible starch delivery of MOS <i>in vivo</i>.</p> <p>In Chapter II of this dissertation, we reported a significantly higher stimulatory effect of MOS on GLP-1 and OXM secretion compared to glucose in mouse and human L-cells, respectively. Additionally, maltotriose enhanced the relative expression of the gastrointestinal peptide, cholecystokinin. Moreover, MOS exhibited protective effects on barrier function and monolayer integrity of intestinal epithelial cells. </p> <p>In Chapters III and IV, we performed a multiomics approach where transcriptomic analysis and global protein profiling of mouse L-cells treated with different types of MOS showed that the carbohydrates exhibit their effects through the induction of exocytosis of GLP-1- or OXM-containing vesicles and not through a positive regulation of the proglucagon gene expression. It is suggested that MOS induce higher secretion, but not higher synthesis, of the proglucagon gene products. In addition, maltotriose treatment downregulated the relative expression of the glucotoxicity marker, thioredoxin-interacting protein, and upregulated the relative expression of tight junction proteins supporting a role of MOS in barrier function integrity.</p> <p>Translating the <i>in vitro</i> findings into an <i>in vivo</i> application that is beneficial for human health required the use of controllable tool for the delivery of MOS throughout the small intestine for sensing by a higher number of L-cells. Slowly digestible starch (SDS), compared to rapidly digestible starch, provided such a tool. For this purpose, we used alginate-entrapped SDS microspheres that digest distally into the ileum to examine the role of SDS in the intervention and prevention of obesity in C57BL/6J diet-induced obese (DIO) and lean mice models.</p> <p>Results showed that 20% SDS in low-fat diets significantly improved weight loss and food intake reduction in DIO mice converted to low-fat diet for 12 weeks. Similarly, 15% SDS in high-fat diets showed significant reduction in body fat percent and significant increase in lean body mass as well as considerable reduction in weight gain rate and food intake in lean mice fed on 45% of calories high-fat diet. Immunohistochemistry of small intestine of mice in both the intervention and prevention studies revealed an even and thorough distribution of GLP-1 positive L-cells.</p> <p>Overall, this dissertation proposes several insights into L-cell sensation of dietary starch-degraded MOS delivered by the consumption of slowly digestible starch. MOS exhibit unique influences on L-cell sensitivity and gut hormone productivity. Future research investigating the mechanisms of intestinal sensing of MOS, as well as the development of bioactive carbohydrate structures that could preserve body weight and modulate glucose tolerance <i>in vivo</i> is needed to translate these findings into nutritional recommendations and food products beneficial for human health. The intricate role of dietary carbohydrates on gut physiological response, related to satiety and food intake could be a new approach for design of foods for health applications.</p>

L'objectif de ce travail était d'améliorer la compréhension et la modélisation de la propagation de la houle au-dessus d'une topographie lentement variable et en présence d'un courant inhomogène. Nous nous sommes en particulier intéressés à l'influence d'un courant cisaillé linéairement et verticalement sur la dynamique de la houle. Dans ce but un modèle linéaire de propagation de la houle a été développé et une campagne expérimentale a été menée en bassin de génie océanique. Au cours de cette campagne expérimentale les paramètres de la houle et du courant ont été mesurés avec une haute résolution spatio-temporelle. Nous avons pu décrire l'interaction complexe entre la houle et le courant, en particulier les effets de l'évolution spatiale des gradients verticaux et horizontaux de ce dernier sur la propagation de la houle. / The purpose of this work was the improvement of the understanding and the modelling of wave propagation over a slowly varying topography in presence of a inhomogeneous current. Particularly we focus on the influence of a linearly vertically sheared current on the wave behaviour. To this end, we develop a new wave propagation model and we carry out an experimental study in an ocean engineering basin.During the experiments, wave parameters and currents parameters have been measured with a high spatial and temporal resolution. This allows us to describe the complex interaction between the wave and the current, particularly its horizontal and vertical gradients effects on the wave propagation.

<p>Einstein's theory of general relativity is a cornerstone in the process of gaining increased understanding about problems of gravitational nature. It can be applied to problems on the huge length scales of cosmology and as far as we know it does not break down before the Planck scale is approached. Irrespective of scale, a perturbative approach is often a very useful way to reduce the Einstein system to manageable complexity and size.</p><p>The projects included in this thesis can be divided into three subcategories. In the first category the keyword is photon-photon scattering. General relativity predicts that scattering can take place on a flat background due to the curvature of space-time caused by the photons themselves. The coupling equations and cross-section are found and a comparison with the corresponding quantum field theoretical results is done to leading order. Moreover, photon-photon scattering due to exchange of virtual electron-positron pairs is considered as an effective field theory in terms of the Heisenberg-Euler Lagrangian resulting in a possible setup for experimental detection of this phenomenon using microwave cavities. The second category of projects is related to cosmology. Here linear perturbations around a flat FRW universe with a cosmological constant are considered and the corresponding temperature variations of the cosmic microwave background radiation are found. Furthermore, cosmological models of Bianchi type V are investigated using a method based on the invariant scheme for classification of metrics by Karlhede. The final category is slowly rotating stars. Here the problem of matching a perfect fluid interior of Petrov type D to an exterior axisymmetric vacuum solution is treated perturbatively up to second order in the rotational parameter.</p>

Einstein's theory of general relativity is a cornerstone in the process of gaining increased understanding about problems of gravitational nature. It can be applied to problems on the huge length scales of cosmology and as far as we know it does not break down before the Planck scale is approached. Irrespective of scale, a perturbative approach is often a very useful way to reduce the Einstein system to manageable complexity and size. The projects included in this thesis can be divided into three subcategories. In the first category the keyword is photon-photon scattering. General relativity predicts that scattering can take place on a flat background due to the curvature of space-time caused by the photons themselves. The coupling equations and cross-section are found and a comparison with the corresponding quantum field theoretical results is done to leading order. Moreover, photon-photon scattering due to exchange of virtual electron-positron pairs is considered as an effective field theory in terms of the Heisenberg-Euler Lagrangian resulting in a possible setup for experimental detection of this phenomenon using microwave cavities. The second category of projects is related to cosmology. Here linear perturbations around a flat FRW universe with a cosmological constant are considered and the corresponding temperature variations of the cosmic microwave background radiation are found. Furthermore, cosmological models of Bianchi type V are investigated using a method based on the invariant scheme for classification of metrics by Karlhede. The final category is slowly rotating stars. Here the problem of matching a perfect fluid interior of Petrov type D to an exterior axisymmetric vacuum solution is treated perturbatively up to second order in the rotational parameter.

Different modes of assisted ventilation were investigated in cats before and after lung lavage and after instillation of surfactant. The activity of single units of slowly adapting pulmonary stretch receptors (PSRs) in the vagal nerve and the integrated phrenic nerve activity were recorded. The instantaneous impulse frequency (fimp) of PSRs was calculated and related to transpulmonary pressure (Ptp), tidal volume (Vt) and the calculated energy storage of the lung (ΣP*ΔV). Respiratory rate (RR), inspiratory and expiratory time, and Vt were measured, and their coefficients of variation were calculated. During assist control (A/C) ventilation with different pressure waveforms, PNA was shorter and lower in amplitude with squarewave pressure waveform than with linear and sinusoidal pressure waveforms in cats with normal lungs, concomitantly with earlier peak fimp during inspiration and prolonged fimp during expiration. The type of pressure waveform can thus influence the spontaneous breathing effort during A/C ventilation. Proportional assist ventilation (PAV) is a new mode of assisted ventilation which servo-controls the applied airway pressure continuously in proportion to the breathing effort. After lung lavage and surfactant instillation, PAV improves ventilation markedly, with lower PNA and oesophageal pressure deflection and higher RR and variability of breathing, compared to CPAP. In addition, an earlier and higher maximal fimp was observed during PAV. Under conditions of low work and maintained control of breathing, PAV seems to be an attractive mode of ventilatory support. Low-threshold (LT) and high-threshold (HT) PSRs respond to the surfactant content of the lung partly independent of Ptp and Vt in spontaneously breathing cats, implying a possible effect of surfactant on PSRs. The PSR fimp normalized to ΣP*ΔV confirmed these findings and showed that LT and HT PSRs are intrinsically the same. After instillation of surfactant, compliance and PSR activity increased, but the breathing still remained shallow and rapid, suggesting a control of breathing less dominated by PSR activity.

The heterogeneous structure of fractured media can lead to complex spatiotemporal fluid invasion dynamics. It thus brings forward challenging fundamental questions in the context of out-of-equilibrium dynamical systems, but also relevant to many processes of interest. The goal of the Thesis is to study the spatio-temporal dynamics of the oil-air interface between displaced air and invading oil, in imbibition through a model open fracture. The research combines exhaustive experimental work with accurate data analysis based on methods of nonlinear statistical physics. The mean postion of the interface h(t) is studied in capillary rise experiments, giving rise to a new analytical solution for h(t). The fluctuations of the interface in forced-flow experiments are analysed in the context of kinetic roughening, characterizing a super-rough scaling scenario. Finally, the burst-like dynamics is studied by analysing the local and global velocities of the front, which are widely distributed and display complex spatio-temporal correlations. We define local and global avalanches whose sizes and durations are also widely distributed, with cutoffs that diverge with the capillary number. Intermittentcy of the global signal is quantified. The ensemble of results presented in this Thesis supports a very general picture of the nonequilibrium dynamics of slowly-driven fronts in open fractures: the lateral propagation of interfacial fluctuations is controlled by local mass conservation, through the lateral correlation length; and the advancement of the interface in the direction of propagation is controlled by the characteristic extent of the disorder d and by the mean front velocity.