Théorèmes d'existence pour des systèmes d'équations différentielles et d'équations aux échelles de temps.

Nous présentons dans cette thèse des théorèmes d’existence pour des systèmes d’équations différentielles non-linéaires d’ordre trois, pour des systèmes d’équa- tions et d’inclusions aux échelles de temps non-linéaires d’ordre un et pour des systèmes d’équations aux échelles de temps non-linéaires d’ordre deux sous cer- taines conditions aux limites. Dans le chapitre trois, nous introduirons une notion de tube-solution pour obtenir des théorèmes d’existence pour des systèmes d’équations différentielles du troisième ordre. Cette nouvelle notion généralise aux systèmes les notions de sous- et sur-solutions pour le problème aux limites de l’équation différentielle du troisième ordre étudiée dans [34]. Dans la dernière section de ce chapitre, nous traitons les systèmes d’ordre trois lorsque f est soumise à une condition de crois- sance de type Wintner-Nagumo. Pour admettre l’existence de solutions d’un tel système, nous aurons recours à la théorie des inclusions différentielles. Ce résultat d’existence généralise de diverses façons un théorème de Grossinho et Minhós [34]. Le chapitre suivant porte sur l’existence de solutions pour deux types de sys- tèmes d’équations aux échelles de temps du premier ordre. Les résultats d’exis- tence pour ces deux problèmes ont été obtenus grâce à des notions de tube-solution adaptées à ces systèmes. Le premier théorème généralise entre autre aux systèmes et à une échelle de temps quelconque, un résultat obtenu pour des équations aux différences finies par Mawhin et Bereanu [9]. Ce résultat permet également d’obte- nir l’existence de solutions pour de nouveaux systèmes dont on ne pouvait obtenir l’existence en utilisant le résultat de Dai et Tisdell [17]. Le deuxième théorème de ce chapitre généralise quant à lui, sous certaines conditions, des résultats de [60]. Le chapitre cinq aborde un nouveau théorème d’existence pour un système d’in- clusions aux échelles de temps du premier ordre. Selon nos recherches, aucun résultat avant celui-ci ne traitait de l’existence de solutions pour des systèmes d’inclusions de ce type. Ainsi, ce chapitre ouvre de nouvelles possibilités dans le domaine des inclusions aux échelles de temps. Notre résultat a été obtenu encore une fois à l’aide d’une hypothèse de tube-solution adaptée au problème. Au chapitre six, nous traitons l’existence de solutions pour des systèmes d’équations aux échelles de temps d’ordre deux. Le premier théorème d’existence que nous obtenons généralise les résultats de [36] étant donné que l’hypothèse que ces auteurs utilisent pour faire la majoration a priori est un cas particulier de notre hypothèse de tube-solution pour ce type de systèmes. Notons également que notre définition de tube-solution généralise aux systèmes les notions de sous- et sur-solutions introduites pour les équations d’ordre deux par [4] et [55]. Ainsi, nous généralisons également des résultats obtenus pour des équations aux échelles de temps d’ordre deux. Finalement, nous proposons un nouveau résultat d’exis- tence pour un système dont le membre droit des équations dépend de la ∆-dérivée de la fonction.

Existence et multiplicité de solutions de systèmes d'équations et de systèmes d'inclusions différentielles avec opérateurs maximaux monotones

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Existence et multiplicité de solutions de systèmes d'équations et de systèmes d'inclusions différentielles avec opérateurs maximaux monotones

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

An analytical solution for solid stresses in a silo with an inner tube

This paper presents an analytical solution for the solid stresses in a silo with an internal tube. The research was conducted to support the design of a group of full scale silos with large inner concrete tubes. The silos were blasted and formed out of solid rock underground for storing iron ore pellets. Each of these silos is 40m in diameter and has a 10m diameter concrete tube with five levels of openings constructed at the centre of each rock silo. A large scale model was constructed to investigate the stress regime for the stored pellets and to evaluate the solids flow pattern and the loading on the concrete tube. This paper focuses on the development of an analytical solution for stresses in the iron ore pellets in the silo and the effect of the central tube on the stress regimes. The solution is verified using finite element analysis before being applied to analyse stresses in the solid in the full scale silo and the effect of the size of the tube.

Visualization of thermal characteristics around the absorber tube of a standard parabolic trough thermal collector by 3D simulation

Three dimensional conjugate heat transfer simulation of a standard parabolic trough thermal collector receiver is performed numerically in order to visualize and analyze the surface thermal characteristics. The computational model is developed in Ansys Fluent environment based on some simplified assumptions. Three test conditions are selected from the existing literature to verify the numerical model directly, and reasonably good agreement between the model and the test results confirms the reliability of the simulation. Solar radiation flux profile around the tube is also approximated from the literature. An in house macro is written to read the input solar flux as a heat flux wall boundary condition for the tube wall. The numerical results show that there is an abrupt variation in the resultant heat flux along the circumference of the receiver. Consequently, the temperature varies throughout the tube surface. The lower half of the horizontal receiver enjoys the maximum solar flux, and therefore, experiences the maximum temperature rise compared to the upper part with almost leveled temperature. Reasonable attributions and suggestions are made on this particular type of conjugate thermal system. The knowledge that gained so far from this study will be used to further the analysis and to design an efficient concentrator photovoltaic collector in near future.

Magnetohydrodynamic unsteady flow in a tube of variable cross section in an axial magnetic field

Oscillatory flow in a tube of slowly varying cross section is investigated in the presence of a uniform magnetic field in the axial direction. A perturbation solution including steady streaming is presented. The pressure and shear stress on the wall for various parameters governing the flow are discussed. Physics of Fluids is copyrighted by The American Institute of Physics.

Stability of the viscous flow of a fluid through a flexible tube

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (rho VR/eta), the ratio of the viscosities of the wall and fluid eta(r) = (eta(s)/eta), the ratio of radii H and the dimensionless velocity Gamma = (rho V-2/G)(1/2). Here rho is the density of the fluid, G is the coefficient of elasticity of the wall and V is the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter epsilon = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate s((0)), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctuations due to the Reynolds stress. There is an O(epsilon(1/2)) correction to the growth rate, s((1)), due to the presence of a wall layer of thickness epsilon(1/2)R where the viscous stresses are O(epsilon(1/2)) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Gamma and wavenumber k where s((1)) = 0. At these points, the wall layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(epsilon) correction to the growth rate s((2)) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s((2)) increases proportional to (H-1)(-2) for (H-1) much less than 1 (thickness of wall much less than the tube radius), and decreases proportional to H-4 for H much greater than 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube

Stability of the flow of a fluid through a flexible tube at high Reynolds number

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (ρVR / η), the ratio of the viscosities of the wall and fluid ηr = (ηs/η), the ratio of radii H and the dimensionless velocity Γ = (ρV2/G)1/2. Here ρ is the density of the fluid, G is the coefficient of elasticity of the wall and Vis the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter ε = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate do), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctruations due to the Reynolds strees. There is an O(ε1/2) correction to the growth rate, s(1), due to the presence of a wall layer of thickness ε1/2R where the viscous stresses are O(ε1/2) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Γ and wavenumber k where s(l) = 0. At these points, the wail layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(ε) correction to the growth rate s(2) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s(2) increases [is proportional to] (H − 1)−2 for (H − 1) [double less-than sign] 1 (thickness of wall much less than the tube radius), and decreases [is proportional to] (H−4 for H [dbl greater-than sign] 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube.

Riemann shock tube: 1D normal shocks in air, simulations and experiments

This paper presents numerical simulation of the evolution of one-dimensional normal shocks, their propagation, reflection and interaction in air using a single diaphragm Riemann shock tube and validate them using experimental results. Mathematical model is derived for one-dimensional compressible flow of viscous and conducting medium. Dimensionless form of the mathematical model is used to construct space-time finite element processes based on minimization of the space-time residual functional. The space-time local approximation functions for space-time p-version hierarchical finite elements are considered in higher order GRAPHICS] spaces that permit desired order of global differentiability of local approximations in space and time. The resulting algebraic systems from this approach yield unconditionally positive-definite coefficient matrices, hence ensure unique numerical solution. The evolution is computed for a space-time strip corresponding to a time increment Delta t and then time march to obtain the evolution up to any desired value of time. Numerical studies are designed using recently invented hand-driven shock tube (Reddy tube) parameters, high/low side density and pressure values, high- and low-pressure side shock tube lengths, so that numerically computed results can be compared with actual experimental measurements.

Bypass transition to sustained thermoacoustic oscillations in a linearly stable rijke tube

In this paper we examine triggering in a simple linearly-stable thermoacoustic system using techniques from flow instability and optimal control. Firstly, for a noiseless system, we find the initial states that have highest energy growth over given times and from given energies. Secondly, by varying the initial energy, we find the lowest energy that just triggers to a stable periodic solution. We show that the corresponding initial state grows first towards an unstable periodic solution and, from there, to the stable periodic solution. This exploits linear transient growth, which arises due to nonnormality in the governing equations and is directly analogous to bypass transition to turbulence. Thirdly, we introduce noise that has similar spectral characteristics to this initial state. We show that, when triggering from low noise levels, the system grows to high amplitude self-sustained oscillations by first growing towards the unstable periodic solution of the noiseless system. This helps to explain the experimental observation that linearly-stable systems can trigger to self-sustained oscillations even with low background noise. © 2010 by University of Cambridge. Published by the American Institute of Aeronautics and Astronautics, Inc.

Analysis of estrogens in environmental waters using polymer monolith in-polyether ether ketone tube solid-phase microextraction combined with high-performance liquid chromatography

A simple, rapid and sensitive on-line method for simultaneous determination of four endocrine disruptors (17 beta-estradiol, estriol, bisphenol A and 17 alpha-ethinylestradiol) in environmental waters was developed by coupling in-tube solid-phase microextraction (SPME) to high-performance liquid chromatography (HPLC) with fluorescence detection (FLD). A poly(acrylamide-vinylpyridine-NAP-methylene bisacrylamide) monolith, synthesized inside a polyether ether ketone (PEEK) tube, was selected as the extraction medium. To achieve optimum extraction performance, several parameters were investigated, including extraction flow-rate, extraction time, and pH value, inorganic salt and organic solvent content of the sample matrix. By simply filtered with nylon membrane filter and adjusting the pH of samples to 6.0 with phosphoric acid, the sample solution then could be directly injected into the device for extraction. Low detection limits (S/N = 3) and quantification limits (S/N = 10) of the proposed method were achieved in the range of 0.006-0.10 ng/mL and 0.02-0.35 ng/mL from spiked lake waters, respectively. The calibration curves of four endocrine disruptors showed good linearity ranging from quantification limits to 50 ng/mL with a linear coefficient R-2 value above 0.9913. Good method reproducibility was also found by intra- and inter-day precisions, yielding the RSDs less than 12 and 9.8%, respectively. Finally, the proposed method was successfully applied to the determination of these compounds in several environmental waters. (c) 2006 Elsevier B.V. All rights reserved.

Determination of mercury with a flow injection quartz tube atomic absorption spectrometry

A method was developed for the determination of micro mercury in the soil, plants and the traditional Chinese medicine using flow injection quartz tube-atomic absorption spectrometry. The effect of the factors such as acidity,. the carrier solution, the flow rate of reductive solution and argon gas, etc. on the determination was studied. When vanadic oxide, nitric acid and sulfuric acid were used to decompose the sample reliable result could be obtained. The characteristic mass of the method is 59 pg, the detection limit is 0.028 mug/L, RSD is < 3.9% and the recovery is in the range of 94% &SIM; 102%.

AN IMPEDANCE TUBE FOR THE IN-SITU CLASSIFICATION OF BUBBLY LIQUIDS

It is well documented that the presence of even a few air bubbles in water can signifi- cantly alter the propagation and scattering of sound. Air bubbles are both naturally and artificially generated in all marine environments, especially near the sea surface. The abil- ity to measure the acoustic propagation parameters of bubbly liquids in situ has long been a goal of the underwater acoustics community. One promising solution is a submersible, thick-walled, liquid-filled impedance tube. Recent water-filled impedance tube work was successful at characterizing low void fraction bubbly liquids in the laboratory [1]. This work details the modifications made to the existing impedance tube design to allow for submersed deployment in a controlled environment, such as a large tank or a test pond. As well as being submersible, the useable frequency range of the device is increased from 5 - 9 kHz to 1 - 16 kHz and it does not require any form of calibration. The opening of the new impedance tube is fitted with a large stainless steel flange to better define the boundary condition on the plane of the tube opening. The new device was validated against the classic theoretical result for the complex reflection coefficient of a tube opening fitted with an infinite flange. The complex reflection coefficient was then measured with a bubbly liquid (order 250 micron radius and 0.1 - 0.5 % void fraction) outside the tube opening. Results from the bubbly liquid experiments were inconsistent with flanged tube theory using current bubbly liquid models. The results were more closely matched to unflanged tube theory, suggesting that the high attenuation and phase speeds in the bubbly liquid made the tube opening appear as if it were radiating into free space.

Novel semi-interpenetrating hydrogel networks with enhanced mechanical properties and thermoresponsive engineered drug delivery, designed as bioactive endotracheal tube biomaterials

Thermoresponsive polymeric platforms are used to optimise drug delivery in pharmaceutical systems and bioactive medical devices. However, the practical application of these systems is compromised by their poor mechanical properties. This study describes the design of thermoresponsive semi-interpenetrating polymer networks (s-IPNs) based on cross-linked p(NIPAA) or p(NIPAA-co-HEMA) hydrogels containing poly(e-caprolactone) designed to address this issue. Using DSC, the lower critical solution temperature of the co-polymer and p(NIPAA) matrices were circa 34 °C and 32 °C, respectively. PCL was physically dispersed within the hydrogel matrices as confirmed using confocal scanning laser microscopy and DSC and resulted in marked changes in the mechanical properties (ultimate tensile strength, Young's modulus) without adversely compromising the elongation properties. P(NIPAA) networks containing dispersed PCL exhibited thermoresponsive swelling properties following immersion in buffer (pH 7), with the equilibrium-swelling ratio being greater at 20 °C than 37 °C and greatest for p(NIPAA)/PCL systems at 20 °C. The incorporation of PCL significantly lowered the equilibrium swelling ratio of the various networks but this was not deemed practically significant for s-IPNs based on p(NIPAA). Thermoresponsive release of metronidazole was observed from s-IPN composed of p(NIPAA)/PCL at 37 °C but not from p(NIPAA-co-HEMA)/PCL at this temperature. In all other platforms, drug release at 20 °C was significantly similar to that at 37 °C and was diffusion controlled. This study has uniquely described a strategy by which thermoresponsive drug release may be performed from polymeric platforms with highly elastic properties. It is proposed that these materials may be used clinically as bioactive endotracheal tubes, designed to offer enhanced resistance to ventilator associated pneumonia, a clinical condition associated with the use of endotracheal tubes where stimulus responsive drug release from biomaterials of significant mechanical properties would be advantageous. © 2012 Elsevier B.V. All rights reserved.