Nesse trabalho, usamos métodos da teoria de homogeneização para analisar o compor- tamento assintótico das soluções da equação do p-Laplaciano com condição de contorno de Neumann posto numa família de domínios finos do tipo. De maneira geral, trabalhamos com funções G:(0,1)\\ x R - R uniformemente limitadas, suaves e L-periódicas na segunda variável. Note que o efeito de domínio fino é estabelecido passando ao limite no parâmetro \\varepsilon>0 com \\varepsilon\\to 0. Além disso, introduzimos um parâmetro \\alpha>0 com o objetivo de representar rugosidades via comportamento oscilat\\\'orio na fronteira superior de R^\\varepsilon. Em nossos resultados mostramos que no limite, uma equação unidimensional é obtida, preservando a quasilinearidade do problema original e capturando tanto o efeito da compressão como das oscilações. / In this work we apply homogenization theory methods in order to analyze the asymptotic behavior of the solutions of a p-Laplacian equation with Neumann boundary condition set in bounded thin domains of the type. Generally, we with functions G:(0,1) x R - R uniformly bounded, smooth and L-periodic in the second variable. The thin domain situation is established passing to the limit in the positive parameter \\varepsilon with \\varepsilon \\to 0. In our results we obtain a one dimensional equation that preserves the quasilinearity from the original problem and capturing the effects of compression and oscillations.

Utilizando uma faixa de temperatura entre 5° a 45°C, observou-se duas regiões de diferentes tendências para com o aumento da temperatura durante as oscilações (eletro-oxidação galvanostática, mesma corrente normalizada aplicada) no sistema ácido fórmico sobre platina policristalina em meio ácido. Até 25°C, o comportamento cinético operou de modo convencional, do tipo Arrhenius, sendo que acima desse ponto crítico observou-se o fenômeno de (sobre)compensação de temperatura. O sistema foi caracterizado fazendo uso de técnicas eletroquímicas clássicas e espectroscopia de impedância eletroquímica tendo ficado evidente um ponto de inflexão a 25°C que marca uma quebra na tendência em todas as frequências do sistema (f, Hopf,Sosc) e taxa de envenenamento. Os resultados foram discutidos em termos do papel-chave das espécies de PtO, que acoplam quimicamente as dinâmicas rápidas/lentas. Fomos capazes de: (i) identificar a competição entre duas etapas de reação como responsáveis pelos dois domínios de temperatura; (ii) comparar as energias de ativação relativas dessas duas etapas; E ademais (iii) especulamos sobre o papel de uma determinada etapa de reação no conjunto de reações responsáveis pelo aumento do período oscilatório. Com ajuda de métodos deconvolutivos, reforçamos a hipótese de que as etapas por trás do drift possuem menor energia de ativação que as etapas LH durante tais dinâmicas. Também estão aqui discutidos experimentos de monitoramento de temperatura local durante as dinâmicas oscilatórias. Duas estratégias experimentais foram empregadas: uma utilizando eletrodos-termômetros a base de termistores e outra utilizando um micro calorímetro onde sensores piroelétricos monitoraram as oscilações na temperatura do eletrodo de trabalho, altamente em fase com as oscilações de potencial. Destacamos que ambas configurações foram capazes de acompanhar as diferenças de temperatura durante as dinâmicas oscilatórias (na faixa de 0,1~0,5mK por ciclo). Os resultados obtidos para a reconstrução dos fluxos de calor (ø) corroboram com o atual modelo mecanístico da eletro-oxidação oscilante de ácido fórmico em Pt em meio ácido. Observamos que as etapas de envenenamento do eletrodo são acompanhadas pelo aumento no ø enquanto a reativação do eletrodo é acompanhada pela diminuição no ø. / The oscillating electro-oxidation of formic acid on polycrystalline platinum in acidic media, as a model system, was employed to investigate the temperature effects on the coupling of fast and slow dynamics processes belonging to its oscillatory dynamics, i.e. the core oscillator (fast dynamics) and the slow term deactivation of surface caused by the oxygen place-exchange process. Using a temperature range from 5 to 45°C, we observed two disparate regions of tendencies upon temperature increment on the galvanostatic oxidation. The system exhibits conventional Arrhenius behavior for T up to 25°C and, on the other hand, T > 25° revealed the occurrence of temperature (over)compensation. The system was characterized by means of conventional electrochemical techniques and electrochemical impedance spectroscopy. Clearly, we observed an inflexion point at 25°C marked by a break on the tendency of oscillatory frequency ( f, hopf, Sosc) and poisoning rates. Results were discussed in terms of the key role of PtO species, which chemically couple slow and fast dynamics. In summary we were able to: (i) identify the competition between two reaction steps as responsible for the two temperature domains; (ii) compare the relative activation energies of these two steps; and (iii) suggest the role of a given reaction step on the period-increasing set of reactions involved in the oscillatory dynamics. In addition, we performed experiments to monitor the local temperature of the interface during oscillatory dynamics. Two experimental strategies were applied: low cost thermometers-electrodes and a more sophisticated experimental set up based on pyroelectric detection. It should be noted that both configurations were able to monitor temperature differences during oscillatory dynamics (in the range of 0.1 ~ 0.5mK per cycle). The results obtained for the reconstruction of the heat fluxes (ø) corroborate with the current mechanistic model of the oscillating electro-oxidation of formic acid in Pt in acidic medium. We observed that the poisoning stages of the electrode are accompanied by the increase in ø while the reactivation of the electrode is accompanied by the decrease in ø.

Wormlike micelles are viscoelastic fluids that present an intermediate behavior between solids and ordinary liquids since they are elastic at short time scales but flow easily at large time scales. In opposition to Newtonian fluids, which have constant viscosity, these fluids usually exhibit a non-Newtonian response with a rate-dependent shear viscosity. Wall-bounded oscillatory flows of Newtonian and complex fluids are found in many practical situations. Oscillatory pipe flows are especially important in physiology in connection with the circulatory and respiratory systems of human beings, as well as in industrial processes such as fluid pumping, secondary oil recovery or filtration, and in acoustics. Pulsating flows are of particular interest also in the rheological characterization of complex fluids. We analyze the laminar oscillatory flow of viscoelastic fluids using the Maxwell and Oldroyd-B models. We have shown that in wall-bounded oscillatory flows of viscoelastic fluids the two characteristic lengths of the Ferry waves, the damping length and wavelength, together with the characteristic separation of the walls, define all the flow properties for fluid models with a linear shear-stress equation in unidirectional flow. In wall-bounded settings there exists the possibility that shear waves generated at different locations superpose themselves before decaying so that the shear waves interfere, giving rise to a resonant flow at well defined frequencies of driving. The theoretical predictions obtained for the laminar velocity profiles are validated by carrying out time-resolved Particle Image Velocimetry (PIV) experiments in a vertical pipe at small driving amplitudes. The oscillatory pipe flow has been investigated in the whole range of experimentally accessible driving frequencies and amplitudes, and classified in three main flow regimes: laminar, vortical, and non-axisymmetric vortical. By ramping up and down the driving amplitude at constant frequency we have been able to characterize the transition from laminar to more complex flows, under controlled driving conditions. The first hydrodynamic instability occurs when the laminar base flow becomes unstable against the formation of axisymmetric toroidal vortices that appear distributed along the cylinder. The calculation of root-mean-square fluctuations in the vertical direction, of the vertical and radial components of the velocity (averaged in time or over the tube diameter) has allowed to determine the critical amplitude at which the instability sets in with high accuracy. In the vortical flow an abrupt increase of the fluctuations is observed, that accounts for the loss of the vertical translational symmetry and the formation of vortices in the flow. This transition exhibits hysteresis when the driving amplitude is ramped up and down, which makes us presume that the bifurcation from the laminar flow has a subcritical nature. A second hydrodynamic instability occurs when the vortical flow loses the axial symmetry. In this flow regime the vortices are heavily distorted and no longer axisymmetric. The velocity and vorticity maps of the vortical flow measured in a meridional plane of the tube appear periodic in time, on time scales comparable to the driving period. Interestingly, the vortex formation is favored in the acceleration phases of the piston oscillation. Besides, we have uncovered a spatio-temporal dynamics on long time scales (much larger than the relaxation time of the fluid) that substantially modifies the flow organization. This slow dynamics is more effective in the bottom half of the cylinder, specially next to the driving piston. A global inspection of the vortical flow along the tube length reveals that the instability takes place earlier in the bottom part of the tube, in the vicinity of the driving piston. At increasing the driving amplitude the boundary between laminar and vortical flow progressively raises towards the top regions. And above a critical driving amplitude the entire fluid flow is vortical. The mechanism triggering the hydrodynamic instability from the laminar to the axisymmetric vortical flow is not yet clear. / L'objectiu d'aquesta Tesi és estudiar el flux oscil•latori vertical en fluids micel•lars. Els fluids micel•lars són fluids complexos amb propietats viscoelàstiques, de manera que mostren un comportament intermedi entre els sòlids i els líquids: són elàstics a escales de temps curtes però flueixen a escales de temps més llargues. En contraposició als fluids Newtonians, que tenen una viscositat constant, els fluids complexos mostren un comportament no-Newtonià, amb una viscositat que depèn del ritme de deformació. El fluxos oscil•latoris de fluids Newtonians o complexos en geometries confinades són especialment importants en fisiologia, en relació amb el sistema circulatori i respiratori d'éssers humans, i també en processos industrials com el bombejat de fluids, l'extracció de petroli, i en particular són interessants en la caracterització reològica de fluids complexos. Primer estudiem el flux oscil•latori des d'una perspectiva teòrica i analitzem el flux laminar de fluids viscoelàstics utilitzant els models de Maxwell i Oldroyd-B en un tub vertical. Hem mostrat que en fluxos confinats existeix la possibilitat que les ones de cisalla generades a les diferents parets se sobreposin abans d'esmorteir-se i que eventualment donin lloc a un fenomen de ressonància. Les prediccions teòriques obtingudes pel flux laminar són validades duent a terme experiments de Velocimetria d'Imatges de Partícules (PIV) en un tub vertical, per amplituds petites del forçament oscil•latori. Quan s'incrementa l'amplitud de l'oscil•lació el flux laminar evoluciona cap a fluxos que presenten una dependència espai-temporal més complexa. Fent rampes d'amplitud creixent a una freqüència fixada hem pogut caracteritzar experimentalment la transició del flux laminar a aquests fluxos més complexos, sota condicions de forçament ben controlades. La primera inestabilitat apareix quan el flux laminar esdevé inestable amb la corresponent formació d'anells de vorticitat apilats al llarg del tub. Es manifesta una segona inestabilitat per amplituds del forçament més grans, per la qual el flux vortical perd la simetria axial. En aquest nou règim els vòrtex estan fortament distorsionats i no són axisimètrics. Fent rampes d’amplitud creixent i decreixent hem observat que aquestes dues transicions presenten histèresi, i que per tant són de caràcter subcrític.

Concerns exist regarding the ability of HFOV to provide the needed lung protective ventilation for adult patients with ARDS. HFOV is increasingly being used as a lung protecting ventilation mode even if some of its protective attributes may be lost as the airway resistance (Raw) increases or decreases. In fact, in cases of shifting air resistance, HFOV may have caused lung injury. PURPOSE: The purpose of this study was to investigate the effect of airway resistance on tidal volume (Vt) delivered by HFOV to adult patients. Also, the study intended to determine direction for volume change when resistance increases or decreases. METHODS: An in vitro model was used to simulate an adult passive patient with ARDS using a breathing simulator (Active Servo Lung 5000, Ingmar Medical, Pittsburgh, PA, USA). Adjustable resistance and compliance for each lung was used. The resistance levels of 15, 30, 45 (cm H2O/L/sec) were used for upper and lower Raw and CL was fixed at 40 mL/cm H2O. The ventilator (Sensormedics 3100B) was set to MAP = 35 cm H2O, to insp-time of 33%, to bias flow =30 L/min, to delta-P of 80, and to 50% oxygen. Vt was recorded (n=3) for each Raw, and the data was collected on the host computer. Approximately 200-250 breaths of data for each Raw were captured via the ASL software and then converted to Excel for analysis. An average of 80 breathes (following the steady Vt level) was used in each analysis. DATA ANALYSIS: The data analysis was performed with one way ANOVA and with a post hoc Bonferroni test in order to determine the statistical significance of the delivered Vt with each Raw. A probability of (p < 0.05) was accepted as statistically significant. RESULTS: The descriptive statistics of the average delivered Vt with regard to each Raw (15, 30, 45 cm H2O/L/sec) were the number of experiments (n=3), mean Vt (93.52, 89.09, 85.99 mL), and standard deviations (SD) (1.38, 1.11, 1.10) respectively. There was an inverse relationship between tidal volume and airway resistance during HFOV. With all other variables kept constant, higher resistance caused less volume, whereas lower resistance caused more volume. The one-way ANOVA test showed that there were significant differences between the delivered tidal volumes. When the post hoc Bonferroni test was used, the data showed significant differences between airway resistances of 15 cm H2O/L/sec and 30 cm H2O/L/sec and between 15 cm H2O/L/sec and 45 cm H2O/L/sec. In contrast, no significant differences were found between airway resistances of 30 cm H2O/L/sec and 45 cm H2O/L/sec. CONCLUSION: Vt is not constant during HFOV. Airway resistance is one of the determinants of delivered tidal volume in adults with ARDS during HFOV. Airway resistance should be an important factor in ventilator management and in clinical experiments of patients on HFOV. Without a proper Vt measurement device HFOV should not be used as lung protective ventilation for adult patients with ARDS.

Understanding the mechanisms of cardiovascular disease progression is essential in developing novel therapies to combat this disease that contributes to 1 in 3 deaths in the United States every year. Endothelial dysfunction and its effects on vessel growth and remodeling are key factors in the progression and localization of atherosclerosis. Much of our understanding in this area has come from in-vivo and in-vitro experiments however perfused organ culture systems provide an alternative approach. Organ culture systems can provide a more controlled mechanical and biochemical environment compared to in-vivo models. This study focused on furthering development of this organ culture model by introducing a novel device to produce flow waveforms at the high frequencies and low mean flows seen in the mouse model. The device is capable of monitoring pressure, flow, diameter, and nitric oxide release. Each individual mechanism in the system was integrated via a computer using a custom Labview interface. The performance of the device was characterized by developing physiologic, physiologic-oscillatory, low, low-oscillatory waveforms and sinusoidal waveforms at frequencies ranging from 1-10 Hz. Overall this system provides a robust model to test the effects of flow on various biological markers both in real-time and after culture.

The purpose of this thesis is to implement Finite Volume Weighted Essentially Non-Oscillatory (FV-WENO) scheme to solution of one and two-dimensional discretised Euler equations with different flux algorithms. The effects of the different fluxes on the solution have been tested and discussed. Beside, the effect of the grid on these fluxes has been investigated. Weighted Essentially Non-Oscillatory (WENO) schemes are high order accurate schemes designed for problems with piecewise smooth solutions that involve discontinuities. WENO schemes have been successfully used in applications, especially for problems containing both shocks and complicated smooth solution structures. Fluxes are used as building blocks in FV-WENO scheme. The efficiency of the scheme is dependent on the fluxes used in scheme The applications tested in this thesis are the 1-D Shock Tube Problem, Double Mach Reflection, Supersonic Channel Flow, and supersonic Staggered Wedge Cascade. The numerical solutions for 1-D Shock Tube Problem and the supersonic channel flow are compared with the analytical solutions. The results for the Double Mach Reflection and the supersonic staggered cascade are compared with results from literature.

In this thesis, we study homogenization of optimal control problems in various oscillatory domains. Specifically, we consider four types of domains given in Figure 1 below. Figure 1: Oscillating Domains The thesis is organized into six chapters. Chapter 1 provides an introduction to our work and the rest of the thesis. The main contributions of the thesis are contained in Chapters 2-5. Chapter 6 presents the conclusions of the thesis and possible further directions. A brief description of our work (Chapters 2-5) follows: Chapter 2: Asymptotic behaviour of a fourth order boundary optimal control problem with Dirichlet boundary data posed on an oscillating domain as in Figure 1(A) is analyzed. We use the unfolding operator to study the asymptotic behavior of this problem. Chapter 3: Homogenization of a time dependent interior optimal control problem on a branched structure domain as in Figure 1(B) is studied. Here we pose control on the oscillating interior part of the domain. The analysis is carried out by appropriately defined unfolding operators suitable for this domain. The optimal control is characterized using various unfolding operators defined at each branch of every level. Chapter 4: A new unfolding operator is developed for a general oscillating domain as in Figure 1(C). Homogenization of a non-linear elliptic problem is studied using this new un-folding operator. Using this idea, homogenization of an optimal control problem on a circular oscillating domain as in Figure 1(D) is analyzed. Chapter 5: Homogenization of a non-linear optimal control problem posed on a smooth oscillating domain as in Figure 1(C) is studied using the unfolding operator.

Accurate hydraulic conductivity values are necessary for understanding groundwater flow. Methods for estimating hydraulic conductivity show limitations because measured values vary several orders of magnitude in high permeability aquifers. Slug tests, while cost and time efficient, result in values lower than expected. It is proposed that underdamped behavior of water in a well is similar to mass on a damped spring; hence, models constructed to simulate behavior independent of aquifer effects might replicate some tests. The Poiseuille and Darcy-Weisbach models, and extensions of these models considering entry/exit effects, are applied to an aquifer-free laboratory test, and real wells. Aquifer-free laboratory tests are modeled well using both Poiseuille and Darcy-Weisbach models with entry/exit effects. The Poiseuille model for wells does not agree with observed data, possibly because of high Reynolds numbers. The Darcy-Weisbach model does agree with well data significantly better, although the friction factor relies on a single Reynolds number.

This thesis presents methods for efficient numerical approximation of linear and non-linear systems of highly oscillatory ordinary differential equations. Phenomena of high oscillation is considered a major computational problem occurring in Fourier analysis, computational harmonic analysis, quantum mechanics, electrodynamics and fluid dynamics. Classical methods based on Gaussian quadrature fail to approximate oscillatory integrals. In this work we introduce numerical methods which share the remarkable feature that the accuracy of approximation improves as the frequency of oscillation increases. Asymptotically, our methods depend on inverse powers of the frequency of oscillation, turning the major computational problem into an advantage. Evolving ideas from the stationary phase method, we first apply the asymptotic method to solve highly oscillatory linear systems of differential equations. The asymptotic method provides a background for our next, the Filon-type method, which is highly accurate and requires computation of moments. We also introduce two novel methods. The first method, we call it the FM method, is a combination of Magnus approach and the Filon-type method, to solve matrix exponential. The second method, we call it the WRF method, a combination of the Filon-type method and the waveform relaxation methods, for solving highly oscillatory non-linear systems. Finally, completing the theory, we show that the Filon-type method can be replaced by a less accurate but moment free Levin-type method.

No description available.