Fluid mixing that is induced by hydrodynamic instability is ubiquitous in nature; the material interface between two fluids when perturbed even slightly, changes shape under the influence of hydrodynamic forces, and an additional zone called the mixing layer where the two fluids mix, develops and grows in size. This dissertation reports a study on the role of thermal fluctuations in fluid mixing at the interface separating two perfectly miscible fluids of different densities. Mixing under the influence of two types of instabilities is studied; the Rayleigh-Taylor (RTI) and Richtmyer-Meshkov (RMI) instabilities. The study was conducted using numerical simulations after verification of the simulation methodology. Specifically, fluctuating hydrodynamic simulations were used; the fluctuating compressible Navier-Stokes equations were the physical model of the system, and they were solved using numerical methods that were developed and implemented in-house. Our results indicate that thermal fluctuations can trigger the onset of RTI at an initially unperturbed fluid-fluid interface, which subsequently leads to mixing of multi-mode character. In addition we find that for both RMI and RTI, whether or not thermal fluctuations quantitatively affect the mixing behavior, depends on the magnitude of the dimensionless Boltzmann number of the hydrodynamic system in question, and not solely on its size. When the Boltzmann number is much smaller than unity, the quantitative effect of thermal fluctuations on the mixing behavior is negligible. Under this circumstance, we show that mixing behavior is the average of the outcome from several stochastic instances, with the ensemble of stochastic instances providing the bounds on mixing-related metrics such as the mixing width. Most macroscopic hydrodynamic systems fall in this category. However, when the system is such that the Boltzmann number is of order unity, we show that thermal fluctuations can significantly affect the mixing behavior; the ensemble-averaged solution shows a departure from the deterministic solution. We conclude that for such systems, it is important to account for thermal fluctuations in order to correctly capture their physical behavior.

Small unsteady disturbances of boundary-layer flow fields are often encountered in engineering applications, as for example, in the aerodynamics of a helicopter rotor or a turbine cascade or in a fluttering airfoil as well as in a variety of bioengineering problems. The present dissertation is a unified attempt to study some special classes of unsteady two- and three-dimensional incompressible and compressible . boundary-layer flows. The general character of the mathematical problem is investigated first for each particular area. Asymptotic solutions are then provided based on the assumption of small amplitude and small frequency of oscillation. Systems of general differential equations in a single variable are obtained and solved numerically by the shooting technique. A straightforward fourth order Runge-Kutta integration scheme is employed and the values of the functions at the edge of the boundary-layer are checked against the outer flow boundary conditions. In the first chapter we study simultaneously the effects of three dimensionality coupled with the response to outer flow oscillations. It is believed that the coupling will have significant implications in cascade flows where the finite span blocks the development of cross flows. Some interesting features of oscillatory three-dimensional flows are disclosed. In particular it is found that the coupling of the momentum equations permits the transfer of momentum from the chordwise to the spanwise direction. In this way it is possible to excite a fluctuating boundary layer flow in the spanwise direction even though there is no outer flow fluctuations. In the second chapter the response of laminar compressible boundary layers to fluctuations of the skin of the body or the outer flow are studied in the special case of a wall at the adiabatic temperature. Unsteady outer pressure fluctuations are considered for the first time and their effects to the energy equation and heat transfer is estimated. The analysis holds both for two-dimensional and axisymmetric configurations. / Ph. D.

Reduction of surface pressure fluctuations is desirable in various aerodynamic and hydrodynamic applications. Over the past few years, studies on canopy surface treatments have been conducted to investigate the fundamental mechanisms of surface pressure attenuation termed as pressure shielding. This work talks about the design, development and experimental testing of unidirectional canopy surface treatments which are evenly spaced arrays of streamwise rods placed parallel to the wall without an entrance condition. The canopy designs are based on surface treatments tested by Clark et al. (2014) inspired by the downy coating on owl wings. The main objective of the work is to establish fundamental physical and mathematical basis for treatments that shield aerodynamic surfaces from turbulent pressure fluctuations, while maintaining the wall-normal transport of momentum and low aerodynamic drag. Experimental testing of these canopy treatments are performed in the Anechoic Wall-Jet facility at Virginia Tech. Different canopy configurations are designed to understand the effect of various geometric parameters on the surface pressure attenuation. The treatment is found to exhibit broadband reduction in the surface pressure spectrum. Attenuation develops in two frequency regions which scale differently depending on two different mechanisms. Canopies seems to reduce the large-scale turbulent fluctuations up to nearly twice the height. Semi-analytical model is developed to predict surface pressure spectra in a wall-jet and canopy flow. The rapid term model shows that the inflection in the streamwise mean velocity profile is the most dominant source of surface pressure fluctuations. Synchronized pressure and velocity measurements elucidate significant features of the sources that could be affecting surface pressure fluctuations. Overall, this study explores the qualitative and quantitative physics behind pressure shielding mechanism which find application particularly in trailing edge noise reduction. / Doctor of Philosophy / Unsteady pressure fluctuations originating from interaction of turbulent flow over surfaces often cause undesirable effects. Trailing edge noise in wind turbines and helicopter blades, cabin noise and interior wind noise are some of noise sources which originate from surface pressure fluctuations. Previous studies have demonstrated that surface treatments help in reducing the unsteady surface pressure fluctuations therefore shielding surfaces and this phenomenon is termed as 'Pressure Shielding'. These are surface treatments inspired from the downy coating on owl's wings. This study is motivated by recent works conducted at Virginia Tech on experimental investigation of unidirectional canopy treatments. These are evenly spaced arrays of streamwise rods held horizontal at the downstream end. Most previous surface treatments contain some entrance condition such as steps, supports or gaps which effect the surface pressure measurements and disturb the incoming flow. In this study, the canopies are developed without any entrance condition therefore assist in capturing the fundamental mechanisms of the flow interaction with the canopy rods.

A railroad yard in Oneida, Tennessee was contaminated with creosote in the 1950s and 1960s through cross tie treatment. The problem was discovered in 1990 and phytoremediation in combination with an interception trench was chosen as the remediation strategy. Hybrid poplar trees (1,036) were planted in 1997 within 0.7 acres. The goals of the phytoremediation system are to prevent migration of the contaminant off the site and clean up the contaminant in-situ. This study is focused on quantifying the rate of evapotranspiration of the phytoremediation system and then determining the effect on groundwater flow. This will be accomplished by quantifying evapotranspiration using a water budget, applying White's Equation, comparing groundwater recession curves, creating a groundwater flow model, and examining water table elevations obtained at the site. Calculations of water use by the poplar trees in early September 1999 ranged from 0.62 to 1.34 gal/day/tree. The volume of evapotranspiration calculated for the trees during 1999 is 140,292 gallons. Total evapotranspiration determined by the water budget for 1998 is 1,570,064 gallons. Evaluation of the water level data over a period of several years shows significant lowering of the water table (fluctuations of up to four feet) during the summer and fall months due to evapotranspiration. Although calculated evapotranspiration rates are not as high as seen in the literature, continued monitoring of the site should show large increases in evapotranspiration rates in the future as the poplar trees mature. / Master of Science

L'objectif de cette thèse est d'étudier la dynamique et le désordre spatial de l'orientation de l'axe facile, d'un cristal liquide nématique. La première partie du manuscrit est consacrée à l'étude de la dynamique de l'axe facile. Cette dynamique est généralement décrite au niveau moléculaire par deux procédés différents impliquant un mécanisme d'adsorption / désorption (AD) à la surface et la relaxation conformationelle d'un polymère. Nous avons élaboré une expérience et un modèle originaux capables de séparer l'influence de ces deux mécanismes microscopiques. Dans la deuxième partie, nous avons caractérisé statistiquement le désordre orientationnel de l'axe de facile pour différentes couches d'ancrage. Le désordre a des propriétés universelles, c'est à dire qu'il est le même sur toutes les surface analysées. Nous avons ensuite construit un modèle basé sur le « quenching » en surface des fluctuations nématique orientationnelles causé par le processus d'AD. Dans la dernière partie, nous avons mis en place une méthode avec une résolution spatiale et temporelle capable de capturer l'orientation moyenne de l'axe facile et sa distribution spatiale en fonction du temps. Nous montrons que le glissement de l'axe facile moyen se produit avec un changement relativement faible de son désordre spatial. / The aim of this PhD is to investigate the dynamics and the spatial disorder of the easy axis orientation, in the case of a nematic liquid crystal. The first part of the manuscript is devoted to the study of the easy axis dynamics. This dynamics is usually described at molecular level by two different processes involving adsorption/desorption (AD) at the surface and polymer conformal relaxations. We devise an original experiment and we build a general model able to separate the influence of these two microscopic mechanisms. In the second part, we statistically characterize the orientational disorder of the easy axis in a whole set of different anchoring layers. This disorder is found to have universal properties, i.e. it is the same on all the analyzed layers. We then build up a model based on the surface quenching of the nematic orientational fluctuations due to the AD-process. In the final part, we set up a method with spatial and temporal resolution capturing the average easy axis orientation and its spatial distribution as function of time. We show that the drift of the average easy axis occurs with a relatively small change of its spatial disorder.

L’objectif de cette thèse est de mettre en avant le rôle de la psychologie dans les fluctuations de la production, de la redistribution et des inégalités. Notre travail s’articule autour de deux axes : i) l’importance de la psychologie à l’égard des inégalités dans la détermination des croyances des agents concernant le rôle de l’effort ii) l’impact de ces croyances sur les dynamiques des grandeurs économiques. L’objectif du premier chapitre est de présenter une revue de littérature sur la relation entre croyances et faits économiques. Au second chapitre, nous développons un modèle théorique, dans lequel nous introduisons une composante psychologique immuable dans les croyances des agents. Nous aboutissons à une explication d’ordre psychologique des disparités entre pays de la volatilité de la TFP, de la production, de la redistribution et des inégalités. Dans le troisième chapitre, nous vérifions, économétriquement, les implications du modèle. / The objective of this doctoral thesis is to put forth the role of psychology in the fluctuations of production, redistribution and inequalities. Our work is centered on two axes : i) the importance of psychology with regards to inequalities in determining individual beliefs about the role of effort ii) the impact of beliefs on the dynamics of economic aggregates. The objective of the first chapter is to provide a literature review on the relationship between beliefs and economic events. In the second chapter, we develop a theoretical model, in which we introduce an unchanging psychological component in individual beliefs. We end at an explanation, of a psychological nature, for cross-country disparities in TFP, production, redistribution and inequalities volatilities. In the third chapter, we provide an empirical verification of the model implications.

Fluctuation phenomena are important to many physical systems, such as the fusion plasma. Noise theory is used to study the time and space correlations of stationary Markovian fluctuations that are statistically homogeneous and isotropic. The relaxation of the fluctuations is modeled by the diffusion equation. The spatial correlations are modeled by the exponential decay. Based on these models, the correlation function and the power spectral density of random fluctuations. We also find that the fluctuation-induced transport coefficients may be estimated by the correlation length and the correlation time. The theoretical results are compared with the observed plasma density fluctuations from tokamak and helimak experiments.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

La recherche scientifique contemporaine en matière de matériaux est largement orientée autour de l’optimisation et l’élaboration de nouveaux matériaux poly-fontionnels, multi-structurés et aux dimensions réduites. De tels matériaux conduisent à s’intéresser à la problématique des comportements spécifiques résultant des différentes interfaces mises en jeu ; il peut s’agir d’interfaces physiques entre différents milieux (états différents, compositions chimiques différentes …) ou des interfaces entre différentes propriétés. Dans ce contexte, nous nous sommes intéressés aux corrélations pouvant exister entre les propriétés de luminescence et la réactivité de surface de films mésoporeux d’oxyde métalliques dopés avec des ions EuIII. Ces deux propriétés étant fortement dépendantes de la structure des matériaux, une grande partie de notre travail a été dédiée à la caractérisation de cette dernière. Un intérêt particulier a été porté à l’étude des conséquences de la présence des ions EuIII et à la localisation de ces derniers au sein des matrices étudiées. Finalement, il est apparu que la luminescence des ions EuIII au sein des films mésoporeux à base de TiO2 peut permettre de suivre les réactions redox se produisant au sein des pores, comme par exemple la photo-dégradation de composés organiques ou la photo-réduction de sels métalliques. La photo-réduction in situ permet la formation de réseaux périodiques de nanoparticules métalliques. Ces matériaux offrent donc de nombreuses perspectives d’applications dans des domaines aussi variés que les télécommunications optiques, la photonique, la photocatalyse… / Materials contemporary scientific research is largely devoted to the optimization and the elaboration of new poly-functional, multi-structured and size-reduced materials. Then, specific behaviors due to the different interfacial aspects of those materials – physical interfaces between different matter states, different chemical phases… or properties interfaces – have become a major issue requiring further investigations. In this context, our work deals with correlations that could be established between luminescence properties and surface reactivity of EuIII-doped metal oxide mesoporous thin films. As properties can be linked to materials structure, an important part of our work has been dedicated to structural characterization. EuIII ions incorporation specific effects and ions location within film walls have been particularly studied. Finally, it appeared that EuIII ions luminescence could provide a mean to follow redox reactions occurring within pores, such as organic compounds photo-degradation or metallic salts photo-reduction. In situ photo-reduction can lead to periodic arrays of metallic nanoparticles. La photo-réduction in situ permet la formation de réseaux périodiques de nanoparticules métalliques. Those materials can open up the way in many applications such as optical telecommunication, photonics, photocatalysis…

Cette thèse comprend une analyse d'un système de N bosons de masse m, à une dimension (1D). Vue des efforts expérimentaux récents et de la perspective d'étudier plusieurs effets quantiques intéressants, nous choisissons une géométrie circulaire avec une circonférence L. Un potentiel extérieur dépendant du temps nous permet d'introduire un mécanisme qui change l'état du moment angulaire des bosons. Ce potentiel est de la forme d'une fonction delta de Dirac qui se déplace le long de l'anneau à une vitesse v et la force de ce potentiel vaut U_0. Il peut être vu comme une barrière qui met les bosons en rotation. Les interactions entre les bosons sont des interactions de contact, décrites dans le modèle de Lieb et Liniger. Puisque le potentiel extérieur ne garde pas la symétrie de translation de L'Hamiltonien du système l'équation de Schrödinger n'est pas résoluble de manière exacte en utilisant un Ansatz de Bethe. Cependant, dans les limites des bosons libres et des bosons impénétrables de Tonks et Girardeau des méthodes alternatives existent pour trouver une solution exacte. Le but de cette thèse est de résoudre l'équation de Schrödinger dans ces cas limites. La solution nous permet d'accéder aux observables intéressantes concernant les propriétés superfluides des bosons libres et du gaz de Tonks. Nous effectuons une analyse du courant des particules, de ses fluctuations et de la force de traînée. Nous trouvons un comportement superfluide en-dessous d'une vitesse critique v_c=ħπ/(mL) de la barrière. Une oscillation du courant et la force de traînée est observée pour une vitesse de la barrière v=n*v_c, avec n un entier naturel. De plus, nous étudions la nature de l'état quantique du gaz de Tonks. Dans les analyses de la distribution des impulsions, de la fonction de Wigner et des images ``temps de vol'' pour une vitesse de la barrière v=n*v_c, on trouve que l'état du système est une superposition macroscopique de deux sphères de Fermi, l'une centrée autour de l'impulsion égale à zéro et l'autre autour de l'impulsion égale à 2q, avec q=mv/ħ. Cet état est un état fortement corrélé, non-classique car la fonction de Wigner atteint des valeurs négatives. / Recent experimental activities of boson trapping on a ring geometry open the way to explore a novel topology. We focus on a tight ring trap with strong transverse confinement leading to an effectively one-dimensional motion along its circumference. We consider a strongly interacting bose gas on the ring subjected to a localized barrier potential which is suddenly set into motion. The Bose-Fermi mapping allows to obtain an exact solution for the many-body wavefunction in the impenetrable-boson (Tonks-Girardeau) limit of infinitely strong interactions between the particles with arbitrary external potential, not treatable with the Bethe Ansatz. Using the time-dependent extension to BF mapping an exact solution for the dynamical evolution of the many-body wavefunction is obtained. The exact solution allows to calculate the particle current, the particle current fluctuations and the drag force acting on the barrier. In the weak barrier limit the stirring drives the system into a state with net zero current and vanishingly small current fluctuations for velocities smaller than v_c=ħπ/(mL), with m the atomic mass and L the ring circumference. The existence of a velocity threshold for current generation indicates superfluid-like behavior of the mesoscopic Tonks-Girardeau gas, different from the non-superfluid behavior predicted for the TG gas in an infinite tube. At velocities approaching integer multiples of v_c angular momentum can be transferred to the fluid and a nonzero drag force arises. At these velocities we predict the formation of a macroscopic superposition of a rotating and a nonrotating Fermi sphere of the mapped Fermi gas. We calculate the momentum distribution, time of flight images and the Wigner function of the Bose gas, the latter allowing to identify quantum interferences in the superposition. We find that the barrier velocity should be larger than the sound velocity for a better discrimination of the two components of the superposition.