Understanding flow and transport in porous media is critical as it plays a central role in many biological, natural, and industrial processes. Such processes are not limited to one length or time scale; they occur over a wide span of scales from micron to Kilometers and microseconds to years. While field-scale simulation relies on a continuum description of the flow and transport, one must take into account transport processes occurring on much smaller scales. In doing so, pore-scale modeling is a powerful tool for shedding light on processes at small length and time scales.<br><br>In this work, we look into the multi-phase flow and transport through porous media at two different scales, namely pore- and Darcy scales. First, using direct numerical simulations, we study pore-scale Eulerian and Lagrangian statistics. We study the evolution of Lagrangian velocities for uniform injection of particles and numerically verify their relationship with the Eulerian velocity field. We show that for three porous media velocity, probability distributions change over a range of porosities from an exponential distribution to a Gaussian distribution. We thus model this behavior by using a power-exponential function and show that it can accurately represent the velocity distributions. Finally, using fully resolved velocity field and pore-geometry, we show that despite the randomness in the flow and pore space distributions, their two-point correlation functions decay extremely similarly.<br><br>Next, we extend our previous study to investigate the effect of viscoelastic fluids on particle dispersion, velocity distributions, and flow resistance in porous media. We show that long-term particle dispersion could not be modulated by using viscoelastic fluids in random porous media. However, flow resistance compared to the Newtonian case goes through three distinct regions depending on the strength of fluid elasticity. We also show that when elastic effects are strong, flow thickens and strongly fluctuates even in the absence of inertial forces.<br><br>Next, we focused our attention on flow and transport at the Darcy scale. In particular, we study a tertiary improved oil recovery technique called surfactant-polymer flooding. In this work, which has been done in collaboration with Purdue enhanced oil recovery lab, we aim at modeling coreflood experiments using 1D numerical simulations. To do so, we propose a framework in which various experiments need to be done to quantity surfactant phase behavior, polymer rheology, polymer effects on rock permeability, dispersion, and etc. Then, via a sensitivity study, we further reduce the parameter space of the problem to facilitate the model calibration process. Finally, we propose a multi-stage calibration algorithm in which two critically important parameters, namely peak pressure drop, and cumulative oil recovery factor, are matched with experimental data. To show the predictive capabilities of our framework, we numerically simulate two additional coreflood experiments and show good agreement with experimental data for both of our quantities of interest.<br><br>Lastly, we study the unstable displacement of non-aqueous phase liquids (e.g., oil) via a finite-size injection of surfactant-polymer slug in a 2-D domain with homogeneous and heterogeneous permeability fields. Unstable displacement could be detrimental to surfactant-polymer flood and thus is critically important to design it in a way that a piston-like displacement is achieved for maximum recovery. We study the effects of mobility ratio, finite-size length of surfactant-polymer slug, and heterogeneity on the effectiveness of such process by looking into recovery rate and breakthrough and removal times.

<div>The growing need to improve the power density of compact thermal systems necessitates developing new techniques to modulate the convective heat transfer efficiently. In the present research, acoustic streaming is evaluated as a potential technology to achieve this objective. Numerical simulations using the linearized and fully non-linear Navier-Stokes equations are employed to characterize the physics underlying this process. The linearized Navier-Stokes equations accurately replicate the low-frequency flow unsteadiness, which is used to find the optimal control parameters. Local and global stability analysis tools were developed to identify the modes with a global and positive heat transfer effect.</div><div><br></div><div>High-fidelity numerical simulations are performed to evaluate the effect of the excitation at selected frequencies, directed by the linear stability analysis, on the heat and momentum transport in the flow. Results indicate that, under favorable conditions, superimposing an acoustic wave, traveling along with the flow, can <i>resonate</i> within the domain and lead to a significant heat transfer enhancement with minimal skin friction losses. Two main flow configurations are considered; at the fixed Reynolds number Re_b=3000, in the supersonic case, 10.1% heat transfer enhancement is achieved by an 8.4% skin friction increase; however, in the subsonic case, 10% enhancement in heat transfer only caused a 5.3% increase to the skin friction. The deviation between these two quantities suggests a violation of the Reynolds analogy. This study is extended to include a larger Reynolds number, namely Re_b=6000 at M_b=0.75 and a similar response is observed. The effect of excitation amplitude and frequency on the resonance, limit-cycle oscillations, heat transfer, and skin friction are also investigated here.</div><div><br></div><div>Applying acoustic waves normal to the flow in the spanwise direction disrupts the near-wall turbulent structures that are primarily responsible for heat and momentum transport near the solid boundary. Direct numerical simulations were employed to investigate this technique in a supersonic channel flow at M_b=1.5 and Re_b=3000. The external excitation is applied through a periodic body force in the spanwise direction, mimicking loudspeakers placed on both walls that are operating with a 180^o phase shift. By keeping the product of forcing amplitude A_f and pulsation period (<i>T</i>) constant, spanwise velocity perturbations are generated with a similar amplitude at different frequencies. Under this condition, spanwise pulsations at <i>T</i>=20 and <i>T</i>=10 show up to 8% reduction in Nusselt number as well as the skin friction coefficient. Excitation at higher or lower frequencies fails to achieve such high level of modulations in heat and momentum transport processes near the walls.<br> <br>In configurations involving a spatially-developing boundary layer, a computational setup that includes laminar, transitional, and turbulent regions inside the domain is considered and the impact of acoustic excitation on this flow configuration has been characterized. Large-eddy simulations with dynamic Smagorinsky sub-grid scale modeling has been implemented, due to the excessive computational cost of DNS calculations at high-Reynolds numbers. The optimal excitation frequency that resembles the mode chosen for the fully-developed case has been identified via global stability analysis. Fully non-linear simulations of the spatially-developing boundary layer subjected to the excitation at this frequency reveal an interaction between the <i>pulsations</i> and the perturbations originated from the tripping which creates a re-laminarization zone traveling downstream. Such technique can locally enhance or reduce the heat transfer along the walls.<br></div>

This thesis deals with the stability of particle laden flows. Both modal and non-modal linear analyses have been performed on two-way coupled particleladen flows, where particles are considered spherical, solid and either heavy or light. When heavy particles are considered, only Stokes drag is used as interaction term. Light particles cannot be modeled with Stokes drag alone, therefore added mass and fluid acceleration are used as additional interaction forces. The modal analysis investigates the asymptotic behavior of disturbances on a base flow, in this thesis a pressure-driven plane channel flow. A critical Reynolds number is found for particle laden flows: heavy particles increase the critical Reynolds number compared to a clean fluid, when particles are not too small or too large. Neutrally buoyant particles, on the other hand, have no influence on the critical Reynolds number. Non-modal analysis investigates the transient growth of disturbances, before the subsequent exponential behavior takes over. We investigate the kinetic energy growth of a disturbance, which can grow two to three orders of magnitude for clean fluid channel flows. This transient growth is usually the phenomenon that causes transition to turbulence: the energy can grow such that secondary instabilities and turbulence occurs. The total kinetic energy of a flow increases when particles are added to the flow as a function of the particle mass fraction. But instead of only investigating the total energy growth, the non-modal analysis is expanded such that we can differentiate between fluid and particle energy growth. When only the fluid is considered in a particle-laden flow, the transient growth is equal to the transient growth of a clean fluid. Besides thes Stokes drag, added mass and fluid acceleration, this thesis also discusses the influence of the Basset history term. This term is often neglected in stability analyses due to its arguably weak effect, but also due to difficulties in implementation. To implement the term correctly, the history of the particle has to be known. To overcome this and obtain a tractable problem, the square root in the history term is approximated by an exponential. It is found that the history force as a small effect on the transient growth. Finally, Direct numerical simulations are performed for flows with heavy particles to investigate the influence of particles on secondary instabilities. The threshold energy for two routes to turbulence is considered to investigate whether the threshold energy changes when particles are included. We show that particles influence secondary instabilities and particles may delay transition. / QC 20111013

Les gens infectés par la rougeole subissent une suppression immunitaire. Ce mémoire porte sur l’influence de cette caractéristique de la rougeole sur un autre pathogène, ici la grippe. Il s’agit donc de modéliser la réponse immunitaire d’une interaction virus-virus, problème d’une grande pertinence durant la pandémie causée par le SRAS-CoV-2 alors que les interactions de celui-ci avec le virus de l’influenza demeurent à déterminer. Nous avons également que la grippe augmente la production d’autres pathogènes. Un modèle de chaque pathogène va être développé et analysé. On cherchera les points fixes, leurs conditions de stabilité et on observera quelques résultats numériques pour constater leurs évolutions dans le temps. Ensuite un modèle suivant l’évolution des deux pathogènes ayant infecté un individu au même moment sera conçu. Dans ce modèle nous inclurons les interactions d’un pathogène l’un sur l’autre pour déterminer théoriquement les effets chez les individus infectés à la fois par la grippe et la rougeole. On pourra par la suite comparer entre les différentes populations lorsqu’il n’y a aucune interaction et avec les différentes interactions entre les deux pathogènes. / People infected with measles experience immune suppression. This work focuses on the influence of this characteristic of measles on another pathogen, here the flu. We also have that the flu will increase the production of other pathogens in a co-infection model. Modeling the immune response to such virus-virus interaction is currently of signficant relevance, given the limited knowledge on SARS-CoV-2/influenza interactions. A model of each pathogen will be developed and analysed. We will look for the fixed points, conditions for their stability and we will observe some numerical results of their evolution over time. Then a model following the evolution of the two pathogens having simultaneously infected an individual will be designed. In this model we will include the interactions of the pathogens on each other to theoretically determine the effects in individuals infected with both influenza and measles. Then we can compare between the different populations when there is no interaction and with the different interactions between the two pathogens.

Les Jupiters chaudes sont des exoplanètes possédant des caractéristiques uniques. En raison de leur proximité avec leur étoile hôte elles présentent une non-symétrie remarquable. Cette proximité provoquant la rotation synchrone force un côté de la planète à toujours faire face à l'étoile et l'autre à être plongé dans une nuit perpétuelle. Cette géométrie donne lieu à une différence d'allant de 200 K jusqu'à 2000 K entre les deux côtés de la planète, engendrant des écoulements zonaux pouvant atteindre des vitesses de l'ordre du km/s afin de redistribuer la chaleur. Le point chaud, le point le plus chaud de la planète, est un témoin de ces vents intenses. Les observations et les simulations hydrodynamiques montrent que les écoulements zonaux se font d'ouest en est. Cependant, les observations de deux planètes ne se conforment pas aux prédictions. En effet, CoRoT-2 b et HAT-P-7 b montrent des points chauds à l'ouest. L'explication la plus répandue est que le champ magnétique de ces planètes, en interaction avec leur atmosphère partiellement ionisée, peut renverser la direction des écoulements zonaux, si ce champ est assez puissant. Une diffusivité magnétique variable dans l'espace peut générer localement des champs magnétiques lorsque son gradient s'aligne correctement avec le courant électrique. Nous présentons ici un modèle magnétohydrodynamique en une dimension possédant une diffusivité magnétique dépendante de la température dans le plan équatorial dans le contexte de Jupiters chaudes. Les résultats des simulations présentent des oscillations torsionnelles de type alfvéniques reflétant les effets non linéaires dus au couplage des équations aux dérivées partielles de la magnétohydrodynamique et de la température avec la diffusivité magnétique dépendante de la température. Nous explorons un espace des paramètres afin d'établir l'influence de ceux-ci sur les oscillations. Nous avons aussi développé un modèle local afin de dériver des équations analytiques nous permettant de mieux comprendre les résultats observés en plus de comparer les résultats du modèle en une dimension avec ceux du modèle local. Nous finissons par établir que les oscillations générées par notre modèle en une dimension possèdent des périodes équivalentes allant de 225 à 473 jours et des déplacements longitudinaux équivalant à quelques degrés jusqu'à environ 40° pour une planète de la taille de Jupiter. Ces intervalles de périodes et de déplacements sont encourageants, puisque cela signifie que les oscillations pourraient être observées. / Hot Jupiters are exoplanets with unique features. Due to their proximity to their host stars, they show remarkable non-symmetry. This proximity with the star causes tidal locking, meaning one side of the planet is always exposed to intense radiation from its host and the other side is immersed in a perpetual night. This geometry means there is a difference of temperature ranging from 200 K up to 2000 K between the day and night side. This gradient in temperature induces zonal winds that can reach the order of 1 km/s to redistribute heat to the night side. The hot spot is the hottest spot of the planet and is a telltale of these strong winds. Observations and hydrodynamic numerical simulations show that zonal winds on these planets go eastward. However, two recent observations are showing westward winds. These planets are CoRoT-2 b and HAT-P-7 b. The most common explanation to this contradiction is that the magnetic field, which is interacting with the partially ionized atmosphere, can reverse these winds. It was previously shown that a magnetic diffusivity varying in space can locally generate magnetic fields when its gradient aligns correctly with the electric current density. We present here a one-dimensional magnetohydrodynamic model with a temperature-dependent magnetic diffusivity in the equatorial plane in the context of hot Jupiters. The simulations develop growing torsional alfvénic oscillations due to the non-linear coupling of the magnetohydrodynamics and the temperature partial differential equations and the temperature-dependent magnetic diffusivity. We explore the parameter space and study their influence on the oscillations. We have also developed a local model in order to derive analytical equations characterizing these waves and compare its results with the results of the one-dimensional model. We end by calculating the corresponding periods and longitudinal displacement of the one-dimension model oscillations for a Jupiter-sized planet. The periods correspond to an interval from 225 to 473 days and the displacements range from a few degrees up to 40°. This means that the oscillations could be observed with a few orbits.

>Magister Scientiae - MSc / Warrant pricing has become very crucial in the present market scenario. See, for example, M. Hanke and K. Potzelberger, Consistent pricing of warrants and traded options, Review Financial Economics 11(1) (2002) 63-77 where the authors indicate that warrants issuance affects the stock price process of the issuing company. This change in the stock price process leads to subsequent changes in the prices of options written on the issuing company's stocks. Another notable work is W.G. Zhang, W.L. Xiao and C.X. He, Equity warrant pricing model under Fractional Brownian motion and an empirical study, Expert System with Applications 36(2) (2009) 3056-3065 where the authors construct equity warrants pricing model under Fractional Brownian motion and deduce the European options pricing formula with a simple method. We study this paper in details in this mini-thesis. We also study some of the mathematical models on warrant pricing using the Black-Scholes framework. The relationship between the price of the warrants and the price of the call accounts for the dilution effect is also studied mathematically. Finally we do some numerical simulations to derive the value of warrants.

No description available.

The focus of this thesis is the effect of planetary curvature on the heat transfer efficiencyaccross latitudes in planetary atmospheres and oceans. We investigate both theoreticallyand numerically a physically-based parametrization of baroclinic turbulence inthe Boussinesq Eady model to include variations of the Coriolis parameter with latitude.In this model, a rapidly rotating density-stratified fluid is subjected to a meridional temperaturegradient in thermal wind balance with a uniform vertically sheared zonal flowand the effect of planetary curvature is captured by the parameter β.A normal mode projection of the Eady model with β was inconclusive to properlydescribe meridional heat transfers and the zonal structures usually observed in planetaryflows. However, the DNS solver CORAL allows us to perform 3D high-Reynolds numericalsimulations to seek an extension of the ’vortex-gas’ scaling theory for baroclinic turbulence.Planetary curvature reduces heat transfer between latitudes through the emergenceof coherent zonal structures while the flow remain mainly quasi-geostrophic. The meridionalbuoyancy flux displays the same functional dependence on the control parametersthan for the two-layer model within the framework of quasi-geostrophy.With similar arguments than for the Eady problem, it is shown that in a perturbativefashion for small β, the vertical profiles of meridional buoyancy flux are no longer depthinvariant.The flux decreases at least exponentially with height. The buoyancy transportis shown to be along mean isopycnals, whereas potential vorticity is transported onlyalong instantaneous isopycnals. Overall, the vortex-gas theory and its extension to theβ-plane lead to good predictions for heat transfer in the quasi-geostrophy limit for 3Dflows and weak β. The theory becomes less precise as we increase β. / Fokus för denna avhandling är effekten av planetarisk krökning på värmeöverföringseffektivitetenöver breddgrader i planetariska atmosfärer och hav. Vi undersöker båda teoretisktoch numeriskt en fysiskt baserad parametrisering av baroklinisk turbulens iBoussinesq Eady-modellen för att inkludera variationer av Coriolis-parametern med latitud.I denna modell utsätts en snabbt roterande densitetsskiktad vätska för en meridional temperaturgradient i termisk vindbalans med ett jämnt vertikalt klippt zonflödeoch effekten av planetarisk krökning fångas av parametern β.En normallägesprojektion av Eady-modellen med β var inte övertygande till korrektbeskriv meridionala värmeöverföringar och de zonstrukturer som vanligtvis observeras i planetariskaflöden. DNS-lösaren CORAL tillåter oss dock att utföra 3D high-Reynolds numeriskasimuleringar för att söka en förlängning av skalningsteorin för 'virvelgas' för baroklinisk turbulens.Planetarisk krökning minskar värmeöverföringen mellan breddgrader genom uppkomstenav koherenta zonstrukturer medan flödet förblir huvudsakligen kvasi-geostrofiskt. Meridionalenflytkraftsflöde visar samma funktionella beroende av styrparametrarnaän för tvåskiktsmodellen inom ramen för kvasi-geostrofi.Med liknande argument än för Eady-problemet visas det i ett störandeFör små β är de vertikala profilerna för meridional flytkraft inte längre djupvarianta.Fluxet minskar åtminstone exponentiellt med höjden. Flyttransportenhar visat sig vara längs genomsnittliga isopycnals, medan potentiell vorticitet endast transporteraslängs momentana isopycnals. Sammantaget, vortex-gasteorin och dess utvidgning tillβ-plan leder till goda förutsägelser för värmeöverföring i kvasi-geostrofigränsen för 3Dflyter och svagt β. Teorin blir mindre exakt när vi ökar β.

La couche la plus externe de l’atmosphère solaire, la couronne, est composée de plasma dont la température dépasse de plusieurs ordres de grandeur celle de la surface.Expliquer comment la couronne est chauffée à des températures de l’ordre d’un million de degrés constitue un défi majeur de la physique solaire.Dans ce contexte, je m’intéresse au chauffage des boucles coronales (qui sont des structures composées de plasma confiné dans des tubes de champ magnétique) et plus particulièrement aux cycles de non-équilibre thermique (TNE).L’étude de ces cycles permet de caractériser le chauffage des boucles.Ces cycles se développent dans des boucles soumises à un chauffage fortement stratifié, localisé près de leurs pieds.Ils se traduisent notamment par une variation périodique de la température et de la densité du plasma dans la boucle.Ces variations engendrent des pulsations d’intensité de longue période, qui sont détectées depuis peu dans l’émission en extrême-ultraviolet (EUV) de certaines boucles coronales.Par ailleurs, des écoulements périodiques de plasma à températures coronales se produisent durant ces cycles.Dans certains cas, le plasma qui s’écoule peut refroidir de plusieurs ordres de grandeur et former de la pluie coronale périodique.Durant ma thèse, j’ai travaillé à la première détection de ces écoulements à haute et à basse température.En utilisant des séries temporelles de spectres EUV de l’instrument Hinode/EIS, j’ai mesuré la vitesse Doppler du plasma dans des boucles dans lesquelles on détecte des pulsations d’intensité.Cela m’a permis de détecter des écoulements de plasma à température coronale associé à certaines pulsations d’intensité.Par ailleurs, j’ai participé à la détection d’un événement de pluie coronale périodique (à température plus froide) dans des séries d’images de l’instrument SDO/AIA.Ces détections permettent de confirmer que les pulsations d’intensité de longue période sont bien le résultat de cycles de TNE, ainsi que d’apporter de nouvelles contraintes sur le chauffage des boucles coronales.Cela permet notamment de conclure que le chauffage des boucles coronales est localisé près de leurs pieds et que son temps de répétition est inférieur au temps de refroidissement du plasma.Afin de détecter les écoulements à haute température, j’ai dû corriger de nombreux effets instrumentaux de EIS.J’ai notamment développé une nouvelle méthode pour aligner les spectres avec des images de l’instrument AIA, qui permet de corriger l’angle de roulis et la variation aléatoire du pointage de EIS.En appliquant cette méthode à un grand nombre de spectres, j’ai réalisé la première mesure systématique de l’angle de roulis de l’instrument.Par la suite, j’ai réalisé des simulations numériques du cas de pluie coronale périodique.Dans ces simulations, j’ai calculé l’évolution du plasma dans la boucle pour différents paramètres de chauffage et différentes géométries du champ magnétique.Cela m’a permis d’identifier les paramètres de chauffage permettant de reproduire le comportement observé.Avec ces simulations, j’ai par ailleurs pu comprendre comment l’asymétrie de la boucle et du chauffage conditionnent la température minimale atteinte par les écoulements qui se forment lors des cycles de non-équilibre thermique. / The outermost layer of the solar atmosphere, the corona, is composed of plasma which is hotter than the surface by several orders of magnitude.One of the main challenges in solar physics is to explain how the corona is formed and heated to temperatures of a few million degrees.In this context, I focus on the heating of coronal loops (which are structures composed of plasma confined in magnetic field tubes), and more precisely on thermal non-equilibrium (TNE) cycles.Studying these cycles allows us to characterize the heating of coronal loops.These cycles occur in loops with a highly stratified heating, localized near their footpoints.Among other effects, they cause periodic variations of the temperature and density of the plasma in the loop.These variations result in long-period intensity pulsations, which have recently been detected in the extreme-ultraviolet (EUV) emission of some coronal loops.In addition, periodic flows of plasma at coronal temperatures occur during these cycles.In some cases, the flowing plasma can cool down by several orders of magnitude, and thus form periodic coronal rain.During my thesis, I worked on the first detection of these periodic plasma flows at coronal and lower temperatures.Using time series of spatially-resolved EUV spectra from the instrument Hinode/EIS, I measured the Doppler velocity of plasma in loops undergoing long-period intensity pulsations.This allowed me to detect flows of plasma at coronal temperatures associated with some maxima of the intensity pulsations.In addition, I took part in the detection of an event of periodic coronal rain (at cooler temperatures), using series of images from the instrument SDO/AIA.These detections confirm that the long-period intensity pulsations detected in coronal loops are indeed the result of TNE cycles, and allow better constrain the heating of the loops.From this, conclude that the heating of coronal loops is highly stratified, localized near their footpoints, with a repetition time shorter than the cooling time of the plasma.Detecting the flows of plasma at coronal temperatures required that I correct many EIS instrumental effects.To that aim, I developed a new method for coalinging EIS spectra with images from AIA.This method can correct the roll angle and the jitter (a random variation of the pointing) of EIS.By applying it to a large number of spectra, I carried out a comprehensive determination of the EIS roll angle.I also performed numerical simulations of the periodic coronal rain event.In these simulations, I computed the evolution of the plasma in the loop for different values of the heating parameters, as well as several magnetic field geometries.This allowed me to determine the heating parameters which are required to reproduce the observed behavior of this loop.By analyzing these simulations, I was also able to understand how the asymmetry of the loop and of the heating determine the minimum temperature of the plasma flows which form during thermal non-equilibrium cycles.

This dissertation introduces a general, predictive and cost-efficient reduced-order modeling (ROM) technique for characterization of flame response under acoustic modulation. The model is built upon the kinematic flame model–G-equation to describe the flame topology and dynamics, and the novelties of the ROM lie in i) a procedure to create the compatible base flow that can reproduce the correct flame geometry and ii) the use of a physically-consistent acoustic modulation field for the characterization of flame response. This ROM addresses the significant limitations of the classical kinematic model, which is only applicable to simple flame configurations and relies on ad-hoc models for the modulation field. The ROM is validated by considering the acoustically-excited premixed methane/air flames in conical and M-shape configurations. To test the model availability to practical burners, a confined flame configuration is also employed for model evaluation. Furthermore, to investigate the generality of the ROM to the burner flame, the performance of the ROM with respect to the V-shape and the swirled V-shape is investigated. The model accuracy is evaluated concerning flame geometrical features and flame describing function, and assessed by comparing the ROM results with both experimental measurements and direct- numerical-simulation results. It is found that the flame describing/transfer functions predicted by the ROM compare well with reference data, and are more accurate than those obtained from the conventional kinematic model built upon heuristically-presumed modulation fields.