This thesis deals with receptivity mechanisms of three-dimensional, crossflow-dominated boundary layers. The receptivity of two model problems, a swept-flat-plate and a swept-wing boundary layer, is investigated by solving the parabolised stability equations (PSE) as well as by performing direct numerical simulations (DNS).Both flow cases are known to exhibit strong inflectional instabilities, the crossflow disturbances, whose excitation by external disturbances such as surface roughness or free-stream vorticity is studied. One focus is on worst-case scenarios. This involves the determination of optimal conditions, i.e. those disturbance environments yielding the largest possible response inside the boundary layer. A new method on the basis of the PSE is presented which allows to study optimal disturbances of swept-flat-plate boundary layers. These take the form of tilted streamwise vortices. While convected downstream they develop into streamwise streaks experiencing strong non-modal growth. Eventually, they turn into crossflow disturbances and undergo exponential growth. Non-modal growth is thus found to optimally excite crossflow disturbances and can be related to a receptivity mechanism of three-dimensional boundary layers. Evaluating effects of compressibility reveals that the potential for both non-modal and modal growth increases for higher Mach numbers. It is shown that wall cooling has diverse effects on disturbances of non-modal and modal nature. While destabilising the former it attenuates the growth of modal disturbances. Concave curvature on the other hand is found to be equally destabilising for both types of disturbances. The adjoint of the linearised Navier-Stokes equations is solved for a swept-wing boundary layer by means of DNS. The adjoint solution of a steady crossflow disturbance is computed in the boundary layer as well as in the free-stream upstream of the leading edge. This allows to determine receptivity to incoming free-stream disturbances and surface roughness as well as the corresponding worst-case scenarios. Upstream of a swept wing the optimal initial free-stream disturbance is found to be of streak-type which convects downstream towards the leading edge. It entrains the boundary layer a short distance downstream of the stagnation line. While minor streamwise vorticity is present the streak component is dominant all the way into the boundary layer where the optimal disturbance turns into a crossflow mode. Futher, the worst-case surface roughness is determined. It takes a wavy shape and is distributed in the chordwise direction. It is shown that, under such optimal conditions, the swept-wing boundary layer is more receptive to surface roughness than to free-stream disturbances. Another focus of this work has been the development and evaluation of tools for receptivity prediction. Both DNS and direct and adjoint solutions of the PSE are used to predict the receptivity of a swept-wing boundary layer to localised surface roughness. The configuration conforms to wind tunnel experiments performed by Saric and coworkers at the Arizona State University. Both the DNS and the PSE are found to predict receptivity amplitudes which are in excellent agreement with each other. Though the predicted disturbance amplitudes are slightly lower than experimental measurements the overall agreement with experimental results is very satisfactory. Finally, a DNS of the stabilisation of a transitional swept-wing boundary layer by means of discrete roughness elements is presented. This control approach is found to completely suppress transition to turbulence within the domain studied and confirms experimental results by Saric & coworkers. / QC 20111124

<p>The stability and the receptivity of three-dimensional flat plate boundary layers is studied employing parabolised stability equations. These allow for computationally efficient parametric studies. Two different sets of equations are used. The stability of modal disturbances in the form of crossflow vortices is studied by means of the well-known classical parabolised stability equations (PSE). A new method is developed which is applicable to more general vortical-type disturbances. It is based on a modified version of the classical PSE and describes both modal and non-modal growth in three-dimensional boundary layers. This modified PSE approach is used in conjunction with a Lagrange multiplier technique to compute spatial optimal disturbances in three-dimensional boundary layers. These take the form of streamwise oriented tilted vortices initially and develop into streaks further downstream. When entering the domain where modal disturbances become unstable optimal disturbances smoothly evolve into crossflow modes. It is found that non-modal growth is of significant magnitude in three-dimensional boundary layers. Both the lift-up and the Orr mechanism are identified as the physical mechanisms behind non-modal growth. Furthermore, the modified PSE are used to determine the response of three-dimensional boundary layers to vortical free-stream disturbances. By comparing to results from direct numerical simulations it is shown that the response, including initial transient behaviour, is described very accurately. Extensive parametric studies are performed where effects of free-stream turbulence are modelled by filtering with an energy spectrum characteristic for homogeneous isotropic turbulence. It is found that a quantitative prediction of the boundary layer response to free-stream turbulence requires detailed information about the incoming turbulent flow field. Finally, the adjoint of the classical PSE is used to determine the receptivity of modal disturbances with respect to localised surface roughness. It is shown that the adjoint approach yields perfect agreement with results from Finite-Reynold-Number Theory (FRNT) if the boundary layer is assumed to be locally parallel.  Receptivity is attenuated if nonlocal and non-parallel effects are accounted for. Comparisons to direct numerical simulations and extended parametric studies are presented.</p>

La thèse se compose de 5 articles. Le premier article considère une économie monétaire à horizon infini avec actifs financiers collatéralisés. La Banque Centrale fait des prêts à court et à long terme aux ménages. Les agents peuvent déposer ou/et emprunter à court ou à long terme. Néanmoins un plafond est imposé sur les emprunts de long terme. Tous les agents ont accès aux marchés financiers. Toutefois les agents doivent posséder suffisamment de collatéral en biens de consommations pour vendre un actif financier. Les agents font face à des contraintes de liquidité aussi bien lorsqu’ils achètent des biens de consommation que des actifs financiers. Sous des hypothèses de ”Gains `a l’échange”, l’existence de l’équilibre est démontrée. Dans un tel cadre, plusieurs propriétés des équilibres sont démontrées, notamment l’existence d’une trappe à liquidité. Le deuxième considère un modèle d’équilibre général à la Ramsey avec agents hétérogènes, contraintes d’emprunt, et offre de travail exogène. D’abord, l’existence d’un équilibre est démontrée même si les capitaux ne sont pas bornés uniformément et si les fonctions de production ne sont pas stationnaires. Ensuite (i) nous définissons la bulle du capital physique comme la différence strictement positive entre son prix et sa valeur fondamentale (ii) nous montrons qu’une bulle existe si, et seulement si, la somme des rendements du capital est finie. Enfin, lorsque les fonctions de production sont linéaires, tout équilibre intertemporel est efficient. De plus, on peut avoir des équilibres à la fois efficients et avec bulle. Le troisième étudie la nature de la bulle financière dans un modèle d’équilibre général à l’horizon infini avec agents hétérogènes, contraintes d’emprunt endogènes. Nous démontrons l’existence d’un équilibre sans aucune condition sur des dotations initiales des agents. Nous disons qu’il y a une bulle financière à l’équilibre si le prix d’actif financier est supérieur à sa valeur fondamentale. Nous démontrons que les trois conditions suivantes sont équivalentes : (i) Il y a une bulle, (ii) le coût d’emprunt est strictement positif, (iii) les taux d’intérêt sont bas, i.e., la somme des taux d’intérêt au cours du temps est finie. Nous donnons aussi une condition sur les variables exogènes pour que la bulle financière apparaisse à l’équilibre. Le quatrième concerne l’interaction entre le marché financier et le secteur productif. Pour étudier cela, nous construisons un modèle d’équilibre général à horizon infini avec agents hétérogènes, contraintes d’emprunt endogènes dans lequel les agents investissent en actif financier ou/et en capital physique. Il y a une firme qui maximise son profit. D’abord, l’existence d’un équilibre est démontrée. Nous montrons que si la productivité est suffisamment élevée, l’économie ne tombe jamais en récession. Si la productivité est basse, l’économie va tomber en récession avec un nombre infini de fois. Cependant, dans certains cas, l’actif financier pourrait bénéficier à l’économie en finançant l’achat du capital physique. Grâce à cela, une récession économique pourrait être évitée. [...] / No English summary available.

The concept of dynamic programming was originally used in late 1949, mostly during the 1950s, by Richard Bellman to describe decision making problems. By 1952, he refined this to the modern meaning, referring specifically to nesting smaller decision problems inside larger decisions. Also, the Bellman equation, one of the basic concepts in dynamic programming, is named after him. Dynamic programming has become an important argument which was used in various fields; such as, economics, finance, bioinformatics, aerospace, information theory, etc. Since Richard Bellman's invention of dynamic programming, economists and mathematicians have formulated and solved a huge variety of sequential decision making problems both in deterministic and stochastic cases; either finite or infinite time horizon. This thesis is comprised of five chapters where the major objective is to study both deterministic and stochastic dynamic programming models in finance. In the first chapter, we give a brief history of dynamic programming and we introduce the essentials of theory. Unlike economists, who have analyzed the dynamic programming on discrete, that is, periodic and continuous time domains, we claim that trading is not a reasonably periodic or continuous act. Therefore, it is more accurate to demonstrate the dynamic programming on non-periodic time domains. In the second chapter we introduce time scales calculus. Moreover, since it is more realistic to analyze a decision maker’s behavior without risk aversion, we give basics of Stochastic Calculus in this chapter. After we introduce the necessary background, in the third chapter we construct the deterministic dynamic sequence problem on isolated time scales. Then we derive the corresponding Bellman equation for the sequence problem. We analyze the relation between solutions of the sequence problem and the Bellman equation through the principle of optimality. We give an example of the deterministic model in finance with all details of calculations by using guessing method, and we prove uniqueness and existence of the solution by using the Contraction Mapping Theorem. In the fourth chapter, we define the stochastic dynamic sequence problem on isolated time scales. Then we derive the corresponding stochastic Bellman equation. As in the deterministic case, we give an example in finance with the distributions of solutions.

A lot has changed since that day on December 17, 1903 when the Wright brothers made the first powered manned flight. Even though the concepts behind flying are unaltered, appearance of stat-of-the-art modern aircrafts has undergone a massive evolution. This is mainly owed to our deeper understanding of how to harness and optimize the interaction between fluid flows and aircraft bodies. Flow passing over wings and different junctions on an aircraft faces numerous local features, for instance, acceleration or deceleration, laminar or turbulent state, and interacting boundary layers. In our study we aim to characterize some of these flow features and their physical roles. Primarily, stability characteristics of flow over a wing subject to a negative pressure gradient are studied. This is a common condition for flows over swept wings. Part of the current numerical study conforms to existing experimental studies where a passive control mechanism has been tested to delay laminarturbulent transition. The same flow type has also been considered to study the receptivity of three-dimensional boundary layers to freestream turbulence. The work entails investigation of effects of low-level freestream turbulence on crossflow instability, as well as interaction with micron-sized surface roughness elements. Another common three-dimensional flow feature arises as a resultof stream-lines passing through a junction, the so-calledcorner-flow. For instance, thisflow can be formed in the junction between the wing and fuselage on aplane.A series of direct numerical simulations using linear Navier-Stokes equationshave been performed to determine the optimal initial perturbation. Optimalrefers to perturbations which can gain the maximum energy from the flow overa period of time. In other words this method seeks to determine theworst-casescenario in terms of perturbation growth. Here, power-iterationtechnique hasbeen applied to the Navier-Stokes equations and their adjoint to determine theoptimal initial perturbation. Recent advances in super-computers have enabled advance computational methods to increasingly contribute to design of aircrafts, in particular for turbulent flows with regions of separation. In this work we investigate theturbulentflow on an infinite wing at a moderate chord Reynolds number of Re= 400,000 using a well resolved direct numerical simulation. A conventional NACA4412 has been chosen for this work. The turbulent flow is characterizedusing statistical analysis and following time history data in regions with interesting flow features. In the later part of this work, direct numerical simulation has been chosen as a tool to mainly investigate the effect of freestream turbulence on the transition mechanism of flow from laminar to turbulent around a turbine blade. / <p>QC 20151125</p>

The stability and the receptivity of three-dimensional flat plate boundary layers is studied employing parabolised stability equations. These allow for computationally efficient parametric studies. Two different sets of equations are used. The stability of modal disturbances in the form of crossflow vortices is studied by means of the well-known classical parabolised stability equations (PSE). A new method is developed which is applicable to more general vortical-type disturbances. It is based on a modified version of the classical PSE and describes both modal and non-modal growth in three-dimensional boundary layers. This modified PSE approach is used in conjunction with a Lagrange multiplier technique to compute spatial optimal disturbances in three-dimensional boundary layers. These take the form of streamwise oriented tilted vortices initially and develop into streaks further downstream. When entering the domain where modal disturbances become unstable optimal disturbances smoothly evolve into crossflow modes. It is found that non-modal growth is of significant magnitude in three-dimensional boundary layers. Both the lift-up and the Orr mechanism are identified as the physical mechanisms behind non-modal growth. Furthermore, the modified PSE are used to determine the response of three-dimensional boundary layers to vortical free-stream disturbances. By comparing to results from direct numerical simulations it is shown that the response, including initial transient behaviour, is described very accurately. Extensive parametric studies are performed where effects of free-stream turbulence are modelled by filtering with an energy spectrum characteristic for homogeneous isotropic turbulence. It is found that a quantitative prediction of the boundary layer response to free-stream turbulence requires detailed information about the incoming turbulent flow field. Finally, the adjoint of the classical PSE is used to determine the receptivity of modal disturbances with respect to localised surface roughness. It is shown that the adjoint approach yields perfect agreement with results from Finite-Reynold-Number Theory (FRNT) if the boundary layer is assumed to be locally parallel.  Receptivity is attenuated if nonlocal and non-parallel effects are accounted for. Comparisons to direct numerical simulations and extended parametric studies are presented.

A focus has been put on the stability characteristics of different flow types existing on air vehicles. Flow passing over wings and different junctions on an aircraft face numerous local features, ranging from different pressure gradients, to interacting boundary layers. Primarily, stability characteristics of flow over a wing subject to negative pressure gradient is studied. The current numerical study conforms to an experimental study conducted by Saric and coworkers, in their Arizona State University wind tunnel experiments. Within that framework, a passive control mechanism has been tested to delay transition of flow from laminar to turbulence. The same control approach has been studied here, in addition to underling mechanisms playing major roles in flow transition, such as nonlinear effects and secondary instabilities. Another common three-dimensional flow feature arises as a result of streamlines passing through a junction, the so called corner-flow. For instance, this flow can be formed in the junction between the wing and fuselage on a plane. A series of direct numerical simulations using linear Navier-Stokes equations have been performed to determine the optimal initial perturbation. Optimal refers to a perturbation which can gain the maximum energy from the flow over a period of time. Power iterations between direct and adjoint Navier- Stokes equations determine the optimal initial perturbation. In other words this method seeks to determine the worst case scenario in terms of perturbation growth. Determining the optimal initial condition can help improve the design of such surfaces in addition to possible control mechanisms. / <p>QC 20130604</p> / RECEPT

The master thesis is focused on how a local volatility surfaces can be extracted by optimization with respectto smoothness and price error. The pricing is based on utility based pricing, and developed to be set in arisk neutral pricing setting. The pricing is done in a discrete multinomial recombining tree, where the timeand price increments optionally can be equidistant. An interpolation algorithm is used if the option that shallbe priced is not matched in the tree discretization. Power utility functions are utilized, where the log-utilitypreference is especially studied, which coincides with the (Kelly) portfolio that systematically outperforms anyother portfolio. A fine resolution of the discretization is generally a property that is sought after, thus a seriesof derivations for the implementation are done to restrict the computational encumbrance and thus allow finer discretization. The thesis is mainly focused on the derivation of the method rather than finding optimal parameters thatgenerate the local volatility surfaces. The method has shown that smooth surfaces can be extracted, whichconsider market prices. However, due to lacking available interest and dividend data, the pricing error increasessymmetrically for longer option maturities. However, the method shows exponential convergence and robustnessto different initial (flat) volatilities for the optimization initiation. Given an optimal smooth local volatility surface, an arbitrary payoff function can then be used to price thecorresponding option, which could be path-dependent, such as barrier options. However, only vanilla optionswill be considered in this thesis. Finally, we find that the developed

本研究探討長期信託基金（諸如退休基金，人壽保險公司等）之固定收益債券多期資產配置，利用時間可加性之效用函數描述投資者於投資期限時對財富大小之風險偏好程度，滿足基金之長期最適效益目標，為避免模型過於複雜，本文假設於動態完備市場中針對基金所持有之資產執行動態資產配置，建立財務動態調整機制以評量基金到期之獲利表現。為實際反應市場之風險程度，持有資產將利用隨機擴散過程表示，短期市場利率採用單因子Vasicek隨機模型表示，本文以給定金融市場之情境假設，說明不同到期日之債券為適當之獲利投資及避險工具，本研究之多期資產配置模型主要參考Cox與Huang (1989, 1991)與Sorensen (1999)，將未來財富過程利用平賭過程表示，給定不同投資限制條件、風險偏好程度與市場系統風險，以擬似動態規劃實際計算與比較每期之最適資產配置。 / This study attempts to investigate the hedging behavior through multi-period asset allocation strategy for the long-term fund manager, i.e., pension fund managers, life insurers, etc. Time additive utility function is employed to depict the risk preference of the investors during his investment time horizon. Based on their long-duration liabilities, assets held by the fund manager are employed in hedging and speculating under dynamic complete market assumption. To fully reflect the financial risks from the market, a risk management mechanism is implemented to monitor the long-term financial soundness. Short-term interest rate model proposed by Vasicek is employed to characterize the diffusion pattern of the invested assets. Current financial market information are incorporated and investigated to portray the hedging strategy through fixed income securities with various maturities. The quasi-dynamic approach proposed in Cox and Huang (1989, 1991) and Sorensen (1999) are implemented to construct the optimal asset allocation model. The optimal strategy is examined through maximizing the indirect utility function through the optimal growth portfolio. Finally, the hedging behaviors are compared and fully explored under various market scenarios.

La reconstruction et la résurrection moléculaire de protéines ancestrales est au coeur de cette thèse. Alors que les données moléculaires fossiles sont quasi inexistantes, il est possible d'estimer quelles étaient les séquences ancestrales les plus probables le long d'un arbre phylogénétique décrivant les relations de parentés entre séquences actuelles. Avoir accès à ces séquences ancestrales permet alors de tester de nombreuses hypothèses biologiques, de la fonction des protéines ancestrales à l'adaptation des organismes à leur environnement. Cependant, ces inférences probabilistes de séquences ancestrales sont dépendantes de modèles de substitution fournissant les probabilités de changements entre acides aminés. Ces dernières années ont vu le développement de nouveaux modèles de substitutions d'acides aminés, permettant de mieux prendre en compte les phénomènes biologiques agissant sur l'évolution des séquences protéiques. Classiquement, les modèles supposent que le processus évolutif est à la fois le même pour tous les sites d'un alignement protéique et qu'il est resté constant au cours du temps lors de l'évolution des lignées. On parle alors de modèle homogène en temps et en sites. Les modèles récents, dits hétérogènes, ont alors permis de lever ces contraintes en permettant aux sites et/ou aux lignées d'évoluer selon différents processus. Durant cette thèse, de nouveaux modèles hétérogènes en temps et sites ont été développés en Maximum de Vraisemblance. Il a notamment été montré qu'ils permettent d'améliorer considérablement l'ajustement aux données et donc de mieux prendre en compte les phénomènes régissant l'évolution des séquences protéiques afin d'estimer de meilleurs séquences ancestrales. A l'aide de ces modèles et de reconstruction ou résurrection de protéines ancestrales en laboratoire, il a été montré que l'adaptation à la température est un déterminant majeur de la variation des taux évolutifs entre lignées d'Archées. De même, en appliquant ces modèles hétérogènes le long de l'arbre universel du vivant, il a été possible de mieux comprendre la nature du signal évolutif informant de manière non-parcimonieuse un ancêtre universel vivant à plus basse température que ses deux descendants, à savoir les ancêtres bactériens et archéens. Enfin, il a été montré que l'utilisation de tels modèles pouvait permettre d'améliorer la fonctionnalité des protéines ancestrales ressuscitées en laboratoire, ouvrant la voie à une meilleure compréhension des mécanismes évolutifs agissant sur les séquences biologiques / The molecular reconstruction and resurrection of ancestral proteins is the major issue tackled in this thesis manuscript. While fossil molecular data are almost nonexistent, phylogenetic methods allow to estimate what were the most likely ancestral protein sequences along a phylogenetic tree describing the relationships between extant sequences. With these ancestral sequences, several biological hypotheses can be tested, from the evolution of protein function to the inference of ancient environments in which the ancestors were adatapted. These probabilistic estimations of ancestral sequences depend on substitution models giving the different probabilities of substitution between all pairs of amino acids. Classicaly, substitution models assume in a simplistic way that the evolutionary process remains homogeneous (constant) among sites of the multiple sequence alignment or between lineages. During the last decade, several methodological improvements were realised, with the description of substitution models allowing to account for the heterogeneity of the process among sites and in time. During my thesis, I developed new heterogeneous substitution models in Maximum Likelihood that were proved to better fit the data than any other homogeneous or heterogeneous models. I also demonstrated their better performance regarding the accuracy of ancestral sequence reconstruction. With the use of these models to reconstruct or resurrect ancestral proteins, my coworkers and I showed the adapation to temperature is a major determinant of evolutionary rates in Archaea. Furthermore, we also deciphed the nature of the phylogenetic signal informing substitution models to infer a non-parsimonious scenario for the adaptation to temperature during early Life on Earth, with a non-hyperthermophilic last universal common ancestor living at lower temperatures than its two descendants. Finally, we showed that the use of heterogeneous models allow to improve the functionality of resurrected proteins, opening the way to a better understanding of evolutionary mechanisms acting on biological sequences