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Using statistical physics principles to solve problems in biology is one of the most promising directions due to the complexity and non-equilibrium fluctuations in biological systems. In this work, we try to describe the dynamics at both cellular and molecular levels. Microtubule dynamics and dynamic disorder of enzyme proteins are two of the examples we investigated. The dynamics of microtubules and the mechanical properties of these polymers are essential for many key cellular processes. However, critical discrepancies between experimental observations and existing models need to be resolved before further progress towards a complete model can be made. We carried out computational studies to compare the mechanical properties of two alternative models, one corresponding to the existing, conventional model, and the other considering an additional type of tubulin lateral interaction described in a cryo-EM structure of a proposed trapped intermediate in the microtubule assembly process. Our work indicates that a class of sheet structures is transiently trapped as an intermediate during the assembly process in physiological conditions. In the second part of the work, we analyzed enzyme slow conformational changes in the context of regulatory networks. A single enzymatic reaction with slow conformational changes can serve as a basic functional motif with properties normally discussed with larger networks in the field of systems biology. The work on slow enzyme dynamics fills the missing gap between studies on intramolecular and network dynamics. We also showed that enzyme fluctuations could be amplified into fluctuations in phosphorylation networks. This can be used as a novel biochemical "reporter" for measuring single enzyme conformational fluctuation rates. / Ph. D.

The aerodynamic flow and fluctuating surface pressure of a plane, turbulent, two-dimensional wall jet flow into still air over smooth and rough surfaces has been investigated in a recently constructed wall jet wind tunnel testing facility. The facility has been shown to produce a wall jet flow with Reynolds numbers based on the momentum thickness, Re<SUB>&delta</SUB> = &deltaU<SUB>m</SUB>/&nu, of between 395 and 1100 and nozzle exit Reynolds numbers, Re<SUB>j</SUB> = U<SUB>m</SUB>b/&nu, of between 16000 and 45000. The wall jet flow properties (&delta, &delta<SUP>*</SUP>, &theta, y<SUB>1/2</SUB>, U<SUB>m</SUB>, u<SUP>*</SUP>, etc.) were measured and characterized over a wide range of initial flow conditions and measurement locations relative to the wall jet source. These flow properties were measured for flow over a smooth flow surface and for flow over roughness patches of finite extent. The patches used in the current study varied in length from 305 mm to 914 mm (between 24 and 72 times the nozzle height, b) and were placed so that the leading edge of the patch was fixed at 1257 mm (x/b = 99) downstream of the wall jet source. These roughness patches were of a random sand grain roughness type and the roughness grain size was varied throughout this experiment. The tests covered roughness Reynolds numbers (k<SUP>+</SUP>) ranging from less than 2 to over 158 (covering the entire range of rough wall flow regimes from hydrodynamically smooth to fully rough). For the wall jet flows over 305 mm long patches of roughness, the displacement and momentum thicknesses were found to vary noticeably with the roughness grain size, but the maximum velocity, mixing layer length scale, y<SUB>/2</SUB>, and the boundary layer thickness were not seen to vary in a consistent, determinable way. Velocity spectra taken at a range of initial flow conditions and at several distinct heights above the flow surface showed a limited scaling dependency on the skin friction velocity near the flow surface. The spectral density of the surface pressure of the wall jet flow, which is not believed to have been previously investigated for smooth or rough surfaces, showed distinct differences with that seen in a conventional boundary layer flow, especially at low frequencies. This difference is believed to be due to the presence of a mixing layer in the wall jet flow. Both the spectral shape and level were heavily affected by the variation in roughness grain size. This effect was most notable in overlap region of the spectrum. Attempts to scale the wall jet surface pressure spectra using outer and inner variables were successful for the smooth wall flows. The scaling of the rough wall jet flow surface pressure proved to be much more difficult, and conventional scaling techniques used for ordinary turbulent boundary layer surface pressure spectra were not able to account for the changes in roughness present during the current study. An empirical scaling scheme was proposed, but was only marginally effective at scaling the rough wall surface pressure. / Ph. D.

We examine the relaxed minimization problem for ferromagnetic bodies using the nonlocal exchange energy model. We show that the model possesses a wide range of phenomena including hysteresis, hysteresis subloops, Barkhausen effect, and demagnetization. The results are in three parts. First, we examine analytically the problem of a unit sphere of ferromagnetic material. We show that when the exchange energy is zero we duplicate De Simone's model which has a wide range of measure-valued minimizers. As the exchange energy grows our model stabilizes at the saturated solutions of the Stoner-Wohlfarth model. Here, the measure-valued minimizers are eliminated. Next, we examine numerically the problem of a body composed of several unit spheres of ferromagnetic material. We show that a constrained problem that focuses on the resultant field energy produces results similar to the unconstrained problem with considerable savings in time and resources. Finally, we examine numerically the constrained problem on a moderately large body. It is shown that the constrained problem contains all the hysteresis phenomena mentioned above. / Ph. D.

In this thesis, the benefits of boundary layer control (BLC) in improving aerodynamic performance and engine stability were examined in a compact, serpentine inlet exhibiting flow separation. A 1/14-scale turbofan engine simulator provided the flow through the inlet. The inlet's mass flow was measured to be 759 scfm (0.939 lbm/s) with an average throat Mach number of 0.23 when the simulator speed was 40 krpm. Boundary layer suction, blowing, and their combination were used to minimize the inlet's flow separation. The effectiveness of the suction alone and the blowing alone was shown to be approximately equivalent, and the effectiveness of the combined use of both was seen to be better than either one by itself. With blowing and suction flowrates around 1% of the simulator's core flow, the inlet's distortion was lowered by 40.5% (from 1.55% to 0.922%) while the pressure recovery was raised by 9.7% (from 87.2% to 95.6%). With its reduction in distortion, BLC was shown to allow the simulator to steadily operate in a range that would have otherwise been unstable. Minimizing the flow separation within the inlet was shown to directly relate to measurements from flush-mounted microphones along the inlet wall: as the exit distortion decreased the microphone spectrum also decreased in magnitude. The strong relationship between the aerodynamic profiles and the microphone signal suggests that microphones may be used in an active flow control scheme, where the BLC effort can be tailored for different engine operating conditions. Unfortunately, the sensing scheme used in this experiment showed the microphone signal to continue to decrease even when the separation is overly compensated; therefore refinements must be made before it would be practical in a real application. / Master of Science

Yes / When fixating on a stationary object, the power of the eye’s lens fluctuates. Studies have suggested that changes in these so-called microfluctuations in accommodation may be a factor in the onset and progression of short-sightedness. Like many physiological signals, the fluctuations in the power of the lens exhibit chaotic behaviour. A breakdown or reduction in chaos in physiological systems indicates stress to the system or pathology. The purpose of this study was to determine whether the chaos in fluctuations of the power of the lens changes with refractive error, i.e. how short-sighted a subject is, and/or accommodative demand, i.e. the effective distance of the object that is being viewed. Six emmetropes (EMMs, non-short-sighted), six early-onset myopes (EOMs, onset of short-sightedness before the age of 15), and six late-onset myopes (LOMs, onset of short-sightedness after the age of 15) took part in the study. Accommodative microfluctuations were measured at 22 Hz using an SRW-5000 autorefractor at accommodative demands of 1 D (dioptres), 2 D, and 3 D. Chaos theory analysis was used to determine the embedding lag, embedding dimension, limit of predictability, and Lyapunov exponent. Topological transitivity was also tested for. For comparison, the power spectrum and standard deviation were calculated for each time record. The EMMs had a statistically significant higher Lyapunov exponent than the LOMs ( 0.64±0.330.64±0.33 vs. 0.39±0.20 D/s0.39±0.20 D/s ) and a lower embedding dimension than the LOMs ( 3.28±0.463.28±0.46 vs. 3.67±0.493.67±0.49 ). There was insufficient evidence (non-significant p value) of a difference between EOMs and EMMs or EOMs and LOMs. The majority of time records were topologically transitive. There was insufficient evidence of accommodative demand having an effect. Power spectrum analysis and assessment of the standard deviation of the fluctuations failed to discern differences based on refractive error. Chaos differences in accommodation microfluctuations indicate that the control system for LOMs is under stress in comparison to EMMs. Chaos theory analysis is a more sensitive marker of changes in accommodation microfluctuations than traditional analysis methods.

High Reynolds number turbulent boundary layers over both smooth and rough surfaces subjected to a systematically defined family of continually varying, bi-directional pressure gradient distributions are investigated in both wind tunnel experiments and steady 2D and 3D Reynolds Averaged-Navier-Stokes (RANS) computations. The effects of pressure gradient, pressure gradient history, roughness, combined roughness and pressure gradient, and combined roughness and pressure gradient history on boundary growth and the behavior of the underlying surface pressure spectrum are examined. Special attention is paid to how said pressure spectra may be effectively modeled and predicted by assessing existing empirical and analytical modeling formulations, proposing updates to those formulations, and assessing RANS flow modeling as it pertains to successful generation of spectral model inputs. It is found that the effect of pressure gradient on smooth wall boundary layers is strongly non-local. The boundary layer velocity profile, turbulence profiles, and associated parameters and local skin friction at a point that has seen non-constant upstream pressure gradient history will be dependent both on the local Reynolds number and pressure gradient as well as the Reynolds number and pressure gradient history. This shows itself most readily in observable downstream lagging in key observed behaviors. Steady RANS solutions are capable of predicting this out-of-equilibrium behavior if the pressure gradient distribution is captured correctly, however, capturing the correct pressure gradient is not as straightforward as may have previously been thought. Wind tunnel flows are three-dimensional, internal problems dominated by blockage effects that are in a state of non-equilibrium due to the presence of corner and juncture flows. Modeling a 3D tunnel flow is difficult with the standard eddy viscosity models, and requires the Quadratic Constitutive Relation for all practical simulations. Modeling in 2D is similarly complex, for, although 3D effects can be ignored, the absence of two walls worth of boundary layer and other interaction flows causes the pressure gradient to be captured incorrectly. These effects can be accounted for through careful setup of meshed geometry. Pressure gradient and history effects on the pressure spectra beneath smooth wall boundary layers show similar non-locality, in addition to exhibiting varying effects across different spectral regions. In general, adverse pressure gradient steepens the slope of the mid-frequency region while favorable shallows it, while the high frequency region shows self-similarity under viscous normalization independent of pressure gradient. The outer region is dominated by history effects. Modeling of such spectra is not straightforward; empirical models fail to incorporate the subtle changes in spectral shape as coherent functions of flow variables without becoming overly-defined and producing non-physical spectral shapes. Adopting an analytical formulation based on the pressure Poisson equation solves this issue, but brings into play model inputs that are difficult to predict from RANS. New modeling protocols are proposed that marry the assumptions and limitations of RANS results to the analytical spectral modeling. Rough surfaces subjected to pressure gradients show simplifications over their smooth wall relatives, including the validity of Townsend's outer-layer-Reynolds-number-similarity Hypothesis and shortened history effects. The underlying pressure spectra are also significantly simplified, scaling fully on a single outer variable scaling and showing no mid-frequency slope pressure gradient dependence. This enables the development of a robust and accurate empirical model for the pressure spectra beneath rough wall flows. Despite simplifications in the flow physics, modeling rough wall flows in a steady RANS environment is a challenge, due to a lack of understanding of the relationship between the rough wall physics and the RANS model turbulence parameters; there is no true physical basis for a steady RANS roughness boundary condition. Improvements can been made, however, by tuning a shifted wall distance, which also factors heavily into the mathematical character of the pressure spectrum and enables adaptations to the analytical model formulations that accurately predict rough wall pressure spectra. This work was sponsored by the Office of Naval Research, in particular Drs. Peter Chang and Julie Young under grants N00014-18-1-2455, N00014-19-1-2109, and N00014-20-2821. This work was also sponsored by the Department of Defense Science, Mathematics, and Research for Transformation (SMART) Fellowship Program and the Naval Air Warfare Center Aircraft Division (NAWCAD), in particular Mr. Frank Taverna and Dr. Phil Knowles. / Doctor of Philosophy / Very near to a solid surface, air or water flow tends to be highly turbulent: chaotic and random in nature. This is called a boundary layer, which is present on almost every system that involves a fluid and a solid with motion between them. When the boundary layer is turbulent, the surface of the solid body experiences pressures that fluctuate very rapidly, and this can fatigue the structure and create noise that radiates both into the structure to passengers and out from the structure to observers far away. These pressure fluctuations can be described in a statistical nature, but these statistics are not well understood, particularly when the surface is rough or the average pressure on the surface is changing. Improving the ability to predict the statistics of the pressure fluctuations will aid in the design of vehicles and engineering systems where those fluctuations can be damaging to the structure or the associated noise is detrimental to the role of the system. Wind turbine farm noise, airport community noise, and air/ship-frame longevity are all issues that stand to benefit from improved modeling of surface pressure fluctuations beneath turbulent boundary layers. This study aims to improve said modeling through the study of the effects of changing average surface pressure and surface roughness on the statistics of surface pressure fluctuations. This goal is accomplished through a combination of wind tunnel testing and computer simulation. It was found that the effect of gradients in the surface pressure is not local, meaning the effects are felt by the boundary layer at a different point than where the gradient was actually applied. This disconnect between cause and effect makes understanding and modeling the flow challenging, but adjustments to established modeling ideas are proposed that prove more effective than what exists in the literature for capturing those effects. Roughness on the surface causes the flow to become even more turbulent and the surface pressure fluctuations to become louder and more damaging. Fortunately, it is found that the combination of roughness with a gradient in surface pressure is actually simpler than equivalent smooth surfaces. These simplifications offer significant insight into the underlying physics at play and enable the development of the first analytically based model for rough wall pressure fluctuations.

Dans l'étang de Berre, les apports excessifs en eau douce entraînent souvent des variations brusques de la salinité et des apports en azote parfois abondants. Les processus de régénération sédimentaire et d'élimination d'azote constituent des phénomènes majeurs pouvant expliquer le développement phytoplanctoniques et contrôler l'eutrophisation. L'étude de ces processus a été réalisée dans 2 stations ayant subi des historiques de variations de salinité différents. RDNA et anammox étaient négligeables. La dénitrification (couplée à la nitrification) serait le principal processus de sortie de N2 de l'étang. La forte production primaire pélagique utilisant l'ammonium a pu être expliquée par les processus de régénération, contrairement au nitrate dont la demande pélagique serait soutenue par des apports externes. Comme la salinité est susceptible d'influencer les processus d'azote, des microcosmes ont été utilisés afin d'évaluer la sensibilité de ces processus (résistance, résilience, shift) face aux variations à court terme de la salinité. Les 2 stations ont présenté des réponses différentes (dénitrification et nitrate réduction plus résilientes que la nitrification), suggérant que les stress halins à long terme influencent les réponses à court terme. Une hypothèse serait que la diversité et la structure des communautés joueraient un rôle crucial dans le maintien des taux d'activité. Dans cette étude, seule la communauté nitrifiante (AO) a été étudiée. Les AO et leurs transcrits étaient spécifiques aux sites et leurs abondances changeaient faiblement entre les microcosmes (résistance plus forte dans le site fréquemment soumis à des fluctuations de salinité). / The Berre lagoon receives excess freshwater leading to strong changes in the ecosystem salinity and in the nutrient inputs. Regeneration processes and the N2 removal of nitrogen are of a particular interest as they can explain the planktonic development and control the eutrophication state. These processes were studied in 2 stations with different patterns of long term stresses. DNRA and anammox were negligible. Denitrification (particularly the one coupled to nitrification) would be the main N2 removal in the lagoon. The high primary production based on N-NH4+ can be explained by the regeneration processes, while the primary production based on N-NO3- might be sustained by external inputs. As salinity susceptible to influence directly or indirectly the nitrogen processes, a microcosm approach was used in order to assess their sensitivity (resistance, resilience, shifts) to short term salinity fluctuations. Overall, towards the same kind of perturbations, the two stations responded differently (denitrification and nitrate reduction exhibited showed higher resilience than nitrification.), suggesting that long-term saline stresses would influence short-term responses. We suggest that the diversity and the structure of the communities would be crucial in their functional redundancy and thereby in the maintenance of the rates. In this study, we focused on the total structure of the nitrifying community (AO). AO and their transcripts were site-specific and their abundances changed slightly between microcosms (higher resistance in the site subject to frequent salinity fluctuations compared to the other site which is not affected by changes in the in situ salinity).

Dans cette thèse, nous nous intéressons à des matrices aléatoires en lien avec des permutations. Nous abordons l'étude de leurs spectres de plusieurs manières, et à différentes échelles d'observation. Dans un premier temps, nous prolongeons l'étude de Wieand à propos des nombres de valeurs propres appartenant à certains arcs fixés du cercle unité. Pour cela nous tirons parti des travaux réalisés par Ben Arous et Dang sur les statistiques linéaires du spectre de matrices de permutation pour une famille de lois à un paramètre englobant le cas de la loi uniforme sur le groupe symétrique, appelée famille des lois d'Ewens. Une partie innovante de notre travail réside dans la généralisation à des arcs non nécessairement fixés. Nous obtenons en effet des résultats similaires en autorisant les longueurs des arcs à décroître lentement vers zéro avec la taille des matrices. Dans un deuxième temps, nous regardons le spectre à échelle microscopique. En nous inspirant des travaux de Najnudel et Nikeghbali en rapport avec la convergence de mesures empiriques des angles propres normalisés, nous commençons par donner un sens à la convergence en terme de comptages de points sur des intervalles fixés. A partir du processus ponctuel limite, nous montrons que le nombre de points dans un intervalle a des fluctuations asymptotiquement gaussiennes lorsque la longueur de l'intervalle tend vers l'infini. Enfin, nous adaptons certains résultats de Chhaibi, Najnudel et Nikeghbali sur le polynôme caractéristique de matrices du CUE à échelle microscopique, et les développons dans notre cadre. De manière analogue mais avec d'autres techniques de preuves, nous obtenons des convergences des polynômes caractéristiques vers des fonctions entières, et cela pour une grande famille de lois pour le tirage des permutations, incluant les lois d'Ewens. / In this thesis, our goal is to study random matrices related to permutations. We tackle the study of their spectra in various ways, and at different scales. First, we extend the work of Wieand about the numbers of eigenvalues lying in some fixed arcs of the unit circle. We take advantage of the results of Ben Arous and Dang on the linear statistics of the spectrum of permutation matrices for a one-parameter family of deformations of the uniform law on the symmetric group, called Ewens' measures. One of the most innovative parts of our work is the generalization to non-fixed arcs. Indeed we get similar results when we let the lengths of the arcs decrease to zero slower than 1/n. Then, we look at the spectrum at microscopic scale. Inspired by the work of Najnudel and Nikeghbali about the convergence of empirical measures of rescaled eigenangles, we give a meaning to the convergence in terms of indicator functions of intervals. From the limiting point process, we show that the number of points in any interval is asymptotically normal as the length of the interval goes to infinity. Finally, we adapt some results of Chhaibi, Najnudel and Nikeghbali on the characteristic polynomial of the CUE at microscopic scale, and develop them in our framework. Analogously but with different techniques of proof, we get that the characteristic polynomials converge to entire functions, and this for a large family of laws including the Ewens' measures.

Cette thèse propose une analyse de la dynamique macroéconomique de l’économie camerounaise. On commence par une analyse quantitative générale du cycle des affaires au Cameroun, fondée sur des données macroéconomiques annuelles que nous avons nous-mêmes assemblées. Cette première exploration laisse apparaître un certain nombre de caractéristiques qui se prêtent bien à une modélisation de type néo-keynesien. Nous construisons alors un modèle dynamique stochastique d’équilibre général (DSGE) de l’économie camerounaise. Ce modèle comporte les blocs de construction de modèles DSGE néo-keynésiens standards (par exemple, la rigidité des prix et des salaires des rigidités, et des coûts d'ajustement), mais il inclut également un certain nombre de caractéristiques spécifiques (telles que l'exportation des matières premières et les revenus du pétrole entre autre) dont on montre qu’elles jouent un rôle important dans la dynamique de l'économie camerounaise. Le modèle est estimé et évalué selon une approche bayésienne. La performance du modèle DSGE en termes de prévision est comparée à celle d’un modèle de marche aléatoire, à celle d’un modèle vectoriel auto-régressif (VAR) et, enfin, à celle d’un modèle vectoriel auto-régressif de type Bayesien (BVAR). Nous trouvons que, le modèle DSGE est plus précis en matière de prévision au moins dans un horizon de court-terme. Pour ce qui est des fluctuations macroéconomiques, les chocs des prix des produits de base génèrent une expansion de la production, une augmentation de l'emploi et une baisse de l'inflation tandis que des chocs liés aux prix du pétrole ont un impact direct sur le coût marginal de production qui augmente et provoque une augmentation de l'inflation en même temps que production et emploi baissent. Notons que, les chocs extérieurs et les chocs d'offre domestiques représentent une grande part des fluctuations de la production et de l'investissement. Aussi, l'évolution de la production sur l'ensemble de l'échantillon est dominée par le choc de prix des matières premières et le choc des prix du pétrole. / This thesis aims at analyzing the macroeconomic dynamics of the Cameroonian economy. It begins with a quantitative analysis of the business cycle in Cameroon, based on annual macroeconomic data, especially gathered for this purpose. This preliminary inquiry highlights a number of features that can be accounted for in a new-keynesian modelling framework. A dynamic stochastic general equilibrium (DSGE) model of the new-keynesian family is thus constructed as a mean of describing the salient feautures of the Cameroonian economy. It has the traditional blocks of new-keynesian DSGE models (Sticky prices and wages, adjustment costs, etc). But it also accounts for a number of characteristics of the Cameroonian economy that are shown to be influential in the dynamics of the cameroonian economy (e.g. oil revenues or primary goods exports). The model is then estimated and evaluated, based on a Bayesian approach. Its forecasting performance is also assessed through comparison to the performances of a random walk model, a vector autoregressive (VAR) model and a Bayesian VAR (BVAR) model. It turns out that, at least for short horizons, the DSGE model shows the highest perfromance. As to macroeconomic fluctuations, the estimated model suggests that commodity price shocks generate an output expansion, an increase in employment and a fall in inflation. In addition, oil price shocks have a direct impact on marginal costs which increase and provoke a rising in inflation while output and employment tend to fall. Foreign shoks and domestic supply shocks account for a large share of output and investment fluctuations. The evolution of output over the whole sample is dominated by commodity price shocks and oil price shocks as one would expect.