Cette thèse est dédiée à l'étude d'opérateurs de composition pondérés sur plusieurs espaces fonctionnels sous fond du problème du sous-espace invariant. Cet important problème ouvert pose la question de l'existence pour tout opérateur sur un espace de Hilbert, complexe, séparable de dimension infinie, d'un sous-espace fermé, non-trivial et invariant par cet opérateur. La première partie est consacrée à l'étude spectrale et à la caractérisation des vecteurs cycliques d'un opérateur de composition à poids particulier sur L^2([0,1]^d) : l'opérateur de type Bishop, introduit comme possible contre-exemple au problème du sous-espace invariant. Les seconde, troisième et quatrième parties abordent ce problème sous un autre aspect : celui de l'universalité d'un opérateur. Ces opérateurs universels possèdent la propriété d'universalité : la description complète des sous-espaces invariants d'un opérateur universel permettrait de répondre au problème du sous-espace invariant. Déterminer l'universalité d'un opérateur repose sur l'établissement de propriétés spectrales fines de l’opérateur considéré (théorème de Caradus). Dans ce but, nous établissons des propriétés spectrales ad-hoc de classes d’opérateurs de composition à poids sur L^2([0,1]), les espaces de Sobolev d’ordre n, sur les espaces de Hardy du disque unité et du demi-plan supérieur, permettant de déduire des résultats d’universalité. Nous obtenons aussi une généralisation du critère d’universalité. Dans la dernière partie, nous donnons une caractérisation des opérateurs de composition rsid16415432 inversibles et une caractérisation partielle des opérateurs de composition isométriques sur les espaces de Hardy de l’anneau / In this thesis, we study classes of weighted composition operators on several functional spaces in the background of the invariant subspace problem. This important open problem asks the question of the existence for every operator, defined on a complex and separable infinite dimensional Hilbert space, of a non trivial closed subspace invariant under the operator. The first part is dedicated to the establishment of the spectrum and the characterization of cyclic vectors of a special weighted composition operator defined on L^2([0,1]^d) : the Bishop type operator, introduced as possible counter-example of the invariant subspace problem. The second, third and fourth part approach the problem from the point of view of universal operators. More precisely, universal operators have the universal property in the sense of the complete description of all the invariant subspaces of a universal operator could solve the invariant subspace problem. A sufficient condition for an operator to be universal (Caradus’theorem) is given in terms of spectral properties. To this aim, we establish ad-hoc spectral properties of a class of weighted composition operators on L^2([0,1]) and Sobolev spaces of order n, of composition operator in the Hardy space of the unit disc and of the upper half-plane, which lead us to deduce universality results. We also obtain a generalization of the universality criteria mentioned above. In the last part, we give a characterization of invertible composition operators and a partial characterization of composition operators on the Hardy space of the annulus

[pt] Este trabalho apresenta o crescimento de pressão no anular causado pela fluência do sal e relaciona com o cálculo deste fenômeno quanto ao efeito térmico, que é normalmente conhecido por APB (annular pressure build-up). Este fenômeno não é modelado em softwares comerciais e deve ser considerado em poços de pré-sal. O cálculo de APB considera três mecanismos geradores de pressão no anular: expansão térmica do fluido do anular, expansão do tubing e influxo e efluxo do fluido confinado no anular. Mudanças no volume do anular, causados pela fluência do sal, podem ser tratadas como um quarto mecanismo, equivalente ao influxo de fluido no cálculo do APB. O cálculo deste fenômeno pode ser incorporado a um modelo de cálculo acoplado ( multistring casing design ) através da programação do APB causado pelo efeito de expansão térmica dos fluidos confinados e o APB causado pela fluência do sal. Para isso é necessário adotar um modelo constitutivo para descrever o comportamento de fluência desta rocha em função do estado de tensão, perfil de temperatura, tipo de sal, tempo decorrido, energia de ativação e outros fatores. Os efeitos de APB devido à fluência do sal podem ser mais pronunciados quando a sapata do revestimento é assentada em um intervalo de sal com elevado gradiente de sobrecarga e elevado gradiente geotérmico. Não considerar o efeito da fluência do sal no crescimento de pressão do anular (APB) pode causar um dimensionamento inadequado de revestimento ou packoff e levar a perda da integridade do poço. / [en] This paper presents the annular pressure build-up caused by salt creep and link to current calculation of this phenomenon due to thermal effect, which is commonly known as APB. This phenomenon is not currently modeled on commercial software and should be considered in subsalt wells. The calculation of APB considers three generator mechanisms: thermal expansion of annular fluid, influx or efflux and tubing buckling. Changes in the annular volume, caused by salt creep, may be treated as a fourth mechanism, equivalent to the influx in current calculation of APB. The calculation of this phenomenon can be incorporated into a multistring casing design model by programming the thermal expansion effect and the APB caused by salt creep. This requires adopting a constitutive model to describe the creep behavior of rock for differential stress, temperature profile, salt type, salt thermal activation and other factors. When the casing shoe is seated in deep salt sections with high overburden gradient and high temperature from the produced hydrocarbons, effects of APB due to salt creep and thermal effects may be more pronounced. Not considering the salt creep effect in the annular pressure build-up (APB) can lead to inadequate casing design and possible loss of well integrity.

<p dir="ltr">With increasing demand for reduced carbon emissions and increased fuel costs, novel aircraft designs are being developed that reduce the wetted area of the aircraft leading to complex inlet installations for engine integrations. With this, an understanding of the effects of inlet distortion on the compression system is paramount. One key parameter that defines the response of the compression system to inlet distortions is that of the critical angle of distortion. This is the circumferential angle that a distortion must occupy before performance and stability of the compression system is changed. This effort investigates the mechanism by which the critical angle of distortion alters the performance and stability of a high-speed centrifugal compressor. With this, a more accurate estimate of the critical angle of distortion for compressors is developed that allows for characterization of this angle without the need for copious simulations and experimental test campaigns. This investigation was driven by computational fluid dynamic simulations that were utilized to determine the critical angle of inlet distortion. Once this was understood, inlet distortion screens were designed via use of porous inlet-only CFD models to generate similar distortion profiles to those used in the CFD campaign. Finally, these screens were tested and the distortion profiles of the screens investigated along with the performance and stability changes of the compressor due to increasing distortion extents.</p><p dir="ltr">To determine the critical angle of distortion for the centrifugal compressor investigated, a computational fluid dynamics study of the compressor was conducted. In this effort, pure once-per-rev total pressure distortions were delivered to the compression system with the extent varied in terms of number of impeller main blade pitches. The effects of this on performance and machine static pressure rise characteristics was analyzed. These simulations were conducted using a full-annulus transient model to allow for distortion propagation through the passages to be as realistic as possible. The critical angle of distortion of the compressor was found to correspond to 4.5 pitches (or 95.3°) as at this point the compressor efficiency and total pressure ratio were exponentially deteriorated for any increase in distortion extent.</p><p dir="ltr">With knowledge of the critical angle, an understanding of the mechanism by which this alters performance was presented in terms of reduced frequency. Advective, acoustic, and relative acoustic definitions of reduced frequency were analyzed to determine which correlated best with physical flow disturbances from the inlet distortion propagation through the impeller passage. Furthermore, rothalpy was investigated as a tool to track distortion through the passage as it is maintained along a streamline but contains information of the relative frame temporal pressure gradient due to disturbances in the absolute frame. Utilizing distortion tracking and reduced frequencies, the critical angle of inlet distortion was found to correlate with the acoustic reduced frequency. For acoustic reduced frequencies below unity, the compressor performance was degraded.</p><p dir="ltr">With an understanding of the critical extent, inlet-only simulations were conducted to generate designs of total pressure screens to precipitate similar total pressure distortion profiles to the compressor for a design of experiment. These designs were evaluated experimentally using rotatable inlet rakes upstream of the compressor. A comparison between the experimental and CFD data for these distortion profiles showed discrepancies, which were investigated. The findings from this allowed an outline of best practices for future design work for generating total pressure distortion profiles using porous inlet-only models for design of experimental testing of inlet distortion related effects.</p><p dir="ltr">Finally, the centrifugal compressor’s response to the designed inlet distortion screens was analyzed. The compressor was mapped from choke to surge at 80%, 90%, and 100% speed. These corresponded to subsonic, transonic, and supersonic inlet relative Mach numbers for the impeller. The compressor was found to be sensitive above the critical distortion extent with efficiency and stage total pressure ratio degraded. Surge margin was enhanced by use of the screens at 100% speed, but severely degraded at 80% and this was found to correlate with the work characteristic slope. The typical understanding of a more negative work characteristic slope being a more stable operating condition for the compressor was found to be untrue for the distortion screens tested. The compressor entered instability at the same value of work coefficient for all distortion conditions, which lead to a more positive slope of the work characteristic allowing for a wider operating range in terms of flow coefficient.</p>