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Parmi les scénarios accidentels hypothétiques étudiés dans le cadre des études de sûreté des Réacteurs à Eau Pressurisée (REP), figure l’Accident par Perte de Réfrigérant Primaire (APRP). Dans ce scénario, les gaines en alliage de zirconium qui contiennent le combustible nucléaire sont soumises à une oxydation importante à haute température (T≈ 1200 °C) dans de la vapeur d’eau. Les gaines étant la première barrière de confinement des radioéléments, il est primordial qu’elles conservent une certaine ductilité résiduelle après la trempe pour conserver son intégrité. Cette propriété est directement liée aux cinétiques de croissance de la zircone et de la phase αZr(O), ainsi qu’au profil de diffusion de l’oxygène dans le métal au cours du régime transitoire. Dans ce cadre, la compréhension et la modélisation du phénomène d’oxydation et de diffusion de l’oxygène dans les alliages de zirconium à haute température ont fait l’objet de cette thèse. Le modèle cinétique (EKINOX-Zr), développé au cours de cette thèse, est basé sur la résolution numérique d’un problème de diffusion/réaction avec des conditions aux limites sur trois interfaces mobiles : gaz/oxyde, oxyde/αZr(O) et αZr(O)/βZr. Le couplage du code cinétique avec le logiciel ThermoCalc et la base de données thermodynamiques Zircobase permet de prendre en compte l’influence des éléments d’alliages (Sn, Fe, Cr, Nb) et de l’hydrogène. Cette étude s’est plus particulièrement intéressée à deux aspects de l’APRP : l’influence d’une couche de pré-oxyde (formée aux températures des conditions de service du réacteur) et les effets de l’hydrogène. Grâce au couplage avec la base thermodynamique Zircobase, l’effet de l’hydrogène sur les limites de solubilité de l’oxygène dans les différentes phases a pu être pris en compte dans le modèle cinétique. Les simulations ont ainsi permis de reproduire les profils de concentration en oxygène mesurés sur différents échantillons pré- hydrurés. Par ailleurs, l’existence de couche de pré-oxyde de forte épaisseur peut conduire à une réduction transitoire de la couche de pré-oxyde dans les premiers instants du palier à haute température sous vapeur d’eau, avant formation de l’oxyde haute température. Une première série de simulations à l’aide du modèle cinétique EKINOX-Zr a permis de reproduire qualitativement ce chemin cinétique et a montré que cette couche formée à basse température possède des propriétés de diffusion particulières. Des expériences de traceurs sous 16O2/18O2 ont été réalisées sur des gaines pré-oxydées en autoclave pour étudier la diffusion de l’oxygène à haute température dans ces couches formées à basse température. D’autre part, le modèle cinétique EKINOX-Zr a été modifié pour prendre en compte la diffusion des traceurs. La confrontation des expériences avec les calculs a permis d’étudier les propriétés de diffusion particulières de la couche d’oxyde basse-température ainsi qu’une évolution des propriétés de diffusion de la phase αZr(O) formée par dissolution de l’oxyde à haute température. / One of the hypothetical accident studied in the field of the safety studies of Pressurized light Water Reactor (PWR) is the Loss-Of-Coolant-Accident (LOCA). In this scenario, zirconium alloy fuel claddings could undergo an important oxidation at high temperature (T≈ 1200 °C) in a steam environment. Cladding tubes constitute the first confinement barrier of radioelements and then it is essential that they keep a certain level of ductility after quenching to ensure their integrity. These properties are directly related to the growth kinetics of both the oxide and the αZr(O) phase and also to the oxygen diffusion profile in the cladding tube after the transient. In this context, this work was dedicated to the understanding and the modeling of the both oxidation phenomenon and oxygen diffusion in zirconium based alloys at high temperature. The numerical tool (EKINOX-Zr) used in this thesis is based on a numerical resolution of a diffusion/reaction problem with equilibrium-conditions on three moving boundaries : gas/oxide, oxide/αZr(O), αZr(O)/ βZr. EKINOX-Zr kinetics model is coupled with ThermoCalc software and the Zircobase database to take into account the influence of the alloying elements (Sn, Fe, Cr, Nb) but also the influence of hydrogen on the solubility of oxygen. This study focused on two parts of the LOCA scenario : the influence of a pre-oxide layer (formed in-service) and the effects of hydrogen. Thanks to the link between EKINOX-Zr and the thermodynamic database Zircobase, the hydrogen effects on oxygen solubility limit could be considered in the numerical simulations. Thus, simulations could reproduce the oxygen diffusion profiles measured in pre-hydrided samples. The existence of a thick pre-oxide layer on cladding tubes can induce a reduction of this pre-oxide layer before the growth of a high-temperature one during the high temperature dwell under steam. The first simulations performed using the numerical tool EKINOX-Zr showed that this particular kinetics pathway was qualitatively well reproduced by the modeling. It was also showed that the pre-oxide layer (formed at low-temperature) has particular diffusion properties. Consequently, some 18O tracer experiments were performed on pre-oxidized cladding tubes (pre-oxidizing done in autoclave) in order to study the diffusion properties of this oxide layers formed at low-temperature. Furthermore, EKINOX-Zr was modified to take into account the diffusion of tracer species. Both the diffusion properties of the low-temperature oxide layer and the evolution of the diffusion properties of the αZr(O) phase (formed by reduction of the oxide layer) were studied by comparing experiments and numerical simulations.

In molecules, electronic state transitions can occur via quantum coupling of the states. If the coupling is due to the kinetic energy of the molecular nuclei, then electronic transitions are best represented in the adiabatic frame. If the coupling is instead facilitated through the potential energy of the nuclei, then electronic transitions are better represented in the diabatic frame. In our study, we modeled these latter transitions, called ``nonadiabatic transitions.'' For one nuclear degree of freedom, we modeled the de-excitation of a diatomic molecule. For two nuclear degrees of freedom, we modeled the de-excitation of an ethane-like molecule undergoing cis-trans isomerization. For both cases, we studied the dependence of the de-excitation on the nuclear configuration and potential energy of the molecule. We constructed a numerical model to solve the time-dependent Schr\"{o}dinger Equation for two coupled wave functions. Our algorithm takes full advantage of the sparseness of the numerical system, leading to a final set of equations that is solved recursively using nothing more than the Tridiagonal Algorithm. We observed that the most effective de-excitation occurred when the molecule transitioned from a stable equilibrium configuration to an unstable equilibrium configuration. This same mechanism is known to drive fast electronic transitions in the adiabatic frame. We concluded that while the adiabatic and diabatic frames are strongly opposed physically, the mathematical mechanism driving electronic transitions in the two frames is in some sense the same.

Cette thèse s'intéresse à des méthodes de points intérieurs et de quasi-Newton en optimisation non linéaire et à leurs mises en oeuvre. On présente le code NOPTIQ utilisant les formules de BFGS à mémoire limitée pour résoudre des problèmes de grande taille. L'originalité de cette approche est l'emploi de ces formules dans le cadre des méthodes de points intérieurs. L'espace mémoire et le coût en opérations du calcul d'une itération sont alors faibles. Le code NOPTIQ est robuste et a des performances comparables avec les codes de références l-BFGS-B et LANCELOT. On présente aussi un algorithme non réalisable utilisant les méthodes précédentes pour résoudre un problème non linéaire avec contraintes d'inégalité et contraintes d'égalité linéaire. L'idée est de pénaliser le problème à l'aide de variables de décalage et d'une variante de la méthode big-M. La convergence q-superlinéaire des itérés internes et la convergence globale des itérés externes sont démontrées.

The idea of obtaining a best approximation in some sense of a function gained considerable importance with the introduction of electronic computers. The Remez algorithm, which is known as the exchange method, is used in this paper to find the best approximating polynomial of a given degree for a real continuous function f(x) on a real finite interval (a,b). The comparison of such an algorithm written in the FORTRAN and the PL/I languages is the main purpose of this paper. A review of the approximation theory is made as well as a discussion of the steps in the programming process. The outstanding features used in the programs of the languages are pointed out and illustrated with examples taken from the programs. The accuracy of the results, the speed, and the storage requirements are analyzed. Also ideas of program organization are discussed.Ball State UniversityMuncie, IN 47306

In this paper the mechanical behaviour, both elastic and plastic, of single-crystal nickel-based superalloys has been investigated. A theoretic base has been established in crystal plasticity, with concern taken to the shearing rate on the slip systems. A model of the mechanical behaviour has been implemented, by using FORTRAN, as a user defined material model in three major FEM-programmes. To evaluate the model a simulated pole figure has been compared to an experimental one. These pole figures match each other very well. Yielding a realistic behaviour of the model.

<p>In this paper the mechanical behaviour, both elastic and plastic, of single-crystal nickel-based superalloys has been investigated. A theoretic base has been established in crystal plasticity, with concern taken to the shearing rate on the slip systems. A model of the mechanical behaviour has been implemented, by using FORTRAN, as a user defined material model in three major FEM-programmes. To evaluate the model a simulated pole figure has been compared to an experimental one. These pole figures match each other very well. Yielding a realistic behaviour of the model.</p>

Computational electromagnetic modeling involves generating system matrices by discretizing integral equations and solving the resulting system of linear equations. Many methods of solving the system of linear equations exist and one such method is the factorization of the matrix using the so called local-global solution (LOGOS) modes. Computer codes to perform the discretization of the integral equations, filling of the matrix, and the subsequent LOGOS factorization have previously been developed by others. However, these codes are limited to complex double precision arithmetic only. This thesis extends and expands the existing computer by creating a more general implementation that is able to analyze a problem not only in complex double precision but also in real double precision and both complex and real single precision. The existing code is expanded using "templates" in Fortran 90 and the resulting generic code is used test the performance of the LOGOS (both OL- and NL-LOGOS) factorization on matrices generated by discretization of the volume integral equation. As part of this effort, we demonstrate for the first time that the LOGOS factorization provides an O(N log N) complexity solution to the volume integral equation formulation of low-frequency electromagnetic problems.

Submitted by Algacilda Conceição (algacilda@sibi.ufrj.br) on 2018-03-16T19:13:47Z No. of bitstreams: 1 130278.pdf: 5399051 bytes, checksum: 04fe5ab53ca6f5bf3abd35c033cdbc7d (MD5) / Made available in DSpace on 2018-03-16T19:13:47Z (GMT). No. of bitstreams: 1 130278.pdf: 5399051 bytes, checksum: 04fe5ab53ca6f5bf3abd35c033cdbc7d (MD5) Previous issue date: 1972-09 / Visando otimizar-se um sistema decomponível não-linear, estuda-se um algoritmo primal de direções viáveis. No decurso desse estudo formalizam-se e demonstram-se alguns resultados conhecidos e desenvolvem-se interpretações econômicas. Um critério para testar a diferenciabilidade das funções pertubação envolvidas no algoritmo é desenvolvido, podendo tal propriedade ser utilizada com vantagens computacionais. Rapidamente se discute o conceito de Ɛ-atividade de vínculos ligado à convergência do algoritmo. Finalmente, apresenta-se uma sub-rotina em FORTRAN IV que obtém, em cada iteração do algoritmo, uma direção viável. / A primal feasible directions algorithm is studied to optimize non-linear decomposable systems. In the course of these studies some known results are formalized and proved, and economical interpretations are developed. A criterion is derived to detect the different hability of the pertubation functions involved in the algorithm, and this property is used with some computational advantages. The concept of Ɛ-activity of constraints is discussed, and related to the convergente of the algorithm. Finally, a FORTRAN IV subroutine is presented capable of finding a feasible direction in each iteration of the algorithm.