La description des propriétésspectrales des plasmas hautement ionisés –comme ceux rencontrés en fusion nucléaire,en astrophysique et en expérimentationlaser-plasmas –peut nécessiter différentstypes d’interprétation, parmi lesquelsl’approche détaillée ou raie-par-raieimpliquant de la diagonalisation del’Hamiltonien du système et, l’approchestatistique basée sur la caractérisation desstructures spectrales à travers les momentsde distribution.Ce travail de thèse a pour objectif d'étudier etde mettre en œuvre les méthodes statistiquestraitant des cas où de nombreuses raies seregroupent en faisceaux de transition nonrésolus (UTA pour Unresolved TransitionArray).Pour cela, des études analytique et numériqueont été menées. D’une part, les momentsd’ordre élevé de la distribution d’énergies spinorbiteont été obtenus, en utilisant lestechniques de calcul de moyennes qui fontintervenir les résultats de la secondequantification et de l’algèbre de momentangulaire. D’autre part, après avoir implémentéun programme de post-traitement des donnéesatomiques produites par le code FAC (FlexibleAtomic Code), en mode détaillée comme enmode UTA, les spectres d’émission et / The description of spectralproperties of highly ionized plasmas – asthose studied in stellar atmospheres, facilitiesfor nuclear fusion, or laser-plasmasexperiments – may require different types ofinterpretation, among which the detailed line by-line accounting which relies on Hamiltoniandiagonalization and the statistical approachbased on the characterization of spectralstructures through distribution moments.My PhD work aims at developing statisticalmethods dealing with situations whereabundant lines gather in Unresolved TransitionArrays (UTA).To this end, analytical and numerical analysishave been carried out. On one hand, high-ordermoments of spin-orbit energy have beenderived using averaging calculation techniquesbased on second quantization results andangular momentum algebra. On the other hand,after implementing a post-processing programfor both detailed and UTA computations of theFlexible Atomic Code (FAC), emission andabsorption spectra of tungsten plasmas havebeen studied in tokamak-equivalentthermodynamic conditions.Results of this thesis should hopefully stimulatefurther analysis on averages computationinvolving complex transition processes.

Doctor of Philosophy / Department of Physics / Brett D. Esry / The nuclear rotational period of the simplest molecule H[subscript]2[superscript]+ is about 550 fs, which is more than 35 times longer than its vibrational period of 15 fs. The rotational time scale is also much longer than widely available ultra short laser pulses which have 10 fs or less duration. The large difference in rotational period and ultra short laser pulse duration raises questions about the importance of nuclear rotation in theoretical studies of H[subscript]2[superscript]+ dissociation by these pulses. In most studies, reduced-dimensionality calculations are performed by freezing the molecular axis in one direction, referred to as the aligned model. We have systematically compared the aligned model with our full-dimensionality results for total dissociation probability and field-free dynamics of the dissociating fragments. The agreement between the two is only qualitative even for ultra short 10 fs pulses. Post-pulse dynamics of the bound wave function show rotational revivals. Significant alignment of H[subscript]2[superscript]+ occurs at these revivals. Our theoretical formulation to solve the time-dependent Schrodinger equation is an important step forward to make quantitative comparison between theory and experiment. We accurately calculate observables such as kinetic energy, angular, and momentum distributions. Reduced-dimensionality calculations cannot predict momentum distributions. Our theoretical approach presents the first momentum distribution of H[subscript]2[superscript]+ dissociation by few cycle laser pulses. These observables can be directly compared to the experiment. After taking into account averaging steps over the experimental conditions, we find remarkable agreement between the theory and experiment. Thus, our theoretical formulation can make predictions. In H[subscript]2[superscript]+ dissociation by pulses less than 10 fs, an asymmetry in the momentum distribution occurs by the interference of different pathways contributing to the same energy. The asymmetry, however, becomes negligible after averaging over experimental conditions. In a proposed pump-probe scheme, we predict an order of magnitude enhancement in the asymmetry and are optimistic that it can be observed.

The flexural capacity of the new hollow flange steel section known as LiteSteel beam (LSB) is limited by lateral distortional buckling for intermediate spans, which is characterised by simultaneous lateral deflection, twist and web distortion. Recent research based on finite element analysis and testing has developed design rules for the member capacity of LiteSteel beams subject to this unique lateral distortional buckling. These design rules are limited to a uniform bending moment distribution. However, uniform bending moment conditions rarely exist in practice despite being considered as the worst case due to uniform yielding across the span. Loading position or load height is also known to have significant effects on the lateral buckling strength of beams. Therefore it is important to include the effects of these loading conditions in the assessment of LSB member capacities. Many steel design codes have adopted equivalent uniform moment distribution and load height factors for this purpose. But they were derived mostly based on data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. In contrast LSBs are made of high strength steel and have a unique crosssection with specific residual stresses and geometrical imperfections along with a unique lateral distortional buckling mode. The moment distribution and load height effects for LSBs, and the suitability of the current steel design code methods to accommodate these effects for LSBs are not yet known. The research study presented in this thesis was therefore undertaken to investigate the effects of nonuniform moment distribution and load height on the lateral buckling strength of simply supported and cantilever LSBs. Finite element analyses of LSBs subject to lateral buckling formed the main component of this study. As the first step the original finite element model used to develop the current LSB design rules for uniform moment was improved to eliminate some of the modelling inaccuracies. The modified finite element model was validated using the elastic buckling analysis results from well established finite strip analysis programs. It was used to review the current LSB design curve for uniform moment distribution, based on which appropriate recommendations were made. The modified finite element model was further modified to simulate various loading and support configurations and used to investigate the effects of many commonly used moment distributions and load height for both simply supported and cantilever LSBs. The results were compared with the predictions based on the current steel code design rules. Based on these comparisons, appropriate recommendations were made on the suitability of the current steel code design methods. New design recommendations were made for LSBs subjected to non-uniform moment distributions and varying load positions. A number of LSB experiments was also undertaken to confirm the results of finite element analysis study. In summary the research reported in this thesis has developed an improved finite element model that can be used to investigate the buckling behaviour of LSBs for the purpose of developing design rules. It has increased the understanding and knowledge of simply supported and cantilever LSBs subject to non-uniform moment distributions and load height effects. Finally it has proposed suitable design rules for LSBs in the form of equations and factors within the current steel code design provisions. All of these advances have thus further enhanced the economical and safe design of LSBs.

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