Neutral two- and three-pion productions in proton-proton collisions at a center of mass energy of 2.465 GeV have been studied using the WASA detector and an internal pellet target at the CELSIUS storage ring in Uppsala. An important part of the detector for the measurments was a central electromagnetic calorimeter composed of 1012 CsI crystals, which measured the photons originating from neutral pion decays. Test measurements and calibration procedures for this detector part were carried out. An important part of the analysis was the identification of the neutral pions from the invariant mass of the decay gammas and the use of Monte Carlo simulations to understand the detector responds. Total cross sections for the pp→ppπ0π0 and pp→ppπ0π0π0 reactions are presented as well as distributions of relevant kinematical variables for the pp→ppπ0π0 reaction. The distributions show significant deviations from phase space predictions. These deviations are typical for resonance production. The excitation of two simultaneous Δ resonances seems to be the main reaction mechanism.

No description available.

This study explores the use of hierarchical models to represent three-dimensional solids in a computationally inexpensive way. First, it is investigated the choice of the finite element spaces and how it affects the convergence in relation to the thickness parameter. It was studied three different models. It was shown that the best lowest order suitable combination of spaces grows in all fields as the model order is enriched. After, it is presented a theory to evaluate the error in the discretization and the kinematical hypothesis. It is shown that the implemented error in discretization technique is capable of capturing the boundary layer in automated way for any model. It is also given a posteriori error procedure for kinematical hypothesis. The method is based on the equilibrium error of higher order models. Good results are shown. In the end, it is presented a geometrical nonlinear hierarchical shell model and its discretization. It is shown that the model succeeds in representing the three-dimensional solution when compared with solid elements in a commercial code. / Este estudo explora o uso de modelos hierárquicos para representar sólidos tridimensionais de forma computacionalmente barata. Em primeiro lugar, é explorada a escolha dos espaços de elementos finitos e como isso afeta a convergência em relação ao parâmetro da espessura. Foram estudados três modelos diferentes. Mostrou-se que a menor ordem adequada do espaço de discretização cresce para todos os campos conforme a ordem do modelo é enriquecida . Isso impõe um problema, já que um maior polinômio exige maior custo computacional e modelos de alta ordem só são necessários perto do contorno. Depois, são usados estimadores de erro na discretização e na hipótese cinemática. Mostra-se que o erro implementado na discretização é capaz de capiturar a camada limite de forma automatizada para qualquer modelo. Também é apresentada uma técnica de erro a posteriri na hipótese cinemática com base no erro no equilíbrio de modelos de ordem superior. No final, é apresentado um modelo hierárquico de casca geométricamente não linear e sua discretização. Mostra-se que o modelo consegue representar a solução tridimensional quando comparado com o um software comercial.

No description available.

This study explores the use of hierarchical models to represent three-dimensional solids in a computationally inexpensive way. First, it is investigated the choice of the finite element spaces and how it affects the convergence in relation to the thickness parameter. It was studied three different models. It was shown that the best lowest order suitable combination of spaces grows in all fields as the model order is enriched. After, it is presented a theory to evaluate the error in the discretization and the kinematical hypothesis. It is shown that the implemented error in discretization technique is capable of capturing the boundary layer in automated way for any model. It is also given a posteriori error procedure for kinematical hypothesis. The method is based on the equilibrium error of higher order models. Good results are shown. In the end, it is presented a geometrical nonlinear hierarchical shell model and its discretization. It is shown that the model succeeds in representing the three-dimensional solution when compared with solid elements in a commercial code. / Este estudo explora o uso de modelos hierárquicos para representar sólidos tridimensionais de forma computacionalmente barata. Em primeiro lugar, é explorada a escolha dos espaços de elementos finitos e como isso afeta a convergência em relação ao parâmetro da espessura. Foram estudados três modelos diferentes. Mostrou-se que a menor ordem adequada do espaço de discretização cresce para todos os campos conforme a ordem do modelo é enriquecida . Isso impõe um problema, já que um maior polinômio exige maior custo computacional e modelos de alta ordem só são necessários perto do contorno. Depois, são usados estimadores de erro na discretização e na hipótese cinemática. Mostra-se que o erro implementado na discretização é capaz de capiturar a camada limite de forma automatizada para qualquer modelo. Também é apresentada uma técnica de erro a posteriri na hipótese cinemática com base no erro no equilíbrio de modelos de ordem superior. No final, é apresentado um modelo hierárquico de casca geométricamente não linear e sua discretização. Mostra-se que o modelo consegue representar a solução tridimensional quando comparado com o um software comercial.

Gegenstand dieser Arbeit ist die Bereitstellung eines geeigneten Simulationswerkzeuges für die numerische Untersuchung der beim Rollkontakt zwischen Rad und Schiene auftretenden Phänomene. Hierbei liegt das Hauptaugenmerk auf der kontinuumsmechanischen Formulierung des mechanischen Feldproblems kontaktierender Körper sowie dessen numerischer Lösung mittels der Finite-Element-Methode. Zur Reduzierung des bei der Simulation von Rollkontakt aus der notwendigen sehr feinen Diskretisierung der Kontaktgebiete resultierenden numerischen Aufwandes wird eine relativkinematische Beschreibung herangezogen. Diese gemischte LAGRANGE-EULER-Betrachtungsweise beruht auf der Zerlegung der Bewegung in einen Starrkörperanteil und eine dazu relative Deformation. Die Herleitung der Bewegungsgleichung für das Kontaktproblem erfordert die relativkinematische Formulierung der kontinuumsmechanischen Grundgleichungen, d.h. der Bilanzgleichungen sowie der konstitutiven Beziehungen. Eine geeignete Kontaktmechanik einschließlich der Berücksichtigung des Kontakts rauer Oberflächen und veränderlicher Kontaktrandbedingungen ist ebenfalls notwendig. Die physikalische Einbindung der Körper in die Umgebung erfolgt über NEUMANNsche und DIRICHLETsche Randbedingungen. Auf dieser Basis können die Bewegungsgleichungen der Elastomechanik hergeleitet werden, welche sich jedoch einer analytischen Lösung verschließen. Somit werden sie in ihrer schwachen Form im integralen Mittel formuliert, was der Anwendung des Prinzips der virtuellen Verschiebungen als Ausgangspunkt für die numerische Lösung entspricht. Die rechentechnische Umsetzung erfordert die inkrementelle und diskrete Formulierung der Bewegungsgleichungen unter besonderer Beachtung der Trägheits-und Kontaktterme, wobei auf die Unterscheidung zwischen Haften und Gleiten beim Tangentialkontakt besonderes Augenmerk gelegt wird. Die numerische Lösung des Finite-Element-Gleichungssystems liefert den aktuellen Beanspruchungszustand zweier Körper im Rollkontakt. Die Funktionsfähigkeit der entwickelten Algorithmen wird abschließend anhand aussagekräftiger Beispielrechnungen zum statischen Kontakt und zum stationären Rollkontakt demonstriert, deren Ergebnisse gute Übereinstimmung mit analytischen Vergleichslösungen, soweit verfügbar, aufweisen. / Scope of this work is the preparation of a suitable simulation tool for the numerical investigation of rolling contact phenomena. The main focus lies on the continuum–mechanical formulation of the mechanical field problem of contacting bodies and its numerical solution within the framework of the Finite Element Method. For reducing the numerical effort in rolling contact simulation, induced by the necessity of a very fine discretization within the expected contact area, a relative–kinematical description is utilized. This arbitrary LAGRANGian–EULERian approach is based upon the decomposition of the total motion into a rigid body motion and a superimposed deformation. The derivation of the equation of motion for the contact problem requires the relative–kinematical formulation of the continuum–mechanical fundamental equations, i. e. the balance equations and the constitutive relations. A suitable contact model including the contact of rough surfaces and varying contact boundary conditions is also necessary. The physical embedding into the environment is accomplished by NEUMANN and DIRICHLET boundary conditions. Based upon that foundation the elastomechanics’ equations of motion are derived, which however can not be solved analytically in general. Hence, the equations of motion are transferred into their weak form by the application of the principle of virtual displacements serving for the numerical solution. The implementation of the problem demands for an incremental and discrete formulation of the equations, especially regarding the terms of inertia and the contact terms. Thereby, special attention has to be paid to the distinction between sticking and sliding within the framework of the tangential contact analysis. The numerical solution of the finite elements’ system of equations provides the state of stress, displacement and contact of two bodies in rolling contact. The reliability of the developed algorithms is finally verified by means of meaningful numerical examples for both static contact and for stationary rolling contact, whereby the numerical results coincide well with available analytical reference solutions.

In this work, different double ionization (DI) mechanisms of various atomic and molecular targets by electron impact at different intermediate incident energies have been studied by so-called (e, 3-1e) and (e, 3e) experiments. Four and five fold differential cross sections in angle and in energy have been measured and analyzed in a coplanar geometry. The experimental measurements are compared with both first order and second order theoretical model calculations. The results shows that the theories including second order mechanism (such as Two Step 2, TS2) are generally in better agreement with the experimental data than these only including first order mechanisms (such as Shake Off and Two Step 1). This demonstrates that under present kinematics, second order mechanism plays an important role or even dominates over first order mechanisms. Besides, all DI results are compared with the predictions of TS2 kinematical analysis developed by Lahmam-Bennani et al (2010). Most of the structures shown in the measured angular distribution can be correctly explained by the TS2 kinematical analysis predictions. Besides, we extend this model by including the recoil contribution in each step. Some structures which cannot be explained by the previous model are well explained by the extended TS2 kinematical model. The isoelectronic target structure influence in DI is investigated preliminarily. The (e, 3-1e) results on Ne and CH₄ indicate the differences under same kinematics. The data analysis is underway.

Cette thèse traite des problèmes des concentrations de contraintes locales, en particularité des effets des bords libres dans des structures stratifiés. À l'interface entre deux couches avec des propriétés élastiques différentes, les contraintes ont un comportement singulier dans le voisinage du bord libre en supposant un comportement de matériau élastique linéaire. Par conséquent, ils sont essentiels pour promouvoir le délaminage. Via Formulation unifiée de la Carrera (CUF) différents modèles cinématiques sont testés dans le but de capter les concentrations de contraintes. Dans la première partie de ce travail, les approches de modélisation dimensionnelle réduits sont comparées. Deux classe principale sont présentés: la couche équivalent (ESL) et l'approche par couche, LW. Par la suite leurs capacités à capter les singularités sont comparées. En utilisant une fonction a priori singulière, via une expression exponentielle, une mesure des contraintes singulières est introduite. Seulement deux paramètres décrivent pleinement les composantes des contraintes singulières au voisinage du bord libre. Sur la base des paramètres obtenus les modèles sont comparés et aussi les effets sous des charges d'extension et de flexion et pour différents stratifiés. Les résultats montrent une nécessité des modèles complexes dans le voisinage du bord libre. Cependant loin des bords libres, dans le centre de plaques composite, aucune différence significative ne peut être noté pour les modèles plutôt simples. La deuxième partie de ce travail est donc dédiée au couplage de modèles cinématique incompatibles. Modèles complexes et coûteux sont utilisés seulement dans des domaines locaux d'intérêt, tandis que les modèles économiques simples seront modéliser le domaine global. La eXtended Variational Formulation (XVF) est utilisé pour coupler les modèles de dimensionnalité homogènes mais de cinématique hétérogènes. Ici pas de recouvrement de domaine est présent. En outre, le XVF offre la possibilité d'adapter les conditions imposées à l'interface en utilisant un paramètre scalaire unique. On montre que, pour le problème de dimensionnalité homogène, que deux conditions différentes peuvent être imposées par ce paramètre. Un correspondant à des conditions fortes des Multi Point Constraints (MPC) et un second fournir des conditions faibles. La dernière offre la possibilité de réduire extrêmement le domaine qui utilise le modèle cinématique complexe, sans perte de précision locale. Comme il s'agit de la première application de la XVF vers les structures composites, le besoin d'un nouvel opérateur de couplage a été identifié. Un nouveau formulaire est proposé, testé et sa robustesse sera évaluée. / This work considers local stress concentrations, especially the free-Edge effects of multilayered structures. At the interface of two adjacent layers with different elastic properties, the stresses can become singular in the intermediate vicinity of the free edge. This is valid while assuming a linear elastic material behaviour. As a consequence this zones are an essential delamination trigger. Via the Carrera Unified Formulation (CUF), different kinematical models are testes in order to obtain the correct local stress concentration. In the first part of this work, the reduced dimensional modelling approaches are compared. Two main class are presented: Equivalent Single Layer (ESL) models treating the layered structure like one homogenous plate of equal mechanical proper- ties, and the Layer Wise approach, treating each layer independently. Subsequently their capabilities to capture the appearing singularities are compared. In order to have a comparable measurement of those singularities, the obtained stress distributions will be expressed via a power law function, which has a priori a singular behaviour. Only two parameters fully describe therefore the singular stress components in the vicinity of the free edge. With the help of these two parameters not only the different models capabilities will be compared, but also the free edge effect itself will be measured and compared for different symmetrical laminates and the case of extensional and uniform bending load. The results for all laminates under both load cases confirm the before stated need for rather complex models in the vicinity of the free edge. However far from the free edges, in the composite plates centre, no significant difference can be noted for rather simple models. The second part of this work is therefore dedicated to the coupling of kinematically incompatible models. The use of costly expensive complex models is restricted to local domains of interest, while economic simple models will model the global do- main. The Extended Variational Formulation (XVF) is identified as the most suitable way to couple the kinematically heterogenous but dimensional homogenous models. As it uses a configuration with one common interface without domain overlap, the additional efforts for establishing the coupling are limited. Further the XVF offers the possibility to adapt the conditions imposed at the interface using a single scalar parameter. It will be shown that for the homogenous dimensional problem under consideration only two different conditions can be imposed by this parameter. One matching the strong conditions imposed by the classical Multi Point Constrains (MPC) and a second one providing a weak condition. The last one is shown to provide the possibility to reduce further the domain using the complex kinematical model, without the loss of local precision. As this is the first application of the XVF towards composite structures, the need for a new coupling operator was identified. A new form is proposed, tested and its robustness will be evaluated.

Gegenstand dieser Arbeit ist die Bereitstellung eines geeigneten Simulationswerkzeuges für die numerische Untersuchung der beim Rollkontakt zwischen Rad und Schiene auftretenden Phänomene. Hierbei liegt das Hauptaugenmerk auf der kontinuumsmechanischen Formulierung des mechanischen Feldproblems kontaktierender Körper sowie dessen numerischer Lösung mittels der Finite-Element-Methode. Zur Reduzierung des bei der Simulation von Rollkontakt aus der notwendigen sehr feinen Diskretisierung der Kontaktgebiete resultierenden numerischen Aufwandes wird eine relativkinematische Beschreibung herangezogen. Diese gemischte LAGRANGE-EULER-Betrachtungsweise beruht auf der Zerlegung der Bewegung in einen Starrkörperanteil und eine dazu relative Deformation. Die Herleitung der Bewegungsgleichung für das Kontaktproblem erfordert die relativkinematische Formulierung der kontinuumsmechanischen Grundgleichungen, d.h. der Bilanzgleichungen sowie der konstitutiven Beziehungen. Eine geeignete Kontaktmechanik einschließlich der Berücksichtigung des Kontakts rauer Oberflächen und veränderlicher Kontaktrandbedingungen ist ebenfalls notwendig. Die physikalische Einbindung der Körper in die Umgebung erfolgt über NEUMANNsche und DIRICHLETsche Randbedingungen. Auf dieser Basis können die Bewegungsgleichungen der Elastomechanik hergeleitet werden, welche sich jedoch einer analytischen Lösung verschließen. Somit werden sie in ihrer schwachen Form im integralen Mittel formuliert, was der Anwendung des Prinzips der virtuellen Verschiebungen als Ausgangspunkt für die numerische Lösung entspricht. Die rechentechnische Umsetzung erfordert die inkrementelle und diskrete Formulierung der Bewegungsgleichungen unter besonderer Beachtung der Trägheits-und Kontaktterme, wobei auf die Unterscheidung zwischen Haften und Gleiten beim Tangentialkontakt besonderes Augenmerk gelegt wird. Die numerische Lösung des Finite-Element-Gleichungssystems liefert den aktuellen Beanspruchungszustand zweier Körper im Rollkontakt. Die Funktionsfähigkeit der entwickelten Algorithmen wird abschließend anhand aussagekräftiger Beispielrechnungen zum statischen Kontakt und zum stationären Rollkontakt demonstriert, deren Ergebnisse gute Übereinstimmung mit analytischen Vergleichslösungen, soweit verfügbar, aufweisen. / Scope of this work is the preparation of a suitable simulation tool for the numerical investigation of rolling contact phenomena. The main focus lies on the continuum–mechanical formulation of the mechanical field problem of contacting bodies and its numerical solution within the framework of the Finite Element Method. For reducing the numerical effort in rolling contact simulation, induced by the necessity of a very fine discretization within the expected contact area, a relative–kinematical description is utilized. This arbitrary LAGRANGian–EULERian approach is based upon the decomposition of the total motion into a rigid body motion and a superimposed deformation. The derivation of the equation of motion for the contact problem requires the relative–kinematical formulation of the continuum–mechanical fundamental equations, i. e. the balance equations and the constitutive relations. A suitable contact model including the contact of rough surfaces and varying contact boundary conditions is also necessary. The physical embedding into the environment is accomplished by NEUMANN and DIRICHLET boundary conditions. Based upon that foundation the elastomechanics’ equations of motion are derived, which however can not be solved analytically in general. Hence, the equations of motion are transferred into their weak form by the application of the principle of virtual displacements serving for the numerical solution. The implementation of the problem demands for an incremental and discrete formulation of the equations, especially regarding the terms of inertia and the contact terms. Thereby, special attention has to be paid to the distinction between sticking and sliding within the framework of the tangential contact analysis. The numerical solution of the finite elements’ system of equations provides the state of stress, displacement and contact of two bodies in rolling contact. The reliability of the developed algorithms is finally verified by means of meaningful numerical examples for both static contact and for stationary rolling contact, whereby the numerical results coincide well with available analytical reference solutions.

Des modèles géométriques ont été proposés pour reconstruire la géométrie de plis associés aux rampes (par exemple pli sur flexure de faille), en identifiant en particulier la profondeur de niveau de décollement et le déplacement total sur la rampe. Ces méthodes de reconstruction géométrique sont appliquées pour des plis partiellement érodés. Au cours de l'érosion, le cut-off de la rampe peut être érodé et, par conséquent, le déplacement sur la rampe est difficile à quantifier. Dans cette thèse, nous développons onze modèles thermo-géométriques. Les modèles combinent les données géométriques et les données d’enfouissement pour proposer une évolution cinématique d’un pli avec cut-off érodé. Nous supposons que la mise en place d'une unité tectonique produit une anomalie thermique dans le mur de la faille, et que cette anomalie thermique pourrait indiquer une épaisseur de bloc chevauchant. Les modèles fournissent une estimation de la profondeur de décollement et le déplacement total sur une rampe érodée, qui ne dépend pas de taux d’érosion. Dans le cas de chevauchements actifs, les modèles proposent un taux de déplacement et un âge de l'initiation de la faille en fonction de taux d'érosion. Ces données sont utilisées pour proposer un développement cinématique de coupes érodées. Nous appliquons les modèles sur les plis érodés et actif à Taiwan dans les zones de Choshui et Miaoli. On propose des coupes régionales équilibrées en utilisant la technique de modélisation directe. Dans la section Choshui, nous proposons un niveau de détachement de ~5 km à ~14 km, marquée par deux sauts successifs de rampes de ~5 km and ~4 km. En supposant un taux d'érosion à 4 mm/an, l'âge de l’initiation de chevauchement active est entre 3,3 Ma dans la partie intérieure de prisme (Chevauchement de Tili) à 0,9 Ma dans la partie extérieur (Chevauchement de Chelungpu). Le raccourcissement totale sur la coupe de Choshui est ~100 km et le taux de déplacement calculé est ~1 cm/an. Pour tester nos modèles thermo-géométriques dans une chaîne plissée inactive, on applique nos modèles sur les plis érodés associés aux failles de Pine Mountain et Jones Valley dans la chaîne plissée des Appalaches. L'application des modèles thermo-géométriques nous permet d’estimer une quantité de déplacement sur les deux failles et expliquer de manière satisfaisante l'anomalie thermique dans le mur des failles de Pine Mountain et Jones Valley. Afin d'améliorer la description de l’anomalie thermique qui se développe dans le soubassement des failles, on a étudié l'évolution des minéraux magnétiques des roches argileuses le long de quatre sections dans la chaîne plissée à Taiwan. On a remarqué que la greigite (Fe3S4) domine l'assemblage magnétique dans les roches enfouies à moins à moins de de 70°C. La magnétite (Fe3O4) se développe pour des températures d’enfouissement de ~50°C et domine l’assemblage magnétique jusqu'à ~350° C. A partir ~300°C, la pyrrhotite monoclinique (Fe7S8) se développe aux dépens de la magnétite, et à ~350°C, la magnétite n'est plus détecté. Ces résultats peuvent être utilisés en complément d'autres géothermomètres pour identifier les anomalies thermiques dans une gamme de de 50-70°C et de 300-350°C où les caractéristiques des minéraux magnétiques sont identifiées / Geometric models have been proposed to account satisfactorily for ramp-related folds (e.g. fault-bend fold), identifying in particular detachment depth and total shortening. These methods of geometric reconstruction are applied on partially eroded folds. During erosion, the fault cut-off may be removed and as a result, the displacement is difficult to quantify. In this thesis, we develop 11 thermo-geometric models combining geometric description of folds and burial data to propose kinematic evolution of folds with eroded cut-offs. We assume that the emplacement of a tectonic unit will result in a thermal anomaly in the footwall, and that this thermal anomaly might indicate a thickness of the overriding unit. The models provide an estimation of the detachment depth and the total shortening on an eroded ramp, independent of the erosion rate. In the case of active thrusts, the models provide an estimation of the slip rate and the age of the initiation of the thrust as a function of the erosion rate. These data are used to unravel the kinematic development of eroded cross-sections. We apply the models on eroded folds from Taiwan underlined by active thrusts in the Choshui and Miaoli sections. We propose regional balanced cross-sections using forward modeling technique. In the Choshui section, we propose a detachment profile with a depth between ~ 5 km and ~ 14 km, marked by two steps of ~ 5 km. Assuming erosion rate at 4 mm/a, the age of initiation of the active thrusts is ranging from 3.3 Ma inward (Tili thrust) to 0.9 Ma outward (Chelungpu thrust). The total shortening from the whole section is ~100 km and the calculated slip rate is about 1 cm/a. To test our models in a non-active fold-and-thrust belt, we study eroded folds associated to the Pine Mountain thrust and Jones Valley thrust from the Appalachian belt. The application of the thermo-geometric models provides a value of the total shortening and explains satisfactorily the thermal anomaly in the footwall of the Jones Valley thrust. In order to improve the description of the thermal anomaly, we have studied the evolution of magnetic minerals of argillaceous rocks in four sections from the Taiwan thrust belt. We found that the iron sulfide greigite (Fe3S4) is dominating the magnetic assemblage in the less buried rocks (<70°C). The magnetite (Fe3O4) develops at burial temperature of ~50°C and is dominating the magnetic assemblage up to ~350°C. By ~300°C, the monoclinic pyrrhotite (Fe7S8) develops at the expense of magnetite, and at ~350°C, the magnetite is no longer detected. These results can be used complementary to other geothermometers to identify thermal anomalies in the range 50-70°C and 300-350°C where characteristic magnetic minerals are identified