Дисертації з теми "Stabilité des equilibres"

Les robots parallèles continus (RPCs) sont des manipulateurs utilisant plusieurs tiges flexibles disposées en parallèle et connectées à une plateforme rigide. Les RCPs promettent des capacités de charge et une précision plus élevée queles robots sériels continus, tout en gardant une grande flexibilité. Puisque le risque de blessure lors d’un contact accidentel entre un humain et un CPR devrait être réduit, les RCPs peuvent être utilisés dans des tâches collaboratives à grande échelle ou dans de tâches de chirurgie robotique assistée. Différentes architectures de RCP existent, mais la conception du prototype est rarement basée sur des considérations de performance, et la réalisation de RCPs est principalement à partir d’intuitions en utilisant d’architectures de manipulateurs parallèles rigides. Les thèmes de recherche de cette thèseportent sur l’analyse des performances des RCPs, et sur les outils nécessaires à une telle évaluation, ainsi que sur les algorithmes de calcul de leur espace de travail. En particulier, les stratégies de calcul de l’espace de travail pour les RCPs sont essentielles pour l’´évaluation de la performance, car l’espace de travail peut être utilisé comment un indice deperformance, par exemple pour des outils de conception optimale. Deux nouveaux algorithmes de calcul de l’espace de travail sont proposés dans ce manuscrit, le premier se concentrant sur le calcul du volume de l’espace de travail et la certification de ses résultats numériques, et le second sur le calcul des bords de l’espace de travail uniquement. Enraison de la nature ´élastique des RCPs, un indicateur de performance essentiel pour ces robots est la stabilité de leurs configurations d’équilibre. Cette thèse propose la validation expérimentale de l’´évaluation de la stabilité des équilibres sur un prototype réel, démontrant les limites de certaines hypothèses couramment utilisées. De plus, un indice de performance mesurant la distance à l’instabilité est proposé dans ce manuscrit. Contrairement à la majorité des approches existantes, l’avantage évident de l’indice proposé est une signification physique bien défini
Continuum parallel robots (CPRs) are manipulators employing multiple flexible beams arranged in parallel and connected to a rigid endeffector. CPRs promise higher payload and accuracy than serial CRs while keeping great flexibility. As the risk of injury during accidental contact between a human and a CPR should be reduced, CPRs may be used in large-scalecollaborative tasks or assisted robotic surgery. There exist various CPR designs, but the prototype conception is rarely based on performance considerations, and the CPRs realization in mainly based on intuitions or rigid-link parallel manipulators architectures. This thesis focuses on the performance analysis of CPRs, and the tools needed for such evaluation, such as workspace computation algorithms. In particular, workspace computation strategies for CPRs are essential for the performance assessment, since the CPRs workspace may be used as a performance index or it can serve for optimal-design tools. Two new workspace computation algorithms are proposed in this manuscript, the former focusing on the workspace volume computation and the certification of its numerical results, while the latter aims at computing the workspace boundary only. Due to the elastic nature of CPRs, a key performance indicator for these robots is the stability of their equilibrium configurations. This thesis proposes the experimental validation of the equilibrium stability assessment on a real prototype, demonstrating limitations of some commonly used assumptions. Additionally, a performance index measuring the distance to instability is originally proposed in this manuscript. Differently from themajority of the existing approaches, the clear advantage of the proposed index is a sound physical meaning; accordingly, the index can be used for a more straightforward performance quantification, and to derive robot specifications

Cette thèse a deux parties. La première traite des jeux stratégiques non-atomiques, la seconde propose des applications de la théorie des jeux aux réseaux de télécommunications. Dans la première partie, les modèles de jeux non-atomiques proposés par Schmeidler (1973) et par Mas-Colell (1984) sont décrits et comparés. Nous montrons alors que ces jeux non-atomiques sont de bonnes approximations de jeux avec un nombre finis de joueurs et dans lesquels l'influence de chacun sur le paiement des autres joueurs est évanescente. Nous proposons ensuite une extension et des variations du modèle de Mas-Colell afin d'obtenir un cadre unificateur pour diverses applications des jeux non-atomiques, telles les jeux de routage, les jeux de foule et les jeux évolutionnaires. Ces trois types de jeu sont étudiés. Enfin nous étendons le concept de stratégie évolutionnairement stable au modèle de Schmeidler, ce qui donne un critère de sélection des équilibres. La deuxième partie traite de problèmes de routage dans les réseaux. Tout d'abord nous modélisons des situations où deux types de joueur partagent un réseau, des joueurs ayant une influence certaine sur la répartition des paquets dans le réseau et des joueurs n'en ayant pas. Puis, nous étudions la convergence de dynamiques de meilleures réponses dans des réseaux d'architecture simple. Finalement, nous modélisons le problème du routage mutipoint-à-multipoint.

The Lyapunov function method is used in proving stability, asymptotic or globally asymptotic stability of discrete dynamic systems. We show that the slightly relaxed versions of the well known sufficient conditions are also necessary. The stability of the equilibria of time-invariant nonlinear dynamical systems with discrete time scale is investigated. We present an elementary proof showing that in the case of a stable equilibrium and continuously differentiable state transition function, all eigenvalues of the Jacobian computed at the equilibrium must be inside or on the unit circle. We also demonstrate via numerical examples that if some eigenvalues are on the unit circle and all other eigenvalues are inside the unit circle, then the equilibrium maybe unstable, or stable, or even asymptotically stable, which show that the necessary condition cannot be further restricted in general. In addition, the necessary condition is given in terms of spectral radius and matrix norms. The asymptotic stability of equilibria in a number of discrete dynamic oligopolies is analyzed. First the equivalence of the equilibrium problem of a large class of nonlinear games and the equilibrium problem of a class of discrete dynamic systems is verified. Stability conditions are then derived for a certain class of dynamic models, and these results are finally applied to single-product oligopolies, multiproduct oligopolies, and labor-managed oligopolies. The economic interpretation of the stability conditions are also presented. The stability properties of a special class of homogeneous dynamic economic systems are examined. The nonlinearity of the models and the presence of eigenvalues with zero real parts in a normally hyperbolic invariant set make the application of the classical theory impossible. Some principles of the modern theory of dynamical systems and invariant manifolds are applied. The local and global strong attractivity of the set of equilibria is verified under mild conditions. As an application, special labor-managed oligopolies are investigated.

In Hamiltonian systems with symmetry, many previous studies have centred their attention on compact symmetry groups, but relatively little is known about the effects of noncompact groups. This thesis investigates the properties of the system of N point vortices on the hyperbolic plane H2, which has noncompact symmetry SL (2, R).The Poisson Hamiltonian structure of this dynamical system is presented and the relative equilibria conditions are found. We also describe the trajectories of relative equilibria with momentum value not equal to zero. Finally, stability criteria are found for a number of cases, focusing on N = 2, 3. These results are placed in context with the study of point vortices on the sphere, which has compact symmetry.

This thesis is concerned with aspects of the surface and colloid chemistry of various microemulsion systems stabilised by pure nonionic surfactants and alcohol as well as mixtures of nonionic and anionic surfactants. Phase equilibria and interfacial characteristics of the systems are studied with a view to their potential usefulness for enhanced oil recovery, in which salinity and temperature are important parameters. The equilibrium microemulsion phases are scanned at different temperatures and salinities and thus interfacial boundaries can be determined and optimum salinity scans can be performed accurately using a modified spectrophotometer. Several analytical techniques (e.g., high performance liquid chromatography, gas chromatography, ion-exchange chromatography, mass spectrometry, viscometry, electrical conductivity, photon correlation spectroscopy, UV-spectrophotometry, thermogravimetric analysis, transmission electron microscopy, surface and interfacial tension techniques) have been used to characterise and understand the microchemistry of the microemulsion systems. Ultra-low interfacial tensions (>0.1 µN/m) can be achieved in the microemulsion systems. Surfactant transfer between phases, and phase inversion of micro emulsions are shown to occur around the condition which produces minimum interfacial tension. Adsorption of the surfactants from aqueous and nonaqueous solutions has been investigated and the results show that the extent of adsorption can be reduced significantly in the presence of alcohols (co-solvent). The extent of adsorption increases with increasing temperature and salinity; however, it decreases with an increase in the hydrophilic head group of the surfactant. Adsorption of nonionic surfactants on quartz from the nonaqueous solution (decane) is much greater than from aqueous solution. In microemulsion applications, droplet combustion of w/o microemulsions is also studied for different surfaces (i.e. silica, oxidised Fecralloy and catalyst coated Fecralloy) in the temperature range of 313-573K. Formaldehyde and acetaldehyde are formed as intermediate combustion products. Thus the microemulsion combustion can lead to new oxygenate products. The w/o microemulsion route is used to synthesize colloidal silica of controlled particle size and morphology. The particle size can be varied by changing the molar ratio of water to TEOS using a water pH of 10.5.

La prima parte della tesi tratta le definizioni e i risultati essenziali della teoria dei sistemi di equazioni differenziali ordinarie; il discorso viene poi incentrato, nel secondo capitolo, sul problema della dipendenza continua e differenziabile della soluzione dalle condizioni iniziali e da eventuali parametri; il terzo capitolo tratta invece la teoria della stabilità dei punti di equilibrio nel caso particolare in cui il sistema sia autonomo. Si è data dunque la definizione di punto di equilibrio e si è detto precisamente in che senso esso è stabile o asintoticamente stabile; l'attenzione è stata poi rivolta ad alcuni criteri (come quello della funzione di Lyapunov) che danno condizioni necessarie e/o sufficienti affinché un dato punto di equilibrio sia stabile/asintoticamente stabile. Infine, sono stati presentati due esempi esplicativi: il modello preda predatore di Lotka-Volterra e l'esempio del pendolo.

Quel que soit le type d'exosquelettes de jambes, la question d’équilibre du système est très importante, puisqu'il s'agit de robots physiquement attachés à l'utilisateur. Dans le but de respecter au maximum la volonté de l'utilisateur ainsi que ses mouvements, cette thèse a pour objectif de développer des stratégies de commande de gestion d'équilibre pour un exosquelette d’assistance. Il s'agit alors d'assister l'équilibre du système couplé (utilisateur valide + exosquelette), en gérant l'équilibre de l'exosquelette soumis à l'action de l'utilisateur. La commande de gestion d'équilibre proposée s'inspire des commandes développées par le CEA-LIST sur les exosquelettes Hercule et des stratégies de récupération d'équilibre observées chez l'humain. Elle est essentiellement basée sur le concept du point de capture instantané. En effet,le point de capture instantané est un bon outil qui englobe aussi bien le cas statique que le cas dynamique et surtout, qui contient une information sur la direction de mouvement, ce qui nous permet d'anticiper certaines actions comme l'action de faire un pas. Les contributions de cette thèse sont alors :• l'application d'une commande du point de capture à un exosquelette d'assistance ;• la proposition d'une nouvelle répartition des efforts sur les deux jambes de l'exosquelette permettant d'anticiper les perturbations et le pas ;• la gestion du sous-actionnement (toutes les articulations ne sont pas motorisées) en phase de double support via un calcul d'optimisation qui a pour objectif de suivre la répartition des efforts désirée et de maîtriser les forces d'interaction entre l'utilisateur et l'exosquelette
The postural stability of leg exoskeletons, no matter their purposes (medical, military or civil), is a real issue since the user is fastened to them. Indeed, in order to respect the will of the user and his movements to the maximum, we have to study the system balance. Therefore, the purpose of this thesis is to develop balance strategies for a leg exoskeleton designed for industrial applications such as static work. It is about assisting the balance of the coupled system (user +exoskeleton) by dealing with the exoskeleton’s balance subjected to the user’s action. We present a balance control which is inspired by control methods developed by CEA-LIST for the Hercule exoskeleton, as well as by human balance strategies. It is mainly based on the instantaneous capture point concept. The first contribution of this thesis is the application of a classical instantaneous capture point control to a leg exoskeleton that assists a user. The user’s intention is first detected through the position of the instantaneous capture point and the assistance provided by the exoskeleton differs. The second contribution focuses on how we candistribute the effort to the legs. The experience of the «Master-Slave » control of CEA-LIST showed that the main difficulty, for a user, is to handle the weight transfer in order to take the swing leg off and make a step. We suggest a newleg distribution, that is able to anticipate a step. The last contribution is related to the underactuation of the exoskeleton in the double support phase. We propose an optimization algorithm that aims at following the leg distribution, and at managing the interaction forces between the user and the exoskeleton

Equilibrium relations between garnet and orthopyroxene have been investigated by reversal experiments in the range of 20-45Kb and 975-1400°C in the FeO-MgO-Al₂O₃-SiO₂(FMAS) system. The Fe-Mg exchange reaction seems to have little or no compositional dependence at these conditions. The experimental results can be fitted adequately by the linear relation: ln K(D) = 2243/T°K - 0.9522 at 25Kb where K(D) = (X(Fe)/X(Mg))ᴳᵗ/(X(Fe)/X(Mg))ᴼᵖˣ. Combination of the available data for the mixing properties of garnet and V° for the Fe-Mg exchange reaction with the above experimental results yields the following geothermometric expression for the common natural assemblages that can be represented essentially within the system CaO-MnO-FeO-MgO-Al₂O₃-SiO₂. T°K = (1968 + 11P(Kb) + 1510(X(Ca)+X(Mn))ᴳᵗ)/(ln K(D) + 0.9522). The stability field of pyrope+quartz, defined by the reaction pryope+quartz=opx+sill, has been calculated as a function of P,T,X(Fe)ᴳᵗ in the FMAS system using the reversal experimental data of Perkins (1983) in the MAS system, and the present data on K(D)(Fe-Mg) between garnet and orthopyroxene. This reaction is very sensitive to pressure and compositional effects. Combination of P,T conditions for the garnet stability and that defined by (K(D)(Fe-Mg))ᴳᵗ⁻ᴼᵖˣ yields a simultaneous solution for both P and T of equilibration of garnet and orthopyroxene in the presence of Al₂SiO₅ and SiO₂. The effect of FeO on Al₂O₃ solubility in orthopyroxene in equilibrium with garnet has been determined experimentally at several pressures at 975 and 1200°C. These data have been modeled to develop a thermodynamic method for the calculation of Al₂O₃ in orthopyroxene as a function of P,T and composition. The Al₂O₃ isopleths have moderate P-T slopes, and provide virtually the only means of determining the pressure of mantle derived rocks.

We have focussed on the study of the linear stability of some particular periodic orbits (called relative equilibria) in planar singular mechanical systems with SO(2)-symmetry, and we have achieved the results using quite advanced mathematical techniques. These involve some homotopy invariants, such as the spectral flow, and some index theory, namely a theorem stating the equality between the Morse index of an orbit seen as a critical point of a Lagrange action functional and the Maslov index of the fundamental solution of the associated Hamiltonian system. Moreover, what we have found meets one of its most important applications in a generalised n-body problem, that is, an n-body problem with a more general potential.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Nuclear Science and Engineering, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references.
In this work, two separate aspects of ideal MHD theory are considered. In the first part, analytic solutions to the Grad-Shafranov equation (GSE) are presented, for two families of source functions: functions which are linear in the flux function T , and functions which are quadratic in T. The solutions are both simple and very versatile, since they describe equilibria in standard tokamaks, spherical tokamaks, spheromaks, and field reversed configurations. They allow arbitrary aspect ratio, elongation, and triangularity as well as a plasma surface that can be smooth or possess a double or single null divertor X-point. The solutions can also be used to evaluate the equilibrium beta limit in a tokamak and spherical tokamak in which a separatrix moves onto the inner surface of the plasma. In the second part, the reliability of the ideal MHD energy principle in fusion grade plasmas is assessed. Six models are introduced, which are constructed to better describe plasma collisonality regimes for which the approximations of ideal MHD are not justified. General 3-D quadratic energy relations are derived for each of these six models, and compared with the ideal MHD energy principle. Stability comparison theorems are presented. The main conclusion can be summarized in two points. (1) In systems with ergodic magnetic field lines, ideal MHD accurately predicts marginal stability, even in fusion grade plasmas. (2) In closed field line geometries, however, the ideal MHD predictions must be modified. Indeed, it is found that in collisionless plasmas, the marginal stability condition for MHD modes is inherently incompressible for ion distribution functions that depend only on total energy. The absence of compressibility stabilization is then due to wave particle resonances. An illustration of the vanishing of plasma compressibility stabilization in closed line systems is given by studying the particular case of the hard-core Z-pinch.
by Antoine Julien Cerfon.
Ph.D.

Il contenuto della tesi consiste in definizioni di stabilità nel senso di Lyapunov, classificazione dei punti di equilibrio per sistemi differenziali lineari nel piano, criteri per determinare la stabilità dei punti di equilibrio per sistemi differenziali non necessariamente lineari ed infine si passa all'aspetto applicativo dei risultati esposti.

03etude de la stabilite de l'etat d'equilibre d'un plasma confine par des champs magnetiques a l'interieur d'un tokamak et represente par les equations de la mhd. Pour deux des principaux types d'instabilite, la convection et l'instabilite de dechirement des surfaces magnetiques, on fait une etude non lineaire des solutions, en considerant le probleme mathematique comme un probleme de bifurcation

Conception et validation d’un nouvel outil d’évaluation de la stabilité posturale en position érigée(SAP3D : Système d’Analyse Postural 3D)La stabilité posturale en position debout est la capacité d'un sujet à maintenir un état d'équilibre ou à le retrouver en cas de perturbation. De nombreux organes sont mis à contribution par le système nerveux central afin d'aider l'organisme à maintenir sa stabilité. L'atteinte d'une ou plusieurs de ces structures (suite à un traumatisme, une pathologie, ou tout simplement du fait du vieillissement) modifie le comportement du sujet et altèrent sa capacité à maintenir sa stabilité. Les outils d’évaluation posturale actuels reposent essentiellement sur des mesures du centre des pressions et/ou du centre de masse, négligeant le comportement postural inter-segmentaire : les outils capables de les prendre en compte sont souvent inaccessibles, car complexes et coûteux. Le SAP3D a été développé comme un nouvel outil d’évaluation de la stabilité posturale, il permet une reconstruction tridimensionnelle multi-segmentaire et du centre de masse à partir d’une seule caméra bon marché. La validation du SAP3D comparativement à un système de référence optoélectronique met en évidence une excellente corrélation et un faible résidu moyen entre les deux systèmes. En situation clinique, le SAP3D confirme que les mécanismes de stabilisation posturale sont i) moins efficaces en condition yeux fermés ; ii) influencés négativement par le vieillissement ; iii) influencés positivement par la pratique régulière d’une activité telle que de la danse, au moins chez les jeunes femmes ; iv) altérés par plusieurs antécédents traumatiques et/ou pathologiques. Bien que des améliorations techniques soient envisagées, le SAP3D constitue une alternative clinique fiable, rapide, accessible et peu coûteuse aux systèmes d'analyse posturographique existants.Mots-clés : équilibre ; contrôle moteur ; analyse cinématique ; centre de masse ; personnes âgées ; vieillissement ; danse ; faible coût
Design and validation of a new tool for assessing postural stability in quiet standing(SAP3D: 3D Postural Analysis System)Postural stability in quiet standing is a subject’s ability to maintain its balance or to regain it after a perturbation. Multiple organs contribute to ensure postural stability, under a regulation ensured by the central nervous system. The alteration of one or several of these organs (following a trauma, a pathology or simply due to ageing) modifies the subject’s behavior and its ability to maintain stability. Current systems for postural evaluation rely mostly on center of pressure and/or center of mass assessment, disregarding the intersegmental postural behavior: such measurements are possible, but most tools are complex and expensive. The SAP3D system was developed as a new tool for postural stability assessment, allowing for center of mass and multi-segmental three dimensional modeling based on a single inexpensive camera. Validation of the SAP3D system compared to a standard optoelectronic system shows excellent agreement and a satisfyingly low average residue between the two systems. In a clinical setup, the SAP3D system confirms that postural steadiness mechanisms are i) less efficient with eyes closed than eyes opened; ii) negatively affected by ageing; iii) positively affected by regular practice of an activity such as dancing, at least for young women; iv) altered in pathological or injured patients. Although many technical improvements are being considered, the SAP3D system is a reliable, quick, accessible and low-cost clinical alternative to the existing systems for postural evaluation.Keywords: balance; steadiness; motor control; kinematics; center of mass; elderly; ageing; dance; low-cost

The work in this thesis focuses primarily on equilibrium and stability properties of collisionless current sheet models, in particular of the force-free Harris sheet model. A detailed investigation is carried out into the properties of the distribution function found by Harrison and Neukirch (Physical Review Letters 102, 135003, 2009) for the force-free Harris sheet, which is so far the only known nonlinear force-free Vlasov-Maxwell equilibrium. Exact conditions on the parameters of the distribution function are found, which show when it can be single or multi-peaked in two of the velocity space directions. This is important because it may have implications for the stability of the equilibrium. One major aim of this thesis is to find new force-free equilibrium distribution functions. By using a new method which is different from that of Harrison and Neukirch, it is possible to find a complete family of distribution functions for the force-free Harris sheet, which includes the Harrison and Neukirch distribution function (Physical Review Letters 102, 135003, 2009). Each member of this family has a different dependence on the particle energy, although the dependence on the canonical momenta remains the same. Three detailed analytical examples are presented. Other possibilities for finding further collisionless force-free equilibrium distribution functions have been explored, but were unsuccessful. The first linear stability analysis of the Harrison and Neukirch equilibrium distribution function is then carried out, concentrating on macroscopic instabilities, and considering two-dimensional perturbations only. The analysis is based on the technique of integration over unperturbed orbits. Similarly to the Harris sheet case (Nuovo Cimento, 23:115, 1962), this is only possible by using approximations to the exact orbits, which are unknown. Furthermore, the approximations for the Harris sheet case cannot be used for the force-free Harris sheet, and so new techniques have to be developed in order to make analytical progress. Full analytical expressions for the perturbed current density are derived but, for the sake of simplicity, only the long wavelength limit is investigated. The dependence of the stability on various equilibrium parameters is investigated.

La thèse Analyse multifactorielle de l’influence de l’environnement sur la stabilité et la locomotion humaine, propose des recherches théoriques et expérimentales dans le domaine complexe des influences du milieu environnant, à travers ses paramètres spécifiques, sur les performances de la locomotion et d’équilibre stable du corps humain. Elle met ensemble plusieurs domaines pour l’obtention d’une évaluation statistique des influences provenant des paramètres signifiants du milieu environnant sur la locomotion et sur l’équilibre stable, représentés par le centre de pression et par les forces générées dans la zone plantaire. La thèse est structurée en huit chapitres dont quatre sont concernés à l’introduction, les objectifs de la thèse, les conclusions, les contributions originales et le mode de valorisation de la recherche, ainsi qu’aux directions futures de développement, alors que les quatre suivants développent successivement, d’une manière consistante, le sujet de thèse débutant avec l’étude bibliographique dans le domaine spécifique, suivi de l’étude et l’analyse des paramètres spécifiques du milieu environnant, l’analyse de la locomotion et de la stabilité humaine et l’analyse expérimentale des influences de l’environnement sur la stabilité et la locomotion humaine. Elle contient 195 pages, 147 de figures, 22 tableaux et 5 annexes étendues sur 50 pages concernant les recherches expérimentales.Durant le programme de recherche, l’auteur a élaboré et publié 13 articles dans les proceedings des manifestations scientifiques en Roumanie et à l’étranger et a participé à deux contrats de recherche
The thesis Contributions to research concerning the influences of the environment on human stability and locomotion proposes theoretical and experimental researches in the very complex domain of the influences of environment, described through its specific parameters, on locomotion and stable equilibrium of human body’s performances, characterized by pressure center and by the forces generated in the plantar area. The thesis is structured in eight chapters and, among them: four are concerned on introduction, thesis objectives, conclusions, original contribution and thesis valorization (published papers and research grants)/future research directions. The next four develop, consistently, the thesis subject, beginning with critical analyze of the specialized literature that is followed by the analyze of specific parameters of the environment, the analyze of the human locomotion and stability and of influences of environment on human locomotion and stable equilibrium. It contains 195 pages, 147 figures and 22 tables and is accompanied by 5 annexes on 50 pages concerning the experimental research. During the research program, the author elaborated and published 13 papers in the proceedings of different scientific events in Romania and abroad and was a part of two research teams for scientific grants

The rigid body has been one of the most noteworthy applications of Newtonian mechanics. Applying the principles of classical mechanics to the rigid body is by no means routine. The equations of motion, though discovered two hundred and fifty years ago by Euler, have remained quite elusive since their introduction. Understanding the rigid body has required the applications of concepts from integrable systems, algebraic geometry, Lie groups, representation theory, and symplectic geometry to name a few. Moreover, several important developments in these fields have in fact originated with the study of the rigid body and subsequently have grown into general theories with much wider applications.In this work, we study the stability of equilibria of non-degenerate orbits of the generalized rigid body. The energy-Casimir method introduced by V.I. Arnold in 1966 allows us to prove stability of certain non-degenerate equilibria of systems on Lie groups. Applied to the three dimensional rigid body, it recovers the classical Euler stability theorem [12]: rotations around the longest and shortest principal moments of inertia are stable equilibria. This method has not been applied to the analysis of rigid body dynamics beyond dimension n = 3. Furthermore, no conditions for the stability of equilibria are known at all beyond n = 4, in which case the conditions are not of the elegant longest/shortest type [10].Utilizing the rich geometric structures of the symmetry group G = SO(2n), we obtain stability results for generic equilibria of the even dimensional free rigid body. After obtaining a general expression for the generic equilibria, we apply the energy-Casimir method and find that indeed the classical longest/shortest conditions on the entries of the inertia matrix are suffcient to prove stability of generic equilibria for the generalized rigid body in even dimensions.

La methode proposee consiste a combiner la methode de la surface potentiometrique de bye-lefebvre, une methode de regression non lineaire et une methode de simulation statistique. Etude des equilibres de formation des isopolyanions molybdiques. On propose un mecanisme de type sn2 pour les reactions de decondensation et d'hydrolyse des ions trimolybdiques et tetramolybdiques

Le crissement des freins a disque est une vibration auto entretenue due au frottement. Ce phenomene est interprete dans cette these comme une instabilite par flottement de la solution frottante stationnaire. Les equations qui regissent la solution frottante stationnaire sont analysees (existence et unicite de la solution). Une analyse theorique de la stabilite de cette solution est menee. Une approche numerique par elements finis est proposee pour le calcul de cette stabilite. Cette approche est mise en uvre pour etudier le crissement des freins a disque. L'approche numerique est validee par confrontation a des resultats analytiques (stabilite du glissement d'une couche elastique sur un massif rigide, et des deux couches elastiques l'une sur l'autre).

Trois exemples d'equilibres contraints dans les materiaux sont etudies. Couches ga#xin#1##xp deposees en phase vapeur aux organo-metalliques en epitaxie sur des substrats de gaas voisins de (001): par microscopie electronique en transmission (m. E. T. ) on identifie une mise en ordre de type cupt sur le sous-reseau iii et une selection des variants par la polarite et la desorientation du substrat. Un modele original d'ordre induit par la croissance explique qualitativement ces resultats et d'autres donnees de la litterature. Couches gaas implantees si, se et recuites: la microstructure et les amas de defauts residuels identifies par m. E. T. Montrent que le defaut d'activation du si n'est pas lie a cette microstructure, mais qu'il l'est pour se. Dans ce cas une couche amorphe est formee, sa recristallisation induit la precipitation d'amas tetraedriques polaires, correles a un manque d'activation local du dopant. Theorie des equilibres dynamiques dans les composes sollicites: on donne une description stochastique (equation pilote et de fokker planck) d'un compose ou les echanges heteroatomiques se font par sauts forces (pouvant se produire par cascade) parallelement aux sauts thermiquement actives. En l'absence de sollicitation, le modele est ajuste sur une thermodynamique simple de champ moyen. En presence de la sollicitation, le potentiel stochastique trouve permet de construire des diagrammes d'equilibre dynamique. Le comportement complexe de ni#4mo sous irradiation (bistabilite, inversion de stabilite) est elucide. Des effets de taille de cascade sont prevus

The subject that concerns this thesis is the modelling and control of plasma equilibria in the RFX-mod device operating as shaped tokamak. The aim was to develop an overall model of the plasma-conductors-controller system of RFX-mod shaped tokamak configuration for electromagnetic control purposes, with particular focus on vertical stability. Thus, the RFX-mod device is described by models of increasing complexity and involving both theoretical and experimental data. The CREATE-L code is used to develop 2D linearized plasma response models, with simplifying assumptions on the conducting structures (axisymmetric approximations). Such models, thanks to their simplicity, have been used for feedback controller design. The CarMa0 code is used to develop linearized plasma response models, but considering a detailed 3D description of the conducting structures. These models provide useful hints on the accuracy of the simplified models and on the importance of 3D structures in the plasma dynamics. The CarMa0NL code is used to model the time evolution of plasma equilibria, by taking into account also nonlinear effects which can come into play during specific phases (e.g. disruptions, limiter-to-divertor transitions, L-H transition etc.). The activity can be divided into two main parts: the first one involves the modelling of numerically generated low-β plasmas, which are used as a reference for the design and implementation of the plasma shape and position control system; the second part is related to the results of the experimental campaigns on shaped plasmas from low-β to H-mode regime, with particular efforts on the development of a novel plasma response model for the new equilibrium regimes achieved. Several challenges and peculiarities characterize the project in both the modelling and control frameworks. Strong plasma shape and different plasma regimes (i.e. low-β to H-mode plasmas), deeply affect the modelling activity and require the development of several numerical tools and methods of analysis. From the control system point of view, non-totally observable dynamic and model order reduction requirements allowed a full application of the model based approach in order to successfully design the plasma shape and vertical stability control system. The first part is based on theoretical data generated by the MAXFEA equilibrium code and used to derive the linearized model through the CREATE-L code. Two reference models have been produced for the magnetic configurations interested in shaped operations: the lower single null (LSN) and the upper single null (USN). The CREATE-L models are the most simple in terms of modelling complexity, because the conducting structures are described within the axisymmetric approximation. On the other hand, the simple but reliable properties of the CREATE-L model led to the successful design of the RFX-mod plasma shape and control system, which has been successfully tested and used to increase plasma performances involved in the second part of the thesis. Then, an investigation on the possible 3D effects of the conducting structures on these numerically generated plasma configurations has been carried out by producing plasma linearized models with an increased level of complexity. A detailed 3D volumetric description of the conducting structures of RFX-mod has been carried out and included in the plasma linearized models through the CarMa0 code. A comparison between the accuracy of this model and the previous 2D one has been performed. The different assumptions and approximations of the various models allow a clear identification of the key phenomena ruling the evolution of the n=0 vertical instability in RFX-mod tokamak discharges, and hence, provide fundamental information in the planning and the execution of related experiments and in refining the control system design. Finally, the nonlinear evolutionary equilibrium model including 3D volumetric structures CarMa0NL has been used to model nonlinear effects by simulating a "fictitious" linear current quench. The second part involves a modelling activity strictly related to the results of the experimental campaigns. In particular, new linearized models for the experimental plasmas in USN configuration have been carried out for all the plasma regimes involved in the experimental campaign, i.e. from low-β to H-mode. An iterative procedure for the production of accurate linearized plasma response models has been realized in order to handle the experimental data. The new plasma linearized models allowed further investigations on vertical stability, including 3D wall effects, in the three different plasma regimes (i.e. low-β, intermediate-β, H-mode). Furthermore, the axisymmetric plasma linearized models (CREATE-L) have been analyzed in the framework of the control theory revealing peculiar features in terms of associated SISO transfer function for vertical stability control and in terms of full MIMO model for shaping control. The MIMO model has been used to investigate the plasma wall-gaps oscillations experimentally observed in some intermediate-β plasma shots. A non-linear time evolution of the plasma discharge for a low-β plasma has been carried out by using the evolutionary equilibrium code CarMa0NL. Finally, it was investigated the vertical instability for the experimental plasmas in terms of a possible relation between plasma parameters and the occurrence of it; for these purposes, the solution of the inverse plasma equilibrium problem for the production of numerically generated plasma equilibria with variations on the plasma parameters observed experimentally was performed. This involves a wide class of numerical methods that will be described in details. Then, statistical hypothesis test has been adopted to compare the mean values of the parameters of both experimental and numerically generated plasmas showing different behaviours in terms of vertical stability.
La presente tesi tratta la modellazione e il controllo di plasmi in equilibrio, a sezione non circolare e relativi all’esperimento RFX-mod operante come tokamak. L’obiettivo è di sviluppare un modello complessivo di RFX-mod (includendo plasmaconduttori- controllore) con finalità di controllo elettromagnetico del plasma. L’esperimento RFX-mod è stato descritto con modelli caratterizzati da un crescente livello di complessità, coinvolgendo sia dati teorici che sperimentali. Il codice CREATE-L è stato usato per lo sviluppo di modelli linearizzati di risposta di plasma, con ipotesi semplificative sulla rappresentazione delle strutture conduttrici (approssimazione assialsimmetrica). Questi modelli, grazie alla loro semplicità, sono stati utilizzati per la progettazione del sistema di controllo. Il codice CarMa0 è stato usato per sviluppare modelli analoghi ma con una rappresentazione tridimensionale delle strutture conduttrici; questi permettono di verificare l’accuratezza dei modelli semplificati e indagare l’importanza delle strutture tridimensionali sulla dinamica del sistema. Il codice CarMa0NL ha permesso la trattazione di fenomeni evolutivi nel tempo e nonlineari (e.g. disruzioni, transizioni limiter-divertor, transizioni L-H etc.). L’attività può essere suddivisa in due parti: la prima riguarda la modellizzazione di plasmi a basso β teorici, non ottenuti sperimentalmente, usati come riferimento per la progettazione e l’implementazione del sistema di controllo della forma e della posizione verticale del plasma; la seconda parte, è legata ai risultati delle campagne sperimentali sui plasmi a sezione non circolari in diversi regimi, dal basso β al modo H, con particolare attenzione allo sviluppo di un nuovo modello linearizzato di risposta di plasma per i nuovi regimi di equilibrio raggiunti. L’attività di ricerca è caratterizzata da molteplici problematiche e peculiarità sia in termini di modellazione che di controllo. La pronunciata non circolarità della forma di plasma e i diversi regimi coinvolti hanno influenzato fortemente l’attività di modellazione che ha richiesto, infatti, lo sviluppo di molteplici strumenti computazionali e di analisi dati. Per quanto concerne il controllo, la non completa osservabilità della dinamica del sistema e la necessità di ridurre l’ordine del modello sono solo alcuni degli aspetti che hanno determinato la progettazione del sistema di controllo di forma e di posizione verticale. La prima parte è basata su dati teorici generati dal codice di equilibrio MAXFEA e poi utilizzati per derivare il modello linearizzato attraverso il codice CREATE-L. In questo contesto, sono stati prodotti due modelli di riferimento per le configurazioni magnetiche relative a plasmi non circolari: il singolo nullo inferiore (LSN) e il singolo nullo superiore (USN). I modelli CREATE-L sono i più semplici in termini di complessità di modellazione, in quanto le strutture conduttive della macchina sono descritte nell’approssimazione assialsimmetrica. D’altro canto, le proprietà semplici ma affidabili del modello CREATE-L hanno portato alla progettazione del sistema di controllo di forma e posizione verticale del plasma di RFX-mod, che è stato in seguito testato e utilizzato con successo per aumentare le prestazioni del plasma. Successivamente, è stata condotta un’analisi sui possibili effetti 3D delle strutture conduttrici sulle due configurazioni di plasma di riferimento, producendo dunque modelli linearizzati caratterizzati da un sempre maggiore livello di complessità. Una dettagliata descrizione volumetrica (3D) delle strutture conduttrici di RFX-mod è stata eseguita e inclusa nei modelli linearizzati di plasma attraverso il codice CarMa0. Successivamente, è stato eseguito un confronto tra l’accuratezza di questo modello e quello precedente 2D. Le diverse ipotesi e approssimazioni dei vari modelli consentono una chiara identificazione dei fenomeni chiave che governano l’evoluzione dell’instabilità verticale n = 0 in scariche RFX-mod tokamak e quindi forniscono informazioni fondamentali nella pianificazione ed esecuzione di esperimenti correlati oltre che nella raffinazione del progetto del sistema di controllo. Infine, il modello di equilibrio evolutivo non lineare CarMa0NL, che comprende le strutture volumetriche 3D, è stato utilizzato per modellare gli effetti non lineari simulando una variazione di corrente lineare "fittizia". La seconda parte è costituita da un’attività di modellazione strettamente correlata ai risultati delle campagne sperimentali. In particolare, sono stati eseguiti nuovi modelli linearizzati per i plasmi sperimentali nella configurazione USN per tutti i regimi di plasma coinvolti, cioè dal basso β fino al modo H. È stata ideata e sviluppata una procedura iterativa per la produzione di modelli linearizzati di risposta di plasma estremamente accurati, al fine di riprodurre al meglio i dati sperimentali. I nuovi modelli hanno consentito ulteriori studi sulla stabilità verticale, inclusi gli effetti della parete 3D, nei tre diversi regimi studiati (basso β, β intermedio, modo H). I modelli linearizzati assialsimmetrici (CREATE-L) sono stati analizzati dal punto di vista della teoria dei controlli, rilevando caratteristiche peculiari in termini di funzione di trasferimento SISO associata al controllo della stabilità verticale e in termini di modello completo MIMO relativo al controllo di forma. Il modello MIMO è stato utilizzato per indagare le oscillazioni nella forma del plasma osservate sperimentalmente in alcune scariche a β intermedio. L’evoluzione temporale non lineare della scarica di plasma, per plasmi sperimentali a regimi a basso β, è stata effettuata usando il codice di equilibrio evolutivo CarMa0NL. Infine, è stata studiata l’instabilità verticale per i plasmi sperimentali in termini di un possibile rapporto tra i parametri del plasma e il suo verificarsi; a tal fine è stata eseguita la soluzione del problema inverso per la produzione di equilibri di plasma teorici di riferimento, prodotti come variazioni sui parametri dei plasmi osservati sperimentalmente, il che comporta una vasta gamma di metodi numerici descritti in dettaglio. Successivamente, è stato adottato un test di ipotesi statistica per confrontare i valori medi dei parametri di plasma, sia sperimentali che teorici, associati a due diversi comportamenti in termini di stabilità verticale.

L'elaborato di tesi si occupa di due modelli deterministici essenziali per l'Epidemiologia. Dopo aver introdotto alcuni preliminari di teoria delle equazioni differenziali, si studia il modello SIR nelle varianti epidemica ed endemica: la formulazione delle equazioni, i punti di equilibrio e l'andamento della soluzione. Un approccio analogo è rivolto al modello SEIR di tipo endemico. Infine, si propone un modello deterministico per la pandemia da SARS-CoV-2: se ne descrivono le equazioni e si accenna all'andamento della soluzione numerica.

Foram estudados os equilíbrios dos complexos de Mn (II) com íons azoteto, em meio aquoso, por método potenciométrico indireto, através de medidas de pH, em meio de azoteto 0 a 1,8 M, e a 25,0 ºC, utilizando força iônica 2,00 M mantida com perclorato de sódio. Nas diferentes concentrações de íon metálico empregadas, 20, 40, 60, 80 e 100 mM, obteve-se uma mesma curva de formação de número médio de ligantes vs. concentração de ligante livre, o que configura a inexistência de complexos polinucleares nessas condições experimentais. Os valores de número médio de ligantes n¯, e de concentração de ligante livre, [L], foram utilizados para a integração de função de Bjerrum, obtendo-se a função de Fronaeus, F0(L), a partir da qual calcularam-se, por métodos gráficos e matemáticos, as quatro sucessivas constantes globais de equilíbrio: β1 = 4,15 ± 0,02 M-1 , β2 = 6,61 ± 0,04 M-2 , β3 = 3,33 ± 0,02 M-3 , β4 = 0,63 ± 0,01 M-4 . Avaliando os valores das constantes, observa-se que os complexos formados são fracos e, em obediência à regra de Irving e Williams, são menos estáveis que os complexos de cobalto (II) e de níquel (II). Em concentrações de ligante superiores a 1M há condições para lenta oxidação espontânea dos complexos de manganês(II) a manganês(III) com significativas mudanças espectrais.
The equilibria of complex formation between manganese(II) cations and azide anions were studied in aqueous medium by an indirect potentiometric method, at 25°C and ionic strengh 2.0 M (NaClO4). The equilibrium data were based on pH measurements of Mn(II) in N3¯/HN3 buffers. Metal ion concentration changing from 20 to 100 mM have defined one single formation curve of n_ (Bjerrum function) vs. [N 3 ¯ ] which is an evidence that only mononuclear species ara present in the working solutions. Integration of the formation curve from the best n¯vs. [N3¯] data leads to Fronaeus function data. They were properly treated to obtain the formation by a variety of methods (graphic and mathematical). The best set formed is: β1 = 4,15 ± 0,02 M-1 , β2 = 6,61 ± 0,04 M-2 , β3 = 3,33 ± 0,02 M-3 , β4 = 0,63 ± 0,01 M-4 . The complex are weaks and are is agreement with the Irving and Williams rule, i. e., less stable than the corresponding complexes of Ni(II) and Co(II). At ligand concentration higher t than 1,0 M there were conditions for a slow spontaneous oxidation of manganese(II) complexes to manganese to manganese(III), with remarkable spectral changes.

La presente tesis compila el resultado de cuatro estudios siguiendo una línea de investigación. Los cuatro articulos han sido publicados. Esta línea tiene una vertiente metodológica y otra clínica, ya que se han utilizado tres tipos de estudios, como son las revisiones sistemáticas (RS), los estudios de validación y el ensayo clínico aleatorio (ECA), sobre un tema en común como son los trastornos del equilibrio y control del tronco en pacientes que han experimentado un ictus. En las siguientes páginas se pone en contexto el problema del ictus y sus secuelas, con un especial énfasis en la debilidad muscular y las alteraciones de la sensibilidad, lo cual conduce a deficiencias en el control postural y equilibrio. El control postural es una habilidad muy compleja; en la que intervienen diferentes sistemas, y que resulta imprescindible para una vida independiente, para la realización de cualquier tarea de la vida diaria y en la deambulación. En esta tesis se aborda una línea de investigación para mejorar dichas deficiencias, como es un enfoque fisioterapéutico basado en ejercitar y potenciar la musculatura central del cuerpo o Core. El primer trabajo de investigación consistió en la realización de una RS para analizar qué evidencia existía hasta el momento referente a la efectividad de los ejercicios de tronco o de Core Stability para mejorar el equilibrio en sedestación y control de tronco en los pacientes que han sufrido un ictus. La revisión sirvió para constatar las deficiencias metodológicas de los ECAs realizados hasta la fecha, así como para detectar la ausencia de escalas validadas a la lengua española, para evaluar el equilibrio en sedestación y control postural en este tipo de pacientes. A partir de la revisión y en base a las deficiencias detectadas se diseñó un ECA para evaluar el efecto de los ejercicios de Core Stability en la población que ha sufrido su primer ictus y se encuentra en la fase subaguda (≤ 3 meses). Así mismo dos escalas utilizadas en el ECA y de uso frecuente en neurología, fueron validadas a la lengua española.

Cosa determina la stabilità di un sistema politico internazionale? L’anarchia sistemica determina sempre una minaccia alla sopravvivenza? Il modello strutturale qui proposto integra le variabili della concentrazione del potere e della localizzazione geografica delle Grandi Potenze, per dimostrare come specifiche configurazioni strutturali contribuiscano a plasmare le motivazioni che stanno alla base dei comportamenti statali, condizionando i risultati sistemici osservabili. Viene, inoltre, inquadrato il processo di socializzazione come variabile interveniente, attivata da specifiche condizioni strutturali, in grado di inibire la ricorrenza della tendenza sistemica al bilanciamento attraverso la riduzione delle opzioni di politica estera a disposizione degli Stati. Dal punto di vista teorico, concentrandosi sul ruolo svolto dal potere e dalla geografia nell’orientare le motivazioni di base degli attori, il modello modifica l’assunto realista di incentivi strutturali costanti all’azione degli Stati, ipotizzando che questi varino al variare dei livelli di concentrazione del potere. Inoltre, mitiga il carattere meccanicistico del realismo strutturale, considerando il bilanciamento come una tra tante opzioni disponibili. Dal punto di vista empirico, il modello viene applicato a tre casi di studio, nel tentativo di evidenziare come la stabilità o l’instabilità sistemica siano determinate dall’esistenza di strutture di potere diffuse o concentrate.
What does effectively determine systemic stability? Does international anarchy always determine a threat to survival? The structural model introduced in this work focuses on two main variables, power concentration and geography, to demonstrate how structural constraints shape States’ base motivations to action, and how the resulting behaviors condition the observable systemic outcomes. Furthermore, I introduce the socialization process as an intervening variable, enabled by specific structural conditions. Socialization could inhibit the systemic balancing tendency by narrowing States’ foreign policy options. From the theoretical point of view, the model modifies the realist assumption towards constant structural incentives to action. By focusing on the role played by power concentration and geography in shaping States’ motivations, it is possible to link together the shifts in international power distribution with shifts in structural incentives. Nonetheless, the model loses the rather mechanistic character of structural realism, making balancing one among many viable options. From the empirical point of view, I apply the model against three case studies, trying to demonstrate how the existence of concentrated or diffused power structures determines systemic stability or instability.

Cosa determina la stabilità di un sistema politico internazionale? L’anarchia sistemica determina sempre una minaccia alla sopravvivenza? Il modello strutturale qui proposto integra le variabili della concentrazione del potere e della localizzazione geografica delle Grandi Potenze, per dimostrare come specifiche configurazioni strutturali contribuiscano a plasmare le motivazioni che stanno alla base dei comportamenti statali, condizionando i risultati sistemici osservabili. Viene, inoltre, inquadrato il processo di socializzazione come variabile interveniente, attivata da specifiche condizioni strutturali, in grado di inibire la ricorrenza della tendenza sistemica al bilanciamento attraverso la riduzione delle opzioni di politica estera a disposizione degli Stati. Dal punto di vista teorico, concentrandosi sul ruolo svolto dal potere e dalla geografia nell’orientare le motivazioni di base degli attori, il modello modifica l’assunto realista di incentivi strutturali costanti all’azione degli Stati, ipotizzando che questi varino al variare dei livelli di concentrazione del potere. Inoltre, mitiga il carattere meccanicistico del realismo strutturale, considerando il bilanciamento come una tra tante opzioni disponibili. Dal punto di vista empirico, il modello viene applicato a tre casi di studio, nel tentativo di evidenziare come la stabilità o l’instabilità sistemica siano determinate dall’esistenza di strutture di potere diffuse o concentrate.
What does effectively determine systemic stability? Does international anarchy always determine a threat to survival? The structural model introduced in this work focuses on two main variables, power concentration and geography, to demonstrate how structural constraints shape States’ base motivations to action, and how the resulting behaviors condition the observable systemic outcomes. Furthermore, I introduce the socialization process as an intervening variable, enabled by specific structural conditions. Socialization could inhibit the systemic balancing tendency by narrowing States’ foreign policy options. From the theoretical point of view, the model modifies the realist assumption towards constant structural incentives to action. By focusing on the role played by power concentration and geography in shaping States’ motivations, it is possible to link together the shifts in international power distribution with shifts in structural incentives. Nonetheless, the model loses the rather mechanistic character of structural realism, making balancing one among many viable options. From the empirical point of view, I apply the model against three case studies, trying to demonstrate how the existence of concentrated or diffused power structures determines systemic stability or instability.

In questo elaborato si è effettuato una caratterizzazione meccanica completa (tramite prove di stato e meccaniche) dei materiali rocciosi, che costituiscono il versante in cui è scavato uno dei monumenti più importanti della Georgia: la città rupestre di Vardzia. La roccia tenera e la fratturazione sistematica dell'ammasso creano i presupposti per l'attivazione di movimenti franosi, che possono compromettere l'integrità fisica dei migliaia di turisti che vengono a visitare il monumento ogni anno e l'integrità strutturale ed architettonica del sito, fondamentale per la sua selezione nella lista UNESCO dei patrimoni dell'umanità. Per questo, tramite anche un'analisi numerica agli elementi finiti, si studia la stabilità allo scivolamento di uno dei possibili cunei rocciosi che interessano il sito.

Bright and stable near-infrared (NIR) and infrared (IR) emitting chromophores are in high demand for applications in telecommunication, solar cells, security barcodes, and as fluorescent reporters in bioimaging studies. The best choice for wavelengths >750 nm are semiconductor nanocrystals, especially ternary or alloy nanocrystals like CdHgTe, which enable size and composition control of their optical properties. Here, we report on the influence of growth time and surface chemistry on the composition and optical properties of colloidal CdHgTe. Up to now, these are the only NIR and IR emissive quantum dots, which can be synthesized in high quality in water, using a simple one-pot reaction. For this study we utilized and compared three different thiol ligands, thioglycolic acid (TGA), 3-mercaptopropionic acid (MPA), and glutathione (GSH). Aiming at the rational design of bright NIR- and IR-emissive alloy materials, special emphasis was dedicated to a better understanding of the role of the surface ligand and adsorption–desorption equilibria on the photoluminescence quantum yield and stability. In this respect, dilution and protonation studies were performed. Our results show that with this simple synthetic procedure, strongly fluorescent CdHgTe colloids can be obtained with MPA as stabilizing ligand revealing quantum yields as high as 45% independent of particle concentration.

Nous considérons les équations différentielles stochastiques (EDS) de Mc Kean-Vlasov, qui sont des EDS dont les coefficients de dérive et de diffusion dépendent non seulement de l'état du processus inconnu, mais également de sa loi de probabilité. Ces EDS, également appelées EDS à champ moyen, ont d'abord été étudiées en physique statistique et représentent en quelque sorte le comportement moyen d'un nombre infini de particules. Récemment, ce type d'équations a suscité un regain d'intérêt dans le contexte de la théorie des jeux à champ moyen. Cette théorie a été inventée par P.L. Lions et J.M. Lasry en 2006, pour résoudre le problème de l'existence d'un équilibre de Nash approximatif pour les jeux différentiels, avec un grand nombre de joueurs. Ces équations ont trouvé des applications dans divers domaines tels que la théorie des jeux, la finance mathématique, les réseaux de communication et la gestion des ressources pétrolières. Dans cette thèse, nous avons étudié les questions de stabilité par rapport aux données initiales, aux coefficients et aux processus directeurs des équations de McKean-Vlasov. Les propriétés génériques de ce type d'équations stochastiques, telles que l'existence et l'unicité, la stabilité par rapport aux paramètres, ont été examinées. En théorie du contrôle, notre attention s'est portée sur l'existence et l'approximation de contrôles relaxés pour les systèmes gouvernés par des EDS de Mc Kean-Vlasov
We consider Mc Kean-Vlasov stochastic differential equations (SDEs), which are SDEs where the drift and diffusion coefficients depend not only on the state of the unknown process but also on its probability distribution. These SDEs called also mean- field SDEs were first studied in statistical physics and represent in some sense the average behavior of an infinite number of particles. Recently there has been a renewed interest for this kind of equations in the context of mean-field game theory. Since the pioneering papers by P.L. Lions and J.M. Lasry, mean-field games and mean-field control theory has raised a lot of interest, motivated by applications to various fields such as game theory, mathematical finance, communications networks and management of oil resources. In this thesis, we studied questions of stability with respect to initial data, coefficients and driving processes of Mc Kean-Vlasov equations. Generic properties for this type of SDEs, such as existence and uniqueness, stability with respect to parameters, have been investigated. In control theory, our attention were focused on existence, approximation of relaxed controls for controlled Mc Kean-Vlasov SDEs

La tesi tratta di alcuni modelli matematici che descrivono l’andamento di una popolazione e l’interazione tra due specie in un ecosistema. Dopo una prima esposizione di alcuni concetti teorici necessari alla comprensione degli argomenti trattati, un primo modello presentato è quello di Malthus. Esso descrive la crescita esponenziale o la decrescita esponenziale di una popolazione. In seguito si è studiato un perfezionamento del modello precedente, il modello logistico, che tiene conto delle risorse ambientali e secondo il quale una popolazione, ad un certo punto, raggiunge una situazione di equilibrio. Infine è stato descritto il modello preda-predatore sulla base delle equazioni di Lotka-Volterra, che spiega l’andamento di due specie interagenti tra loro in un ecosistema. Attraverso questo modello si è arrivati alla conclusione che, ad un picco della numerosità delle prede, segue un picco della numerosità dei predatori.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Métodos de otimização que utilizam condições de otimalidade de primeira e/ou segunda ordem são conhecidos por serem eficientes. Comumente, esses métodos iterativos são desenvolvidos e analisados à luz da análise matemática do espaço euclidiano n-dimensional, cuja natureza é de caráter local. Consequentemente, esses métodos levam a algoritmos iterativos que executam apenas as buscas locais. Assim, a aplicação de tais algoritmos para o cálculo de minimizadores globais de uma função não linear,especialmente não-convexas e multimodais, depende fortemente da localização dos pontos de partida. O método de Otimização Global Topográfico é um algoritmo de agrupamento, que utiliza uma abordagem baseada em conceitos elementares da teoria dos grafos, a fim de gerar bons pontos de partida para os métodos de busca local, a partir de pontos distribuídos de modo uniforme no interior da região viável. Este trabalho tem dois objetivos. O primeiro é realizar uma nova abordagem sobre método de Otimização Global Topográfica, onde, pela primeira vez, seus fundamentos são formalmente descritos e suas propriedades básicas são matematicamente comprovadas. Neste contexto, propõe-se uma fórmula semi-empírica para calcular o parâmetro chave deste algoritmo de agrupamento, e, usando um método robusto e eficiente de direções viáveis por pontos-interiores, estendemos o uso do método de Otimização Global Topográfica a problemas com restrições de desigualdade. O segundo objetivo é a aplicação deste método para a análise de estabilidade de fase em misturas termodinâmicas,o qual consiste em determinar se uma dada mistura se apresenta em uma ou mais fases. A solução deste problema de otimização global é necessária para o cálculo do equilíbrio de fases, que é um problema de grande importância em processos da engenharia, como, por exemplo, na separação por destilação, em processos de extração e simulação da recuperação terciária de petróleo, entre outros. Além disso, afim de ter uma avaliação inicial do potencial dessa técnica, primeiro vamos resolver 70 problemas testes, e então comparar o desempenho do método proposto aqui com o solver MIDACO, um poderoso software recentemente introduzido no campo da otimização global.
Optimization methods that use optimality conditions of first and/or second order are known to be efficient. Commonly, such iterative methods are developed and analyzed in the light of knowledge concerning the mathematical analysis in n-dimensional Euclidean spaces, whose nature is of local character. Consequently, these methods lead to iterative algorithms that perform only local searches. Thus, the application of such algorithms to the calculation of global minimizers of a non-linear function, especially non-convex and multimodal, depends strongly on the location of the starting points. The Topographical Global Optimization method is a clustering algorithm, which uses an ingenious approach based on elementary concepts of graph theory, in order to generate good starting points for local search methods, from points distributed uniformly in the interior of the feasible set. The purpose of this work is two-fold. The first is a revisit to the Topographical Global Optimization method, where, for the first time, its foundations are formally described and its basic properties are mathematically proven. In this context, we propose a semi-empirical formula for computing the key parameter of this clustering algorithm, and, using a robustand efficient direction interior-point method, we extend the use of the Topographical Global Optimization method to problems with inequality constraints. The second objective is the application of this method to the phase stability analysis of mixtures, a difficult and important global optimization problem of the chemical engineering thermodynamics. Furthermore, in order to have an initial assessment of the power of this technique,first we solve 70 test problems, and then compare the performance of the method considered here with the MIDACO solver, a powerful software recently introduced in the field of global optimization.

Cette etude theorique se consacre a la description de la dynamique des surfaces vicinales portees hors de l'equilibre thermodynamique. Elle s'insere dans la problematique plus generale de la croissance cristalline dont l'importance tient a la fois des enjeux technologiques les plus actuels mais aussi de la place majeure qu'elle occupe dans les developpements de la physique non lineaire, des systemes hors equilibre et d'une maniere plus generale, des phenomenes de morphogenese. Les surfaces vicinales sont obtenues par clivage d'un cristal le long d'une direction legerement inclinee par rapport a un plan dense. La structure qui en resulte est composee d'une succession de terrasses separees par des marches monoatomiques. Une telle surface presente un reel interet pour la croissance par jet moleculaire. Les marches etant des sites de nucleations preferentiels, lorsque les conditions de croissances sont favorables, on serait en principe capable de faire croitre le solide couche par couche, donc de controler la croissance a l'echelle de l'atome. Or, et c'est la le point principal du present travail, la croissance d'une surface vicinale conduit inevitablement a des instabilites qui puisent leurs origines dans les processus hors de l'equilibre, moteur de la croissance. Deux instabilites principales se manifestent couramment : le meandre des marches (les marches droites deviennent spontanement modulees, conduisant par la meme a des modulations de la surface) et la mise en paquets des marches (les marches se regroupent par paquets formant des macro-marches separees par de larges terrasses ; on peut dire qu'il s'agit d'une instabilite de facettage dynamique). C'est sur ces deux instabilites qu'a porte notre etude.

Les récentes recherches sur les rotors d'hélicoptère conduisent au développement de pales de nouvelle génération présentant des géométries courbes. La double flèche de la pale BlueEdgeTM proposée par Eurocopter impose de reconsidérer les outils de calcul des charges rotors pour déterminer le torseur des efforts appliqués aux pales et aux éléments constitutifs du moyeu rotor afin de satisfaire aux exigences de conception et de certification. Les charges rotors se décomposent en contributions aéro- et élasto-dynamiques prises en compte par des modélisations distinctes. La thèse vise à définir une méthodologie de calcul de charges applicable aux pales à double flèche. Ainsi sont présentés les modèles aérodynamiques bi-dimensionnels pour calculer les vitesses induites du rotor et déterminer la répartition des efforts aérodynamiques sur le rotor. Le calcul des charges rotor nécessite de recourir à des modèles élasto-dynamiques. En résolvant les équations de la dynamique des solides pour un système mécanique, le code de mécanique du vol HOST considère une modélisation élastique de pale pour déterminer le torseur des efforts, les efforts de commande étant fournis par l'ensemble bielle de pas et plateaux cycliques. Le comportement non linéaire des adaptateurs de traînée interpales est décrit par des modèles de force de restitution. Ces travaux ont utilisé des caractérisations expérimentales sur des machines de traction de laboratoire ainsi que des essais en vol afin d'évaluer le niveau de représentativité des outils et méthodes proposés. La mise en oeuvre de l'ensemble de ces modèles détermine avec satisfaction les charges dynamiques du rotor pour des vols stabilisés
New generation blades have led to new load computation problems due to the evolution of the general shape, with forward and backward sweep. The BlueEdgeTM blade pattented by Eurocopter imposes to reconsider the development methodology and thus it is no longer possible to speak of straight blades and the models used for load computation have to be evaluated. The objective of this thesis is to determine what has to be modified and improved in current load computation methodology in order to reach an acceptable predictive level. This work considers both aerodynamic and dynamic models implemented in the HOST multi-body computer code. The aerodynamics models are based on the hypothesis of a two dimensional flow. The use of the CFD software \emph{elsA} is evaluated. Attention is given to rotor dynamics models that have an impact on loads, such as lead-lag damper models, blade element models and hub models. This thesis presents the different models and gives orientations relating to efficient load computation methodology. The aerodynamics models are compared to windtunnels experiments from the literature. This study leads also to perform flight tests and to investigate the dampers behavior on test benches in order to confront the computed loads to the reality of the helicopter operation. The proposed methodology is able to compute with a good accuracy rotor loads for stabilized flight cases

La croissante demande d'énergie électrique a conduit à la conception de systèmes électriques de grande complexité où les combustibles fossiles constituent la principale source d'énergie. Néanmoins, les préoccupations environnementales poussent à un changement majeur dans les pratiques de production d'électricité, avec un passage marqué des énergies fossiles aux énergies renouvelables et des architectures centralisées à distribuées. Les problèmes de stabilité dus à la présence de ce qu'on appelle les Charges à Puissance Constante (CPLs) constituent l’un des principaux défis auxquels sont confrontés les systèmes électriques distribués. On sait que ces charges, que l’on trouve couramment dans les installations de technologie de l’information et de la communication, réduisent l’amortissement effectif des circuits qui les alimentent, ce qui peut provoquer des oscillations de tension, voire une chute. Dans cette thèse, les principales contributions sont centrées sur la compréhension et la résolution de divers problèmes rencontrés dans l'analyse et le contrôle de systèmes électriques contenant des CPLs. Les contributions sont énumérées comme suit. (i) Des conditions simplement vérifiables sont proposées pour certifier la non existence d'états en régime permanent pour des réseaux multi-ports, à courant alternatif avec une distribution de CPLs. Ces conditions, qui reposent sur les inégalités matricielles linéaires, permettent d’écarter les valeurs des puissances des charges qui produiraient certainement un effondrement de la tension sur l’ensemble du réseau. (ii) Pour des modèles généraux de certains systèmes électriques modernes, y compris les réseaux de transmission à courant continu haute tension et les microréseaux, il est montré que, si des équilibres existent, il existe un équilibre caractéristique à haute tension qui domine tous les autres. En outre, dans le cas des systèmes d'alimentation en courant alternatif sous l'hypothèse de découplage standard, cet équilibre caractéristique s'avère stable à long terme. (iii) Une classe de systèmes port-Hamiltoniens, dans laquelle les variables de contrôle agissent directement sur l'équation du balance de puissance, est explorée. Il est démontré que ces systèmes sont décalés de manière passive lorsque leurs trajectoires sont contraintes à des ensembles facilement définissables. Ces dernières propriétés sont exploitées pour analyser la stabilité de leurs équilibres intrinsèquement non nuls. Il a également été montré que la stabilité des réseaux électriques à courant continu multiports et des générateurs synchrones, tous deux connectés à des CPLs, peuvent naturellement être étudiée avec le cadre proposé. (iv) Le problème de la régulation de la tension de sortie du convertisseur buck-boost alimentant une CPL non connu est résolu. L'un des principaux obstacles à la conception de commandes linéaires classiques provient du fait que le modèle du système est de phase non minimale par rapport à chacune de ses variables d'état. Cette thèse rapporte un contrôleur adaptatif non linéaire capable de rendre un équilibre souhaité asymptotiquement stable; de plus, une estimation de la région d'attraction peut être calculée. (v) La dernière contribution concerne l'amortissement actif d'un système d'alimentation de petite taille à courant continu avec une CPL. Au lieu de connecter des éléments passifs peu pratiques et énergétiquement inefficaces au réseau existant, l’ajout d’un convertisseur de puissance contrôlé est exploré. La contribution principale rapportée ici est la conception d'une loi de contrôle non linéaire basée sur l'observateur pour le convertisseur. La nouveauté de la proposition réside dans le fait qu'il n'est pas nécessaire de mesurer le courant électrique du réseau ni la valeur de la CPL, soulignant ainsi son applicabilité pratique. L'efficacité du schéma de contrôle est ensuite validée par des expériences sur un réseau à courant continu réel
The continuously increasing demand of electrical energy has led to the conception of power systems of great complexity that may extend even through entire countries. In the vast majority of large-scale power systems the main primary source of energy are fossil fuels. Nonetheless, environmental concerns are pushing a major change in electric energy production practices, with a marked shift from fossil fuels to renewables and from centralized architectures to more distributed ones. One of the main challenges that distributed power systems face are the stability problems arising from the presence of the so-called Constant Power Loads (CPLs). These loads, which are commonly found in information and communication technology facilities, are known to reduce the effective damping of the circuits that energize them, which can cause voltage oscillations or even voltage collapse. In this thesis, the main contributions are focused in understanding and solving diverse problems found in the analysis and control of electrical power systems containing CPLs. The contributions are listed as follows. (i) Simply verifiable conditions are proposed to certify the non existence of steady states in general, multi-port, alternating current (AC) networks with a distributed array of CPLs. These conditions, which are based on Linear Matrix Inequalities, allow to discard the values of the loads' powers that would certainly produce a voltage collapse in the whole network. (ii) For general models of some modern power systems, including High-Voltage Direct Current transmission networks and microgrids, it is shown that if equilibria exist, then there is a characteristic high-voltage equilibrium that dominates, entry-wise, all the other ones. Furthermore, for the case of AC power systems under the standard decoupling assumption, this characteristic equilibrium is shown to be long-term stable. (iii) A class of port-Hamiltonian systems, in which the control variables act directly on the power balance equation, is explored. These systems are shown to be shifted passive when their trajectories are constrained to easily definable sets. The latter properties are exploited to analyze the stability of their---intrinsically non zero---equilibria. It is also shown that the stability of multi-port DC electrical networks and synchronous generators, both with CPLs, can be naturally studied with the proposed framework. (iv) The problem of regulating the output voltage of the versatile DC buck-boost converter feeding an {em unknown} CPL is addressed. One of the main obstacles for conventional linear control design stems from the fact that the system's model is non-minimum phase with respect to each of its state variables. As a possible solution to this problem, this thesis reports a nonlinear, adaptive controller that is able to render a desired equilibrium asymptotically stable; furthermore an estimate of the region of attraction can be computed. (v) The last contribution concerns the active damping of a DC small-scale power system with a CPL. Instead of connecting impractical, energetically inefficient passive elements to the existing network, the addition of a controlled DC-DC power converter is explored. The main contribution reported here is the design of a nonlinear, observer-based control law for the converter. The novelty of the proposal lies in the non necessity of measuring the network's electrical current nor the value of the CPL, highlighting its practical applicability. The effectiveness of the control scheme is further validated through experiments on a real DC network

L'objectif principal de ce travail est de mettre à la disposition des pouvoirs publics un outil de prévision des glissements de terrains naturels, pour leur permettre de prendre les décisions qui s'imposent au bon moment. Vu les incertitudes qui pèsent sur l'analyse a priori des phénomènes d'instabilité et l'imprécision de la cinématique des mouvements, il est nécessaire de pouvoir déterminer, chaque fois qu'il y a risque de mptme d'un ouvrage ou d'un site naturel, une frontière critique dans l'espace des paramètres définissant l'équilibre des masses potentiellement instables. Parmi les paramètres liés directement au comportement de l'ouvrage, seuls les déplacements sont directement mesurables. Dans cet esprit, les métbodes de surveillance portent essentiellement sur la mesure des déplacements, en surface (topographie) et en profondeur (inclinométrie ). La méthode présentée dans cette étude est basée essentiellement sur les mesures inclinométriques effectuées sur site instable et les résultats des essais de cisaillement triaxial réalisés sur des échantillons de sol prélevés sur ce site. Cette méthode a donc été appliqnée à deux sites instables (PONSONNAS et AVIGNONET) dans la région du Trièves (Isère). Au cours de cette étude, nous avons mis au point un outil informatique pour l'analyse de stabilité des pentes et l'étude d'écoulement souterrain en régime permanent par la méthode des éléments finis.

Human papillomavirus (HPV), a major sexually-transmitted disease, causes cervical cancer, in addition to numerous other cancers in females and males. This thesis uses mathematical modeling, theory and simulations to study the transmission dynamics of HPV, and associated dysplasia, in a community. A new deterministic model is designed and used to assess the population-level impact of Pap cytology screening on the transmission dynamics of the disease in a community. The model is rigorously analyzed for its dynamical features, vis-a-vis determining the conditions for the effective control (or elimination) and persistence of the disease. Furthermore, the effect of uncertainties in the estimates of the parameter values used in the numerical simulations of the model is accounted for via uncertainty and sensitivity analysis. Simulations of the model show that Pap screening dramatically reduces the incidence of cervical cancer in the community.

The study of infinitely long cylinders of constant cross-section floating in an infinite fluid bath in zero-gravity environments has primarily been focused on bodies whose cross-sections are strictly convex and sufficiently smooth. In this thesis, our efforts are concentrated on the consideration of bodies that are only convex and piecewise smooth. These types of bodies are seldom considered in current literature. We have worked with a series expansion of the energy function in order to determine when configurations of a given body will be in equilibrium, stable or otherwise. We have proven that any convex body with a straight side cannot float in a stable equilibrium with the fluid interface intersecting the interior of the straight side in a single point. This fact is then used to prove necessary and sufficient conditions for stable equilibrium of polygons, bodies whose cross-sections are comprised of only straight sides. We illustrate these conditions with several examples. In the latter portion of the thesis, we turn our attention to bodies in three dimensions. While past research has again been focused on strictly convex bodies, we began to consider bodies that do not meet these requirements by examining bodies of revolution. A condition for stability with respect to vertical variations of bodies of revolution is derived. We conclude with several examples of bodies of revolution, some of which interestingly relate back to an analogous two-dimensional shape.

Metallic fuels have an important role to play in "fast breeder" Gen-IV type nuclear reactors, and U-Pu-Zr is one of the prototypical systems. Because of the variability in fuel chemistry during burn-up, it is important to understand the effect of minor actinides and fission products on phase stability. Within this framework, we present a study on phase equilibria in the binary Np-Zr alloy system on which little work has been published. To resolve the contradictory reports on the ordering/ clustering trends of the bcc phase, a thermodynamic study is performed using the CALPHAD method. The calculated Np-Zr phase diagram is consistent with two sets of data: formation enthalpies of the bcc phase that are calculated with ab initio KKR-ASA-CPA electronic-structure method and lattice stabilities of solution phases obtained from first-principles technique. Another important feature in the Np-Zr alloy system is the non-stoichiometric delta-NpZr2 phase that forms in a hexagonal C32 structure similar to the delta-phase in the U-Zr system and the w-phase in pure Zr. An increase in the homogeneity range of the delta-phase when going from Pu to Np and to U is attributed to a lowering of its heat of formation that is caused by an increase in d-band occupation. Two different possibilities for the stability of the delta- and w- phases have been proposed in the present work. Additionally, calculated changes in enthalpy versus temperature are plotted for two alloy compositions of the Np-Zr system to guide future experimental work in resolving important issues in this system. Finally, an ab initio study, implemented with the L(S)DA U formalism, is performed for pure Np that reveals a transition from a non-magnetic to a magnetic state at a critical U parameter.

碩士
國立成功大學
材料科學及工程學系
102
High-temperature materials are demanding for high-power electronics, so the material of soldering need to support the high temperature. Currently, Pb is proven to be harmful to the environment and human health, so the searching for high temperature lead-free solders becoming to be a demanding need. In this study, we choose Au-Ge eutectic alloy to be the solder, reactions between Au-Ge solders and Ni or Cu substrates have to be investigated to evaluate the Au-Ge based high-temperature solders. In the results of the interfacial reaction between Au-12wt. % Ge (Au-12Ge) and Ni substrate, after a 8-hour reaction, the formation of F.C.C.-(Au, Ge, Ni)/NiGe alternating layers occurred in the interface. The stability diagrams and the 673 K isothermal section of the Au-Ge-Ni ternary system were calculated using the CALPHAD method to analyze the mechanism of alternating-layer formation. Ge was then determined to be the dominant diffusion specie. When Ge atoms accumulated at the NiGe/Ni2Ge interface, the interface became unstable and a new pair of F.C.C.-(Au, Ge, Ni)/NiGe would form, resulting in the previously-formed F.C.C.-(Au, Ge, Ni)/NiGe layers being separated from the original Ni2Ge/Ni substrate. The periodic thermodynamic instability caused subsequent nucleation of new alternating layers. The diffusion path across the interface is liquid/F.C.C.-(Au, Ge, Ni)/NiGe/⋯/F.C.C.-(Au, Ge, Ni)/NiGe/Ni2Ge/Ni. In the previous research, the alternating-layers structure was always found in the solid/solid interfacial reaction. Our research is the first diffusion couple that found this phenomenon only in the liquid/solid reaction, but not in the solid/solid reaction. In the past, the research of Au-12Ge/Cu interfacial reaction annealing at 400 oC and 300 oC, the unidentified “X” phase has been found and recognized as a ternary phase. The composition of X phase had a range from Au-74.72Cu-16.97Ge to Au-77.65Cu-15.58Ge. Therefore, we constructed the isothermal phase diagram of Au-Ge-Cu ternary system. We focus on the phase area near the ζ and ε1 phase. According to the new isothermal phase diagram, the “X” phase has been identified to be the ε1 phase.

Ideal MHD models are known to be inadequate to describe various physical attributes of a toroidal field with non-continuous symmetry, such as magnetic islands and stochastic regions. Motivated by this omission, a new variational principle MRXMHD was developed; rather than include an infinity of magnetic flux surfaces, MRxMHD has a finite number of flux surfaces, and thus supports partial plasma relaxation. The model comprises of relaxed plasma regions which are separated by nested ideal MHD interfaces (flux surfaces), and can be encased in a perfectly conducting wall. In each region the pressure is constant, but can jump across interfaces. The field and field pitch, or rotational transform, can also jump across the interfaces. Unlike ideal MHD, MRxMHD plasmas can support toroidally non-axisymmetric confined magnetic fields, magnetic islands and stochastic regions. In toroidally non-axisymmetric plasma, the existence of interfaces in MRxMHD is contingent on the irrationality of the rotational transform of flux surfaces. That is, the KAM theorem shows that invariant tori (flux surfaces) continue to exist for sufficiently small perturbations to an integrable system (which describes flux surfaces), provided that the rotational transform is sufficiently irrational. Building upon the MRxMHD stability model, we study the effects of irrationality of the rotational transform at interfaces in MRxMHD on plasma stability. We present an MRxMHD equilibrium model to investigate the effects of magnetic field pitch within the plasma and across the aforementioned flux surfaces within a chosen geometry. In this model, it is found that the 2D system stability conditions are dependent on the interface and resonant surface magnetic field pitch at minimised energy states, and the stability of a system as a function of magnetic field pitch destabilises at particular values of magnetic field pitch. We benchmark the treatment of a two-volume system, along with the calculations for background and perturbed magnetic fields to existing cylindrical working. An expression is formulated for the stability eigenvalues by creating a model for the slab geometry system. The eigenvalues for system stability at a minimum energy state are found to depend upon the rationality of the magnetic field pitch at resonant surfaces. Various system parameter scans are conducted to determine their affect upon system stability and their implications. While tearing instabilities exist at low order rational resonances, investigating the instability of high-order rationals requires study of pressure-driven instabilities.

Il presente lavoro trova come spunto i temi trattati nel convegno “Euro e Fiscal Compact: quali prospettive per l’Euro” ed in particolare le riflessioni suscitate dalle relazioni del Prof. Guarino e del Prof. Tosato. Il successivo approfondimento, svolto in coerenza con le attività di studio e di ricerca legate al dottorato , ha avuto ad oggetto le riforme apportate al Patto di stabilità e crescita durante il periodo 2011 e 2013. Tali riforme hanno inciso nella poltica economica europea, di coordinamento, di sorveglianza economica multiaterale e di controllo sui bilanci pubblici nazionali. Per tale via le decisioni europee si insinuano anche nella fase di preparazione, approvazione e controllo dei bilanci nazionali e inferiscono nella determinazione delle spese pubbliche parlamentarmente assentibili, manifestando un potere che non appare più contenibile nel quadro previgente di governance economica europea. In quanto la riserva di legge che affida l’approvazione del bilancio al Parlamento non è solo un elemento che caratterizza storicamente la forma dello Stato liberale e che trova indirizzo di sviluppo nello Stato sociale, ma misura anche concretamente l’indice di democraticità di uno Stato. Infatti, “i bilanci generali non sono solo materie di calcoli aritmetici, ma in mille modi vanno alla radice della prosperità delle persone, ai rapporti fra le classi sociali, e alla potenza” degli Stati . Il nuovo quadro europeo più che attuare il rafforzamento della disciplina prevista nei Trattati, manifeta l’emersione di un vero e proprio Potere (sia dal punto di vista soggettivo che procedurale) di governo dell’economia. Sebbene ciò la cooperazione economica verso obiettivi comuni quali crescita e sviluppo è e deve essere ancora il tratto fondante del progetto europeo, il suo valore economico ha ancora oggi bisogno di essere letto attraverso la lente di principi, quali ad esempio l’uguaglianza e la solidarietà, per permettere al processo di integrazione europeo di approfondirsi politicamente. Partendo da queste considerazioni, il presente lavoro approfondisce lo studio della poltica economica europea ancorando tale indagine “ai principi ed ai valori fondanti della costruzione europea” ritrovandoli nelle Costituzioni nazionali, che costituiscono l’architettura su cui si poggia l’equilibrio costituzionale dei poteri in un ordinamento composito. In quanto, sebbene la separazione dei poteri sia un principio originariamente “sconosciuto all’organizzazione istituzionale europea” , tale principio e il suo equilibrio istituzionale in ambito di politica di bilancio appartiene “alla struttura fondamentale, politica e costituzionale” degli Stati membri che le Istituzioni eurpee nel loro agire e nei loro atti devono rispettare ai sensi dell’art. 4, par. 2, TUE . L’inferenza della normativa europea su quella nazionale di bilanicio quindi investe il rapporto tra i poteri in un quadro istituzionale multi livello, che coinvolge oltre all’equilibrio istituzionale anche quello costituzionale nazionale. Rispetto a tale assunto, nel presente lavoro dopo un indagine storico ricostruttiva sulla normativa afferente la politica economica europea (Capitolo I), si approfondisce: il nuovo assetto di coordinamento economico rafforzato dalle riforme al Patto di stabilità e crescita (Capitolo II), l’inferenza di questo nel ruolo democratico di approvazione delle scelte di spesa e di bilancio affidate ai Parlamenti nazionali (Capitolo III), i nuovi equilibri emersi tra le prerogative governative europee e nazionali di governo dell’economia (Capitolo IV), la loro incidenza nell’equilibrio dei poteri e rispetto a questo equilibrio il ruolo assunto dalla Corte costituzionale tedesca nell’affermare la tutela delle prerogative democratiche nazionali sulle decisioni afferenti la spesa pubblica (Capitolo V). Concludendo il discorso con un ragionamento che riporta i difetti dell’attuale costrutto di politica economica europea all’imperfezione del modello originario di fusione a freddo delle competenze nazionali in ambito di politca economica europea, rispetto invece a quello di fusione a caldo adopertato in ambito di politica monetaria unica (Capitolo VI). Si premette che lo scrivente ritiene che tale compromesso raggiunto per fondare l’Unione economica e monetaria è stato inevitabile date le esigenze contrapposte di tutela della sovranità nazionale in ambito economico e di bilancio, rispetto a quella di devoluzione all’ordinamento europeo della politica monetaria. Mentre le successive implementazioni normative hanno dimenticato l’approfondimento dell’integrazione politica dal punto di vista democratico. Il presente lavoro ha quindi un tono critico rispetto alla politica economica europea, ma lo stesso non è un giudizio sul valore dell’Unione economica e monetaria. Tale critica è, invece, lo strumento attraverso il quale si è approfondito lo studio della normativa europea e si conclude sulla necessità di una novella al diritto primario europeo per continuare nel cammino di integrazione politica attraverso un modello Istituzionale e procedurale che legittimi democraticamente le decisioni economiche prese, che contempli un bilanciamento tra interessi economici parziali e tutela di diritti generali (ovvero, per tutti i cittadini europei), e che contemperi la politica di stabilità con gli indirizzi alla crescita.