While psychological practice continues to expand, the sobering decline of mental health identified by Hillman and Ventura (1993) is evidenced by increased rates of suicide (Weir, 2019; Hedegaard, 2021; Stone et al., 2018) and psychopathology (Blue Cross Blue Shield Association, 2018; Twenge et al., 2010). Charles Taylor identified, in the same time frame as the noted decline of mental health, a malaise of modernity (1991), that is, the loss of meaning and transcendence in the modern world. Throughout the history of psychology and Western thought and culture, increased rates of psychological distress certainly coincide with what I will refer to as the malaise of psychology: the reliance on immanence-based theories that locate meaning and purpose within (i.e., emergent from) persons themselves, as opposed to being anchored in any genuine transcendence, that provides meaning and purpose to persons by calling them out of themselves, to something higher. Psychological practice has, ironically, come to reject the autonomous individual in favor of a socially/relationally constructed persona while at the same time locating the source of meaning and truth within the individual person and honoring the individual desires and needs as the definitive source of the meaning of life itself. This movement contrasts sharply with a genuinely transcendent approach which recognizes the importance, and even grants the ontological status, of higher goods and commonalities, that is, the existence of something higher in our humanity itself that calls us at once into being and into responsibility. I will propose that to remedy the malaise of psychology, we must locate the foundation of meaning, purpose, healing, and transformative change in our ethical obligations and responsibilities toward others, a recognizing and striving towards being for the other (e.g., P. Marcus, 2008) as opposed to being simply for oneself, within oneself, and, thus, merely with the other. Furthermore, I argue that being for the particular other cannot occur unless human beings are genuinely responsible moral agents capable of an individual power and potential to act for the sake of that responsibility (Williams et al., 2021). That is, only in the transcending encounter with the other wherein we are called out of our self to something greater beyond us can we achieve fundamental and lasting change in mental health and healing for self and others. I will support this assertion by drawing on the work of Emmanuel Levinas, Charles Taylor, and C. Terry Warner, as well as others. Psychology, I will argue, must include this conception of an inherently moral system of human relationships in which each human being is responsible (i.e., able to respond) to the felt moral imperative from the other. Such obligation one might only be able to fulfill as one is attuned to and disposed to be for the other. This mode of being is distinctly not a systemic, nor a technological, solution to be achieved by strategic inner change or insight. Rather, it consists in the recognition and amalgamation of many individual acts of being for the other—by unique individuals for the sake of other unique individuals. I will end by outlining one possible model of application of this approach to clinical practice, viz., Alterity Focused Therapy© proposed by Burdge, Burdge, and Major (2022).

Yes / There is a need to understand the nature of aggregation of cyclodextrins (CDs) with guest molecules in increasingly complex formulation systems. To this end an innovative application of Taylor dispersion analysis (TDA) and comparison with dynamic light scattering (DLS) have been carried out to probe the nature of ICT01-2588 (ICT-2588), a novel tumor-targeted vascular disrupting agent, in solvents including a potential buffered formulation containing 10% hydroxypropyl-β-cyclodextrin. The two hydrodynamic sizing techniques give measurement responses are that fundamentally different for aggregated solutions containing the target molecule, and the benefits of using TDA in conjunction with DLS are that systems are characterised through measurement of both mass- and z-average hydrodynamic radii. Whereas DLS measurements primarily resolve the large aggregates of ICT01-2588 in its formulation medium, methodology for TDA is described to determine the size and notably to quantify the proportion of monomers in the presence of large aggregates, and at the same time measure the formulation viscosity. Interestingly TDA and DLS have also distinguished between aggregate profiles formed using HP-β-CD samples from different suppliers. The approach is expected to be widely applicable to this important class of drug formulations where drug solubility is enhanced by cyclodextrin and other excipients.

La thèse porte sur l'étude de la réduction de traînée par injection de bulles. La réduction de traînée présente un intérêt pour les applications navales puisqu'elle est issue d'une modification des structures cohérentes qui contribuent le plus à la résistance à l'avancement. Le but de cette étude est d'analyser les mécanismes à l'origine de cette diminution du frottement pariétal. L'approche utilisée dans le cadre de cette étude est numérique, elle emploie le code JADIM par une approche Euler-Lagrange : la phase continue est simulée par Simulation Numérique Directe et la phase dispersée est simulée en suivant individuellement chaque bulle. La configuration retenue dans le cadre de cette étude est celle de l'écoulement de Taylor-Couette (écoulement compris entre deux cylindres en rotation). La première partie de la thèse vise à adapter l'outil numérique employé, afin de pouvoir prendre en compte le retour de la phase dispersée via des termes de forçage dans les équations bilan de matière et de quantité de mouvement. La deuxième partie de la thèse vise à étudier l'écoulement porteur en configuration monophasique, afin de disposer d'une référence sur l'écoulement non perturbé. La troisième partie de la thèse a pour objectif d'étudier la dispersion passive des bulles dans le système, afin d'analyser les mécanismes de migrations mis en jeu. Enfin la dernière partie de la thèse vise à étudier l'influence des bulles sur l'écoulement porteur en analysant l'effet de certains paramètres, notamment le taux de vide et la flottabilité. / The study deals with drag reduction induced by bubble injection, its application concerns naval transport. The aim of the study is to shed more light on mechanisms that are involved in this wall friction reduction. The study is based on a numerical approach, and use the JADIM code with an Euler-Lagrange approach: the continuous phase is solved by Direct Numerical Simulation, and the disperse phase by a tracking of each bubble. Within the framework of this study we consider the Taylor-Couette flow configuration (flow between two concentric cylinders in rotation). The first part of the study deals with the modification of the numerical tool, in order to take into account the influence of the disperse phase on the continuous one through forcing terms in the mass and momentum balance equations. The aim of the second part is to study de Taylor-Couette flow in its monophasic configuration, for the purpose of providing a reference of the undisturbed flow. The third part deals with the passive dispersion of bubble in Taylor-Couette flow, in order to analyze the migration mechanisms involved. And the aim of the last part is to study the effects of the disperse phase on the continuous one, by analyzing the influence of bubbly phase parameters (like void fraction and buoyancy).

Cette thèse vise à améliorer la précision numérique des simulations aéroacoustiques d’écoulements dans un contexte précis, celui du cadre industriel avec un partenariat Dassault Aviation. Pour répondre à cette problématique, la modélisation aux grandes échelles est utilisée afin de la rendre plus efficace et adaptée à la méthode numérique des éléments finis stabilisée par SUPG/GLS. Afin de préciser la méthode numérique, une première partie est consacrée à la formulation théorique et pratique du code AETHER utilisé. La précision des schémas numériques spatial et temporel est aussi présentée. L’idéologie principale issue de la famille des modèles Variational Multi-Scale a été retenue afin de construire le nouveau modèle de sous-maille. En effet, une précédente thèse avait démontré la pertinence de ce type d’approche pour les éléments finis. Même si le cadre est applicatif, cette thèse propose une réflexion générale sur le filtrage numérique en éléments finis ainsi qu’un nouveau procédé pour filtrer le plus efficacement l’écoulement calculé. Cette nouvelle approche de filtrage est particulièrement bien adaptée aux éléments finis et à la montée en ordre spatial. Un modèle hybride de gestion des parois est aussi développé afin de pouvoir utiliser le nouveau modèle de sous-maille dans des configurations complexes comprenant des surfaces solides. Le processus de filtrage est testé sur le cas académique des tourbillons de Taylor-Green et présente un réel gain. Enfin le modèle global est utilisé pour calculer une configuration industrielle de tri-corps hypersustenté nommée LEISA II. Grâce au nouveau modèle proposé et validé par les résultats expérimentaux, il a été possible de fournir des interprétations physiques pointues sur le comportement complexe de l’écoulement du bec et du bruit qu’il génère. Cette dernière partie est une illustration pertinente de l’utilisation des modèles aux grandes échelles pourtant coûteux, et cela même dans un contexte industriel. / The goal of this thesis is to improve the numerical accuracy for aeroacoustic flow simulations in a given scope, that is an industrial application for a partnership with the aircraft company Dassault Aviation. These works are then looking for a new large eddy simulation (LES) model which is efficient and well suited for the finite element formulation and the SUPG/GLS stabilisation method. In order to clarify the scientific environment and numerical tools, a first part is devoted to the theoretical and practical framework of the AETHER code. The spatial and temporal performances of its numerical schemes are assessed too. The philosophy of the Variational Multi-scale models has been selected to build an improvement for the new subgrid model. Indeed, a previous thesis had already demonstrated the relevance of this kind of models especially for the finite element method. Despite the industrial framework, a general reflection on the numerical filtering in finite elements is suggested and a new filtering process is developed in order to sort efficiently the scales of the simulated flow. This new filtering method is especially well fitted to finite element simulations and the high spatial order schemes. An hybrid model has been developed too in order to be able to use the new VMS model in complex configurations involving solid bodies. The filtering process is assessed on an academic case called Taylor-Green vortices and shows a real benefit compare to classical approaches. Finally the whole model is used to compute an industrial configuration, a three-element high-lift device called LEISA II. Thank to the validation of the new model with the experimental results, it has been possible to find accurate explanations about the complex flow behaviour of the slat and its noise generation. This last part is a relevant demonstration of the LES models use in the industrial world even if they are still costly in computation ressources.

Submitted by JOSIANE SANTOS DE OLIVEIRA (josianeso) on 2018-05-11T15:32:26Z No. of bitstreams: 1 Odair Camati_.pdf: 1067364 bytes, checksum: 5f0ed114a31bc5d5fcfe07a390e1b15c (MD5) / Made available in DSpace on 2018-05-11T15:32:26Z (GMT). No. of bitstreams: 1 Odair Camati_.pdf: 1067364 bytes, checksum: 5f0ed114a31bc5d5fcfe07a390e1b15c (MD5) Previous issue date: 2018-03-21 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho sustentamos a tese de que o encontro entre as teorias de Charles Taylor e Will Kymlicka oferece boas perspectivas para o estabelecimento de um projeto multicultural em sociedades liberais e democráticas, mas possui limites quando da tentativa de universalização desse mesmo projeto. As dificuldades quanto à universalização se apresentam de formas distintas nos autores referidos. Para o liberal Kymlicka, os valores tradicionais do liberalismo são suficientes para o reconhecimento de todas as diferentes manifestações culturais. Com isso a universalidade estaria pré-concebida, o que, segundo nosso entendimento, impediria um diálogo construtivo com aqueles que não comungam os mesmos valores. Taylor, por sua vez, propõe um modelo de razão prática com raízes hermenêuticas que ofereceria elementos para o estabelecimento de juízos de valor com validade para todas as comunidades humanas que se colocassem em processo de compreensão mútua. As limitações residem na dificuldade para estabelecer condições mínimas para que esse processo se desenvolva sem distorções. Para chegar a esse momento, faremos antes uma retomada dos principais elementos envoltos nas discussões multiculturais no sentido de provar a necessidade de debater tal temática. Na sequência, apresentaremos criticamente os fundamentos conceituais desenvolvidos pelos filósofos canadenses em suas teorias do multiculturalismo. Basicamente, a autonomia é o conceito central em Kymlicka e o reconhecimento ocupa o mesmo espaço em Taylor. Por fim, a partir de um liberalismo brando, da não possibilidade de total neutralidade estatal e da valorização do contexto de escolha, propomos que existem elementos suficientes para desenvolver um projeto multicultural em sociedades liberais e democráticas. O que não significa, necessariamente, que temos elementos para um projeto multicultural com validade universal / In this work, I support the thesis that even though the encounter between Charles Taylor’s and Will Kymlicka’s theories offers good prospects for the establishment of a multicultural project in liberal and democratic societies, it has some limits when we try to universalize it. The difficulties regarding universalization are presented in different ways by the aforementioned authors. On the one hand, Kymlicka’s liberalism holds that the traditional values of liberalism are sufficient for the recognition of all different cultural manifestations. On this view, the universality would be preconceived, which, according to our understanding, would preclude a constructive dialogue with those who do not share the same values. On the other hand, Taylor proposes a model of practical reason with hermeneutical roots that would provide elements for the establishment of value judgments valid for all human communities that put themselves in a process of mutual understanding. The limitations of this model lie in the difficulty of establishing minimum conditions for this process to be developed without distortions. To get this point, we shall first take up the main elements involved in multicultural discussions in order to prove the need to discuss such issues. After that, we shall critically expose the conceptual foundations developed by both Canadian philosophers in their theories of multiculturalism. Basically, while autonomy is Kymlicka’s core concept, recognition is Taylor’s one. Finally, from a soft liberalism, which claims the lack of state neutrality and the valorization of the context of choice, we propose that the encounter between the two theories has enough elements to develop a multicultural project in societies that are both liberal and democratic. Yet this does not necessarily mean that we have elements for a multicultural project with universal validity.

La pertraction est une technologie émergente d’extraction liquide-liquide utilisant une barrière membranaire comme surface d’échange entre la phase aqueuse et le solvant. Un solvant très émulsif et/ou constitué par un extractant pur peut ainsi être utilisé sans la contrainte d’un écart de densité avec la phase aqueuse. Utiliser un extractant pur est d’un grand intérêt dans la perspective d’avoir une forte capacité de charge du solvant (>100 g.L-1). A ce titre, l’étude de la faisabilité de l’usage d’un extractant pur comme solvant dans le procédé de pertraction apparait pertinent. Cette thèse a donc pour objet l’étude du procédé de pertraction pour l’extraction des métaux d’intérêt en utilisant un solvant sans diluant. L’extraction des terres rares (néodyme (Nd), praséodyme (Pr) et dysprosium (Dy)) a été choisi comme objet de cette étude, par une démarche visant tout d’abord la sélection d’un solvant spécifique des lanthanides (le Nd comme modèle), le montage et l’optimisation d’un module de pertraction, et enfin la mise en œuvre d’un modèle de transfert de matière pour étudier l’influence des différents paramètres qui gouvernent le procédé. Le choix du solvant s’appuie ainsi sur 3 critères : son affinité pour le Nd, sa viscosité ainsi que sa solubilité en phase aqueuse. Pour la sureté du procédé son point éclair a également été pris en compte dans la sélection. Par cette approche, le N, N dibutylacétamide (DBAc) a été retenu pour sa viscosité modérée (< 5 mPa.s) mais son utilisation a nécessité l’addition de sels de nitrates en phase aqueuse pour augmenter son affinité pour le Nd par le déplacement de l’équilibre d’extraction dans le sens de la formation des complexes DBAc-Nd. Avec une capacité de charge supérieure 126 g.L-1, une application remarquable du DBAc s’oriente vers le recyclage des terres rares à partir d’un lixiviat de déchet d’aimant NdFeB, précisément dans la récupération sélective du Nd, du Pr, du Dy à partir d’un lixiviat nitrique contenant le fer, le bore, le cobalt et le nickel comme métaux compétiteurs. Les essais de pertraction ont tout d’abord été effectués à co-courant et en circuit fermé sur un module à monofibre creuse en polypropylène hydrophobe. Un modèle de transfert de matière a été développé sur la base des hypothèses classiques de la théorie des résistances en série afin de décrire le mécanisme de transfert à travers la membrane et prédire le profil de concentration du Nd en fonction du temps. L’utilisation du modèle a requis entre autres paramètres d’entrée le coefficient de diffusion du Nd en phase aqueuse et dans le solvant. La technique d’Analyse de la Dispersion de Taylor (TDA) a été développée pour la détermination expérimentale des valeurs du coefficient de diffusion. Les résultats expérimentaux de l’étude du système DBAc pur / Nd sont jugés en bon accord avec les données du modèle. Les valeurs des coefficients de transfert de matière dans les films et dans la membrane indiquent que l’étape limitante dans le transfert de matière est la diffusion des complexes Nd-DBAc dans le solvant, précisément à l’intérieur des pores de la membrane et dans le film coté solvant. Cette limitation pourrait s’expliquer par une viscosité relativement plus importante du DBAc pur en comparaison de la viscosité de la phase aqueuse. Pour rappel, le coefficient de diffusion est inversement proportionnel à la viscosité dans la corrélation de Stock-Einstein. Une perspective de développement de la pertraction comme technique d’extraction/recyclage est la récupération de métaux réfractaires comme le tantale et le niobium. Les études préliminaires de recherche d’un solvant de forte affinité et de grande sélectivité présentent la propriété de la méthylacétophénone pure (MAcPh) à extraire sélectivement le tantale à partir d’un lixiviat fluorhydrique de déchet de condensateur contenant du fer, du manganèse, du nickel et de l’argent comme impuretés, avec une capacité de charge supérieure à 150 g.L-1. / Pertraction is an emerging liquid-liquid extraction technology which use a membrane barrier as surface area between the aqueous phase and solvent. It thus offers the possibility to use very emulsive solvent and / or consisting of a pure extractant without any necessity of different density with the aqueous phase. The advantage of using a pure extractant is the possibility to have a high loading capacty of solvent (>100 g.L-1). So, we have studied the feasibility of pertraction of metals of interest by using a pure extractant as solvent. The extraction of rare earth metals (neodymium (Nd), praseodymium (Pr) and dysprosium (Dy)) was chosen as the aim of this study. The approach was defined by tree steps : identification of selective solvent for lanthanids (Nd as model), set-up and optimization of pertraction module, mass transfer modeling. The screening of solvent was governed by namely three criteria : its affinity for Nd, its viscosity and solubility in water. To avoid fire risk, the flashpoint of solvent was also taken into account in the selection. In this framework, N, N-dibutylacetamide was selected especially for its moderate viscosity (<5 mPa.s) but its employment required the use of nitrates for increase its affinity for Nd. With high loading capacity (> 126 g.L-1), a remarkable application of DBAc could be its use for selectively extract Nd, Pr, Dy and separate them each other from magnet waste containing impurities such as iron, boron, nickel, cobalt. Pertraction of Nd by DBAc pure has been made in recycle mode on polypropylene hollow fiber module. The mass transfer model has been developed on the basis of conventional assumptions of resistances in series theory in order to predict the concentration of Nd at different times. It has required some input parameters such as diffusion coefficient of Nd in aqueous and organic phases. Taylor dispersion analysis (TDA) has been used for the experimental determination of diffusion coefficients. Experimental data and model results were found to be in good agreement for the system DBAc/Nd. The values of mass transfer coefficients in films and membrane indicate that the mass transfer limiting step is the diffusion of DBAc-Nd in the solvent present in the membrane pores and in the diffusional film of the solvent. This can be explained by the relative high viscosity of solvent because diffusion coefficient is inversely proportional to viscosity in Stock-Einstein correlation. A development perspective of pertraction as liquid-liquid technology is the recovery of refractory metals like tantalum (Ta) and niobium (Nb). Preliminary studies for identify selective solvent present the properties of methylacetophenone pure (MAcPh) to extract selectively Ta from hydrofluoric solution of capacitor waste containing iron, manganese, nickel and silver as impurities with a loading capacity superior than 150 g.L-1.

In this thesis I discuss three normative claims that I take to be central elements of Charles Taylor’s political thought. The first of these is Taylor’s contention that, in contemporary pluralistic societies, justifying socially prevailing norms by appealing to universally binding moral values is unlikely to promote social solidarity. Because this approach tends to downplay the goods that people realise through membership in particular associations, Taylor believes we must adopt a model of justification that does not prioritise universal over particular goods if we are to further social co-operation. A second claim Taylor defends is that commitment to the liberal value of collective self-rule implies treating patriotically motivated public service as a non-instrumental good. We should not, Taylor argues, regard collective association as nothing more than a means to satisfying private goals. Taylor advances a third claim, that is, he maintains that liberal toleration for diverse ways of life may require a perfectionist state that supports particularistic ways of life when they are threatened by decline. I offer a qualified defence of the first two claims, but suggest that the third is less compelling. I attempt to do this by evaluating Taylor’s claims against the standards of lucid argumentation that he himself lays down. In discussing social and political norms, which he describes as “advocacy” issues, Taylor argues that our normative commitments necessarily rely on an underlying social ontology. More specifically, Taylor argues that the political values we defend are those that enable us to secure the interests we have as the bearers of an identity possessing both individual and collective dimensions. In setting out the conditions that favour integrated and free identity formation we may thereby reach a clearer understanding of the political norms that we wish to endorse. I argue that, while Taylor’s ontological reflections might well incline us to accept his model of justification and his account of patriotic social commitment, they do not of themselves dispose us to accept state perfectionism.

L’écoulement entre deux cylindres coaxiaux, appelé l’écoulement de Couette-Taylor, a été étudié lorsque le cylindre intérieur tourne. Quatre dispositifs ont été utilisés avec différentes tailles d’entrefer. Les visualisations montrent l’évolution des motifs avec le nombre de Reynolds, Re. La variation du couple sur le cylindre intérieur a été déterminée en utilisant le pseudo-nombre de Nusselt, qui est une mesure du taux de dissipation d’énergie.Pour des faibles valeurs de Re, l’écoulement est laminaire et azimutal, et le couple est proportionnel à Re. Au-delà d’une valeur critique de Re, les rouleaux de Taylor apparaissent et la pente de variation du couple change brutalement. Pour de grandes valeurs de Re, les rouleaux deviennent turbulents et la pente du couple augmente à cause de la dissipation d’énergie turbulente. Le couple a été mesuré jusqu’à Re=45.000 et montre une dépendance avec le rapport de rayons des cylindres et du nombre de vortex. Avant le régime ultime de la turbulence, les états avec plus de rouleaux présentent un couple plus grand et la situation est inversée dans le régime ultime.Une étude du couple agissant sur le cylindre intérieur a été menée en présence d’un liquide viscoélastique contenant des polymères de grande masse molaire. En appliquant des cycles d’accélération-décélération de la rotation du cylindre intérieur, le couple présente une boucle d’hystérèse dont l’aire augmente avec la concentration de polymère. Les statistiques des fluctuations de la turbulence élastique ont été analysées. Le couple exercé par les vortex solitaires obtenus lors de la phase de décélération, avant la relaminarisation complète de l’écoulement, a été étudié. / The flow between two concentric cylinders, i.e., the Couette-Taylor flow, has been investigated when only the inner cylinder rotates. Four set-ups have been employed with 4 values of the radius ratio. Flow visualisations have been performed to analyse the evolution of the flow patterns with the Reynolds number, Re. The variation of the torque acting on the inner cylinder with different parameters has been quantified using the pseudo-Nusselt number, which measures the rate of energy dissipation in the flow.At low Re, the flow is laminar and azimuthal, and the torque is proportional to Re. Above a critical value of Re, Taylor vortices emerge in the flow and the slope of the torque changes drastically. At high values of Re, the vortices become turbulent and the increase rate of torque is enhanced due to the energy dissipation of turbulence. The torque measured up to Re=45 000 depends on the radius ratio of the cylinders and on the number of vortices. Below the ultimate regime of turbulence, flows containing larger number of vortices exert larger levels of torque; above it, flows containing larger number of vortices exert lower levels of torque.A specific study of the torque exerted on the inner cylinder has been carried out with viscoelastic fluids made of large-weight-molecule polymers. If acceleration-deceleration cycles of the rotation of the inner cylinder are applied, the torque exhibits a hysteretic loop, which increases with the polymer concentration. The statistics of the elastic turbulence fluctuations have been analysed. A special focus was made on the torque induced by the solitary vortices obtained in the deceleration phase, before the flow relaminarisation.

Diss. Accademia Alfonsiana, 2005. / Bibliogr.: p. [291]-318.

Στην παρούσα διατριβή αναπτύσσεται η γραμμικοποιημένη μέθοδος των πεπερασμένων διαφορών. Η μέθοδος αυτή αποτελεί νέα αριθμητική τεχνική επιλύσεως των διαφορικών εξισώσεων δευτέρας τάξεως, κανονικών και με μερικές παραγώγους και εφαρμόζεται σε εσωτερικές και εξωτερικές ροές. Συγκεκριμένα, στο πρώτο κεφάλαιο γίνεται εισαγωγή στις μεθόδους διακριτοποιήσεως μιας διαφορικής εξισώσεως και στον τρόπο επίλυσης ενός γραμμικού συστήματος αλγεβρικών εξισώσεων. Στο δεύτερο κεφάλαιο εκτίθεται η μέθοδος των Allen και Southwell για τη λύση της εξισώσεως της στροβιλότητας προκειμένου περί δισδιάστατης ροής και η τροποποίηση και βελτίωση της μεθόδου από τον Dennis. Εν συνεχεία περιγράφεται η περαιτέρω βελτίωση της μεθόδου, διά της οποίας ο πίνακας του συστήματος των συντελεστών των αγνώστων καθίσταται διαγωνίως υπέρτερος. Στο τρίτο κεφάλαιο η βελτιωμένη μέθοδος επεκτείνεται στις τρεις διαστάσεις με μεταβλητούς συντελεστές και εφαρμόζεται στην λύση αντιστοίχου προβλήματος ροής ιδανικού ρευστού εντός σωλήνα. Στο τέταρτο κεφάλαιο η παρούσα μέθοδος γενικεύεται μεταβλητούς συντελεστές. Στο πέμπτο κεφάλαιο επιλύεται η εξίσωση της στροβιλότητας στις τρεις διαστάσεις σε σύστημα κυλινδρικών συντεταγμένων και ο αλγόριθμος εφαρμόζεται στο πρόβλημα του von Kármán. Τέλος, στο έκτο κεφάλαιο εξετάζεται η περίπτωση της αριθμητικής εξομοίωσης στροβίλων Taylor προκειμένου περί ροής ιξώδους ρευστού, το οποίο περιέχεται εντός σφαιρικού κελύφους, η δε κίνηση του ρευστού προκαλείται από την διαφορική περιστροφή των δύο σφαιρών γύρω από την κοινή διάμετρό τους. / In the present dissertation a numerical technique is developed on the solution of ordinary and/or partial differential equations of second order with variable coefficients. In particular, in the first chapter we make a general introduction to the discretisation methods and to the methods of solution of a linear system of algebraic equations. In the second chapter the method of Allen and Southwell on the solution of the vorticity equation in two dimensional flow is presented as well as its modification and improvement by Dennis. The contribution of the present work is on the further improvement of the previous method, such that the matrix of the coefficients of the unknowns becomes diagonally dominant and its extension to three dimensional problems. The consecutive steps of the method (Linearized Finite Difference Method, LFDM) are worked out on the ordinary differential equation with variable coefficients. Next, the method is applied to the solution of two problems from Fluid Mechanics. In the third chapter the improved method is extended to three dimensions with variable coefficients. Accordingly the method is applied to the solution of the equations of motion of a perfect fluid moving in a straight tube. In the fourth chapter the present method is generalized with variable coefficients. In the fifth chapter the three dimensional equation of the vorticity expressed in cylindrical coordinates is solved and the results are applied to the von Kármán problem. Finally in the sixth chapter we use this method to simulate Taylor vortices in spherical annular flow in the presence of heat, the motion of the fluid being induced by the differencial rotation of two spheres about their common diameter.