Les écoulements de mélanges de deux fluides incompressibles, miscibles et ayant des densités très différentes sont gouvernés par les équations de Navier-Stokes non-homogène, couplées à une équation de convection-diffusion décrivant l'évolution de la composition du mélange. Nous proposons un algorithme associant la méthode des caractéristiques, pour la discrétisation des termes de transport, à la méthode des éléments finis avec une adaptation automatique de maillage, et démontrons que la solution de cet algorithme converge vers la solution exacte lorsque les pas de discrétisation tendent vers zéro. La robustesse de cet algorithme permet d'obtenir les premiers résultats de simulations numériques directes d'écoulements d'échange à très forte différence de densité, et de les valider par comparaison avec des expériences. Des écoulements de nuages denses sur des pentes sont simulés, et permettent d'analyser l'influence de la différence de densité sur les écoulements d'avalanches.

<p>The paper contains comment, clarification and criticism, even constructive criticism, of some theses that have been put forward by Laurence Bonjour in his In Defense of Pure Reason.</p><p>It presents a concept of experience that deals with the relation between cognizer and object of experience that has a great similarity to that of Bonjour. Through analysis it is shown that the concept of a priori entails that Bonjour has two concepts of a priori, a narrow and a broad one. The narrow one is, in my own words: According to moderate rationalism a proposition p is a priori justified if and only if you apprehend that p must be true in every possible world. This doesn’t mean that Bonjour doesn’t believe in an epistemological, metaphysical and semantic realm. The broad one does not mention anything about possible worlds.</p><p>Casullo in his A priori justification rejects Bonjour’s argument against Quine’s coherentism. A defense is put forward with the concept ‘an ideal of science for apparent rational insights’. The concept of axiomatic system and foundationalism is used. If we assume that the colour proposition ‘nothing can be red all over and green all over at the same time’ has the meaning that we, in this very moment, are representing a property in the world, thus we have an argument of superposition for the correctness of the proposition. The ground for this argumentation relies on the identification of colours with superposing electromagnetic waves.</p>

<p>The technique of volume rendering can be a powerful tool when visualizing 3D medical data sets. Its characteristic of capturing 3D internal structures within a 2D rendered image makes it attractive in the analysis. However, the applications that implement this technique fail to reach out to most of the supposed end-users at the clinics and radiology departments of today. This is primarily due to problems centered on the design of the Transfer Function (TF), the tool that makes tissues visually appear in the rendered image. The interaction with the TF is too complex for a supposed end-user and its capability of separating tissues is often insufficient. This thesis presents methods for detecting the regions in the image volume where tissues are contained. The tissues that are of interest can furthermore be identified among these regions. This processing and classification is possible thanks to the use of a priori knowledge, i.e. what is known about the data set and its domain in advance. The identified regions can finally be visualized using tissue adapted TFs that can create cleaner renderings of tissues where a normal TF would fail to separate them. In addition an intuitive user control is presented that allows the user to easily interact with the detection and the visualization.</p>

The paper contains comment, clarification and criticism, even constructive criticism, of some theses that have been put forward by Laurence Bonjour in his In Defense of Pure Reason. It presents a concept of experience that deals with the relation between cognizer and object of experience that has a great similarity to that of Bonjour. Through analysis it is shown that the concept of a priori entails that Bonjour has two concepts of a priori, a narrow and a broad one. The narrow one is, in my own words: According to moderate rationalism a proposition p is a priori justified if and only if you apprehend that p must be true in every possible world. This doesn’t mean that Bonjour doesn’t believe in an epistemological, metaphysical and semantic realm. The broad one does not mention anything about possible worlds. Casullo in his A priori justification rejects Bonjour’s argument against Quine’s coherentism. A defense is put forward with the concept ‘an ideal of science for apparent rational insights’. The concept of axiomatic system and foundationalism is used. If we assume that the colour proposition ‘nothing can be red all over and green all over at the same time’ has the meaning that we, in this very moment, are representing a property in the world, thus we have an argument of superposition for the correctness of the proposition. The ground for this argumentation relies on the identification of colours with superposing electromagnetic waves.

Kant is famous for his use of transcendental arguments in the transcendental deduction. This thesis examines how such a transcendental argument is used within Kant’s methodological framework. Following the work of Henrich and Walker, the paper asks whether transcendental arguments in the Critique of Pure Reason are compatible with Kant’s methodology in general. We find that these arguments and Kant’s methodology are compatible, and that transcendental arguments are indeed very weak arguments by Walker’s standards. However, the entire transcendental deduction should be understood as a deduction writing that uses transcendental arguments particularly effectively according to Kant’s own methodological standards.

It is widely believed that we have immediate, introspective access to the content of our own thoughts. This access is assumed to be privileged in a way that our access to the thought content of others is not. It is also widely believed that, in many cases, thought content is individuated according to properties that are external to the thinker's head. I will refer to these theses as privileged access and content externalism, respectively. Though both are widely held to be true, various arguments have been put forth to the effect that they are incompatible. This charge of incompatibilism has been met with a variety of compatibilist responses, each of which has received its own share of criticism. In this thesis, I will argue that a contrastive account of self-knowledge is a novel compatibilist response that shows significant promise.

The technique of volume rendering can be a powerful tool when visualizing 3D medical data sets. Its characteristic of capturing 3D internal structures within a 2D rendered image makes it attractive in the analysis. However, the applications that implement this technique fail to reach out to most of the supposed end-users at the clinics and radiology departments of today. This is primarily due to problems centered on the design of the Transfer Function (TF), the tool that makes tissues visually appear in the rendered image. The interaction with the TF is too complex for a supposed end-user and its capability of separating tissues is often insufficient. This thesis presents methods for detecting the regions in the image volume where tissues are contained. The tissues that are of interest can furthermore be identified among these regions. This processing and classification is possible thanks to the use of a priori knowledge, i.e. what is known about the data set and its domain in advance. The identified regions can finally be visualized using tissue adapted TFs that can create cleaner renderings of tissues where a normal TF would fail to separate them. In addition an intuitive user control is presented that allows the user to easily interact with the detection and the visualization.

Distributed optimal control problems with transient convection dominated diffusion convection reaction equations are considered. The problem is discretized in space by using three types of discontinuous Galerkin (DG) method: symmetric interior penalty Galerkin (SIPG), nonsymmetric interior penalty Galerkin (NIPG), incomplete interior penalty Galerkin (IIPG). For time discretization, Crank-Nicolson and backward Euler methods are used. The discretize-then-optimize approach is used to obtain the finite dimensional problem. For one-dimensional unconstrained problem, Newton-Conjugate Gradient method with Armijo line-search. For two-dimensional control constrained problem, active-set method is applied. A priori error estimates are derived for full discretized optimal control problem. Numerical results for one and two-dimensional distributed optimal control problems for diffusion convection equations with boundary layers confirm the predicted orders derived by a priori error estimates.

In this paper, we study the partial Fourier method for treating the Lamé equations in three-­dimensional axisymmetric domains subjected to nonaxisymmetric loads. We consider the mixed boundary value problem of the linear theory of elasticity with the displacement u, the body force f \in (L_2)^3 and homogeneous Dirichlet and Neumann boundary conditions. The partial Fourier decomposition reduces, without any error, the three­dimensional boundary value problem to an infinite sequence of two­dimensional boundary value problems, whose solutions u_n (n = 0,1,2,...) are the Fourier coefficients of u. This process of dimension reduction is described, and appropriate function spaces are given to characterize the reduced problems in two dimensions. The trace properties of these spaces on the rotational axis and some properties of the Fourier coefficients u_n are proved, which are important for further numerical treatment, e.g. by the finite-element method. Moreover, generalized completeness relations are described for the variational equation, the stresses and the strains. The properties of the resulting system of two­dimensional problems are characterized. Particularly, a priori estimates of the Fourier coefficients u_n and of the error of the partial Fourier approximation are given.

Le contourage des ventricules cardiaques sur IRM est nécessaire à la détermination de la fonction contractile du cœur. Cette tâche est difficile, en particulier pour le ventricule droit (VD), due au flou aux frontières des cavités, aux irrégularités des intensités et à sa forme complexe et variable. Peu de travaux ont cependant été réalisés afin de résoudre cette problématique de segmentation. Dans ce but, nous avons proposé et développé deux méthodes de segmentation basées sur la méthode des coupes de graphe (GC), à laquelle nous avons incorporé des a priori de forme. La première méthode, semi-automatique, repose sur une carte d'a priori statistique créée à base d'Analyses en Composantes Principales et intégrée à la méthode des GC binaires. La seconde, automatique, permet la segmentation d'un ensemble d'objets par GC multi-labels à partir d'un modèle de forme probabiliste basé sur le recalage et la fusion d'atlas. Ces méthodes ont été évaluées sur une base importante d'IRM cardiaques, composée de 48 patients. Une comparaison aux méthodes de l'état de l'art pour cette application à travers le challenge de segmentation du VD MICCAI'12, que nous avons organisé, montre l'efficacité de nos méthodes.