Analysis and Simulations of a Nonlocal Gray-Scott Model

The Gray-Scott model is a set of reaction-diffusion equations that describes chemical systems far from equilibrium. Interest in this model stems from its ability to generate spatio-temporal structures, including pulses, spots, stripes, and self-replicating patterns. We consider an extension of this model in which the spread of the different chemicals is assumed to be nonlocal, and can thus be represented by an integral operator. In particular, we focus on the case of strictly positive, symmetric, $L^1$ convolution kernels that have a finite second moment. Modeling the equations on a finite interval, we prove the existence of small-time weak solutions in the case of nonlocal Dirichlet and Neumann boundary constraints. We then use this result to develop a finite element numerical scheme that helps us explore the effects of nonlocal diffusion on the formation of pulse solutions.Comment: 28 pages, 2 figure

Lamia e le sue metamorfosi

Il lavoro analizza la figura di Lamia alla luce delle testimonianza testuali e iconografiche. L'obiettivo è quello di distinguerla dalle altre figure di demoni femminili presenti nel panorama greco dei demoni rapitori di bambini e di comprendere se la sua androginia sia un elemento originario o acquisito in seguito ai contatti culturali con il Vicino Oriente. Attraverso lo studio delle fonti è quindi possibile seguire questa figura e tutte le metamorfosi da lei subite, sia nella cultura greca sia in quella latina

Las puertas de Ditis: estudio comparativo sobre las posibilidades de interacción entre vivos y muertos en el Mediterráneo antiguo

La presente tesis de doctorado tiene como objetivo el estudio de las puertas de acceso a los infiernos o, por decirlo mejor, los diversos canales de comunicación arquitectónicos que permitían al mundo de los muertos entrar en comunicación con el de los vivos y viceversa. Este estudio está basado en el análisis de los textos, mayoritariamente en lengua original y su traducción, interpretados a la luz de la crítica filológica y la lingüística indoeuropea, aunque también se incluyen los testimonios arqueológicos, pinturas cerámicas y pinturas parietales de las tumbas y esculturas, de modo que estos tipos de fuentes entran en diálogo entre sí, valorándose y complementándose bajo la mirada de los estudios de religión antigua..

Stabilisation non linéaire des équations de la magnétohydrodynamique et applications aux écoulements multiphasiques

The investigations presented in this manuscript focus on the numerical approximation of the magnetohydrodynamics (MHD) equations and on their stabilization for problems involving either large kinetic Reynolds numbers or multiphase flows. We validate numerically a new Large Eddy Simulation (LES) model, called entropy viscosity, on flows driven by precessing cylindrical containers or counter-rotating impellers (Von Kármán flow). These studies are performed with SFEMaNS MHD-code developed by J.-L. Guermond and C. Nore since 2002 for axisymmetric geometries. This code is based on a spectral decomposition in the azimuthal direction and a Lagrange finite element approximation in a meridian plane. We adapt a pseudo-penalization method to report the action of rotating impellers that extends the range of SFEMaNS's applications to any geometry. We also present an original approximation method of the Navier-Stokes equations with variable density. This method uses the momentum as variable and stabilizes both mass and momentum equations with the same entropy viscosity.Les travaux présentés dans ce manuscrit se concentrent sur l'approximation numérique des équations de la magnétohydrodynamique (MHD) et sur leur stabilisation pour des problèmes caractérisés par des nombres de Reynolds cinétique élevés ou par des écoulements multiphasiques. Nous validons numériquement un nouveau modèle de Simulation des Grandes Echelles (ou Large Eddy Simulations, LES), dit de viscosité entropique, sur des écoulements de cylindre en précession ou créés par des turbines contra-rotatives (écoulement de Von Kármán). Ces études sont réalisées avec le code MHD SFEMaNS développé par J.-L. Guermond et C. Nore depuis 2002 pour des géométries axisymétriques. Ce code est basé sur une décomposition spectrale dans la direction azimutale et des éléments finis de Lagrange dans un plan méridien. Nous adaptons une méthode de pseudo-pénalisation pour prendre en compte des turbines en mouvement, ce qui étend le code SFEMaNS à des géométries quelconques. Nous présentons aussi une méthode originale d'approximation des équations de Navier-Stokes à densité variable qui utilise la quantité de mouvement comme variable et la viscosité entropique pour stabiliser les équations de la masse et du mouvement

On the schedulability of deadline-constrained traffic in TDMA Wireless Mesh Networks

In this paper, we evaluate the schedulability of traffic with arbitrary end-to-end deadline constraints in Wireless Mesh Networks (WMNs). We formulate the problem as a mixed integer linear optimization problem, and show that, depending on the flow aggregation policy used in the network, the problem can be either convex or non-convex. We optimally solve the problem in both cases, and prove that the schedulability does depend on the aggregation policy. This allows us to derive rules of thumb to identify which policy improves the schedulability with a given traffic. Furthermore, we propose a heuristic solution strategy that allows good suboptimal solutions to the scheduling problem to be computed in relatively small times, comparable to those required for online admission control in relatively large WMNs