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Modélisation et calcul scientifique

Le séminaire de Modélisation et Calcul Scientifique est une série mensuelle d'exposés destinés aux équipes de mathématiques appliquées au sens large, du doctorant au chercheur, ainsi qu'aux ingénieurs d'entreprises environnantes. Les intervenants - mathématiciens, ingénieurs, physiciens, etc. - exposent leurs méthodes et résultats dans les différents domaines de la modélisation et de la simulation numérique.
D'une durée de 45 minutes suivies de questions/réponses, les exposés ont lieu sur le site de Rocquencourt, bâtiment 1, amphithéâtre A. Turing à 14h, café dès 13h45.

8 février: François Graner, Institut Curie, Paris

"From cells to tissues: physical modelling of the collective behaviour of embryonic cells"
To understand how cellular mechanical properties act on the level of a tissue, where they are implied in morphogenesis, it has been proposed that cells act as soap bubbles or molecules in a liquid. We test these analogies between tissues and physical systems with a computational model, in collaboration with experimentalists.
In the retina of Drosophila, the packing of cells has been compared to soap bubble packing. We find that the resemblance is not due to the physical resemblance of cells and bubbles, but to a similar organisation on the collective level: cells in a tissue tile the space, like bubbles in a foam, thereby influencing each other's shapes.
The spontaneous sorting of cells of different types has been compared to the demixing of liquids. While in liquids this behaviour is due to the attraction between molecules, we find that in aggregates of zebrafish germlayer cells differential contraction of the cytoskeleton plays a role as well.
Compression of an aggregate of cells has been analysed as if the aggregate behaved as a liquid drop, where only the surface tension determines its properties. However, individual cells in the aggregate deform and rearrange, and solid-like stresses inside the aggregate co-determine its shape and forces.
The widely used physical analogies prove thus to be incomplete, but interesting. We propose a distinctive description, in which an aggregate or tissue is a collection of closely packed living cells that change shape and rearrange. This approach allows to study how cell adhesion, cortical tension and the cellular fluctuations govern the behaviour on the collective level, and on morphogenesis.
We are now applying it to the tissue development during the metamorphosis of the fruit fly."

5 mars : Clair Poignard, Inria Bordeaux Sud-Ouest

Titre : QUELQUES RESULTATS SUR LA MODELISATION DE L'ELECTROPORATION DES CELLULES

La modélisation électrique des cellules englobe deux domaines de recherche distincts : l’ ́electrophysiologie qui consiste à décrire évolution des concentrations ioniques intra- et extra- cellulaires afin d’en déduire l'évolution du potentiel transmembranaire de la cellule, et le génie  électrique qui considère la cellule comme un matériau diélectrique et qui décrit le potentiel (ou le champ)  électrique dans toute la cellule. Ces deux approches ne sont généralement pas couplées. Cependant dans le phénomène électroperméabilisation des celllules, il est à la fois nécessaire de connaître le potentiel  électrique dans toute la cellule, afin de savoir s’il y a perméabilisation ou non de la membrane, tout en décrivant les flux ioniques à travers la membrane pour connaître, par exemple, les quantités de substances actives pénétrant dans la cellule, ainsi que l'évolution du volume cellulaire pendant le processus. En se basant sur des résultats d’analyse asymptotique, nous justifierons les modèles électriques des cellules et un premier modèle d'électroporation cellulaire sera présenté. Ensuite nous présenterons une approche  électrophysiologique liant potentiel transmembranaire, volume cellulaire et flux ioniques. Nous concluerons par un couplage possible des deux phénomènes pour apporter des premiers  éléments de réponse dans la modélisation d'électroperméabilisation des cellules.
Ce travail est effectué avec le laboratoire de Vectorologie Physique et Thérapies anti-Cancéreuses de l’IGR, le laboratoire de Mathématiques de Versailles et le LIX de l’Ecole Polytechnique.

5 avril : Marius Tucsnak, Inria Grand Est

Title: Control and Optimization of Low Reynolds number swimming

This presentation considers a class of problems arising in the study of self-propelling of solids in a viscous fluid. The main application we have in mind consists in using control theoretical techniques to understand self-propelled motion of a solid (fishes, swimming robots, submarines, micro-organisms) in a viscous fluid. These problems, in which the solid is propelling by changing its shape, raise important theoretical and computational challenges.
We focus on the low Reynolds number case, appearing in the study of locomotion of microscopic aquatic organisms (like spermatozoids) or of micro and nano swimming robots. Since the fluid is modeled by the elliptic Stokes system, in which the time appears only as a parameter in the coupling equations with the fluid, the coupled model is, in principle, quite simple: we have a system of nonlinear ODE’s on a finite dimensional manifold. However, an important difficulty has to be solved from the first stage of the problem, which consists in obtaining the wellposedness of the system. Indeed, in order to apply Cauchy-Lipschitz type theorems, it is essential to prove that the solution of the exterior Stokes problem depends smooth enough on the shape of the interface.   The next question which is studied is the controllability of the system, which is investigated by combining perturbation results with the classical Chow’s theorem. We end up with time optimal control problems, which are studied from both theoretical and numerical view points.

17 mai : Mike Park, Computational AeroSciences Branch, NASA Langley Research Center

Title: Grid Adaption to Improve Engineering Outputs of Reynolds-Averaged Navier-Stokes Simulations

Controlling discretization error is a challenge in numerical simulation. This difference between the solution to the original continuous partial differential equation and its discrete representation is a product of many factors including the grid. Grid adaptation is specified by an anisotropic metric and local modifications are applied to reduce the errors induced by the grid. Not all errors in the domain impact the outputs of engineering interest equally. The adjoint solution is employed to determine the transport and relative importance of local error sources to focus adaptation on improving the calculation of a specific output or goal. Grid adapted examples from recent workshops include turbulent Reynolds-averaged Navier-Stokes simulations of shock boundary layer interaction and a three dimensional high lift system. A large simulation framework is required to perform these simulations on high performance computing resources. A brief description of the NASA FUN3D simulation framework and its software development practices will also be presented.

Mots-clés : Modélisation et calcul scientifique Paris - Rocquencourt Séminaire

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