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Les événements de juillet 2018

Séminaire

  • Équipe Analyse Appliquée (AA)

    • Mardi 3 juillet 11:00-12:00 - Samir SALEM - CEREMADE, Université Paris Dauphine

      Propagation of chaos for some 2 dimensional fractional Keller Segel equation in dominated diffusion and fair competition cases

      Résumé : In this work we deal with the local in time propagation of chaos without cut-off for some two dimensional fractional Keller Segel models. More precisely the diffusion considered here is given by the fractional Laplacian operator −(−∆) ^(a/2) with a ∈ (1, 2) and the singularity of the interaction is of order |x|^(1−α) with α ∈]1, a]. In the case α ∈ (1, a) we prove a complete propagation of chaos result, proving the Γ-l.s.c property of the fractional Fisher information, already known for the classical Fisher information, using a result of [4]. In the fair competition case ([1]) a = α, we only prove a convergence/consistency result in a sub-critical mass regime, similarly as the result obtained for the classical Keller-Segel equation in [2].
      References
      [1] J. Carrillo, V. Calvez, F. Hoffmann. Equilibria of homogeneous functionals in the fair-competition regime Nonlinear Analysis, (2016).
      [2] N. Fournier, B. Jourdain. Stochastic particle approximation of the Keller-Segel equation and two-dimensional generalization of Bessel processes. Accepted at Ann. Appl. Probab.
      [3] N. Fournier, M. Hauray, S. Mischler. Propagation of chaos for the 2D viscous vortex model. J. Eur. Math. Soc., Vol. 16, No 7, 1423-1466, 2014.
      [4] M. Hauray, S. Mischler. On Kac’s chaos and related problems, J. Funct. Anal., Volume 266, P. 60556157,(2014).

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      Samir SALEM

      Lieu : CMI, salle de séminaire R164 (1er étage) - I2M - Château-Gombert
      39 rue Frédéric Joliot-Curie
      13453 MARSEILLE cedex 13

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  • Équipe Géométrie, Dynamique, Arithmétique et Combinatoire et leurs interactions (GDAC)

    • Vendredi 6 juillet 11:00-12:00 - Diana DAVIS - Swarthmore College

      Tiling billiards and interval exchange transformations

      Résumé : TBA

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      Diana DAVIS

      Lieu : FRUMAM - Aix-Marseille Université - Site St Charles
      3, place Victor Hugo - case 39
      13331 MARSEILLE Cedex 03

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    • Vendredi 13 juillet 11:00-12:00 - Sergei KOROTKIKH - Higher School of Economics, Moscow

      Markov processes on the infinite-dimensional simplex

      Résumé : My talk is devoted to the family of markov processes on the infinite-dimensional simplex, initially constructed as the infinitely-many-neutral-allels diffusion model by Ethier and Kurth in 1981, and later generalised by Petrov, Borodin and Olshanski. These are Feller processes which are defined infinitesimally in terms of generators (operators acting on the space of functions on the simplex). I will describe several global properties which can be recovered form the infinitesimal definition and explain how these properties follow from the study of the generators.

      Lieu : FRUMAM - Aix-Marseille Université - Site St Charles
      3, place Victor Hugo - case 39
      13331 MARSEILLE Cedex 03

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  • Équipe Signal et Image (SI)

    • Vendredi 6 juillet 11:00-12:00 - Herman CLERCX - I2M, Aix-Marseille Université & Fluid Dynamics Laboratory, Department of Applied Physics, Eindhoven University of Technology, Eindhoven

      Rotating Rayleigh-Benard convection : probing the transition to the rotation-dominated regime

      Résumé : Séminaire commun I2M (équipe ALEA-SI) / IRPHE (Seminar I2M / IRPHE)
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      Most geo- and astrophysical flows are driven by strong thermal forcing and affected by high rotation. In these systems, direct measurements of the physical quantities are not possible due to their large scales, remoteness and complexity. A model containing the main physical constituents is rather beneficial. This approach is given by the problem of rotating Rayleigh-Benard convection (RRBC) : a rotating fluid layer heated from below and cooled from above. For large-scale systems, the governing parameters of RRBC take extreme values, leading to a regime of geostrophic turbulence.
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      Background rotation causes different flow structures and heat transfer efficiencies in Rayleigh-Benard convection. Three main regimes are known : rotation-unaffected (regime I), rotation-affected (regime II) and rotation-dominated (regime III). Regimes I and II are easily accessible with experiments and numerical simulations (see right figure [1]), thus they have been extensively studied, see for a recent review [2]. On the other hand, access to regime III is more troublesome. Thus, regime III and the transition to this regime are less explored. Approaching the geostrophic regime of rotating convection, where the flow is highly turbulent and at the same time dominated by the Coriolis force, typically requires dedicated setups with either extreme dimensions or troublesome working fluids (e.g., cryogenic helium). In this study, we explore the possibilities of entering the geostrophic regime of rotating convection with classical experimental tools : a table-top conventional convection cell with a height of 0.2 m and water as the working fluid [3], see figure below. In order to examine our experimental measurements, we compare the spatial vorticity autocorrelations with the statistics from simulations of geostrophic convection reported earlier [4]. Our findings show that we have indeed access to the geostrophic convection regime and can observe the signatures of the typical flow features reported in the aforementioned simulations. As a next step we explored the role of coherent flow structures on the transition to regime III in RRBC. There are two main hypotheses proposed for the driving mechanisms of the transition to regime III one of them directly related to flow coherency. These hypotheses are usually examined through different parameters such as viscous and thermal boundary layers thicknesses and heat transfer efficiency [5,6]. In this work, we study regime III and these hypotheses from a new perspective : Lagrangian velocity and acceleration fluctuations and autocorrelations of tracers from experiments. We have found that the transition to regime III coincides with three phenomena ; the vertical motions are suppressed, the vortical plumes penetrate further into the bulk and the vortical plumes interact less with their surroundings. These findings allow us to evaluate the available hypotheses and to understand more about regime III [7].
      These regime transitions will be discussed in this talk.
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      [1] R.J.A.M. Stevens, H.J.H. Clercx and D. Lohse, PRE 86, 056311 (2012).
      [2] R.J.A.M. Stevens, H.J.H. Clercx and D. Lohse, EJMB/F 40, 41-49 (2013).
      [3] D. Nieves, A.M. Rubio and K. Julien, PoF 26, 086602 (2014).
      [4] H. Rajaei, R.P.J. Kunnen and H.J.H. Clercx, PoF 29, 045105 (2017).
      [5] E.M. King, S. Stellmach, J. Noir, U. Hansen and J.M. Aurnou, Nature 457, 301-304 (2009).
      [6] K. Julien, E. Knobloch, A.M. Rubio and G.M. Vasil, PRL 109, 254503 (2012).
      [7] H. Rajaei, K.M.J. Alards, R.P.J. Kunnen and H.J.H. Clercx, submitted to JFM (2018).
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      Herman CLERCX

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      Accès IRPHE

      Lieu : IRPHE - Technopôle de Château-Gombert
      49, rue Joliot Curie - B.P. 146
      13384 Marseille Cedex 13, France

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  • Équipe Logique de la Programmation (LDP)

    • Jeudi 5 juillet 11:00-12:30 - Valentin BLOT - LRI, Université Paris-Sud

      Extensional and intensional semantic universes : a denotational model of dependent types

      Résumé : We describe a dependent type theory, and a denotational model for it, that incorporates both intensional and extensional semantic universes.
      In the former, terms and types are interpreted as strategies on certain graph games, which are concrete data structures of a generalized form, and in the latter as stable functions on event domains. The concrete data structures themselves form an event domain, with which we may interpret an (extensional) universe type of (intensional) types. A dependent game corresponds to a stable function into this domain ; we use its trace to define dependent product and sum constructions as it captures precisely how unfolding moves combine with the dependency to shape the possible interaction in the game. Since each strategy computes a stable function on CDS states, we can lift typing judgements from the intensional to the extensional setting, giving an expressive type theory with recursively defined type families and type operators. We define an operational semantics for intensional terms, giving a functional programming language based on our type theory, and prove that our semantics for it is computationally adequate. By extending it with a simple non-local control operator on intensional terms, we can precisely characterize behaviour in the intensional model. We demonstrate this by proving full abstraction and full completeness results.

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      Valentin BLOT

      Lieu : Salle des séminaires 304-306 (3ème étage) - Institut de Mathématiques de Marseille (UMR 7373)
      Site Sud - Bâtiment TPR2
      Campus de Luminy, Case 907
      13288 MARSEILLE Cedex 9

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  • Habilitations à Diriger des Recherches (HDR)

    • Vendredi 6 juillet 10:30-12:00 - Stéphane CHARPENTIER - I2M, AGT, Aix-Marseille Université

      Opérateurs de composition sur certains espaces de fonctions - Universalité en théorie des opérateurs

      Résumé : Soutenance HDR
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      Soutenance d’Habilitation à Diriger des Recherches
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      TBA
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      Mots clés : TBA
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      Membres du jury :
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      TBA
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      Stéphane CHARPENTIER

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      (lien à venir)


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      Lieu : CMI, salle de séminaire R164 (1er étage) - I2M - Château-Gombert
      39 rue Frédéric Joliot-Curie
      13453 MARSEILLE cedex 13

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  • Soutenances de thèses de doctorat

    • Vendredi 6 juillet 10:30-12:00 - Stéphane CHARPENTIER - I2M, AGT, Aix-Marseille Université

      Opérateurs de composition sur certains espaces de fonctions - Universalité en théorie des opérateurs

      Résumé : Soutenance HDR
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      Soutenance d’Habilitation à Diriger des Recherches
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      TBA
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      Mots clés : TBA
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      Membres du jury :
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      TBA
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      JPEG - 48.3 ko
      Stéphane CHARPENTIER

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      PNG - 7.7 ko
      (lien à venir)


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      Lieu : CMI, salle de séminaire R164 (1er étage) - I2M - Château-Gombert
      39 rue Frédéric Joliot-Curie
      13453 MARSEILLE cedex 13

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