Internship in Mathematics on Stochastic dynamics of particles in turbulence

_Le descriptif de l’offre ci-dessous est en Anglais_ TYPE DE CONTRAT : Stage NIVEAU DE DIPLÔME EXIGÉ : Bac + 5 ou équivalent FONCTION : Stagiaire de la recherche A PROPOS DU CENTRE OU DE LA DIRECTION FONCTIONNELLE The Inria Université Côte d’Azur center counts 36 research teams as well as 7 support departments. The center's staff (about 500 people including 320 Inria employees) is made up of scientists of different nationalities (250 foreigners of 50 nationalities), engineers, technicians and administrative staff. 1/3 of the staff are civil servants, the others are contractual agents. The majority of the center’s research teams are located in Sophia Antipolis and Nice in the Alpes-Maritimes. Four teams are based in Montpellier and two teams are hosted in Bologna in Italy and Athens. The Center is a founding member of Université Côte d'Azur and partner of the I-site MUSE supported by the University of Montpellier. CONTEXTE ET ATOUTS DU POSTE CONTEXT : The modeling of a turbulent flow, and of the particles transported in it, offers a vast field of investigation for stochastic approaches. These approaches are nowadays enriched and renewed to take into account more and more complex phenomena, extending and improving the existing computational approaches in fluid mechanics, with multiple applications, both environmental and industrial. By adopting an interdisciplinary approach, the Calisto team develops original and coherent stochastic models in this field, based on two complementary points of view, the first is the classical framework of statistical descriptions of turbulence (so-called mean fields) where only limited information is available; the second is the detailed approach, where the fine description of the phenomena is obtained from direct numerical simulations, allowing the extraction of information on the instantaneous structures of the flow. MISSION CONFIÉE The CaliSto team at Inria is looking for a Master trainee, on the topics of stochastic analysis and probabilistic numerical analysis, motivated to pursue with PhD thesis. https://team.inria.fr/calisto/ PRINCIPALES ACTIVITÉS TOPIC DESCRIPTION : The dynamics of a point particle in a homogeneous and isotropic turbulent flow is commonly described (in the mean field sense) by a diffusion process. However, this approach leaves room for significant improvements as soon as one or more of the above hypotheses are made more complex, either with respect to the nature of the particle -non-spherical, non-point (i.e. flexible particle, filament)- or of the turbulence -non-isotropic flow, intermittent effect. In these situations super diffusion effects, non-reversibility effects, memory effects are to be introduced. Starting from relatively simplified particle dynamics situations (Brownian fluctuations), the objective of the internship is to list and study mathematical properties of gradually more complex models, by extending the Brownian fluctuations to Levy fluctuations, for some specific jump measurements, and/or by introducing a coupling of the diffusion with auxiliary stochastic processes, to move away from models with Gaussian responses. The analysis could be completed by aspects of approximations, and the analysis of specific numerical schemes. A continuation of the work in PhD is strongly encouraged, in the continuity of this topic (funding acquired). COMPÉTENCES EXPECTED PROFILE : 3rd year master student in mathematics, (French Master 2) with a background in stochastic analysis. Stochastic modeling and numerical probability will be also appreciate. AVANTAGES * Subsidized meals * Partial reimbursement of public transport costs * Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.) * Possibility of teleworking (after 6 months of employment) and flexible organization of working hours * Professional equipment available (videoconferencing, loan of computer equipment, etc.) * Social, cultural and sports events and activities * Access to vocational training * Social security coverage