Princeton/Hydro, MHD, Astro - Département de Physique de l'Ecole Normale supérieure

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Princeton/Hydro, MHD, Astro

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Stages L3
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Actualités : Séminaire de Recherche ICFP
du 14 au 18 novembre 2022 :
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Contact - Secrétariat de l’enseignement :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

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Prochain Séminaire de la FIP :
Accéder au programme

Retrouvez toutes les informations pour vos stages :
Stages L3
Stages M1 ICFP

Actualités : Séminaire de Recherche ICFP
du 14 au 18 novembre 2022 :
Retrouvez le programme complet

Contact - Secrétariat de l’enseignement :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

Responsable : Daniel LECOANET, Princeton University, Center for Theoretical Science and Department of Astrophysical Sciences
lecoanet@princeton.edu
http://www.princeton.edu/~lecoanet/index.html

Project 1 : Nonlinear optimization and large deviation theory in pattern formation & fluid dynamics

Nonlinear optimization techniques have recently been applied in fluid dynamics to understand the subcritical transition to turbulence in several parallel shear flow configurations. The adjoint method has been used to find the lowest energy single perturbation which can lead to turbulence. The goal of this project is to develop and use similar techniques to find the optimal time-dependent perturbation in a simplified pattern formation system, the Swift-Hohenberg equation. This time-dependent perturbation is the so-called ``instanton’’ of large deviation theory, and is the most likely path to transition between equilibrium states under low amplitude noise. We will use the open-source, pseudo-spectral code Dedalus to simulate the Swift-Hohenberg equation, which exhibits many localized equilibria, and study the transitions between these states. This includes calculating the equilibria, the optimal single perturbations between them, as well as the instantons connecting these states. The optimization techniques developed for the Swift-Hohenberg equation will then be applied to study the evolution of 2D vortex systems.

Project 2 : Testing the mean-field electrodynamic theory of large-scale dynamos

Three dimensional simulations of the magneto-rotational instability in large domains show the organization of small-scale magnetic field into coherent large-scale fields which undergo quasi-regular reversals. One possible explanation of this phenomenon is given by mean-field electrodynamics, in which the correlation of small-scale velocities and magnetic fields are parameterized based on their influence on large-scale fields. However, this theory relies on a scale separation between small and large scales which is seldom realized in systems of interest. The goal of this project is to calculate the small-scale correlations directly from three dimensional simulations of the magneto-rotational instability, and then use these to simulate the simpler equations of mean-field electrodynamics in Dedalus, an open-source pseudo-spectral code. These calculations will test the various assumptions of the mean-field electrodynamics framework, and identify which correlation terms are important to explain the emergence and evolution of the large scale magnetic field.

Accès rapides

Prochain Séminaire de la FIP :
Accéder au programme

Retrouvez toutes les informations pour vos stages :
Stages L3
Stages M1 ICFP

Actualités : Séminaire de Recherche ICFP
du 14 au 18 novembre 2022 :
Retrouvez le programme complet

Contact - Secrétariat de l’enseignement :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr