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Dynamical systems and chaos

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Stages L3
Stages M1 ICFP

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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Lectures : Stephan Fauve
Exercises : Baptiste Coquinot and Antonio Costa
ECTS credits : 3
Language of instruction : English
Key words : Dynamical systems, instabilities, fluctuations, stochastic processes
Exam : written
Covid-19 alternative examination : Oral examination

Description

The first part of the lectures concerns the macroscopic description of out-of-equilibrium systems. We will first consider thermodynamics of irreversible processes in the linear regime and Onsager relations. We will show next how this formalism can be used to find out bounds on the efficiency of thermal engines in realistic conditions for which the output power is finite. We will illustrate these concepts on energy transformations in thermoelectric or photovoltaic devices. We will then study diffusion processes and show how nonlinearities of the diffusion equation can generate anomalous diffusion. Finally, we will study fluctuations of thermodynamic quantities.
In the second part of the lectures, randomness will be modelled by assuming that the system is submitted to fluctuations with simple statistical characteristics. After studying the Langevin equation and fluctuation-dissipation relations, we will show in which limits a system submitted to random noise can be modelled using the Fokker-Planck or the master equations. We will then discuss some extensions of the fluctuation-dissipation relation for strongly out-of-equilibrium systems by mentioning some recent results referred to as fluctuation theorems. Finally, we will consider some effects of external noise on instability phenomena, such as the amplification of fluctuations in the vicinity of a bifurcation, squeezing of noise or on-off intermittency.

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

r>