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DTSTART:19700329T020000
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SUMMARY:Simon Thalabard (IMPA\, Brésil) – Simon Thalabard (IMPA\, Brésil)
UID:evenement303 @ http://www.cpt.univ-mrs.fr
DTSTAMP:20210113T130000ZZ
DTSTART:20210113T130000Z
DTEND:20210113T140000Z
LOCATION: online-for link write to Annalisa Panati
CATEGORIES:Séminaire
DESCRIPTION:In this talk\, I will outline outgoing efforts to analyse self-similar solutions to non-linear diffusions. In the context of hydrodynamic turbulence\, non-linear diffusions arise as closures for the kinetic energy dynamics and are historically referred to as ’’Leith models’’ In the context of wave turbulence\, they arise from an approximation of local interactions within the relevant kinetic equations. Phenomenology of this class of non-linear diffusions can be described from the interplay between scaling solutions and equilibrium solutions. Among salient features\, a subclass of models with physical interest feature explosive behavior leading to finite-time singularity . In those cases\, careful numerics reveal systematic anomalous transients\, whose scalings deviate slightly from Kolmogorov-Zakharov constant-flux exponent. Our efforts aim at characterizing those anomalies in terms of an eigen-value problem involving self-similar solutions to the equations. For models involving second-order derivatives only\, which usually feature direct cascade of energy\, such an approach was shown to be successful and the anomalous exponent relates to well-defined heteroclinic bifurcation. Our recent results show that the approach can be extended to more elaborated fourth-order models\, which appear in the study of gravitational wave turbulence or formation of Bose-Einstein condensates\, and for which one expects a dual cascade scenario. In this case\, the anomalous exponent relates to the presence of an infinitely large limit-cycle in a suitably defined 4-th order autonomous system of ordinary differential equations. If time permits\, I will finally mention recent insights from such non-linear diffusions on the problem of strong hydro-dynamical turbulence\, and in particular on Gallavotti’s conjecture\, which states that in the limit of vanishing viscosity\, replacing viscous damping by a reversible thermostat yield statistical features of turbulence unaltered.
URL:http://www.cpt.univ-mrs.fr/spip.php?page=rubrique&id_rubrique=37
STATUS:CONFIRMED
TRANSP:OPAQUE
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