Centre de Physique Théorique


January 2021

Wednesday 13 January 14:00-15:00, online-for link write to Annalisa Panati

Simon Thalabard (IMPA, Brésil)

Simon Thalabard (IMPA, Brésil)

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.

Wednesday 20 January 16:00-17:00, Online

Controlling active matter: From engines to biased ensembles

Etienne Fodor (University of Luxembourg)

Active matter is a class of nonequilibrium systems where every component extracts energy from its environment to produce an autonomous, directed motion. This directed motion yields some anomalous thermo-mechanical properties, and it can lead to collective states without any equilibrium equivalent. Many previous studies have studied in detail the phase diagrams of active systems, and to which extent some equations of state can be drawn beyond equilibrium. Yet, how to control optimally active matter, with a view either to extracting energy from the system or to promoting specific collective states, remains largely an open question. In this talk, I will discuss how to exploit and control nonequilibrium properties to (i) design innovative engines with thermodynamic cycles, and (ii) induce phase transitions in dissipation-biased ensembles.

Lien zoom: https://zoom.us/j/6813231221?pwd=Tk4vVFJFd1RhWWhndStGRUNGZ2xTZz09

Wednesday 27 January 14:00-15:00, CPT, Amphi 5


Chiara Saffirio, Université de Basel, Suisse