Bypassing fluctuation-dissipation theorems to compute non-equilibrium responses
| When |
Nov 08, 2016
from 10:45 to 12:00 |
|---|---|
| Where | Centre Blaise Pascal |
| Attendees |
Simon Thalabard |
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In this talk, I will expose a dynamical optimization framework to compute non-equilibrium averages, in which the latter are approximated in terms of geodesic paths in probability space. This dynamical response theory was conceptualized in a series of recent work, and will here be exposed in the context of the late stage thermalization of prototypical fluid models, such as inviscid shell models and truncated Burgers-Hopf dynamics.
In conceptual outline, the method imposes a parametric statistical model on the full turbulent dynamics, and ``best-fit'' that model to the underlying dynamics equations by minimizing a certain cost functional over paths of model states. In the context of turbulence modeling these desirable properties guarantee that no realizability issues arise in a best-fit closure.
The best-fit theory is predictive. By recasting the geodesic principle as an optimal control problem, non-equilibrium responses can be computed numerically, and coincide with DNS for moderate perturbations. In this near-equilibrium regime, I will argue that the optimal response theory provides an approximate yet predictive counterpart to fluctuation-dissipation identities.