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This work aims to investigate the well-posedness and the existence of ergodic invariant measures for a class of third grade fluid equations in bounded domain $D\subset\mathbb{R}^d,d=2,3,$ in the presence of a multiplicative noise. First, we…
A simplified thermodynamic approach of the incompressible axisymmetric Euler equations is considered based on the conservation of helicity, angular momentum and microscopic energy. Statistical equilibrium states are obtained by maximizing…
An experimental study is reported of the near-critical reflection of internal gravity waves over sloping topography in a stratified fluid. An overturning instability close to the slope and triggering the boundary-mixing process is observed…
Topological properties of physical systems play a crucial role in our understanding of nature, yet their experimental determination remains elusive. We show that the mean helicity, a dynamical invariant in ideal flows, quantitatively…
These notes present a recent approach to study the high-frequency eigenstates of the Laplacian on compact Riemannian manifolds of negative sectional curvature. The main result is a lower bound on the Kolmogorov-Sinai entropy of the…
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We develop different synthetic notions of Ricci flow in the setting of time-dependent metric measure spaces based on ideas from optimal transport. They are formulated in terms of dynamic convexity and local concavity of the entropy along…
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It has long been suspected that flows of incompressible fluids at large or infinite Reynolds number (namely at small or zero viscosity) may present finite time singularities. We review briefly the theoretical situation on this point. We…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
Recent experiments and realistic flux-gradient-driven computer simulations provide evidence of plastic flow of flux lines in a superconductor. The striking videos of the onset of vortex motion vividly illustrate the existence of flowing…
We develop a variational method for constructing positive entropy invariant measures of Lagrangian systems without assuming transversal intersections of stable and unstable manifolds, and without restrictions to the size of non-integrable…
We show that binary Toeplitz flows can be interpreted as Delone dynamical systems induced by model sets and analyse the quantitative relations between the respective system parameters. This has a number of immediate consequences for the…
We study the two dimensional (2D) stochastic Navier Stokes (SNS) equations in the inertial limit of weak forcing and dissipation. The stationary measure is concentrated close to steady solutions of the 2D Euler equation. For such inertial…
Plane Couette flow of visco-elastic fluids is shown to exhibit a purely elastic subcritical instability in spite of being linearly stable. The mechanism of this instability is proposed and the nonlinear stability analysis of plane Couette…
The superflow in a superfluid is bounded from above by Landau's critical velocity. Within a microscopic bosonic model, I show that below this critical velocity there is a dynamical instability that manifests itself in an imaginary sound…
Measure-theoretic slow entropy is a more refined invariant than the classical measure-theoretic entropy to characterize the complexity of dynamical systems with subexponential growth rates of distinguishable orbit types. In this paper we…
We have developed and characterized two novel micro flow sensors based on measuring the electrical impedance of the interface between the flowing liquid and metallic electrodes embedded on the channel walls. These flow sensors are very…
We introduce a new framework to deal with rough differential equations based on flows and their approximations. Our main result is to prove that measurable flows exist under weak conditions, even solutions to the corresponding rough…
The quantum measurement procedure based on the Lorentz transformation formalism and weak perturbation of the system is considered. In the simple case of a single-qubit it turns out that one can perform 4-dimension pseudo-rotation along with…