Linearization

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Théorie générale des systèmes
Théorie du chaos

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Publications associées (31)

Mass-Zero constrained dynamics and statistics for the shell model in magnetic field

Sara Bonella, Alessandro Coretti, David Daniel Girardier

In several domains of physics, including first principle simulations and classical models for polarizable systems, the minimization of an energy function with respect to a set of auxiliary variables must be performed to define the dynamics of physical degr ...

EDP Sciences, Springer2021

Stability of a Point Charge for the Vlasov–Poisson System: The Radial Case

Klaus Martin Widmayer

We consider the Vlasov–Poisson system with repulsive interactions. For initial data a small, radial, absolutely continuous perturbation of a point charge, we show that the solution is global and disperses to infinity via a modified scattering along traject ...

2021

Null-controllability, exact controllability, and stabilization of hyperbolic systems for the optimal time

Hoài-Minh Nguyên

In this paper, we discuss our recent works on the null-controllability, the exact controllability, and the stabilization of linear hyperbolic systems in one dimensional space using boundary controls on one side for the optimal time. Under precise and gener ...

2020

Invariant states in inclined layer convection. Part 1. Temporal transitions along dynamical connections between invariant states

Tobias Schneider, Florian Reetz

Thermal convection in an inclined layer between two parallel walls kept at different fixed temperatures is studied for fixed Prandtl number . Depending on the angle of inclination and the imposed temperature difference, the flow exhibits a large variety of ...

Cambridge University Press2020

Influence of the inlet velocity profile on the flow stability in a symmetric channel expansion

François Gallaire, Lorenzo Siconolfi, Robin Debuysschère

In a channel flow with a sudden expansion, whether for three-dimensional (3-D) pipe and channel flows, or for two-dimensional (2-D) channel flow, it is known that increasing the Reynolds number beyond a critical value induces a symmetry breaking Pitchfork ...

Cambridge University Press2020

Enhanced Dissipation in the Navier-Stokes Equations Near the Poiseuille Flow

Klaus Martin Widmayer

We consider solutions to the 2d Navier-Stokes equations on T x R close to the Poiseuille flow, with small viscosity nu > 0. Our first result concerns a semigroup estimate for the linearized problem. Here we show that the x-dependent modes of linear solutio ...

SPRINGER2020

Stationary Structures near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations

Klaus Martin Widmayer

We study the behavior of solutions to the incompressible 2d Euler equations near two canonical shear flows with critical points, the Kolmogorov and Poiseuille flows, with consequences for the associated Navier-Stokes problems. We exhibit a large family of ...

2020

Frequency selection in a gravitationally stretched capillary jet in the jetting regime

François Gallaire, Isha Shukla

A capillary jet falling under the effect of gravity continuously stretches while thinning downstream. We report here the effect of external periodic forcing on such a spatially varying jet in the jetting regime. Surprisingly, the optimal forcing frequency ...

Cambridge University Press2020

Second-order sensitivity in the cylinder wake: Optimal spanwise-periodic wall actuation and wall deformation

François Gallaire, Edouard Boujo, Andrea Fani

Two-dimensional (2D) flows can be controlled efficiently using spanwise "waviness," i.e., a control (e.g., wall blowing and suction or wall deformation) that is periodic in the spanwise direction. This study tackles the global linear stability of 2D flows ...

AMER PHYSICAL SOC2019

Flow dynamics of a dandelion pappus: A linear stability approach

François Gallaire, Pier Giuseppe Ledda, Francesco Viola, Lorenzo Siconolfi

The study and control of flow instabilities is a key problem in aerodynamics. Aircrafts are designed not only to generate the lift force needed to balance their weight but, more importantly, to be stable and reasonably steady when in cruise conditions. Sim ...

2019

Turbulent patterns in wall-bounded shear flows: invariant solutions and their bifurcations

Florian Reetz

When laminar shear flows in large wall-bounded domains transition to turbulence, the flow exhibits spatio-temporally chaotic dynamics. Despite its chaotic dynamics, the flow may self-organize into characteristic spatially periodic patterns of unknown origi ...

EPFL2019

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